Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (2017)

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21 C h a p t e r 3 The details of technical approaches and results are provided in this section. Major parameters related to bridge types, load effects, and forces associated with rail–train–structure interaction are studied. A unified design method for bridges subjected to light rail train and/or highway vehicle loads is developed. Load factors for bridges carrying light rail trains or both light rail and highway vehicle loads are examined. 3.1 Response Monitoring of Constructed Bridges 3.1.1 Site Visit Prior to conducting response monitoring, the site condition of five bridges in Denver, CO, was evaluated (Figure 3.1). The purposes of the site visit were to identify potential problems that might influence technical work, and to confirm engineering drawings obtained from a local transit agency (Regional Transportation District, RTD). A plan for instrumentation was established. 3.1.2 Calibration of Rail Response A laboratory experiment was conducted to calibrate the response of a 115RE rail under mechanical loading. A 128-in. long rail was tested with strain gages, as shown in Figure 3.2. The strain gage configuration used is similar to the method recommended by the Associa- tion of American Railroads (AAR) for wheel load calibration. Figure 3.3 exhibits the load- strain behavior of the 115RE rail. Two loading conditions were employed: simply-supported and continuous. According to the RTD design manual (2013), the front wheel of a fully loaded train weighs 12.2 kips (“Full train” in Figure 3.3), whereas that of an empty train has 7.5 kips (“Empty train” in Figure 3.3). The strains measured at the bottom of the rail where a maximum flexural effect takes place were compared with those calculated by structural analysis formulas. The strain values of the continuous rail were less than those of the simply- supported case (e.g., the measured strain of the continuous rail was 39% less than that of its simply-supported counterpart at a load of 7.5 kips). This observation indicates that the proposed test setup can properly represent the response of continuous rails supported by multiple sleepers on site. The response of the strain gages bonded to the rail side is given in Figure 3.4. The gages facing each other in the diagonal direction showed similar behavior. Test data showed slight discrepancy between the G1/G3 and G2/G4 groups, which illustrates that the applied principal stresses in these two diagonal directions (i.e., s1 and s2) were not the same. Linear curve-fitting equations were developed to establish the relationship between the strain and the applied load, so that in situ train load would be measured based on strain reading. Figure 3.5 shows the calibration of a portable data acquisition system Research Program

22 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads using a conventional laboratory data acquisition system. At typical loads of 12 kips and 14 kips in the continuous rail test, the strain reading of these two systems was almost identi- cal. These calibration results corroborate that the use of the portable data acquisition system is adequate to measure the in situ behavior of the five bridges discussed in Section. 3.1.1. The established load-strain relationships (Figure 3.4) were further validated with actual train load on site [Figure 3.6(a)]. The front wheel of an empty stationary train (7.5 kips) generated a maximum strain of 64.5 microstrains, as shown in Figure 3.6(b), which agreed with the laboratory strain of 63.8 microstrains subjected to a load of 7.5 kips (only one gage reading is provided for clarity). 3.1.3 Background and Response of Bridges A total of five constructed bridges in Denver, CO, were monitored. The monitored span of the individual bridges was determined by the following criteria as recommended by RTD that controls all light rail transit systems in Denver: (1) lowest superstructure elevation for safety and (2) accessibility to tracks with minimal disruption to train operation. This section sum- marizes bridge details, in situ data, and technical interpretation, including statistical param- eters useful to develop design recommendations. Typical field monitoring time is 12 hours (from 8:00 am to 8:00 pm) per bridge; however, two days are spent for one bridge owing to a strong wind issue. The behavior of the bridges is converged from a statistics perspective, which means there is no practical need to extend the monitoring time (i.e., sufficient data have been obtained). 3.1.3.1 Bridge Details Broadway Bridge. The Broadway Bridge consists of five spans (2-span plus 3-span con- nected by an expansion joint), having direct fixation tracks, as shown in Figure 3.7. The out- to-out deck width varies from 34 ft to 42 ft with a typical thickness of 10 in. The depth and width of the steel plates (AASHTO M-270 Grade 50) supporting the deck are approximately 5.5 ft and 2 ft, respectively. The 28-day compressive strength of the deck concrete was 4,500 psi. The behavior of the first span was monitored [Figures 3.7(a) and (b)]. Instrumentation included (1) eight strain gages bonded to the rail side in order to measure in situ train wheel load [Fig- ure 3.7(c)]; (2) one strain gage bonded in between the strain gage clusters for temperature monitoring; and (3) three strain gages (one 4.7 in. gage-length and two 0.2 in. gage-length gages) bonded to the bottom of each girder [Figure 3.7(d)] to monitor the flexural response of the bridge at midspan (i.e., bending and live load distribution). Train speed was measured with a digital speed gun confirmed by a portable global positioning system (GPS) inside trains passing the bridge. Indiana Bridge. The Indiana Bridge has no skew and is composed of a hollow prestressed con- crete box girder with a direct fixation track, as shown in Figure 3.8(a). The depth and width of the box girder are 7 ft and 20 ft, respectively, and the 28-day compressive strength of the girder concrete was 5,800 psi. Post-tensioning was conducted with low-relaxation steel strands (Aps = 28.64 in.2 and fpu = 270 ksi, where Aps and fpu are the cross-sectional area and ultimate strength of the steel, respec- tively) at a jacking stress level of 75%fpu. The monitored span is 95 ft long and has expansion and fixed bearings at both ends. Strain gages were bonded to the side of the rail to measure train wheel load and thermal deformation [Figure 3.8(b)]. Unlike other bridges monitored in this research program, one-way travel is allowed along the single track, and light rail trains are alternatively oper- ated from Denver to Golden (east to west) and vice versa, as shown in Figure 3.8(c). Long and short gages (4.7 in. and 0.2 in. gage lengths, respectively) were also bonded to the bottom of the prestressed concrete girder [Figure 3.8(d)].

research program 23 Santa Fe Bridge. The Santa Fe Bridge is a 2-span multicell prestressed concrete box girder bridge, as shown in Figure 3.9(a). The bridge is approximately 28 ft wide and 10 ft deep, and has a total length of 328 ft (172 ft + 156 ft spans). Two train tracks are located on a ballast layer of 1.7 ft. The 28-day compressive strength of the box concrete was 6,000 psi and low- relaxation strands (Aps = 76 in.2 and fpu = 270 ksi) were used for post-tensioning at a jacking stress level of 75%fpu. Strain gages were bonded to the rail side to measure train load and temperature [Figs. 3.9(b) and (c)], and were bonded underneath each web member of the multicell girder [Figure 3.9(d)]. County Line Bridge. The County Line Bridge (L = 990 ft) comprises four prestressed con- crete bulb T-girders (Colorado BT84) for seven spans varying from 114 ft to 160 ft, as shown in Figure 3.10(a). Each girder has a depth of 7 ft with a girder spacing of 8.3 ft, and supports a deck slab (t = 8 in.) with two direct fixation tracks. All girders were connected by diaphragms cast on site (i.e., a continuous system), except the fourth span where expansion joints were placed. Two harping points were used for prestressing strands per girder (Ap = 5.2 in.2 to 12.6 in.2, low- relaxation 270 ksi steel). A 28-day concrete strength of 8,500 psi was used for the girders. Strain gages were bonded to the rail [Figure 3.10(b)] to measure light rail train load [Figure 3.10(c)]. Additional gages were bonded to the bottom of each girder at midspan to monitor the flexural behavior when loaded [Figure 3.10(d)]. 6th Avenue Bridge. The 6th Avenue Bridge has 4 + 2 span prestressed concrete bulb T-girders (BT42) connected by an arch bridge [Figure 3.11(a)]. The non-skew bridge encompasses two bal- lasted train tracks. A waterproofing membrane layer was placed in between the deck concrete (t = 8 in.) and the ballast layer. As in the case of the County Line Bridge, all girders were connected on site to make a continuous system, and each girder had two harping points (Ap = 5.2 in.2 with an effective steel stress of 56%fpu). The compressive strength of the girder concrete was 9,000 psi. Strain gages were bonded like other bridges to measure the in situ wheel load of light rail trains [Figures 3.11(b) and (c)] and the flexural response of the girders at midspan [Figure 3.11(d)]. 3.1.3.2 Temperature Effect on Train Rails As mentioned in Section 3.1.3.1, strain gages were bonded to measure the effects of tem- perature on the behavior of track rails while monitoring train load. The coefficient of thermal expansion (CTE) for steel (115RE) was taken as a = 6.5 × 10-6/°F or 12 × 10-6/°C (Okelo and Olabitman 2011), and a rail temperature (T) was obtained from the relationship between ther- mal strain (eth) and CTE (i.e., T = eth/a). The maximum temperature variation range of each bridge is summarized in Table 3.1: the maximum positive and negative temperatures indicate relative changes in temperature against initial temperatures (e.g., the lower bound for the Broad- way Bridge was -5.3°F, which means that the maximum temperature drop was -5.3°F from the initial temperature when the site work began). A net temperature variation for all bridges was in between 11.1°F and 25.0°F, excluding the temperature of the 6th Avenue Bridge whose strain read- ings were influenced by strong wind blown during the two consecutive days when the field work was conducted (because the response of a bulb-tee superstructure was already measured in the County Line Bridge, further site monitoring for the 6th Avenue Bridge was not carried out). Train loading did not significantly affect the temperature gage readings, since the horizontal-direction gage was bonded at the centroid of the rail where flexural stress was none (although some minor effects were observed in the converted temperature spectra, as typically shown in Figure 3.12). 3.1.3.3 In Situ Wheel Load of Light Rail Trains Figure 3.13 reveals typical strain responses associated with the wheel load of light rail trains running on the bridges monitored. It is worth noting that strain reversals were cor- rected to exhibit consistent positive load values. The strains measured on the rail side were

24 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads converted to the wheel load of the trains using the formulas developed in the laboratory test, which were also calibrated with the stationary light rail trains as mentioned in Section 3.1.2. When interpreting the train load, the temperature effect discussed in Section 3.1.3.2 was com- pensated. Provided that the primary interest of the present site work was in detecting maximum train loads that would control the response of the bridges [i.e., the light rail train has two design loads (fully loaded) for six axles such as 24.375 kips and 16.25 kips, as shown in Figure 3.14, and corresponding wheel loads are 12.188 kips and 8.125 kips], maximum loads (or peak loads) measured during each load cycle were acquired and summarized in Figure 3.15. The number of observations was not consistent for all bridges, because some bridges were used by multiple lines (there are six light rail lines in Denver); however, the mean wheel load measured was almost consistent, irrespective of number of observations. This fact corroborates that the load data are statistically stable. The mean wheel load of the light rail trains varied from 6.2 kips to 6.9 kips [Figs. 3.15(a) to (e)]. The measured load range was reasonable, since the articulated light rail train had a nominal load range between 4.96 kips and 12.19 kips (empty train and fully loaded train, respectively) per train wheel (Figure 3.14). It is presumed that the passenger occupancy increased the train load by 25% to 39%, including some dynamic effects that will be examined in subsequent modeling work (Section 3.2.). Figure 3.15(f) illustrates the relationship between the average train speed measured and the mean train wheel load. In accordance with the regression line, the load has increased with train speed. Although the passenger load was not identical in the individual trains (the number of passengers is stochastic in nature), it appears to be reasonable to adopt the fitted equation because the variation range of the wheel loads was marginal (i.e., 6.2 kips to 6.9 kips). It should be noted that the lower bound of the train wheel loads in Figure 3.15 was intentionally cut to the minimum wheel load of an empty train (i.e., 4.96 kips). The reason is that tremendous amounts of insignificant strain readings were recorded, which are considered noise rather than structural load. The type of a probability distribution for train loading was normal (Figure 3.16); further verification is available later. A probability-based load estimate was con- ducted using a Monte-Carlo simulation in conjunction with the statistical properties acquired from the site (e.g., coefficients of variation), as shown in Figures 3.17(a) to (e). The simulated wheel loads agreed with those measured on site [Figure 3.17(f)], including a maximum margin of 0.28%. This observation supports the adequacy of the simulation technique, which can be used for subsequent technical tasks. 3.1.3.4 Girder Response The flexural behavior of the monitored bridges is provided in Figure 3.18 (only selected cases are shown for brevity because the superstructure responses were intrinsically repeated). The measured strains at midspan of each girder showed periodic spikes when the light rail trains were passing, whose magnitude was a function of girder types and geometric configurations. For instance, the response of the Broadway Bridge (three steel plate I girders with a span length of 119 ft, Figure 3.7) and the Indiana Bridge (one large prestressed concrete box girder with a span length of 95 ft, Figure 3.8) had typical strains of approximately 100 × 10-6 and 35 × 10-6, respectively, as shown in Figures 3.18(a) and (b). Some minor negative strains were detected in all cases, because the bridges were continuous and the behavior of the girders physically moved up and down depending upon the location of train load, particularly for the Broadway Bridge having relatively less flexural rigidity owing to the use of slender steel I plates [Figure 3.18(a)]. As explained in Section 3.1.3.2, the strains of the 6th Avenue Bridge fluctuated due to strong wind; accordingly, close-up views were not provided in Figure 3.18(e). 3.1.3.5 Live Load Distribution Figure 3.19 summarizes the load distribution factors (LDF) of each bridge calculated by Eq. 3.1, depending upon the location of light rail trains:

research program 25 (3.1) 1 LDF m I I i i i ii n∑= ε ε = where m = the number of loaded tracks; Ii and ei = the moment of inertia of the cross section and the strain of the ith girder, respectively; and n = the total number of girders in the superstructure. By including the number of loaded tracks factor m, the results of beam-line analysis with a single-track-loaded case can be expanded to multiple-track-loaded cases. Live LDF are controlled by the position of train wheels, rather than the gross weight of light rail trains. Also presented in Figure 3.19 are the statistical properties of each girder, including mean distribution factors (µ) and corresponding coefficients of variation (V). The shape of the load distribution factor was determined by the location of the train load. The range of the coefficient of variation varied from 0.03 to 0.61 by superstructure types and train configurations. Simultaneous two-track loading was not observed on the Santa Fe and the County Line Bridges [Figures 3.19(c) and (d), respectively]. It is again noted that the 6th Avenue Bridge generated relatively large coefficients of variation due to the strong wind [Figure 3.19(e)]. Figure 3.20 evaluates the application of the Lever Rule and the AASHTO LRFD BDS equations against the measured LDF (the mid-girder strains of the Indiana Bridge [Figure 3.19(b)] were assumed to be equally distributed to the bridge webs when determining the load distribution of the webs [Figure 3.20(b)]). These two existing approaches were by and large conservative, espe- cially for the interior girders. Some notable discrepancy was observed: the steel plate girders in multiple-track loading [Figure 3.20(a)] and the single cell box girder [Figure 3.20(b)]. Modified design equations for live load distribution in light rail bridges are proposed in a later section. The following should be noted: (1) the load distribution of the multiple girders, when the lever rule was applied to the exterior girders, was obtained from the AASHTO LRFD BDS equations and the purpose of the presentation in Figure 3.20 was only to assess the existing design approaches (governing factors are taken when a bridge is designed) and (2) the distribution profile of the Broadway Bridge [Figure 3.20(a)] was not symmetric since the bridge geometry was asymmetric. Table 3.2 lists the statistical parameters attained from the in situ tests. The averaged coefficients of variation of each bridge varied from 0.106 to 0.240, excluding the 6th Avenue Bridge that exhib- ited significant scatter due to the strong wind (i.e., an increased level of dispersion in response, as shown in Figure 3.19). The overall average coefficient of variation for the monitored bridges was found to be 0.161. 3.1.3.6 Dynamic Behavior A non-contact interferometric radar technique called Image By Interferometric Survey (IBIS hereafter) was employed to monitor the dynamic behavior of the bridges. The IBIS system detects a phase-change in reflected radar waves to identify the position of an object. Because the preced- ing response of the light rail bridges was consistent (Section 3.1.3.3 and Section 3.1.3.4), a nomi- nal field monitoring time of 5 hours was planned per bridge. Reflectors were installed along the edge of the bridge deck at mid- and quarter-spans [Figure 3.21(a)] to measure the displacement and frequency of the bridge [Figure 3.21(b)]. The monitored spans were identical to those of the previously conducted field test. The IBIS equipment was set up using a tripod, as shown in Figure 3.21(c), and the radar head was connected to a laptop computer. A laser distance meter mounted to the radar head was used to uniquely link the position of specific bridge members with a peak radar display. This process enabled reviewing in situ technical data at a later time for further data processing such as fast Fourier transform (FFT) analysis. A sampling rate of 200 Hz

26 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads was exploited. Using the IBIS system, the vibration and displacement data of all five bridges were collected and analyzed (to be discussed in a modeling section). 3.2 Finite Element Modeling 3.2.1 Model Development After careful examination and trial modeling of the bridges expounded in Section 3.1, CSIBridge and SAP2000 were selected, in addition to their familiarity, convenience, popularity, and accuracy in bridge modeling. Figure 3.22 illustrates bridge models to predict the field test data obtained from the five bridges monitored in Section 3.1. The following properties were considered per the engineering drawings and documents obtained from RTD, as summarized in Table 3.3: • Superstructure types: steel plate girders, prestressed concrete girders, and prestressed concrete box girders. • Geometric details: depth, width, and length of the girders, rail-supporting plinths, sidewalks, and diaphragms. • Material properties: concrete, steel, and ballast. • Live load: empty and fully loaded light rail trains (total load = 79 kips and 130 kips, respectively, per one articulated train as shown in Figure 3.14). • Number of articulated light rail trains: two to three articulated light rail trains, as observed on site. • Operating speed of light rail trains: average speeds measured on site. • Boundary conditions: hinges and rollers. The average operating speeds of the light rail trains for the Broadway and the 6th Avenue Bridges (23.4 mph and 32.9 mph, respectively) were relatively slower than those for other bridges (Table 3.3). This is attributed to the fact that these two bridges were located near curved tracks; hence, train conductors tended to reduce operating speed. Quadrilateral shell and three-dimensional frame elements were employed to model the bridge structures (Figure 3.22). Link elements were used to define connections between the components such as bridge girders and bearings. All geometric and material properties (Table 3.3) were nominal and nonlinearity was not taken into account. When expansion joints are presented in a continuous system (i.e., physical separation of the bridge girders), the portion of the continued superstructure was modeled without considering other portions. The reason is that the behavior of the modeled portion was not influenced by the other portions owing to the separation (the rail part can provide minor connectivity, whereas its effect is negligible from a structural standpoint). The condition of expansion bearings on site may have partial fixity, when loaded in longitudinal bending; however, insufficient information was available to represent this partial fixity. The models were thus devel- oped with ideal rollers. Perfect connection between the elements was assumed, which is typical in bridge modeling and analysis, because the bridges have full composite action. Following the engineering drawings of each bridge, supports at individual piers and abutments were restrained. Diaphragms were also included to prevent global torsional buckling of the girders. The dead load of each constituent element was taken into consideration by including the density of the materials: reinforced concrete (150 lb/ft3), steel (490 lb/ft3), ballast (120 lb/ft3), and rail-track (200 lb/ft). According to literature (Nielsen 2008), the effects of a ballast layer were modeled with equivalent uniaxial stiffness (6,854 kip/ft) and damping (5.6 kip-sec/ft). These ballast elements were placed underneath the rails. Various load scenarios were modeled: one-track loaded, two-track loaded, and both-track loaded with two to three articulated light rail trains, as observed in the field. Time– history analysis was carried out to predict the dynamic behavior of the bridges, based on the aver- age train speeds measured on site (Table 3.3). Typical bridge behavior is shown in Figure 3.23.

research program 27 3.2.2 Model Validation Against Field Test Data 3.2.2.1 Strain Response and Live Load Distribution Figure 3.24 reveals the strain response of the individual bridges. Two-track loaded cases for the Santa Fe and the County Line Bridges were not observed on site (Figures 3.24(c) and (d), respectively). As illustrated in Figure 3.24, the measured strain responses were generally positioned in between the fully loaded and empty train cases of the model prediction. Some exceptions were, however, observed: (1) the measured stains in Figure 3.24(d) were close to the predicted strain of fully loaded trains because of uncertain site conditions (e.g., material and geometric properties, strain gage locations, and temperature); and (2) the strong wind influenced the strain readings of the 6th Avenue Bridge in Figure 3.24(e), so that the mea- sured values were higher than those predicted. The fully loaded and empty trains include 130 kips and 79 kips, respectively, with six axles per train (Figure 3.14). The model prediction denotes that the in situ trains were loaded with passengers (the average load increase owing to the passengers is provided in Table 3.4). It is estimated that the passenger occupancy has increased the live load of light rail trains by 24.4%, on average, leading to a dynamic train load of 98.6 kips. The average strain readings measured on site were also compared with those predicted with typical service loadings (i.e., empty train load plus the average pas- senger load of each bridge acquired from Table 3.4; the passenger loading of the 6th Avenue Bridge was assumed to be the average passenger loading of the other bridges, since specific loading information was not obtained on account of the wind issue). Although some minor discrepancy was noticed, the predicted strains were within the range of standard deviations of the in situ strains, as shown in the vertical bars of the measured strains in Figure 3.24. It is also important to note that passenger loading is not deterministically predictable because of its stochastic nature; hence, the statistical properties identified in Section 3.1 will be useful to address uncertainty, when developing design recommendations. 3.2.2.2 Dynamic Response of the Five Bridges in Denver, CO For dynamic analysis, the mode superposition method was selected because it is less sensi- tive to time steps (numerically stable) compared with the direct integration. As such, accurate technical results were predicted with reasonable computational effort, including modal analy- sis data, which was a concern in the present research since the number of required simula- tions was substantially large. Constant modal damping was utilized in accordance with the AASHTO LRFD BDS: 1% and 2% for the steel and concrete bridges, respectively. These values are also in an applicable range for railway bridges (Ju 2007; Kim 2010; Martinez-Rodrigo et al. 2010). The train loading was regarded as a transient parameter. First five modes and corresponding frequencies were extracted using Eigenvector analysis. The fundamental fre- quency of each bridge model offered information necessary to assess the user comfort criteria to be described in the next section. The five modes were iteratively calculated with the follow- ing convergence criterion: 1 2 10 (3.2) 1 1 1 9i i µ − µ µ     ≤ + + − where µ is the eigenvalue relative to the frequency shift at the ith iteration. Since all positive frequencies were predicted, it can be stated that the developed dynamic bridge models were stable. Figure 3.25 compares the measured and predicted displacements at midspan of the individual bridges. For consistency, the finite element models included three cases (i.e., empty and fully loaded train loads as well as typical service loading based on the empty train plus the estimated pas- senger load enumerated in Table 3.4) with inbound train loading, which was close to the installed reflector. The sign convention used in Figure 3.25 is as follows: positive and negative values indicate

28 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads downward and upward displacements, respectively. It should be noted that the direction of train operation affected the positive and negative displacements of the monitored span in continuous bridge systems (i.e., downward to upward deflections or upward to downward deflections with time in Figure 3.25). As in the case of the previous model validation, the service response was positioned in between the fully loaded and the empty train loading cases, and the predicted service responses were in agreement with their measured counterparts. 3.2.2.3 Deflection and User Comfort The primary purpose of controlling bridge deflection is to prevent user discomfort (pedestrians and passengers) and structural deterioration induced by excessive bending. The following existing criteria for deflection control were considered: • L/640 for train load (AREMA) • L/800 for vehicular load general (AASHTO LRFD BDS) • L/1,000 for girders (local light rail transit agencies) where L is the span length of the bridge. The maximum average deflection of each bridge is provided in Table 3.5 along with the L/m criterion, where m is a constant. The L/m values of all bridges were significantly less than those mentioned earlier, particularly for the prestressed concrete bridges owing to the relatively large moment of inertia compared with the steel bridges. This implies that the existing deflection control criteria are not sufficient to address serviceability concerns. Another criterion should, therefore, be taken into consideration, namely, the comfort of users such as pedestrians and passengers (further discussions are provided in a later section). The vertical deflection of the bridges under light rail train loading does not seem to influence their track profile. As far as camber requirements are concerned, the AREMA provisions are recommended for light rail bridges. The fundamental frequencies measured and predicted are compared in Table 3.6. Although reasonable agreement was observed in all cases, some discrepancy was noticed possibly because of the noise detected by the sensitive data acquisition. According to a sensitivity study using the finite element models, the effect of miscellaneous members (e.g., concrete plinths and sidewalks) was negligible on the variation of fundamental frequency. Figure 3.26 evaluates user comfort (pedestrian) based on the deflection and fundamental frequency of the in situ bridges. As identified in a preliminary study, the Canadian Highway Bridge Design Code (CHBDC) provides three comfort criteria for bridges: (1) frequent pedestrian use; (2) occasional pedestrian use; and (3) without pedestrian. These criteria were developed based on bridge acceleration limits, which were converted to equivalent static deflections for design purposes. It should be noted that the applicability of the CHBDC criteria was previously assessed in NCHRP Project 20-7 (Roeder et al. 2002) using 12 bridges designed per the AASHTO Specifications. Given that the monitored bridges have right-of-way and do not allow pedestrians for safety reasons, the third criterion was adopted in this section. The predicted fundamental frequency and corresponding maximum deflection of the individual bridges generated specific responses (Figure 3.26), all of which were within the acceptable zone of user comfort. These observations support the fact that the serviceability of the in situ light rail bridges was satisfactory in terms of deflection (Table 3.5) and user comfort (Figure 3.26). 3.2.2.4 Summary of Model Validation Overall, the predicted behavior of the five bridges showed agreement with the measured behav- ior in terms of strain development, live load distribution, and time history responses in conjunc- tion with superstructure deflection and fundamental frequency. It is, therefore, concluded that the proposed modeling approach is reliable to conduct numerical parametric investigations for subsequent technical tasks.

research program 29 3.2.3 Design of Benchmark Bridges Five types of benchmark bridges were designed for a numerical parametric study (Table 3.7): steel plate girder, prestressed concrete multicell box, reinforced concrete T-beam, prestressed concrete I-girder, and steel box girder bridges subjected to light rail trains (the RTD light rail train load discussed in Section 3.1) and HL-93. The following material properties were used: compressive strength ( f ′c) of 4,000 psi and 7,000 psi for reinforced and prestressed concrete, respectively; yield strength (Fy) and modulus (Es) of 50 ksi and 29,000 ksi for structural steel, respectively; and ultimate strength ( fpu) of 270 ksi for low-relaxation prestressing steel strands. Poisson’s ratios for concrete and steel were 0.25 and 0.30, respectively. The light rail train load included a fully loaded axle load of 130 kips (6 axles) for one articulated train (Fig- ure 3.14), and one to four trains were loaded per bridge in accordance with the RTD design manual (RTD 2013). A DLA of 33% was further added to the train (RTD 2013) and HL-93 truck loads. Train derailment was taken into account (RTD 2013). Because the train load is heavier than HL-93 and encompasses wider axle spacing, the train load controlled all design cases. Tables 3.8 to 3.12 summarize details of the bridge design along with Figure 3.27 that shows dimensional configurations. According to the nominal dimensions of the standard track work for light rail transit, a rail gage-length of 4.71 ft was consistently used. A loading gage of 4.9 ft may be an alternative dimension, considering the lateral spacing between the wheel loads of an axle. Nonetheless, these two gages generated virtually identical load effects from a bridge response standpoint, as shown in Figure 3.28: the behavior of two constructed bridges in Denver (County Line and 6th Avenue Bridges) is compared when subjected to two to three articulated Colorado trains with a full design load of 130 kips each (one and two-track loadings), including maximum differences of 0.37% and 0.20% in moment and shear, respectively. For modeling convenience, the flange geometry of each bridge category was assumed to be constant, while its web properties varied. The negative moment of the multiple-span bridges controlled the design; accordingly, conserva- tive sections were selected (i.e., negative moment sections were chosen, rather than positive moment sections). Although variable cross sections are frequently used in practice to save construction costs, constant cross-sectional properties were adopted in this study to facilitate modeling work. Given that LDF are normalized by the moment of inertia of each girder or web (Eq. 3.1) and the effect of the longitudinal stiffness parameter of the girder is insignifi- cant, this modeling approach would not cause any problem in characterizing the behavior of bridge superstructures (i.e., live LDF are reasonably independent of the variation of cross sections). It is worthwhile to note that the properties of the closed steel box girder sections (Table 3.9) can also be used for open steel box girder sections, because (1) these two box girder types are treated equally in AASHTO LRFD BDS and (2) the contribution of the upper flange is marginal to the moment-carrying capacity of the girder due to a short lever-arm distance. The reinforcing schemes associated with Table 3.10 (prestressed concrete I-girder), Table 3.11 (prestressed concrete box girder), and Table 3.12 (reinforced concrete box girder) are provided in Tables 3.13 to 3.15. 3.2.4 Modeling of Bench Mark Bridges The modeling approach explained in Section 3.2.1 was adopted to predict the behavior of the benchmark bridges described in Section 3.2.3. Four representative live load models (Figure 3.29) were identified and used. Most light rail transit agencies do not consider maintenance trains, since multiple articulated light rail trains are generally heavier than a typical maintenance train assembly consisting of a locomotive and ballast trains. One to four articulated train moving loads were applied along the bridge to generate maximum static load effects. Dynamic analysis

30 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads examined the DLA of the benchmark bridges subjected to the light rail trains running at a design speed of 60 mph. One-track-loaded and two-track-loaded cases were modeled. A total of 1,972 static bridge models (116 models for HL-93 plus 1,856 models for the light rail trains) and 2,960 dynamic models (1,856 and 1,104 models for simply-supported and multiple-span cases, respectively) were developed and analyzed. Figures 3.30 and 3.31 show selected bridge models for numerical parametric studies. 3.2.5 Behavior of Benchmark Bridges The behavior of the five simply supported benchmark bridges (Tables 3.8 to 3.12) subjected to the aforementioned light rail train loads (Figure 3.29) is shown in Figures 3.32 to 3.36, which is a function of span length, girder spacing, and the number of articulated trains and loaded tracks. Because DLA is separately dealt with in AASHTO LRFD BDS (i.e., static load + DLA), maximum static moments acquired from the girders are summarized. Irrespective of train type, the maximum moment of the bridges gradually increased when a span length increased. The effects of two-track-loaded cases were more pronounced than those of one-track-loaded cases. There was no significant difference in static moments for the four representative train loads. For example, at a span length of 100 ft in steel plate girder bridges (Figure 3.32), the average maximum static moments of the Colorado, Utah, Minnesota, and Massachusetts trains (two-track-loaded with one to four articulated trains) were 2,263 ft-kip, 2,633 ft-kip, 2,637 ft-kip, and 2,550 ft-kip, respec- tively, which resulted in a relative variation range of less than 16%. The moment of the reinforced concrete girder bridges (Figure 3.36) was lower than the moments of others because of short span length (i.e., 30 ft to 70 ft). Figure 3.37 compares the maximum static moments caused by the light rail train loads with those due to HL-93. Regardless of light rail train type (except for the shortest span of 30 ft in reinforced concrete bridges, Figure 3.37i), the moments induced by one articulated train (designated single train load in Figure 3.37) were lower than or close to unity, which means that the effect of HL-93 was greater than that of the train load. This can be explained by the fact that the HL-93 truck load tended to act like a concentrated load relative to the train loads with much longer axel spacing (Fig- ure 3.29). The high moment ratios of the 30 ft bridges in Figure 3.37(i) are attributable to the fact that only two train axles were positioned within the bridge span, and these train loads (Figure 3.29) were heavier than HL-93 and their middle axle spacing (5.9 ft to 6.0 ft) was much narrower than the axle spacing of the HL-93 truck (14 ft). When multiple trains were loaded (two to four articulated trains), the normalized response was a function of span length (“multiple train load” in Figure 3.37). The HL-93 load controlled the moment of the bridges shorter than 80 ft in all cases (except for the 30 ft reinforced concrete bridges). In contrast, the light rail train loads generally governed the moment of the longer bridges, since the multiple trains were sufficiently loaded on the bridges. This finding is in compliance with AASHTO LRFD BDS and the AREMA manual, in the sense that the behavior of short-span bridges is controlled by the 2-axle design tandem (AASHTO LRFD) and the alternative 4-axle live load (AREMA), rather than the HL-93 and Cooper E80 loads. The responses of various span bridges demonstrated a trend analogous to those of the simply supported cases, as shown in Figure 3.38. 3.2.6 Behavior of Curved and Skewed Bridges As presented in Table 3.7, finite element models were developed to predict the behavior of the bridges with three different radii of curvature (R = 500 ft, 1,000 ft, and 1,500 ft for the steel plate girder, concrete multicell box, and steel box bridges) and three skew angles (20°, 40°, and 60° for all bridge types). Figure 3.31 shows typical curved and skewed bridge models. Superelevation (e) was included in the curved bridges (Unsworth 2010):

research program 31 (3.3) 2 e dV gR = where d = the horizontal projection of the track contact point distance (d = 4.7 ft for light rail trains); V = the speed of the light rail trains (V = 60 mph); g = the acceleration of gravity (g = 32.17 ft/s2); and R = the radius of curvature of the bridge. Four articulated Utah light rail trains that are the heaviest load among the four representative trains (Figure 3.29) were loaded to generate maximum load effects on the bridges, including one- and two-track-loaded cases. Figure 3.39 exhibits the predicted maximum static moments and shear forces of the curved bridges. The difference between the one- and two-track-loaded cases tended to slightly increase, when the span length increased. For example, a difference of 48.9% in static maximum moment was observed between the one- and two-track-loaded 80-ft steel plate bridges, on average, as shown in Figure 3.39(e); however, the discrepancy increased to 50.4% for a span length of 160 ft. Unlike the curved bridges discussed, the behavior of the skewed bridges was influenced by both span length and skew angle (Figure 3.40). The predicted maximum bending moments were reduced with an increase in skew angle, whereas the maximum shear forces revealed an opposite trend [Figs. 3.41(a) and (b), respectively]. These observations are in agreement with the skew correction factors stipulated in AASHTO LRFD BDS. The variation of fundamental frequen- cies in the curved and skewed bridges is given in Figs. 3.42 and 3.43, respectively. Similar to the discussion given above, the effect of curvature radius was negligible; on the other hand, that of skew angle was pronounced. The propensity for decreasing fundamental frequencies with an increased span length is explained by the fact that the frequency is inversely proportional to the square of span length (Bakht and Jaeger 1985). 3.3 Development of a Standard Live Load Model for Light Rail Transit 3.3.1 Background The most critical concern in light rail bridge design is the absence of a standard live load model. Current practice is based on the historical engineering judgment and experience of indi- vidual transit agencies. As such, there is a dearth of uniformity in the level of safety or reliability for bridges designed to resist loadings from light rail transit trains. TCRP Report 155 mentions that the AASHTO Specifications and the AREMA manual do not provide accurate loading infor- mation when designing light rail bridges (Parsons Brinckerhoff et al. 2012). For example, the wheel spacing of the AREMA loading does not represent that of light rail trains, and the service conditions of freight rail bridges are different from those of light rail bridges. It is also stated that the conservative bridge design required by the AREMA manual may not be applicable to light rail bridges. The types and configurations of light rail trains vary depending upon manu- facturers. Consequently, the loadings actually experienced by structures entail a certain level of uncertainty or a lack of surety with regard to actual axle load magnitude and axle spacing (these loadings and spacings are not deterministic). Probability-based live load calibration is a tool that allows for the quantification and management of uncertainty. The standard live load model described in this section uses a simple configuration of concentrated and uniform loadings at set spacings, which will quantify and encompass (or envelope) loading effects (shear and moment). The proposed standard live load model is flexible enough that it can address potential increases in axle loads and modified train configurations in the future, if necessary.

32 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads A blend of deterministic and probabilistic approaches was used in the development of the standard live load model for light rail train gravity loadings. This dual-faceted methodology maximizes the utility and information garnered from each approach (i.e., rapid development of a base or benchmark load model using the results from deterministic finite element models and then subsequently addressing uncertainty by conducting probability analyses with the data produced by the models). Another important aspect of the developed standard live load model is its practical convenience for bridge designers familiar with AASHTO LRFD BDS and its simi- larity to highway traffic gravity loadings (HL-93). With this in mind, the standard light rail load model was developed to be as close as possible to the HL-93 in configuration (e.g., number of axles) and application. The standard live load model for light rail train loadings considered the following aspects: • Integration and consideration of existing light rail train load models used by various transit agencies • Similarity with the live load model of AASHTO LRFD BDS • Familiarity to practicing engineers and straightforward application • Convenience for LRFD implementation for the present and future A schematic of the research approach used is given in Figure 3.44. This approach is derived in part from the method used by the European Railway Research Institute to develop a new train load model, as shown in Figure 3.45. The utility of the LM2000 model is it can cover a wide range of bridge geometries and accommodate potential increases in train loadings during the projected target bridge service life of 100 years (probability-based live load model). Another advantage of the LM2000 model [Figure 3.45(b)] is its straightforward application for design (i.e., simple load configurations) relative to the existing LM71 model [Figure 3.45(a)]. It should also be noted that the configuration of the LM2000 live load model (and other candidate load models [Figure 3.45(c)] considered when LM2000 was developed) is essentially analogous to the HL-93 in AASHTO LRFD BDS (i.e., a simple combination of concentrated loads with a uniformly distributed load, which will expedite bridge design). Figure 3.46 illustrates the layout of the proposed live load model. The model is both general and flexible enough to envelop the structural responses produced by the various potential loading configurations of articulated light rail trains in conjunction with the typical operation schedules of transit agencies. For example, some cases with multiple articulated trains occupying significant portions of a bridge (e.g., four trains during rush hour) require a uniformly distributed load effect, whereas some cases with minimal articulated trains (e.g., two trains during off-peak hour) demand a concen- trated load effect. It is thought that practicing engineers can readily implement the proposed live load model, which is more appropriate than the configuration of the traditional train loading for the design of bridges subjected to light rail loadings. The standard live load model was also probabilisti- cally calibrated to generate reasonable loading effects compared with the existing load models (i.e., the load effects of the proposed load models sufficiently envelope those of the existing load models for light rail bridges). If the standard load model generates similar load effects to con- temporary train loads, bridges designed and constructed as per such a standard load model are expected to have uniform performance, regardless of transit agency. The proposed live load model was calibrated using the matrix of prototype bridges described in Table 3.7. The bending and shear responses of these bridges loaded with the existing live load models (Figure 3.29) were examined until equivalent (and enveloped) responses were achieved with the proposed live load format (Figure 3.46). Iterations of the live load model characteristics (i.e., axle loads and spacings) were a part of this process. According to influ- ence line theory, all the employed live loads were positioned to generate maximum load

research program 33 effects. It is important to note that the effect of small differences in the existing live load models should be insignificant with regard to the behavior of the bridges and, as such, the number of the numerical models employed was not unrealistically large. The calibration work was conducted with all bridges being simply supported to refine the configuration of the proposed model (i.e., loading magnitudes and spacings). Although the deterministic live load models were developed based on the design models used in actual light rail construction (Figure 3.29), additional safety should also be taken into consideration. This is because existing load models may not represent all possible light rail train loads in the United States, and potential increases in actual loadings are quite possible in the near or distant future. As a consequence, a probability analysis was conducted in order to con- trol various levels of risk associated with light rail train loadings. This further calibration work resulted in several property ranges for the load model (Figure 3.46), for instance, the variation of axle loads, axle spacings, and the magnitude of the uniformly distributed load. The type of a probability distribution was determined for the load model (i.e., Gaussian distribution), and corresponding analyses were conducted. The bridge behavior, when subjected to this standard live load model, was compared with the bridge responses from the HL-93 loadings, such that a unified design approach for bridges carrying light rail load and standard highway traffic load can be achieved. The standard live load model developed will significantly contribute to the bridge engineer- ing community. Uniform design outcomes will be available, rather than current agency-specific practice. Post-construction management will also benefit, because light rail bridges can be con- structed based on a single design load. The agreement of bridge behavior with existing design models, in situ load, and the proposed load model was a barometer of measuring the success of this task. 3.3.2 Decomposition of HL-93 Load Effect Section 3.2.5 indicated that the effect of the representative light rail trains loads (Figure 3.29) was comparable to that of the HL-93 load, including the upper and lower margins of 65% and 128%, respectively. Provided that the standard live load model is composed of a lane load and three concentrated loads, as initially proposed (Figure 3.46), and is analogous to the standard live load model of AASHTO LRFD BDS, it was assumed that the lane-to-truck load effect ratio of HL-93 would be valid for the load model of light rail trains. Finite element modeling was conducted using the five types of simply supported benchmark bridges (Table 3.7): 464 bridge models were loaded with the HL-93 lane load of 0.64 k/ft and with the three con- centrated HL-93 truck loads (8 kips + 32 kips + 32 kips at a spacing of 14 ft), as shown in Fig- ures 3.47(a) to (e). The effect of the truck load became pronounced as a span length decreased, whereas that of the lane load was augmented with an increase in span length, irrespective of bridge type. These observations agree with the current loading schemes of AASHTO LRFD BDS and the AREMA manual in the sense that concentrated loads with short-axle spacing (i.e., the design tandem in AASHTO LRFD and the alternative 4-axle live load in AREMA) tend to control the behavior of short-span bridges. Figure 3.47(f) summarizes the load effect ratio of each constituent, including 0.57 and 0.43 for the average truck and lane load components, respectively. 3.3.3 Development of a Standard Live Load Model This section discusses the development of a standard live load model for light rail transit, along with the previously proposed load configuration (Figure 3.46) and probability-based load inference at various risk levels. Unless otherwise stated, the load effects (i.e., moment and shear)

34 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads presented are maximum values along bridge spans, which would represent the behavior (or maximum load effects) of the light rail bridges. 3.3.3.1 Probability-Based Load Inference The development of HL-93 in AASHTO LRFD BDS was based on 75-year anticipated events (NCHRP Report 368), followed by a load-enveloping assessment to be explained in a later sec- tion. For consistency, the current research adopted this probability-based 75-year load inference technique. Three more calibration levels were taken into consideration to ensure that the pro- posed load model has a sufficient level of safety, but is not overly conservative from a practice standpoint. It is important to state that light rail bridges do not have sufficient technical data and application history compared with conventional highway bridges associated with AASHTO LRFD BDS; accordingly, rigorous examinations are necessary at various risk levels. These calibration categories, as described, are used in risk analysis and probability modeling for bridge structures to provide a more complete picture for evaluating the data. The following further explains the use of the probability-based load levels: • 75-year anticipated load: AASHTO LRFD BDS demands the design life of a bridge be 75 years. It is not possible to measure load effects for this long time period; hence, the concept of probability is employed to theoretically infer the occurrence of 75-year antici- pated events based on available technical data. Most technical documents dedicated to LRFD employ this approach, for example, NCHRP Report 368: Calibration of LRFD Bridge Design Code. • 99.9% anticipated load: Various degrees of potential occurrence are conventionally used in probability-based design, namely 99.9%, 95%, and 90% with respective confidence levels. The 99.9% occurrence category is most conservative, and was selected in this research. Sometimes 99.99% is chosen to attain more conservative responses. • Upper 20% anticipated load: A typical bias of 20% exists between the effects of design load and corresponding responses in bridge structures (Barker and Puckett 1997; James 2003). This calibration category can address potential risk induced by overloading of light rail bridges. • Average anticipated load: This load level characterizes the average load effect of the four representative light rail trains (Colorado, Minnesota, Massachusetts, and Utah). Using the technical data obtained from the aforementioned models, anticipated load levels at the potential likelihood of the 75-year and 99.9% events were theoretically predicted. In so doing, the restriction of time (e.g., an occurrence event during a service period of 75 years) is over- come. The equivalent loads to be discussed in Section 3.3.3.2 and Section 3.3.3.3 were plotted on the abscissa in arithmetic scale, and the corresponding inverse normal cumulative distribution function values (z scores to be discussed in Section 3.3.3.2) were generated on the ordinate. A relationship was established between the inverse normal cumulative distribution function and the equivalent loads. The statistical estimation of the equivalent loads at the predefined probability levels was then carried out based on fitted equations. 3.3.3.2 Lane Load Each maximum bending moment of the 1,856 simply supported bridge models subjected to the four representative light rail models (Section 3.2.5) was decomposed into two groups (i.e., lane and concentrated loads). Figure 3.48 exhibits the variation of the lane load compo- nent (equivalent load) sorted by magnitude. The equivalent load is defined by the fact that it can generate the decomposed bending moment of the lane loading portion obtained from the model bridges. Most cases were within a load range in between 0.4 k/ft and 0.7 k/ft, although the

research program 35 shortest span reinforced concrete bridges (L = 30 ft) demonstrated a higher load. To probabilisti- cally infer the intensity of the lane load for developing the standard live load model of light rail trains, a probability distribution type was first examined. Equation 3.4 was used to check if the data were distributed in Gaussian: 1 2 (3.4)1z E a k a i ( )= Φ −+ −− where F = the standard normal quantile function; E = the sorted load; k = the total load case number; and a = a constant (a = 0.375 and 0.5 for k ≤ 10 and k > 10, respectively). As depicted in Figure 3.49, the inverse standard normal distribution of all cases was signifi- cantly linear with an average coefficient of determination of R2 = 0.9371, which indicates that the probability distribution of the lane loads was Gaussian. The slight nonlinearity of the reinforced concrete bridges [Figure 3.49(e)] was considered as a tail response, whose contribution to the nor- mality was not significant. Also shown in Figure 3.49 is the potential occurrence of the lane load at 90.0% and 99.9% probability levels: equivalent z sores are 1.335 and 3.091, respectively. The 75-year anticipated load of each case was estimated by the following assumption: typical articulated light rail trains (one to four trains) are operated every 15 minutes (a typical interval) and a bridge is then subjected to eight articulated trains per hour (back and forth), resulting in N = 5.2 million train loadings for 75 years whose probability of occurrence would lead to z = 5.08. Another infer- ence in potential lane load intensity was the occurrence of upper 20% of the probability domain, as shown in Figure 3.50. A summary of the equivalent lane loads in conjunction with the probability-based approaches is provided in Figure 3.51(a) and Table 3.16. Regardless of bridge type, the 75-year occurrence revealed the highest lane load, followed by the 99.9%, the upper 20%, and the average categories. The average values of these prediction categories varied from 0.61 k/ft to 0.96 k/ft [Figure 3.51(a)]. For evaluation, these lane load intensities are compared with the lane load intensity of the HL-93 load model (0.64 k/ft). The 75-year and 99.9% categories demonstrated 50% and 29% heavier lane loads relative to the HL-93 lane load, on average; however, the upper 20% category was similar to the HL-93 lane load. Given that the nominal load effect of the four representative light rail trains (Figure 3.29) is heavier than that of the HL-93 as reported in Figure 3.37, such probabilistically inferred train load effects are acceptable. 3.3.3.3 Concentrated Load The probability-based approaches expounded in the previous section were adopted to estimate equivalent concentrated loads. The maximum static bending moments of the 1,856 light rail bridge models deducted by the lane load portions (Section 3.3.3.2) were employed to calibrate the concentrated loads. As shown in Figure 3.46, two variables were required to be considered: the magnitude of the concentrated loads and their spacing. A numerical parametric study was conducted with variable axle spacing from 5 ft to 29 ft, which was determined based on the axle spacing of the four representative light rail train loads (Figure 3.29). The number of the equivalent concentrated loads applying to a bridge model was dependent upon the span length of the bridge, as schematically illustrated in Figure 3.52. A total of 46,400 load cases were solved and their indi- vidual responses (sorted) are available in Figure 3.53 and Table 2.17, classified by bridge types. Figure 3.54 summarizes the average equivalent concentrated single-axle loads with respect to their

36 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads spacing. The trend found is that the magnitude of the equivalent concentrated load P gradually rose with an increase in axle spacing. This fact agrees with fundamental structural analysis theory (e.g., a concentrated load at midspan of a simply-supported beam causes more load effect than a distributed load of the same total magnitude). As is for the case of the equivalent lane load, the normality of the concentrated loads was checked (Figure 3.55 shows the load values related to an axle spacing of 14 ft for brevity, while other spacing cases revealed similar trends). Although some locally curved responses were noticed owing to an end-tail effect in probability distributions, linearity was preserved with an average coefficient of determination of R2 = 0.9246. It is, thus, concluded that the probability distribution of the equivalent concentrated load was Gaussian. The four anticipated load levels (i.e., 75-year, 99.9%, upper 20%, and average) were determined based on Figs. 3.55 and 3.56. Depending upon bridge types, Figure 3.57 compares the variation of the load classifications. The magnitudes of the 75-year and 99.9% loads were positioned above the upper 20% and average load groups in most cases. Unlike other bridge types, the load profile of the reinforced concrete bridges exhibited wavy responses in the z-score-based loads (i.e., the 75-year and 99.9% categories) within an axle spacing range between 12 ft and 21 ft [Figure 3.57(e)]. This observa- tion is attributed to the fact that the behavior of the short-span reinforced concrete bridges was controlled by a single-axle loading case, which was not observed in other cases. The variation of the equivalent concentrated loads is illustrated in Figure 3.58. The 75-year, 99.9%, and average load categories were controlled by the steel plate and the prestressed concrete box girder bridges; however, the upper 20% category was governed by the reinforced concrete and the steel plate girder bridges. Figure 3.59 provides a comprehensive evaluation of the equivalent light rail train components against their HL-93 counterparts. The equivalent lane loads based on the upper 20% and average categories were similar to the HL-93 lane load; by contrast, the 99.9% and 75-year categories showed higher ratios [Figure 3.59(a)]. For the concentrated load component [Figure 3.59(b)], the upper 20% and average categories were similar to or less than the HL-93 truck load. The combined load of the concentrated and lane components is compared with the HL-93 load, as shown in Figure 3.59(c). The lane load portion was obtained by the uniformly distributed lane load multiplied by individual axle spacing values; for example, the portion of the HL-93 lane load was 17.9 kips (i.e., 0.64 k/ft × (14 ft + 14 ft) = 17.9 kips). In compliance with AASHTO LRFD BDS, an axle spacing of 14 ft was selected for the can- didate standard live load models representing light rail trains. The upper 20% cases at the 14-ft spacing showed the same load as HL-93 [Figure 3.59(c)], whereas the 99.9% and 75-year cases revealed 21% and 59% higher ratios, respectively. The proposed candidate standard live load models were then: • 75-year load: 0.96 k/ft + three axles of 34 kips at a spacing of 14 ft • 99.9% load: 0.82 k/ft + three axles of 27 kips at a spacing of 14 ft • Upper 20% load: 0.67 k/ft + three axles of 21 kips at a spacing of 14 ft • Average load: 0.61 k/ft + three axles of 16 kips at a spacing of 14 ft Figure 3.60 illustrates the load magnitude of the proposed candidate live load models relative to each of the four light rail train loads (Figure 3.29). For comparison purposes without con- sidering bridge span length, the lane load portion of the candidate loads was calculated using a distance of 28 ft (14 ft + 14 ft = 28 ft) covering the front and rear axles of the individual load models. The 75-year load model shows a magnitude analogous to the Colorado and Massachu- setts trains; in contrast, other load models were positioned below the four train loads. It is worth noting that a standard light rail load model (to be selected from the four candidate models) is intended to generate equivalent load effects, rather than matching the gross load of the existing design live loads (Figure 3.29). This approach is the same as use of the HL-93 representing typi- cal highway traffic loads.

research program 37 3.3.3.4 Assessment of the Candidate Standard Live Load Models All simply supported benchmark bridges (Table 3.7) were loaded with the four candidate live load models developed in Section 3.3.3.3 and corresponding maximum static bending moments were predicted, as shown in Figure 3.61, based on moving load simulation technique. To ensure the adequacy of the simulated results, an independent structural analysis program entitled GoBeam was utilized with selected bridge models and almost identical maximum moments were acquired. A comprehensive comparison is then made against the representative design live loads (Figure 3.61). Conforming to AASHTO LRFD BDS, one-track and two-track loaded cases were specified. The average and the upper 20% candidate load models revealed less bending moments than the representative design loads for all bridges. These two load models may be used for predicting the behavior of light rail bridges in service (i.e., partially occupied trains). The 99.9% load model enveloped the upper boundary of the maximum static moments, except for the several steel plate girder bridges having a span length of 160 ft [Figs. 3.61(g) and (h)]. The 75-year load model provided conservative moment-predictions, irrespective of bridge type and span. The effects of the candidate live load models on the maximum shear of the bridges are avail- able in Figure 3.62. All bridges were subjected to the representative light rail train loads (Fig- ure 3.29), in particular four articulated trains (moving load) that would generate largest shear forces in the bridge structures. Like the moment responses discussed previously, the shear forces resulted from the upper 20% and average load models were less than those of the existing train loads. The 99.9% load model generated shear responses similar to the four representative train loads up to a span length of 100 ft, beyond which the 75-year model enveloped the shear forces induced by the existing loads. The proposed candidate live load models were further assessed against the probabilisti- cally inferred load effects associated with the in situ response of the five bridges in Denver, CO (Table 3.3). Figure 3.63 shows the bending moment of these bridges obtained from the measured girder strains induced by the in situ Colorado light rail trains and composite-section properties (i.e., neutral axis depth and moment of inertia). For comparison, the same risk levels used in the previous examinations were adopted: the average, upper 20%, 99.9%, and 75-year categories. All site responses exhibited a linear trend with an average coefficient of determination of R2 = 0.9506; a summary of the inferred load effects is provided in Table 3.18. These site-based inferred load effects intrinsically represent potential extreme service condi- tions, because the probabilistic inference was made in accordance with in situ train loads. Figure 3.64 compares the site-based moments to those with the candidate live load models. Although the response of the moment ratio was dependent upon the evaluation categories and bridge types, an average ratio of 0.76 was observed. This indicates that the proposed candidate live load models generated about 25% larger moments than the extreme service live loads (e.g., a 75-year occurrence period) inferred by the in situ bridge responses. The proposed candidate load models are, therefore, adequate and appropriate for evaluating the strength limit state of light rail bridges. 3.3.3.5 Proposal of a Standard Live Load Model According to the moment and shear responses discussed in Section 3.3.3.4 (Assessment of the candidate standard live load models), the 75-year load model with a standard track gage width of 4.71 ft was selected for the strength design of light rail bridges (Figure 3.65), and was named to be LRT-16: • LRT-16: 0.96 k/ft + three axles of 34 kips at a spacing of 14 ft It may be allowed to use an alternative site-specific train load model based on the discretion of individual transit agencies.

38 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads 3.3.3.6 Evaluation of Proposed Load Model Using Load-Enveloping Method The proposed standard live load model (Figure 3.65) was evaluated using 33 light rail trains operated in the United States (29 trains) and Canada (with four trains), including a total of 660 load cases. The train-related database obtained from the American Public Transportation Association (APTA) supplies the empty weight of trains (51 kips to 156 kips per train), the num- ber of axles (four to 10 per train), the length of trains (over coupled faces), the number of seats (from 29 to 120 per train), and other non-structural configurations such as car body, doors, and heating systems. The following assumptions were made to generate the load effects of the trains (bending moments and shear forces), because the database did not provide such details: • Structural load (AW4): Empty train weight and fully seated passengers (154 lb/person, TCRP Report 155) plus standees in two groups (205 and 240 persons) were considered. Although standing areas with 6.7 passengers/yd2 (TCRP Report 155) are not available in the database, some design manuals specify the number of standees for AW4 (Denver 160 persons, Minnesota 240 persons, Utah 180 persons, and Washington 240 persons), leading to average standees = 205 people per train and maximum standees = 240 people per train • Axle load: The structural load of an articulated train was distributed according to an expert opinion and reasonable allocation schemes, as shown in Table 3.19 • Axle spacing: Axle spacing was measured from the train drawings available in the database (Tables 3.20 and 3.21 and Figure 3.66) To determine maximum load effects such as bending moments and shear forces induced by the train loads, simply supported beam-line (one-dimensional) bridges were used with a span length varying from 30 ft to 300 ft based on the request of an AASHTO committee. Four articulated trains were exploited to assess the notional load models, so that the bridge span was fully covered by light rail train loading. The moving load feature of the GoBeam program calculated the load effects. Fig- ures 3.67(a) and (b), respectively, show the bending moments and shear forces of the bridges sub- jected to the 33 trains with the average standee load of 205 people per train. The bending moments of all cases were almost enveloped by those obtained from the standard load model [Figure 3.67(c)], while the shear forces of some cases exceeded up to 14.6% at a span length of 300 ft [Figure 3.67(d)]. This discrepancy in load-enveloping is less than or comparable to that of HL-93 against 22 exclusion trucks (AASHTO LRFD BDS). The cases with the maximum standee-load of 240 persons per train are available in Figure 3.68. The difference between the load effects of the standard load model and the 33 trains increased up to 11.4% and 18.7% for the moment and shear, respectively, which are still less than or comparable to that of the HL-93 assessment in AASHTO LRFD BDS. It is, therefore, concluded that the proposed standard live load model for light rail trains represents the load effects of light rail trains and, accordingly, can be used for practice. 3.3.3.7 Discussion on Development of HL-93 and Justification of Proposed Load Model 3.3.3.7.1 Background and calibration methodology of HL-93. It is widely accepted that probability investigations are imperative when a load model is developed, because the effect of live load is controlled by numerous random variables such as vehicle weight, loading position, traffic volume, and bridge configuration. The AASHTO LRFD live load model called HL-93 was developed based on NCHRP Report 368: Calibration of LRFD Bridge Design Code (1993) (this is the reason why it is called HL-93, meaning “highway loading 1993”), and was assessed using 22 exclusion trucks (load enveloping). HL-93 was probabilistically calibrated: survey data with 9,250 truck loadings obtained from various types of bridges constructed in Ontario, Canada, were used to generate 75-year anticipated load effects (extrapolated from the survey data), and the live load model was calibrated against the anticipated load effects with an objective of

research program 39 generating a uniform bias. NCHRP Report 368 justifies use of the probability-based method by stating that “a considerable degree of uncertainty is caused by unpredictability of the future trends with regard to configuration of axles and weights.” After many trials, load effects caused by a combination of HS20 and a lane load of 0.64 k/ft were found to be comparable to the 75-year anticipated maximum load effects with a relatively consistent bias for highway bridges (NCHRP Report 368). It is believed that the reason for keeping the traditional HS20 load in the new model (at that time) was that practitioners were familiar with the use of HS20, although it does not represent modern bridge loading (Nowak and Hong 1991, Baber and Simons 2007; Nowak and Collins 2013), since it was used for over 50 years before AASHTO LRFD BDS was released. So, rather than changing the familiar HS20 truck, the lane load component was added to increase load effects, and the combined load model was probabilistically calibrated to satisfy the demands of the bridge engineering community. 3.3.3.7.2 Justification of proposed load model. It is likely fair to state that the development of the HL-93 loading was a blend of what could be termed “traditional methods (load-enveloping)” and more “modern methods (probability-based methods)”. The trend toward the development of structural design codes that are reliability-based, even after more than 50 years of history, is still typically met with some resistance from certain facets of both the building and bridge engineering communities. The quantification and management of uncertainty provides structural engineers with a much better measure of how safe a structure is or what the true level of safety is. It is fortu- nate that the reliability-based work conducted during this investigation has shown that there is less uncertainty surrounding the configurations of light rail traffic than for other types of vehicles to load highway bridges. At the same time, though, it is likely that not as much time, effort, and monies have been expended on research and development efforts over the years on railway bridge engineering as compared with highway bridge engineering. The result is that the highway bridge engineering community, in all likelihood, had a lot more hard data to work with than was avail- able for this project. As such, the blend of traditional methods and modern methods had to lean more toward emphasizing the modern methods. Reduced uncertainty also means that the initial implementation of light rail provisions by AASHTO can be comfortably conservative, and be economical at the same time. All possible known vehicle configurations are not technically available, unless significant dollars and time are invested as is the case for highway bridges that accompany a substantially long history with abundant technical data. Probability-based modeling was, therefore, an inevitable (and robust) technical option in this project. It is also worth noting that load factor calibration is not related to the 75-year anticipated behavior that AASHTO LRFD BDS demands, because uncertainty is addressed by considering the coefficient of variation and a reliability index. Therefore, the 75-year service life expectation of AASHTO LRFD BDS needs to be addressed, when a load model is developed as in the cases of NCHRP Report 368 and the current research. A number of studies claim that the effects of heavier live load need more research to address technical concerns, and an increase in live load is apparent and expected in both highway and railway bridges (Nowak 1999; Tobias et al. 2004; Fu 2002; Nowak and Collins 2013). To effectively address a potential increase in live load and any uncertain occurrence during the 75-year service life of a bridge, a certain level of conser- vatism relative to current design loading (e.g., the four representative live loads discussed earlier) is necessary. The proposed probability-based live model is technically superior to a model based on simple load-enveloping of design live load effects. Once a load model is proposed and engineers become familiar with it, it is not easy to revise the configuration of the load model. It is thus crucial to propose a load model that may not just represent current live load, but also can represent future load based on probability theory. The original calibration of HL-93 was based on simple analytical models having various spans (Nowak 1999), which is a simplified approach because the capacity of a personal computer was limited in the early 1990s. The present research is based on refined modeling approaches with various types and spans of light rail bridges.

40 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads The approach taken in this research program is basically the same as that of NCHRP Report 368, in that bridge responses were predicted by finite element models (validated against in situ light rail bridge responses) using the representative light rail train loads, and corresponding results were extrapolated up to 75 years using probability theory. Three other anticipated load levels (99.9%, upper 20%, and average) were additionally employed to ensure the load effects generated by the light rail trains were reasonably conservative and reliable, because information on light rail loading is extremely rare so a rigorous and careful evaluation was important. The load effects (moment and shear) induced by the probability-based candidate load models were compared with those generated by the existing train loads (“load-enveloping” with 33 trains), and further assessed using site-data-based probability prediction to justify the use of the proposed live load model. As stated in Section 3.3.1, the idea of the proposed live load model was taken from the European train model (LM2000) and even the existing train load model LM71 has basically a similar format, as shown in Figure 3.45. LM2000 is much simpler and straightforward to use than LM71, which was the primary reason for developing and accepting this new load model by the European Railway Research Institute. Coincidently or not, the LM2000 train model is similar to HL-93 in terms of loading format. It is emphasized that the objective of using a notional live load model for bridge design (either highway bridges or rail bridges) is to conveniently predict the behavior of bridges subjected to certain types of loadings. As long as the model generates reliable bridge responses from design perspectives, its configuration does not matter and there is no need to look different. The European train models are completely different from the Cooper E80 of AREMA; however, the models generate reliable structural responses. All the train load models shown in Figure 3.45 have a uniform load as in the case of HL-93, because trains are physically long and their moving axles generate a so-called uniformly distributed load (UDL) effect, which is the same as the mixed traffic on highway bridges. It was common for practitioners to not fully understand or appreciate the concept of a notional load, when AASHTO LRFD BDS was first published. So, there was a fair amount of resistance at first to the HL-93 load, whereas this sentiment seems to have disappeared to an extent over the years. The concept of a notional load and its usefulness, however, is very powerful and very useful. It is likely that the notional load or the proposed standard live load model for light rail trains will be more readily accepted at first than the HL-93 notional load was. In summary, the proposed live load models (based on 48,256 deterministic light rail loading cases along with the four probability- based examination categories plus load-enveloping assessment using 33 trains) were developed in basically the same approach to HL-93, except that the current models were intended to be a bit more conservative because of the insufficient technical research on light rail loadings and asso- ciated load effects for light rail bridge design, as expounded above. 3.4 Characterization of Live Load Effects 3.4.1 Deflection and User Comfort 3.4.1.1 Deflection Figures 3.69 and 3.70 reveal a comprehensive comparison of the predicted maximum deflec- tions of the 2,960 bridge models against the suggested limits given in Section 3.2.2.3. The simply supported bridge models were loaded with the four representative light rail trains (Figure 3.29), whereas the multiple-span bridges were subjected to the heaviest Utah train load to save compu- tational effort. In accordance with AASHTO LRFD BDS (i.e., dynamic load is applied for deflec- tion check), all train loads were subjected to a design speed of 60 mph. The maximum deflections of the bridges rose with an increase in span length. The prestressed concrete box and reinforced

research program 41 concrete girder bridges exhibited the least deflections because of their substantial flexural rigidity and short span length, respectively, regardless of structural determinacy (i.e., simply supported or multiple spans). The aforementioned deflection limit criteria had noticeable margins com- pared with the predicted deflections. This finding could justify the reason why AASHTO LRFD BDS states that deflection limitations are optional for bridges and several technical documents claimed the L/800 criterion might not be sufficient to control bridge deflections (e.g., NCHRP Project 20-7; SHRP R19B). It is contemplated that the deflection article of AASHTO LRFD BDS is also applicable to light rail bridges (i.e., the L/800 limit can still be optional for light rail bridges), and the subsequent user comfort criteria described in Section 3.4.1.2 can be added. 3.4.1.2 User Comfort The comfort criteria of the CHBDC were adopted in the present research, as discussed in Section 3.2.2.3. All three assessment categories of CHBDC (without pedestrian use, occasional pedestrian use, and frequent pedestrian use) were considered and available in Figs. 3.71 and 3.72, where the maximum static deflections and fundamental frequencies of the 2,960 bridge models were shown. It is worth noting that maximum static deflections were used as stated in CHBDC, and these can be obtained from bridge girders in practice, unless a bridge has a noticeably long overhang (typically over 70 in.) that accommodates traffic loading far away from the exterior girder (i.e., large deflections of the overhang and sidewalk, if any), although sidewalk deflection is mentioned in the code. The responses of all bridges were within acceptable domains when the without pedestrian use and occasional pedestrian use categories were employed. However, the requirement for the frequent pedestrian use category was not satisfied in many cases, except for the prestressed concrete box and reinforced concrete girder bridges, because of the reasons explained earlier (i.e., low deflections owing to their flexural rigidity and short span length). The International Union of Railways (UIC Code 776-2, UIC 2009) employs bridge deflection as a measure of passenger comfort, and provides three comfort levels based on the vertical acceleration of railway bridges (1.0 m/s2, 1.3 m/s2, and 2.0 m/s2 for the Very good, Good, and Acceptable levels, respectively). The deflection limit corresponding to the Very good category is L/600 for bridges carrying trains operating at 60 mph. As examined in Section 3.4.1.1, the bridge deflections were within the L/600 limit and, thus, passenger comfort does not seem to be a concern for light rail bridges. Design recommendations can be made in such a way that user comfort (pedestrians and passengers) may not be critical for light rail bridges when primarily subjected to train loading, whereas care should be exercised to check the pedestrian comfort requirements, if a light rail bridge is intended for frequent pedestrian use, as part of service- ability limit states. 3.4.2 Live Load Distribution 3.4.2.1 Light Rail Train Loading Figure 3.73 illustrates live LDF for selected simply-supported light rail bridges subjected to the standard live load model (Section 3.3). Following AASHTO LRFD BDS, live LDF for light rail trains were developed. The behavior of the simply-supported bridges was the source of the development. It is understood in the research community that structural continuity does not influ- ence live load distribution (Barker and Puckett 1997). Equation 3.1 was used to determine the distribution factors of the light rail bridges. As shown in Figure 3.73, the distribution profile of the live load was controlled by the position and number of light rail trains in the transverse direction. Because there is a lack of information on live LDF for light rail bridges, the lever rule method is frequently employed by practitioners. Figures 3.74 and 3.75 assess existing design methods for bending and shear against the refined LDF attained from the finite element models. The simple mechanics-based lever rule approach largely overestimated the load distribution for both exterior

42 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads and interior girders. The AASHTO LRFD BDS method exhibited better prediction compared with the lever rule; nonetheless, it still demonstrated discrepancy. This fact points out the need to develop live LDF dedicated to light rail bridges. The calibration work shown in Figures 3.76 and 3.77 was based on the format of the AASHTO LRFD BDS equations and minimal adjustment was made, except that the lever rule for single-lane loading recommended by AASHTO LRFD BDS was replaced by equations similar to those for multiple-track-loaded cases since the prediction by the lever rule was overly conservative as discussed earlier. Tables 3.22 to 3.25 summarize the proposed distribution factor equations for moment and shear, including interior and exterior girders. Although the proposed load distribution equations were in agreement with the load dis- tribution predicted by the finite element models (Figure 3.78) and demonstrated better predict- ability against the simple lever rule and the AASHTO LRFD BDS methods, further refinement (or improvement) may be required with a significantly large set of a bridge database as in the case of the load distribution equations in AASHTO LRFD BDS. The proposed equations were employed to predict LDF for the five bridges whose responses were monitored in Section 3.1, as shown in Figure 3.79. The level of prediction was reasonable, while some scatter was inevitable due to the regression nature of the equations. It should be noted that, because its physical geom- etry is not symmetric, the load distribution of the Broadway Bridge in single-track loading was not symmetric [Figure 3.79(a)]. 3.4.2.2 Light Rail Train and Highway Loadings To examine the behavior of the five benchmark bridges subjected to light rail train and highway traffic loadings (the standard live load model and HL-93, respectively), 29 load combinations for each bridge were used (13 and 16 cases for the 2+2+2 and 3+2+3 loading scenarios, respectively, as shown in Figure 3.80). When side-by-side trucks were positioned, their transverse distance (center- to-center of wheels) was 4 ft to generate maximum load effects. The number of the girders varied between 6 and 9, depending upon superstructure types with a span length from 30 ft to 160 ft (Table 3.7). The dimensions related to the load combinations are available in Figure 3.27. Figures 3.81 to 3.100 reveal the moment and shear profiles of the bridges, where maximum responses were pre- dicted. The shape and magnitude of the load distribution were a function of loading position and span length. The load distribution profiles clarify the effects of the combined loading scenarios, in that higher bending moments and shear forces were accompanied with the girders under- neath the light rail train load (girder numbers 3 to 6) compared with those subjected to light rail train loading only (LRT-1 and LRT-2 indicating one- and two-track loaded trains, respectively). Figures 3.101 to 3.102 illustrate increases in moment and shear owing to the combined loads, including normalized load effects with the LRT-1 or LRT-2 scenarios. The variation range of the moment was wider than that of the shear in all cases; however, the breath of the box-type girders (for instance, prestressed concrete box and steel box in Figures 3.101(a) and (e), respectively) was larger than that of the other types. This is attributed to the fact that the box girders were physically integrated with one another, so that the transfer of the live load effect was more effective than discrete girders. Figure 3.103 compares the moment responses of the bridges relative to those of one- and two-track light rail train loadings. The one-track-loaded cases were more sensitive than their two-track-loaded counterparts. The reason for this is that the former had an eccentric loading effect from the centerline of the bridge superstructure (in the lateral direction), unlike the latter that accompanies a uniform load configuration without a noticeable eccentricity. As more lanes were loaded, the shear responses of the bridges increased (Figure 3.104). There was no remarkable difference between the one- and two-track light rail train loading cases, since all gird- ers were supported by pier caps or abutments and, consequently, the eccentricity effect discussed previously was not pronounced. The controlling live LDF for the exterior and interior girders of the bridges carrying light rail train and highway traffic loads are summarized in Tables 3.26 to 3.35, including the 2+2+2

research program 43 and 3+2+3 loading cases (Figure 3.80). The general trend is that the distribution factors for the interior girders were reduced with an increase in span length. This observation can be explained by the fact that the bridge superstructure tended to behave like a single beam, when the span increased (Sennah and Kennedy 1999; Huo et al. 2004; Tobias et al. 2004). By con- trast, the variation of live LDF for the exterior girders was influenced by the location of the loaded lanes, which could illustrate that the applied live load interacted with the edge stiffen- ing of the deck. 3.4.3 Dynamic Load Allowance Figures 3.105 and 3.106 show the DLA of the 1,856 simply supported and 1,104 multiple-span benchmark bridges, respectively, obtained by the following equation: 100 % (3.5)DLA dynamic static static ( )= δ − δδ × where DLA is the dynamic load allowance of the bridge, and ddynamic and dstatic are the maximum deflections of the bridge subjected to the dynamic and static loads generated by the representa- tive light rail trains, respectively. The dynamic deflections were obtained at a train operating speed of 60 mph, and the static ones were attained by the moving load feature of the finite ele- ment program. A total of 2,960 load cases were solved by the finite element models. In the case of simply supported bridges (Figure 3.105), the solved DLA values were typically less than 20%, while the steel box bridges exhibited relatively high values [Figure 3.105(c)]. A similar trend was observed for multiple-span bridges (Figure 3.106). It should be noted that the prestressed concrete I-girder bridges were simply supported (Table 3.7), and in situ continuity diaphragms were not considered. Rocking effects are not an influential parameter in modern light rail transit (typical DLA for railway bridges consists of two components (Unsworth 2010): superstruc- ture-train interaction and rocking effect). Figures 3.107(a) to (e) compare the predicted DLA values with the design equation suggested by ACI-343 (ACI 2012), which is a frequently refer- enced document when designing light rail bridges (Smith and Hendy 2009). The design DLA of ACI-343 was conservative in comparison with the present DLA values. A comprehensive sum- mary of the ACI-343 design DLA is provided in Figure 3.107(f), including the average and maximum values of the five bridge types. To generate design information, probability-based investigations were conducted at three risk levels: 75-year anticipated, 99.9%, and 90.0% DLAs. This approach is identical to the one detailed in Section 3.3.3. Significant normality was observed in all cases with average coeffi- cients of determination of R2 = 0.9466 and 0.9667, as shown in Figures 3.108 and 3.109 for the simply supported and multiple-span bridges, respectively. Figure 3.110 compares the average DLA of the solved models against the probabilistically inferred values (i.e., 90.0%, 99.9%, and 75-year anticipated DLA). The DLA in tandem with a return period of 75 years was the most conservative among others. For strength design purposes, an additional margin of 5% may be added to the 25% DLA determined from the 75-year-anticipated event, because several factors can influence the behavior of constructed light rail bridges (e.g., track shifting, various track defects, and defective train conditions). A DLA of 30% is, therefore, proposed for designing light rail bridges (both distributed and concentrated loads of LRT-16) and its conservative nature was further confirmed via a local dynamic response model (i.e., wheel-rail interaction) developed using an explicit finite element program in a later section. For fatigue design, the proposed DLA of 30% is still recommended owing to the potential existence of deteriorated wheel and track conditions.

44 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads 3.4.4 Multiple Presence Factor A multiple presence factor (MPF) for bridges may be defined as: 1 (3.6) 1 MPF E E N N = where EN and E1 are the load effects of the n-track-loaded and one-track-loaded cases, respectively; and N is the number of loaded lanes. Figure 3.111 illustrates a multiple presence example con- cerning the simultaneous occurrence of two-track loading on the interior span of the steel plate girder bridge (L = 160 ft), when subjected to one articulated six-axle Utah train per track (Fig- ure 3.29). The four candidate standard live load models developed in Section 3.3 were exploited to estimate the MPFs of the light rail bridges, based on maximum static moments. As demonstrated in Figure 3.112, the MPFs of the bridges were close to unity, regardless of the number of loaded tracks. This fact aligns with the AREMA manual, stating that full live load is considered up to two tracks; in other words, a MPF of 1.0 is used for one- and two-track-loaded cases. The MPF of 1.2 for one lane loading specified in AASHTO LRFD BDS does not appear to be applicable to light rail bridges. The multiple presence of in situ light rail trains is given in Figure 3.113. These data were obtained when measuring the behavior of the five light rail bridges in Denver (Section 3.1) in 2014 [Figure 3.113(a)] and were re-counted in 2015 to confirm the occurrence of train presence data [Figure 3.113(b)]. Except for the Indiana Bridge having one-track, all others are two-track bridges. The occurrence of simultaneous two-track loading was insignificant in all cases. It is, therefore, concluded that multiple presence is not a critical concern for light rail bridges, and the proposed MPF of 1.0 can be used for both one- and two-track-loaded cases. 3.4.5 Skew Correction Factor Figure 3.114 evaluates the applicability of the skew correction factors presented in AASHTO LRFD BDS using the response of the skewed light rail bridge models (Figure 3.40). The AASHTO LRFD equations reasonably estimated the moment and shear of the skewed bridges, regardless of bridge type; however, some discrepancy was noticed. To improve the predictive behavior of the skewed light rail bridges, regression analysis was conducted along with the format of the AASHTO LRFD equations. The proposed skew correction factors dedicated to light rail bridges are listed in Table 2.36, and further compared with the model prediction in Figures 3.115 and 3.116. Additional assessment on skew correction factors is available in a later section based on statistical techniques. 3.5 Rail–Train–Structure Interaction and Associated Forces 3.5.1 Centrifugal Force Figure 3.117 exhibits the centrifugal force of the bridges subjected to the heaviest axle load of the Utah train (27 kips was loaded per track) at an operating speed of 60 mph. The centrifugal force was obtained by summing up the largest horizontal force components of the aforemen- tioned curved bridges (Figure 3.31) in the radial direction (perpendicular to the curved super- structure) at a critical location. The use of one axle load is justified by the fact that AASHTO LRFD BDS stipulates a centrifugal force multiplier for each axle load. The AREMA manual prescribes essentially the same approach. The centrifugal forces were reduced as the radius of curvature increased in all cases (Figure 3.117). This is due to the fact that the centrifugal acceleration (ah) associated with the moving axle load decreases, when the radius of the curvilinear track (r) is increased (i.e., ah = V 2/r in which V is the moving speed). Also compared in Figure 3.117 are the

research program 45 centrifugal forces calculated by the equations specified in AASHTO LRFD BDS and AREMA. In general, the AREMA approach underestimated the centrifugal forces resulting from the Utah axle load. The AASHTO LRFD method without MPF (MPF = 1.2 and 1.0, respectively, for one- and two-track-loaded cases) reasonably predicted the forces, whereas it appears to be too close to the centrifugal forces for the one-track-loaded cases. The empirical constant of 4/3 belonging to the AASHTO LRFD equation should be included in the centrifugal force equation for light rail bridges (the empirical constant was involved in AASHTO LRFD BDS to accommodate both truck and lane loadings for HL-93, which can also be valid for the proposed LRT-16 standard live load). Provided that the MPF of light rail trains was proposed to be unity in Section 3.4.4, a modified version of the AASHTO LRFD expression is suggested as follows: 4 3 0.2 1.4 (3.7) 2 C v gR n( )= − + where C = the centrifugal force multiplier for the curved bridge superstructure; g = the gravitational acceleration (32.2 ft/sec2); R = the radius of curvature of the train track; v = the speed of the light rail train (ft/sec); and n = the number of loaded tracks either one or two. Another comparison of the centrifugal forces calculated by the proposed equation against those obtained from the finite element models is given in Figure 3.118. Although Eq. 3.7 conser- vatively predicted centrifugal forces for the bridges with a radius of 500 ft in some cases, it can be acceptable for the design of light rail bridges. 3.5.2 Longitudinal Force When braking action takes place, the kinetic and potential energy of light rail trains can be converted to a longitudinal force (Fb): 1 2 (3.8)2mV mg h F sb+ ∆ = where m = the mass of the light rail train; V = the operating speed; g = the gravitational acceleration (g = 32.2 ft/s2); Dh = the height difference from deceleration to stopping; and s = the braking distance. The longitudinal braking force is transmitted to rails and, consequently, to the supporting members. Rearranging Eq. 3.8 with Fb = ma, in which a is the deceleration of the train, the braking distance s may be calculated: 1 2 (3.9)2s V g h a( )= + ∆ Assuming Dh is zero along a flat operating track, the longitudinal force can then be: F V gs W Wb =     = α 1 2 (3.10) 2

46 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads where W is the weight of the light rail train. Because all wheels of light rail trains are powered, a slope of up to 7% may not cause any problem in train operation (Parsons Brinckerhoff et al. 2012). Figure 3.119 compares the predicted braking distance using Eq. 3.9 with test data taken from the literature (Handoko and Dhanasekar 2006; Nankyo et al. 2006). TCRP Report 155 (Parsons Brinckerhoff et al. 2012) states that the deceleration of light rail trains varies from 6.6 ft/s2 to 8.8 ft/s2, and the corresponding variation of a braking distance is provided in Fig- ure 3.120(a). The effect of train speed is shown in Figure 3.120(b) in conjunction with the TCRP Report 155 deceleration range. It is expected that a typical braking distance required for light rail trains would be from 440 ft to 590 ft. Figure 3.121 reveals the calculated longitudinal force multiplier a, which is independent of train speed as per Eqs. 3.9 and 3.10. The upper decelera- tion limit of a = 8.8 ft/s2 and a design speed of 60 mph (88 ft/s) were taken to propose design recommendations, which resulted in a = 0.273 (Figure 3.121). This value is 8.4% higher than the braking force multiplier a = 0.25 stipulated in AASHTO LRFD BDS. Longitudinal braking force was simulated using the benchmark bridge models (Table 3.7) subjected to one articulated Utah train. The span length of the bridges was 140 ft, except for the reinforced concrete bridge with the longest span length of 70 ft. The train loading was operated at a speed of 60 mph and stopped at 60% of the span length, so that the longitudinal loading was fully transferred to the superstructure. The reaction of the individual girders at the stopping location was summed up to determine a longitudinal braking force. In accordance with Eq. 3.10, the braking force multiplier a was obtained [Figure 3.122(a)]: the reinforced concrete bridges revealed a = 0.24, whereas all other bridges showed a = 0.29, on average. The reason for this relatively low multiplier of the reinforced concrete bridges is that their short span length (70 ft) did not fully accommodate the light rail train loading (162 kips with a spacing of 74 ft from front to rear axles). Figure 3.122(b) compares the theoretical multiplier (a = 0.273) with the finite element prediction. All cases, except for the reinforced concrete bridges, exhibited an average margin of 6.7%, which can be reasonably acceptable. To calibrate the axle plus lane load components of the standard live load model developed in Section 3.3, a comparison was made with the ratio of HL-93 that has a load configuration similar to the proposed standard live load model (LRT-16): Ratio F F b lane b concentrated ( )= ×− − 100 % (3.11) where Fb-lane and Fb-concentrated are the braking forces induced by the lane and concentrated load components, respectively. Within a span length varying from 30 ft to 160 ft, 5% of the axle weight plus lane load of the standard live load model showed agreement with the provision of AASHTO LRFD BDS (Figure 3.123). Conforming to the format of AASHTO LRFD BDS, the longitudinal braking force may be taken as the greatest of (without DLA): • 28% of the light rail design concentrated loads or • 5% of the axle weights plus lane load Literature specifies that the traction force of light rail trains with acceleration is 50% of the braking force with deceleration (RTD 2013). Accordingly, the proposed design expression for longitudinal force can cover both braking and traction components. About 60% of the longi- tudinal force induced by train-braking or tractive effort may be transferred from trains to sup- porting girders (Srinivas et al. 2013); nonetheless, the proposed expressions are conservatively recommended for light rail bridge design. 3.5.3 Thermal Force Pursuant to AASHTO LRFD BDS, the development of interface force for light rail bridges was examined. The coefficients of thermal expansion for steel and concrete were a = 6.5 × 10-6/°F and

research program 47 6.0 × 10-6/°F, respectively. The variation of temperature in steel rails was assumed to be 150°F. Tem- perature gradient was considered to address the non-uniform thermal exposure of a bridge super- structure: thermal zones 1 to 4, based on AASHTO LRFD BDS. The temperature-induced stress (sT) may be obtained by a combination of axial strain (eT) and curvature (yT) (Ghali and Neville 1989): (3.12) A T AT ai i∑ε = α (3.13) I T y A T d IT ai i i i i i∑ψ = α + ∆  where A and Ai = the total cross-sectional area and the ith element area of the bridge superstructure, respectively; Tai = the temperature at the element centroid; I and I _ i = the total moment of inertia and the moment of inertia of the section about its own centroid, respectively; y _ i = the element centroidal axis; DTi = the temperature difference from bottom to top of the element; and di = the element depth. The temperature-induced distress was engaged with the aforementioned thermal zones in AASHTO LRFD BDS. It is worth noting that such distress primarily contributes to increasing internal stresses, rather than causing girder reactions, if expansion joints are designed appropri- ately. Figure 3.124 compares the thermal load of the light rail bridges predicted by the finite ele- ment models with their theoretical counterparts. Irrespective of bridge type, the model prediction agreed with the theoretically determined thermal load. The effect of thermal zones on the thermal load development is provided in Figure 3.125. The thermal load in Zone 1 was higher than that in other zones. For instance, the thermal load of the 140-ft prestressed concrete I-girder bridges under Zone 1 thermal loading (T1 = 54°F) was 33% higher than that under Zone 4 (T1 = 38°F), on average, as shown in Figure 3.125(b). The thermal load tended to decrease with an increase in span length. This observation indicates that the temperature-induced forces were distributed to the bridge girders. As opposed to the thermal responses of the bridges in the longitudinal direc- tion, temperature-induced lateral forces in railway bridges are negligibly transferred to substruc- ture via the bearings (Okelo and Olabimtan 2011). 3.5.4 Rail Break It is common practice to evaluate the effect of rail break at a critical location where an expan- sion joint is installed over the pier. Because the scope of the present research is on the global behavior of light rail bridges (or bridge-level response), local issues related to rail break such as fastener spacing and toe load are not of interest. The range of temperature variation in the rail was taken from the Temperature range for Procedure A of AASHTO LRFD BDS, including a maximum range DT of 120°F and 150°F for Moderate and Cold climates, respectively. The fol- lowing equation was derived from the approach shown in TCRP Report 71, Volume 6 (Dante et al. 2005) to estimate the amount of rail break gap: Gap EA T N P S clip TL ( ) = α∆ µ 2 (3.14)max 2 where E and A = the elastic modulus (E = 29,000 ksi) and cross-sectional area (A = 11.25 in2) of the 115RE rail, respectively;

48 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads a = the CTE of the rail (a = 6.5 × 10-6/°F); DT = the temperature variation; Nclip = the number of rail clips on the fastener (Nclip = 2); µ = the coefficient of friction between the rail and rail clip (an average value of µ = 0.5 was used based on TCRP71-6); PTL = the individual clip toe load (PTL = 6153 lb per fastener based on TCRP Report 71, Volume 6); and S = the spacing of the fastener (30 in. was used as per RTD 2013). The rail gap due to rail break increased in a parabolic manner with an increase in temperature change, and a maximum gap of 3 in. was predicted within the temperature variation range of AASHTO LRFD BDS (Figure 3.126). The rail break simulation, accordingly, had two catego- ries: no break (0 in. gap) and rail break (1, 2, and 3 in. gaps). Unsworth (2010) mentions that a rail-break-induced gap between 2 in. and 6 in. is acceptable for the safety of rail bridges. Figure 3.127 shows a finite element model to predict the effects of rail break on the increase of DLA. The DLA of the bridges subjected to the four articulated Utah trains is revealed in Fig- ure 3.128, which was calculated by maximum negative moments in static and 60-mph dynamic conditions [i.e., DLA = (Rdynamic - Rstatic)/Rstatic, as explained in Section 3.4.3]. Although some scat- ter was noticed in the individual bridge models, the DLA tended to rise as a rail gap increased: the average DLA acquired from the 0-in. gap case (intact rail) was 50%, 59%, and 66% lower than those from the 1-, 2-, and 3-in. gap cases, respectively, as shown in Figure 3.129. The DLAs predicted at the piered location with maximum negative moments (Figure 3.127) were not as high as those obtained at a critical section in positive bending (Figures 3.105 and 3.106). This can be attributed to the fact that the break event was local with discontinued rails, and was not sufficiently large to influence the global response of the bridge structure. Furthermore, all DLA values induced by the rail break were substantially lower than the proposed DLA of 30% for design (Section 3.4.3). There appears to be no technical concern associated with rail break from structural perspectives. 3.5.5 Effect of Bearing Arrangement The effect of bearing arrangement on force transfer from the superstructure to the substruc- ture of the continuous benchmark bridges (Table 3.7) was studied, as shown in Figure 3.130. Because the global behavior of light rail bridges is emphasized, local interaction between track rails and bearings was outside the scope of the present investigation. For consistency with other technical tasks discussed in this document, the Utah train load (162 kips) operated at a speed of 60 mph was employed. Figure 3.131 compares the horizontal forces obtained from each hinged bearing when the bridges (80 ft/span) were subjected to the train loading, includ- ing a force range between 34 kips and 47 kips. The bearing force normalized by the applied train load is summarized in Figure 3.132. The location of the hinged bearings did not notice- ably influence the force transfer from superstructure to substructure. For instance, the average force ratios (bearing force/train loading) of 25.7% and 25.0% were predicted for the two- and three-span bridges, respectively. 3.5.6 DLA Based on Wheel-Rail Interaction To evaluate the global-level (or bridge-level) DLA of 30% proposed in Section 3.4.3, local- level investigations were conducted using the explicit finite element program LS-Dyna. The fun- damental wheel-rail system adapted for the present modeling approach was composed of 115RE rails and AAR-1B wheels (Figure 3.133), as specified in TCRP Report 155 (Parsons Brinckerhoff et al. 2012). The wheel and axle components were made of ASTM A-1 carbon steel with a tensile

research program 49 strength of 60 ksi. Detailed information on the AAR-1B was obtained from TCRP Report 151; for example, wheel diameter = 28 in., wheel gage = 55.7 in., and wheel back to back = 53.4 in. 3.5.6.1 Model Development Figure 3.134 shows the developed wheel-rail interaction model, including AAR-1B wheels, 115RE rails, axle shafts, and suspension and damping systems. The finite element model included 2-node spring elements (MAT_SPRING_ELASTIC), 2-node beam elements (MAT_RIGID), and 8-node hexahedral solid elements (MAT_PIECEWISE_LINEAR_PLASTICITY). The wheels, rails, and axles were modeled with the solid elements, while other components were represented by the beam and spring elements (Figure 3.134). The train load applied was assumed to be a lumped mass linked with the suspension element. A piecewise linear plasticity function built in LS-DYNA (LS-DYNA 2015) was exploited for the bilinear constitutive material models (i.e., stress-strain relationship) of the wheels, rails, and axles. The truck mass connected with the two-axle shafts was modeled as the rigid material function available in LS-DYNA. The suspen- sion and damping system of the model was represented by the beam elements coupled with the discrete springs. Load transfer from the train to the wheel-rail system was assumed to be rigid. The properties of the primary and secondary suspension and damping properties were taken from the literature (Gu and Franklin 2010), including a wheelset mass of 3,924 lb, as summa- rized in Table 3.36. The length of the rail-track was modeled to be 231 ft, which is three times longer than the articulated light rail train operated in Denver (that is, sufficiently long rails were modeled to examine the dynamic effects of the wheel-rail system). The interaction between the wheels and the rails was represented by the automatic surface-to-surface contact function speci- fied in LS-DYNA. This function automatically determines contact components for the slave and master surfaces. The interaction between the wheels and the axle shaft was simulated by the tied surface-to-surface offset function, which utilizes a penalty-based formulation coupled with an offset distance between the contact surfaces. Train velocities were input in two steps: first step = 0 mph and next step = predefined value. 3.5.6.2 Validation The developed wheel-rail interaction model was validated against the DLA reported by Gu and Franklin (2010). For consistency with the global-level simulation discussed in Section 3.4.3, the DLA was obtained by Eq. 3.5 (maximum vertical stresses were taken after solving the explicit finite element model). The suspension and damping properties explained earlier were used in tandem with a mass of 34.3 kips per axle that was used in Gu and Franklin (2010). The operat- ing velocities simulated were 50 mph and 60 mph, which represent those of light rail trains in service. Figure 3.135 shows sequential snapshots for the representative dynamic behavior of the wheel-rail system with vertical stress contours. The predicted and reported DLAs are compared in Figure 3.136. The predicted values were 9.8% higher than the reported ones, on average. Nonetheless, such discrepancy could reasonably be acceptable, because there are a number of parameters influencing the in situ behavior of wheel-rail interaction (e.g., track details and local irregularities along the rail). 3.5.6.3 Response of the Four Representative Light Rail Trains Figure 3.137(a) illustrates the predicted DLA of the four representative light rail trains that are consistently used in this study: Colorado, Utah, Minnesota, and Massachusetts. The axle loads of these trains were input and a design velocity of 60 mph was applied, as in the case of the global-level simulation (Section 3.4.3). An average DLA of 12% was predicted by the explicit finite element models. This value is similar to or higher than the ones shown in Figs. 3.105 and 3.106, which implies that the dynamic energy transferred from the light rail trains to the bridge superstructure via the rail-track could be alleviated by deflection and vibration. The 12% average DLA from the

50 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads representative trains was lower than the proposed DLA of 30% and the 33% of AASHTO LRFD BDS. Figure 3.137(b) reveals the simulated DLA with respect to axle load, and compares the probability-based DLAs developed at the global level: the 75-year, 99.9%, 90.0%, and average occurrences. The wheel-rail responses were positioned in between the 99.9% and 90.0% categories, which were 39% and 59% lower than the 75-year occurrence and the proposed value for design, respectively, on average. It is again confirmed that the proposed DLA of 30% can safely be used. 3.6 A Unified Approach for Designing Bridges Carrying Light Rail and Highway Traffic Loads 3.6.1 Background of Statistical Methods ANOVA was conducted to statistically characterize the behavior of light rail bridges (i.e., load effects), when specific design parameters were considered. The following hypotheses were tested in conjunction with Eq. 3.15 at a level of significance a = 0.05 (95% confidence): H0: All the means of the bridge responses are equal Ha: Not all the means of the bridge responses are equal (3.15) 2 2 1 F ms s k x i i k ∑ =   = where F = the F distribution of the statistically tested bridge behavior; m = the sample size per test group; s2x_ = the sample variance; s2i = the sample variance per group; and k = the number of the means. The degree of freedom is defined as DOF = (k-1, n–k) to determine a critical F distribution value (e.g., F0.05 at a significance level of 0.05). The calculated F distribution was compared with the critical value of F0.05 to conclude that the H0 hypothesis is rejected or not rejected. If the hypothesis H0 is not rejected, the bridge responses caused by a certain design parameter are statistically identical; in this case, the effect of the parameter is found to be insignificant. If the hypothesis H0 is rejected, an opposite decision is made. Another method employed was t-test, which indicates whether the behavior of the bridge is in compliance with AASHTO LRFD BDS or the proposed design recommendations by checking their equivalency at a level of significance a = 0.05. (3.16)t x s n = − µ where x _ = the sample mean; µ = the population mean; s = the standard deviation of the sample; and n = the number of the samples. The number of degrees of freedom is DOF = (n - 1). By setting a specific design value as the population mean taken from either AASHTO LRFD BDS or the proposed design

research program 51 recommendations, the responses of the bridges can be tested if they belong to one of these design guidelines or both, as explained earlier in ANOVA. In so doing, unified approaches for light rail train and standard highway vehicle loadings can be developed to facilitate the design of bridge structures carrying these two distinct live loads. 3.6.2 Implementation of Statistical Methods 3.6.2.1 Effect of Design Parameters on Behavior of Light Rail Bridges Table 3.37 shows the effect of various design parameters on the behavior of the light rail bridges. The arrangement of bearing types did not influence the bridge response (i.e., the magnitude of load transfer from superstructure to substructure), regardless of the number of spans. The contribution of curvature radius was apparent to the centrifugal force of the curved bridges, which was not affected by other geometric parameters like girder spacing and span length. These statistical observations agree with the physical interpretation of the modified AASHTO LRFD BDS equation (Eq. 3.7) for centrifugal force. The bending and shear responses of the curved bridges were controlled by span length, rather than radius and girder spacing. There was no difference in DLA for the bridges with single and multiple spans, which can justify the use of a single DLA value for the superstructure design of light rail bridges. MPFs were independent of bridge types. The presence of rail break altered the statistical response of the DLA in comparison with the case without rail break. It should, however, be noted that this fact does not necessarily imply the proposed DLA of 30% (Section 3.4.3) needs to be revised because (1) the ANOVA result merely informs that the bridge behavior with and without rail break was different; and (2) the proposed value was conservatively developed according to the 75-year anticipated response of the light rail bridges. The behavior of the skewed bridges was not affected by girder spacing, but was affected by span length. 3.6.2.2 Assessment of Design Expression The results of the t-test are summarized in Table 3.38, where absolute F statistic values are also provided. The calculated F value of the AASHTO LRFD BDS braking force exceeded the limit F0.05 = 2.353, which means that the braking force article of AASHTO LRFD BDS cannot be used for light rail loading. By contrast, the braking force expression proposed in Section 3.5.2 was less than the limit. In terms of centrifugal force, the AASHTO LRFD BDS and the pro- posed design expressions (Section 3.5.1) were acceptable for the light rail bridges, irrespective of curvature radius. On the other hand, the AREMA provision was not applicable. Both the AASHTO LRFD BDS and the proposed DLA (Section 3.4.3) were found to be different from the predicted DLA values. This observation is attributable to the fact that these DLAs (33% and 30% in AASHTO LRFD BDS and the proposed, respectively) were sufficiently conserva- tive; hence, their statistical characteristics were not the same as those of the model prediction. MPFs based on AASHTO LRFD BDS were not usable for light rail bridges, whereas the pro- posed factors (Section 3.4.4) were acceptable. The behavior of the bridges with a skew angle of 0° (straight bridges) was appropriately represented by the AASHTO LRFD BDS and the proposed skew correction factors (Section 3.4.5). As the angle of skew increased from 20° to 60°, the applicability of the AASHTO LRFD BDS skew correction factors deviated from the predicted flexural and shear responses in most cases. The proposed equations (Table 3.39), how- ever, demonstrated good agreement with the predicted responses. The last design parameter examined was live LDF in bending and shear. The lever rule method frequently employed in practice failed to represent the live load distribution of all light rail bridge types from statistics perspectives. The proposed load distribution equations (Tables 3.22 to 3.25) were in appropriate agreement.

52 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads 3.6.2.3 Response Comparison of Light Rail Bridges The statistical responses of the light rail bridges was compared with one another, as shown in Table 3.40. The purpose of this comparison was to identify a potential difference in bridge behav- ior along with certain design parameters. Because the t-test requires a reference case (Eq. 3.16), one bridge type was chosen as a reference against which other bridge types were compared. The bearing arrangement of the two- and three-span cases was not a contributing parameter to the behavior of the bridges, provided that all calculated F vales were less than the corresponding F0.05 limit. The braking force of the PC box bridges was statistically indistinguishable from that of the PC I and steel box bridges; however, the force was discernible from that of the steel plate and reinforced concrete bridges. These observations are due to the fact the span length range of the steel plate and reinforced concrete bridges was different from that of other bridge types (i.e., steel plate has 160 ft and reinforced concrete has 30 to 70 ft, Table 3.7), which affected the travel distance of moving trains along the bridge superstructure and associated braking forces. The bridge types did not influence the development of centrifugal force. Live LDF for exterior girders in bending were not controlled by bridge types, while those for interior girders were controlled. The distribution factors for shear were dominated by bridge types for both exterior and interior girders. The response of the curved steel plate bridges was not the same as those of the curved PC box and steel box bridges, which is attributable to their distinct superstructure rigidity. The MPF of the bridges was independent of superstructure types. The response of the bridges experiencing rail break was, in general, governed by span length. The degree of skew angle less than 60° was not influential on the bridge behavior. 3.7 Proposal of Load Factors 3.7.1 Methodology 3.7.1.1 Strength I and Service I For the Strength I limit state, two calibration methods were employed: the refined iterative method (Nowak and Collins 2013) and the approximate direct calculation method (Barker and Puckett 1997). The refined method includes a limit state function (g): (3.17)g R E= − where R and E are the resistance of the bridge and the load effect applied, respectively. After acquiring necessary statistical properties (i.e., coefficients of variation for components R and E), the limit state function is differentiated with respect to its component Zi: G g Z i i i= − ∂ ∂ σ (3.18) where si is the standard deviation of the component i. Because the resistance of the bridge is lognormally distributed, the equivalent parameters of the resistance should be: r VRe Rσ = (3.19) r rRe R ( )µ = − µ 1 ln (3.20) where seR and µeR = the equivalent standard deviation and the mean of the resistance in lognormal distribution, respectively; r = the estimated resistance; VR = the coefficient of variation of the resistance; and µR = the mean resistance of the light rail bridge.

research program 53 Table 3.41 summarizes the coefficient of variation of the resistance (VR) for the bridge structures considered in this calibration. For the first iteration, the limit state function may be set to zero, so that the bridge structure is in a critical condition. A response vector may then be defined as: (3.21) G G G i i T R E { }[ ] [ ]{ } { }{ } { }α = ρ ρ = αα By assuming no correlation between the resistance and the load effect since the probability density functions of load and resistance are independently constructed, the correlation matrix [r] becomes the identity matrix [I]. An estimated design point (zE) is given as: zE E T= α β (3.22) where bT is the target reliability index (according to AASHTO LRFD BDS, bT = 3.5 is used in this calibration). The estimated load effect (e) may be determined by: e z VE E E ( )= µ +1 (3.23) where µE and VE are the mean and the coefficient of variation of the live load effect, respectively. The relationship between the mean resistance (µR) of the light rail bridge and the mean load effect (µE) may be established by: r V R R T R  ( )µ = + α β1 (3.24) As mentioned above, the estimated resistance may be assumed to be the estimated load effect (e*) to make the bridge in a critical condition (i.e., Eq. 3.17 = 0). The current load factor of the live load can be attained from: e E E  γ = λ µ (3.25) where lE is the bias factor of the light rail loading. Equations 3.18 to 3.25 are iterated until convergence of the load factor is achieved. The approximate direct calculation method includes a single equation: VE E( )γ = λ + κ1 (3.26) where k is a conversion constant for the reliability index and standard deviations of the resis- tance and load effects. Nowak (1999) suggested k = 2.0 be used for bridge structures. For the Service I limit state, the present load factor of AASHTO LRFD BDS (g = 1.0) is adopted, since the bridges are subjected to normal operational conditions. An additional load factor for Strength II may not be necessary for light rail bridges, because owner-specified special design trains and evalu- ation permit trains are not analogous to special design and permit loads for highway bridges. In most cases, the load effects of ballast-maintenance train assemblies do not exceed those of the live load model proposed in this document. If a transit agency has specific needs to con- sider unusual live loadings or to design a bridge carrying both light rail and highway traffic loadings, the Strength II limit state of AASHTO LRFD BDS may be employed. A load factor for rail break is considered as an Extreme limit state (gRB = 1.0), as specified in the Guide Specifications developed based on the present research.

54 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads 3.7.1.2 Fatigue I and II Fatigue I is intended to avoid fatigue cracking when subjected to infinitely many fatigue cycles along with stress ranges below an endurance limit. The ratio between the response of a bridge at an occurrence probability of 1/10,000 (Z = 3.719) and the response induced by typical design live load is taken as a load factor for Fatigue I (Fisher et al. 1993). It is important to note that the 1/10,000 probability was initially proposed based on full-scale laboratory testing (Fisher et al. 1993), and can be used for a fatigue limit state that does not cause fatigue cracking (Dexter and Fisher 2000), which is in conformance with the requirement for Fatigue I in either con- ventional highway or light rail bridges. For the Fatigue II limit state, the ratio between the bridge response caused by service live load and that associated with the design load can be its load factor, as the Fatigue II factor of AASHTO LRFD BDS was determined. In order to accomplish consistency with recently published documents such as SHRP R19B and NCHRP Project 12-83, the root mean cube response of the individual bridges may be employed to represent the ser- vice live load component: (3.27)3 1 3 M p Meq i i∑( )= where Meq is the equivalent moment and pi is the occurrence probability of moment Mi. 3.7.2 Calibration of Load Factors 3.7.2.1 Statistical Property of Light Rail Loading The statistical properties obtained from the site in Section 3.1 were used to identify the type of a probability distribution for light rail loading, as shown in Figures 3.138 and 3.139. The loading can be considered to be normally distributed, as per the regression lines having the coefficients of determination of R2 = 0.8453 [Figure 3.138(a)] and 0.9506 (average of Figure 3.139). This finding is in agreement with the types of typical probability distributions in reliability calibration for conventional highway bridges (i.e., traffic loading and corresponding effects are normal and structural resistance is lognormal (Barker and Puckett 1997; Nowak 1999). Monte-Carlo simula- tion was conducted to expand the in situ statistical data, and an average coefficient of variation of 0.165 was attained for light trail loading [Figure 3.138(b)]. 3.7.2.2 Load Factors for Strength I and Service I In accordance with NCHRP Report 368, the bias factor required for Strength I calibration was acquired by a ratio between the 75-year anticipated load effect and the nominal load effect (design load) of the bridges. The average deviation of 1.10 in bridge responses was taken as the bias factor, which was similar to the bias of highway bridges with a typical range from 1.05 to 1.14 (Barker and Puckett 1997). As explained in Section 3.7.1.1, the calibration procedures were iterated until the response of the load factor was converged [Figure 3.140(a)]. The average load factor of Strength I for the light rail bridges was then found to be from 1.53 to 1.63 [Figure 3.140(b)], which could be adjusted to 1.65 for design convenience. The proposed Strength I load factor of 1.65 is less than the factor of highway bridges (gL = 1.75), because the level of uncertainty associated with light rail bridges is lower than that of highway bridges (i.e., the type of train loading is consistent relative to that of highway vehicles). Figure 3.141 compares the load factors obtained from the refined iterative and the approximate direct calculation methods. Both approaches were in reasonable agreement, although the latter was 8.2% lower than the for- mer, on average. The approximate method is easy and straightforward to use without rigorous iteration; however, it typically generates about 10% deviation from the refined load factor. The Service I load factor may not need to be calibrated, and a factor of 1.0 can be used to represent nominal loading conditions.

research program 55 3.7.2.3 Load Factors for Fatigue I and II Figure 3.142(a) illustrates the variation of Fatigue I load factors with span length. The estimated bending moments of the light rail bridges at an occurrence probability of 1/10,000 (Z = 3.719) were obtained from regression lines similar to those shown in Section 3.3, which were then divided by the moments induced by the average design trains. The reinforced concrete bridges demonstrated low Fatigue I factors compared with other bridge types. This implies that the fatigue response of short span bridges was not sensitive. The Fatigue I factors associated with the light rail bridges varied from 1.0 to 1.38 [Figure 3.142(b)], and 1.40 was taken for fatigue design. Figure 3.143 compares the site-based bridge responses (that is, moments calculated by the girder strains measured on site) with (1) their mean, (2) mean plus three standard devia- tions, and (3) root mean cube based on the mean plus three standard deviations. The use of such elevated mean values by three standard deviations (the 99.7 rule in probability theory) is explained by the fact that the number of site samples is limited; hence, there is a need to broadly cover potential service responses up to over 99.7% of possible occurrences (this kind of amplification was also used in SHRP R19B, which had a mean plus 1.5 standard deviations for highway bridge responses). The root mean cube moments were intrinsically higher than their mean counterparts owing to the configuration of Eq. 3.27. Figure 3.144(a) depicts the site-based bending moments relative to the load effect of the standard design load (LRT-16). As discussed in Section 3.7.1.2, the ratio of these two moments is the Fatigue II load factor, and the four bridge cases showed a range from 0.65 to 0.83 (for convenience, the controlling value is rounded to 0.85). The response of the 6th Avenue Bridge was not included because of the wind issue (Section 3.1.3.4). The calibrated Fatigue II factor is the same as the factor of AASHTO LRFD BDS (gFatigueI = 0.85). A comprehensive summary of the load factors proposed in this study and those of AASHTO LRFD BDS is graphically compared in Figure 3.145. Table 3.42 further denotes technical descrip- tions related to the newly calibrated load factors dedicated to light rail bridges. When a bridge is designed to carry both light rail and highway traffic loadings, the proposed load factors of the current research and the existing load factors of AASHTO LRFD BDS are integrated, and conser- vative factors can be utilized. Table 3.43 lists load factors for such loading configurations. Further details about load factors and their combinations are available in the LRFD Guide Specifications for Bridges Carrying Light Rail Transit Loads. 3.8 Chapter 3 Tables Bridge Maximum positive and negative temperatures Net temperature variation Broadway -5.3°F to 8.4°F (-2.9°C to 4.7°C) 13.7°F (7.6°C) Indiana Bridge -5.1°F to 19.9°F (-2.8°C to 11.1°C) 25.0°F (13.9°C) Santa Fe Bridge -3.5°F to 16.4°F (-2.0°C to 9.1°C) 19.9°F (11.1°C) County Line Bridge -8.0°F to 3.1°F (-4.4°C to 1.7°C) 11.1°F (6.1°C) 6th Avenue Bridge -23.5°F to 9.7°F (-13.1°C to 5.4°C)a 33.2°F (18.5°C)a a : strong wind blew when the bridge was monitored so strain reading was influenced Table 3.1. Maximum temperature variation of the monitored bridges. Bridge Type COV Average Broadway Steel plate girder 0.106 0.161a Indiana Prestressed concrete box (single cell) 0.133 Santa Fe Prestressed concrete box (multiple cell) 0.240 County Line Prestressed concrete girder 0.190 6th Avenue Prestressed concrete girder 0.351 a: COV of the 6th Avenue Bridge was not included due to the heavy wind issue Table 3.2. Average coefficient of variation (COV) for live load distribution.

56 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads Bridge Type Typical cross section Spans modeled Materials Speeda Broadway Steel plate girder 2 spans (278 ft) • Concrete deck: f’c = 4,500 psi • Structural steel: Fy = 36 ksi 23.4 mph Indiana Prestressed concrete box 5 spans (628 ft) • Post-tensioned concrete: f’c = 5,800 psi • Prestressing steel: fpu = 270 ksi 40.4 mph Santa Fe Prestressed concrete box 2 spans (334 ft) • Post-tensioned concrete: f’c = 6,000 psi • Prestressing steel: fpu = 270 ksi 46.0 mph County Line Prestressed concrete girders 4 spans (580 ft) • All concrete: f’c = 6,000 psi • Prestressing steel: fpu = 270 ksi 49.0 mph 6th Avenue Prestressed concrete girders 4 spans (328 ft) • Concrete deck: f’c = 4,500 psi • Post-tensioned concrete: f’c = 9,000 psi • Prestressing steel: fpu = 270 ksi 32.9 mph a: Average train speed measured on site. Table 3.3. Summary of bridge details. Bridge Estimated load increment due to passenger loading in servicea Broadway Average increment: 27.6% (100.8 kips) Indiana Average increment: 19.5% (94.4 kips) Santa Fe Average increment: 15.0% (90.9 kips) County Line Average increment: 35.5% (107.0 kips) 6th Avenue Cannot be obtained due to strong wind a: Increases are indicated from empty train load (79 kips). Table 3.4. Average train load increase due to passenger occupancy. Bridge Type Monitored span Test Model Service load Empty train Fully loaded train δmax-average δcontrol δmax δcontrol δmax δcontrol Broadway Steel plate girder 119 ft 0.365 in L/3910 0.252 in L/5670 0.412 in L/3470 Indiana PC box girder 95 ft 0.040 in L/28500 0.038 in L/30000 0.062 in L/18390 Santa Fe PC box girder 155 ft 0.224 in L/8300 0.194 in L/9590 0.311 in L/5980 County Line PC I girder 160 ft 0.250 in L/7680 0.156 in L/12310 0.274 in L/7010 6th Avenue PC I girder 80 ft 0.066 in L/14550 0.054 in L/17780 0.089 in L/10790 Table 3.5. Assessment of deflection control. Bridge Fundamental frequency Measured Predicted Broadway 1.72 ± 0.42 Hz 1.99 Hz Indiana 1.76 ± 0.50 Hz 1.95 Hz Santa Fe 1.84 ± 0.13 Hz 1.70 Hz County Line 2.22 ± 0.85 Hz 2.95 Hz 6th Avenue 1.31 ± 0.11 Hz 1.32 Hz Table 3.6. Comparison between measured and predicted fundamental frequencies.

research program 57 Type Schematica Typeb Span length Girder spacing Number of span Skew angle Radius of curvature Steel plate girder a 80 ft 100 ft 140 ft 160 ft 4 ft 6 ft 8 ft 10ft 1 2 3 0° 20° 40° 60° 500 ft 1000 ft 1500 ft  Cast-in-place concrete multicell box c 80 ft 100 ft 140 ft 8 ft 10 ft 12 ft 1 2 3 0° 20° 40° 60° 500 ft 1000 ft 1500 ft  Cast-in-place concrete T beam e 30 ft 50 ft 70 ft 4 ft 6 ft 8 ft 10 ft 1 2 3 0° 20° 40° 60° N/A Precast concrete I or bulb-tee k 80 ft 100 ft 140 ft 4 ft 6 ft 8 ft 10 ft 1 0° 20° 40° 60° N/A Closed steel boxes b 80 ft 100 ft 140 ft 6 ft 8 ft 10 ft 1 2 3 0° 20° 40° 60° 500 ft 1000 ft 1500 ft  a: Schematic taken from the AASHTO LRFD Specifications (Table 4.6.2.2.1-1). b: Type shown in the AASHTO LRFD Specifications (Table 4.6.2.2.1-1). Table 3.7. Model matrix for the current research. Span L (ft) Gr (ft) Upper FL Lower FL Web Span L (ft) Gr (ft) Upper FL Lower FL Web w (in) t (in) w (in) t (in) h (in) t (in) w (in) t (in) w (in) t (in) h (in) t (in) Si m pl y su pp or te d sp an 80 4 16 1.75 16 1.75 32 1.0 M ul tip le sp an s 80 4 16 1.75 16 1.75 40 1.0 6 16 1.75 16 1.75 32 1.0 6 16 1.75 16 1.75 40 1.0 8 16 1.75 16 1.75 34 1.0 8 16 1.75 16 1.75 43 1.0 10 16 1.75 16 1.75 38 1.0 10 16 1.75 16 1.75 50 1.0 100 4 18 1.75 18 1.75 42 1.0 100 4 18 1.75 18 1.75 55 1.0 6 18 1.75 18 1.75 45 1.0 6 18 1.75 18 1.75 55 1.0 8 18 1.75 18 1.75 48 1.0 8 18 1.75 18 1.75 58 1.0 10 18 1.75 18 1.75 55 1.0 10 18 1.75 18 1.75 66 1.0 140 4 20 2.25 20 2.25 65 1.0 140 4 20 2.25 20 2.25 75 1.0 6 20 2.25 20 2.25 70 1.0 6 20 2.25 20 2.25 75 1.0 8 20 2.25 20 2.25 73 1.0 8 20 2.25 20 2.25 78 1.0 10 20 2.25 20 2.25 76 1.0 10 20 2.25 20 2.25 90 1.0 160 4 24 2.25 24 2.25 76 1.0 160 4 24 2.25 24 2.25 82 1.0 6 24 2.25 24 2.25 78 1.0 6 24 2.25 24 2.25 82 1.0 8 24 2.25 24 2.25 82 1.0 8 24 2.25 24 2.25 85 1.0 10 24 2.25 24 2.25 86 1.0 10 24 2.25 24 2.25 100 1.0 L = span length; Gr = girder spacing; FL = flange; w = width; t = thickness; h = height Table 3.8. Details of the designed benchmark bridge sections (steel plate girders). Span L (ft) Gr (ft) Upper FL Lower FL Web Span L (ft) Gr (ft) Upper FL Lower FL Web w (in) t (in) w (in) t (in) h (in) t (in) w (in) t (in) w (in) t (in) h (in) t (in) Si m pl y su pp or te d sp an 80 6 28 1.5 28 1.5 30 0.75 M ul tip le sp an s 80 6 28 1.5 28 1.5 32 0.75 8 28 1.5 28 1.5 32 0.75 8 28 1.5 28 1.5 36 0.75 10 28 1.5 28 1.5 34 0.75 10 28 1.5 28 1.5 42 0.75 100 6 38 1.5 38 1.5 38 0.75 100 6 38 1.5 38 1.5 42 0.75 8 38 1.5 38 1.5 40 0.75 8 38 1.5 38 1.5 44 0.75 10 38 1.5 38 1.5 42 0.75 10 38 1.5 38 1.5 52 0.75 140 6 48 1.5 48 1.5 52 0.75 140 6 48 1.5 48 1.5 60 0.75 8 48 1.5 48 1.5 60 0.75 8 48 1.5 48 1.5 68 0.75 10 48 1.5 48 1.5 62 0.75 10 48 1.5 48 1.5 78 0.75 L = span length; Gr = girder spacing; FL = flange; w = width; t = thickness; h = height Table 3.9. Details of the designed benchmark bridge sections (steel box girders).

58 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads L (ft) Gr (ft) Girder type L (ft) Gr (ft) Girder type L (ft) Gr (ft) Girder type 80 4 I-Type IV 100 4 I-Type V 140 4 BT84 × 48 6 I-Type IV 6 I-Type V 6 BT84 × 48 8 I-Type IV 8 I-Type V 8 BT84 × 48 10 I-Type V 10 I-Type VI 10 BT84 × 48 L = span length; Gr = girder spacing Table 3.10. Details of the designed benchmark bridge sections (prestressed concrete I girders). Span L (ft) Gr (ft) Upper FL Lower FL Web Span L (ft) Gr (ft) Upper FL Lower FL Web w (in) t (in) w (in) t (in) h (in) t (in) w (in) t (in) w (in) t (in) h (in) t (in) Si m pl y su pp or te d sp an 80 8 384 14 300 10 56 12 M ul tip le sp an s 80 8 384 14 300 10 58 12 10 384 14 300 10 58 12 10 384 14 300 10 60 12 12 384 14 300 10 62 12 12 384 14 300 10 64 12 100 8 384 16 300 12 66 12 100 8 384 16 300 12 68 12 10 384 16 300 12 68 12 10 384 16 300 12 70 12 12 384 16 300 12 70 12 12 384 16 300 12 72 12 140 8 384 18 300 14 80 12 140 8 384 18 300 14 82 12 10 384 18 300 14 82 12 10 384 18 300 14 84 12 12 384 18 300 14 84 12 12 384 18 300 14 86 12 L = span length; Gr = girder spacing; FL = flange; w = width; t = thickness; h = height Table 3.11. Details of the designed benchmark bridge sections (prestressed concrete box girders). Span L(ft) Gr (ft) w (in) ha (in) Span L (ft) Gr (ft) w (in) ha (in) Si m pl y su pp or te d sp an 30 4 12 24 M ul tip le sp an s 30 4 14 25 6 13 25 6 15 27 8 15 26 8 16 29 10 16 28 10 18 30 50 4 16 38 50 4 18 40 6 17 38 6 19 42 8 19 40 8 21 44 10 21 42 10 23 45 70 4 25 55 70 4 27 58 6 27 56 6 29 60 8 29 58 8 30 62 10 30 62 10 32 65 a: without slab (10 in); L = span length; Gr = girder spacing; w = width; t = thickness; h = height Table 3.12. Details of the designed benchmark bridge sections (reinforced concrete girders). L (ft) Gr (ft) Ap (in 2) L (ft) Gr (ft) Ap (in 2) L (ft) Gr (ft) Ap (in 2) 80 4 6.273 (41 tendons) 100 4 8.568 (56 tendons) 140 4 12.699 (83 tendons) 6 6.426 (42 tendons) 6 8.874 (58 tendons) 6 13.005 (85 tendons) 8 6.579 (43 tendons) 8 9.180 (60 tendons) 8 13.464 (88 tendons) 10 7.038 (46 tendons) 10 9.486 (62 tendons) 10 16.830 (110 tendons) L = span length; Gr = girder spacing; Ap = area of tendon (one standard tendon Ap = 0.153 in2) Table 3.13. Cross-sectional area of prestressing steel strands for prestressed concrete I girders.

research program 59 Span L (ft) Gr (ft) Ap (in2) Span L (ft) Gr (ft) Ap (in2) Si m pl y su pp or te d sp an 80 8 16.524 (108 tendons) M ul tip le sp an s 80 8 18.36 (120 tendons) 10 17.44 (114 tendons) 10 19.278 (126 tendons) 12 18.36 (120 tendons) 12 19.89 (130 tendons) 100 8 27.54 (180 tendons) 100 8 30.294 (198 tendons) 10 30.294 (198 tendons) 10 33.05 (216 tendons) 12 32.13 (210 tendons) 12 36.72 (240 tendons) 140 8 36.72 (240 tendons) 140 8 55.08 (360 tendons) 10 38.556 (252 tendons) 10 57.834 (378 tendons) 12 38.556 (252 tendons) 12 57.834 (378 tendons) L = span length; Gr = girder spacing; Ap = area of tendon (one standard tendon Ap = 0.153 in2) Table 3.14. Cross-sectional area of prestressing steel strands for prestressed concrete box girders. Span L (ft) Gr (ft) As (in 2) Span L (ft) Gr (ft) As (in 2) +ve -ve +ve -ve Si m pl y su pp or te d sp an 30 4 12 N/A M ul tip le sp an s 30 4 9 14 6 12 N/A 6 9 14 8 13 N/A 8 9 14 10 14 N/A 10 10 15 50 4 17 N/A 50 4 13 19 6 17 N/A 6 13 19 8 18 N/A 8 13 20 10 20 N/A 10 15 22 70 4 24 N/A 70 4 17 25 6 24 N/A 6 17 25 8 25 N/A 8 18 26 10 28 N/A 10 20 30 L = span length; Gr = girder spacing; As = area of steel reinforcement Table 3.15. Cross-sectional area of steel bars for reinforced concrete girders. PC box PC I Steel box Steel plate RC Average No. of models 288 384 288 512 384 75-year 0.90 k/ft 0.82 k/ft 0.84 k/ft 0.84 k/ft 1.39 k/ft 0.96 k/ft 99.9% 0.80 k/ft 0.73 k/ft 0.75 k/ft 0.73 k/ft 1.11 k/ft 0.82 k/ft Upper 20% 0.69 k/ft 0.63 k/ft 0.64 k/ft 0.61 k/ft 0.78 k/ft 0.67 k/ft Average 0.65 k/ft 0.59 k/ft 0.60 k/ft 0.56 k/ft 0.67 k/ft 0.61 k/ft Table 3.16. Summary of equivalent lane loads. PC box PC I Steel box Steel plate RC AverageNo. of modelsa 7,200 9,600 7,200 12,800 9,600 75-year* 36.2 kips 34.0 kips 35.4 kips 41.6 kips 21.9 kips 33.8 kips 99.9%* 29.2 kips 27.3 kips 28.2 kips 32.3 kips 18.1 kips 27.0 kips Upper 20%* 21.2 kips 19.5 kips 20.1 kips 21.6 kips 21.2 kips 20.7 kips Average* 18.3 kips 16.8 kips 17.1 kips 17.7 kips 12.1 kips 16.4 kips a: Total number of models considered from 5 ft to 29 ft spacing. *: One axle at 14-ft spacing. Table 3.17. Summary of equivalent concentrated loads.

60 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads Bending moment (k-ft): one-track loaded Inference based on site load Inference based on the candidate standard live load models Broadway County Line Santa Fe Indiana 6 th Avenue Broadway County Line Santa Fe Indiana 6th Ave Each Ratio Each Ratio Each Ratio Each Ratio Each Ratio Average 1319 1303 1463 779 615 1329 0.99 1416 0.92 2142 0.68 934 0.83 1359 0.45 Upper 20% 1420 1540 1600 900 830 1620 0.88 1711 0.90 2573 0.62 1140 0.79 1671 0.50 99.9% 1707 2172 1962 918 1402 2040 0.84 2153 1.01 3232 0.61 1439 0.64 2112 0.66 75-year 1953 2740 2283 1058 1912 2499 0.78 2630 1.04 3939 0.58 1764 0.60 2596 0.74 Ratio = Inference based on site load/Inference based on the candidate standard live load models × 100 (%) Table 3.18. Comparison of probabilistically inferred bending moments based on the site data and the candidate standard live load models for the five constructed bridges in Denver, CO. Number of trucks Number of axles Allocation to each truck 2 4 50% + 50% 3 6 35% + 30% + 35% 4 8 25% + 25% + 25% + 25% 5 10 20% + 20% +20% +20% + 20% Table 3.19. Structural load allocation of one articulated light rail train.

No. City Train length (ft) Empty train load (kip) Number of seats Number of axles Axle load (kip) Axle spacing (ft)a Axle spacing between two trainsa Full train load (AW4) Both ends Middle a b c d (e or g) P1, P2 or P5, P6 P3, P4 1 Baltimore 95.00 108 84 6 27 23 7.50 22.50 7.5 27.50 153 2 Boston 74.00 88 44 6 22 19 6.25 17.75 6.25 19.75 126 3 Calgary 81.42 92 52 6 23 20 5.92 19.41 5.92 24.84 131 4 Charlotte 93.50 101 68 6 25 22 6.25 27.68 5.67 19.97 143 5 Cleveland 80.00 91 84 6 24 20 6.08 20.92 6.08 19.92 136 6 Edmonton 81.33 92 60 6 23 20 5.75 19.58 5.75 24.92 133 7 Houston 96.36 99 72 6 25 21 6.23 20.96 5.67 36.31 141 8 Los Angeles 89.00 102 68 6 25 22 7.05 23.958 7.05 19.934 144 9 Minneapolis 93.58 99 68 6 25 21 6.23 27.565 5.9 20.09 141 10 Newark 90.00 99 72 6 25 21 6.25 27.05 6.25 17.15 142 11 Norfolk 93.60 97 68 6 24 21 6.23 20.96 5.67 33.55 139 12 Phoenix 91.50 102 66 6 25 22 6.25 28.00 5.75 17.25 144 13 Pittsburgh 84.67 100 62 6 25 21 6.23 23.19 6.23 19.6 141 14 Portland (TriMet) 92.00 109 73 6 27 23 5.92 28.5 5.92 17.24 152 15 Sacramento 88.50 99 75 6 25 21 5.92 22.33 5.92 26.08 142 16 Saint Louis 89.42 93 72 6 24 20 6.92 24.83 6.92 19.00 136 17 Salt Lake 88.50 99 75 6 25 21 6.25 22.00 6.25 25.75 142 18 Seattle 95.00 102 74 6 25 22 6.25 29.745 5.92 17.09 145 19 San Diego 81.42 97 60 6 24 21 6.23 23.515 5.9 16.03 138 20 San Francisco 75.00 78 60 6 21 18 6.25 17.75 6.25 20.75 119 21 Santa Clara 90.00 100 66 6 25 21 6.25 22.00 6.25 27.25 142 22 Toronto 104.5 108 60 6 26 22 6.07 27.6 6.07 31.09 149 23 Atlanta (Siemens) 79.10 91 60 6 23 20 6.23 23.52 5.89 13.71 132 24 Buffalo 66.83 71 51 4 28 28 6.17 30.00 6.17 24.49 110 25 Philadelphia 55.00 60 50 4 25 25 6.25 18.75 6.25 23.75 99 26 Toronto 52.50 51 46 4 22 22 6.00 19.00 6.00 21.5 90 27 Brookville 66.42 66 47 4 26 26 6.01 32.99 6.01 21.41 105 28 Sacramento 80.06 66 36 4 26 26 5.91 36.27 5.91 31.97 103 29 Tacoma (Skoda) 66.00 56 30 4 23 23 6.17 32.5 6.17 21.16 92 30 Portland (United) 69.58 70 29 4 27 27 6.2 32.5 6.2 24.68 106 31 Portland (Inekon) 66.00 68 30 4 26 26 6.17 32.63 6.17 21.03 104 32 Dallas 123.67 140 96 8 23 23 a = 7, b = d = 24.09, c = 6.83 23.76 186 33 Ottawa 149.00 156 120 10 21 21 a = c = 6.25, b = 29.22, d = f =26.41,e = 19.03 16.68 206 a: Best estimated value based on train drawing. Table 3.20. Dimensional and loading configurations of light rail trains (fully seated passengers plus 205 standees per train).

No. City Train length (ft) Empty train load (kip) Number of seats Number of axles Axle load (kip) Axle spacing (ft)a Axle spacing between two trainsa Full train load (AW4) Both ends Middle a b c d (e or g) P1, P2 or P5, P6 P3, P4 1 Baltimore 95.00 108 84 6 28 24 7.50 22.50 7.5 27.50 158 2 Boston 74.00 88 44 6 23 20 6.25 17.75 6.25 19.75 132 3 Calgary 81.42 92 52 6 24 20 5.92 19.41 5.92 24.84 136 4 Charlotte 93.50 101 68 6 26 22 6.25 27.68 5.67 19.97 149 5 Cleveland 80.00 91 84 6 25 21 6.08 20.92 6.08 19.92 141 6 Edmonton 81.33 92 60 6 24 21 5.75 19.58 5.75 24.92 138 7 Houston 96.36 99 72 6 26 22 6.23 20.96 5.67 36.31 147 8 Los Angeles 89.00 102 68 6 26 22 7.05 23.958 7.05 19.934 149 9 Minneapolis 93.58 99 68 6 26 22 6.23 27.565 5.9 20.09 146 10 Newark 90.00 99 72 6 26 22 6.25 27.05 6.25 17.15 147 11 Norfolk 93.60 97 68 6 25 22 6.23 20.96 5.67 33.55 144 12 Phoenix 91.50 102 66 6 26 22 6.25 28.00 5.75 17.25 149 13 Pittsburgh 84.67 100 62 6 26 22 6.23 23.19 6.23 19.6 147 14 Portland (TriMet) 92.00 109 73 6 28 24 5.92 28.5 5.92 17.24 157 15 Sacramento 88.50 99 75 6 26 22 5.92 22.33 5.92 26.08 147 16 Saint Louis 89.42 93 72 6 25 21 6.92 24.83 6.92 19.00 141 17 Salt Lake 88.50 99 75 6 26 22 6.25 22.00 6.25 25.75 147 18 Seattle 95.00 102 74 6 26 23 6.25 29.745 5.92 17.09 150 19 San Diego 81.42 97 60 6 26 21 6.23 23.515 5.9 16.03 143 20 San Francisco 75.00 78 60 6 22 19 6.25 17.75 6.25 20.75 124 21 Santa Clara 90.00 100 66 6 26 22 6.25 22.00 6.25 27.25 147 22 Toronto 104.5 108 60 6 27 23 6.07 27.6 6.07 31.09 154 23 Atlanta (Siemens) 79.10 91 60 6 24 21 6.23 23.52 5.89 13.71 138 24 Buffalo 66.83 71 51 4 29 29 6.17 30.00 6.17 24.49 115 25 Philadelphia 55.00 60 50 4 26 26 6.25 18.75 6.25 23.75 104 26 Toronto 52.50 51 46 4 24 24 6.00 19.00 6.00 21.5 95 27 Brookville 66.42 66 47 4 28 28 6.01 32.99 6.01 21.41 110 28 Sacramento 80.06 66 36 4 27 27 5.91 36.27 5.91 31.97 109 29 Tacoma (Skoda) 66.00 56 30 4 24 24 6.17 32.5 6.17 21.16 98 30 Portland (United) 69.58 70 29 4 28 28 6.2 32.5 6.2 24.68 111 31 Portland (Inekon) 66.00 68 30 4 27 27 6.17 32.63 6.17 21.03 110 32 Dallas 123.67 140 96 8 24 24 a = 7, b = d = 24.09, c = 6.83 23.76 192 33 Ottawa 149.00 156 120 10 21 21 a = c = 6.25, b = 29.22, d = f =26.41,e = 19.03 16.68 211 a: Best estimated value based on train drawing. Table 3.21. Dimensional and loading configurations of light rail trains (fully seated passengers plus 240 standees per train).

research program 63 PC Box d One lane 45.035.0 11 6.3 75.1 cNL S Two or more lanes 25.03.0 1 8.5 13 L S Nc ( 0.130.7 S ) ( 24060 L ) ( 3bN ) One-track-loaded 0.0770.1381 10.223 19.681 c S L N Two-track-loaded 0.08 0.10613 1 9.989c S N L ( 0.120.8 S ) ( 14080 L ) ( 3bN ) PC I k One lane 1.0 3 3.04.0 0.1214 06.0 s g Lt K L SS Two or more lanes 1.0 3 2.06.0 0.125.9 075.0 s g Lt K L SS ( 0.165.3 S ) ( 0.125.4 st ) ( 24020 L ) ( 4bN ) ( 000,000,7000,10 gK ) One-track-loaded 0.0240.282 0.044 30.19 67.569 12.0 s gKS S L Lt Two-track-loaded 0.0351.556 0.16 30.197 12.734 12.0 s gKS S L Lt ( 104 S ) ( 10st ) ( 14080 L ) ( 3bN ) ( 000,500,2000,500 gK ) Steel Box b,c One lane 0.35 0.25 23.0 12.0 S Sd L Two or more lanes 0.6 0.125 26.3 12.0 S Sd L (6 18S ) ( 20 140L ) (18 65d ) ( 3bN ) One lane 0.308 0.09 268.747 12.0 S Sd L Two or more lanes 0.926 0.022 213.945 12.0 S Sd L (6 10S ) (80 140L ) (33 65d ) (3 5bN ) Steel Plate a One lane 1.0 3 3.04.0 0.1214 06.0 s g Lt K L SS Two or more lanes 1.0 3 2.06.0 0.125.9 075.0 s g Lt K L SS One-track-loaded 0.526 –0.158 30.119 87.720 12.0 s gKS S L Lt 0.096 Two-track-loaded 1.639 0.02 30.209 15.530 12.0 s gKSS L Lt 0.027 ( 0.165.3 S ) ( 0.125.4 st ) ( 24020 L ) ( 4bN ) ( 000,000,7000,10 gK ) ( 104 S ) ( 10st ) ( 16080 L ) ( 3bN ) ( 000,000,5000,400 gK ) RC e One lane 1.0 3 3.04.0 0.1214 06.0 s g Lt K L SS Two or more lanes 1.0 3 2.06.0 0.125.9 075.0 s g Lt K L SS ( 0.165.3 S ) ( 0.125.4 st ) ( 24020 L ) ( 4bN ) ( 000,000,70000,1 gK ) One-track-loaded 0.2141.954 0.085 30.038 14.336 12.0 s gKS S L Lt Two-track-loaded 0.2151.907 0.032 30.074 11.111 12.0 s gKS S L Lt ( 104 S ) ( 10st ) ( 7030 L ) ( 3bN ) ( 000,000,2000,50 gK ) Type of superstructure Applicable cross section in AASHTO LRFD AASHTO LRFD Proposed Table 3.22. Live load distribution calibrated for light rail loading (interior moment).

64 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads PC Box d Regardless of number of lanes 14 eWg ( SWe ) One-track-loaded 28.195 eWg Two-track-loaded 16.745 eWg PC I k One lane Lever Rule Two or more lanes g = eginterior 1.9 77.0 ede ( 5.50.1 ed ) One-track-loaded g = eginterior 0.564 6.559 ede Two-track-loaded g = eginterior 0.789 22.675 ede ( 4 6ed ) Steel Box b,c One lane Lever Rule Two or more lanes g = eginterior 0.97 28.5 ede ( 0 4.5ed ) (6.0 18.0S ) Lever Rule ( 18.0S ) One-track-loaded g = eginterior 0.295 4.765 ede Two-track-loaded g = eginterior 0.797 25.943 ede ( 4 6ed ) (6.0 10.0S ) Steel Plate a One lane Lever Rule Two or more lanes g = eginterior 1.9 77.0 ede ( 5.50.1 ed ) One-track-loaded g = eginterior 0.393 5.637 ede Two-track-loaded g = eginterior 0.689 16.334 ede ( 4 6ed ) RC e One lane Lever Rule Two or more lanes g = eginterior 1.9 77.0 ede ( 5.50.1 ed ) One-track-loaded g = eginterior 0.783 191362.335 ede Two-track-loaded g = eginterior 0.326 73.005 ed Le S ( 4 6ed ) (30 70L ) ( 4 10S ) Type of superstructure Applicable cross section in AASHTO LRFD AASHTO LRFD Proposed Table 3.23. Live load distribution calibrated for light rail loading (exterior moment).

research program 65 PC Box d One lane Lever Rule Two or more lanes g = eginterior 5.12 64.0 ede ( 0.50.2 ed ) One-track-loaded g = eginterior 1.296 3.331* ede S Two-track-loaded g = eginterior 0.67 2.216* ede S ( 64 ed ) (8 12S ) PC I k One lane Lever Rule Two or more lanes g = eginterior 10 6.0 ede ( 5.50.1 ed ) One-track-loaded g = eginterior 0.515 2.348 ede Two-track-loaded g = eginterior 10 6.0 ede ( 4 6ed ) Steel Box b,c One lane Lever Rule Two or more lanes g = eginterior 0.8 10 ede ( 0 4.5ed ) One lane 0.582 2.675 ede Two or more lanes g = eginterior 0.726 28.392 ede ( 4 6ed ) Steel Plate a One lane Lever Rule Two or more lanes g = eginterior 10 6.0 ede ( 5.50.1 ed ) One-track-loaded g = eginterior 1.2 1.871 ede Two-track-loaded g = eginterior 0.065 5.547 ede ( 4 6ed ) RC e One lane Lever Rule Two or more lanes g = eginterior 10 6.0 ede ( 5.50.1 ed ) One-track-loaded g = eginterior 0.088 5.485 ede Two-track-loaded g = eginterior 0.193 11.667 ede ( 4 6ed ) Type of superstructure Applicable cross section in AASHTO LRFD AASHTO LRFD Proposed Table 3.24. Live load distribution calibrated for light rail loading (exterior shear).

66 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads PC Box d One lane 1.06.0 0.125.9 L dS Two or more lanes 3.09.0 0.123.7 L dS ( 0.130.6 S ) ( 24020 L ) ( 11035 d ) ( 3bN ) One-track-loaded 0.303 0.481 16.961 12.0 S d L Two-track-loaded 0.698 0.426 3.971 12.0 S d L ( 0.100.6 S ) ( 14080 L ) ( 9866 d ) ( 3bN ) PC I k One lane 0.25 36.0 S Two or more lanes 0.2 3512 2.0 SS ( 0.165.3 S ) ( 24020 L ) ( 0.125.4 st ) ( 4bN ) One-track-loaded 0.176 47.132 S Two-track-loaded 1.067 0.057 10.928 49.715 S S ( 104 S ) ( 14080 L ) ( 10st ) ( 3bN ) Steel Box b,c One lane 0.6 0.1 10 12.0 S d L Two or more lanes 0.8 0.1 7.4 12.0 S d L ( 20 240L ) (6.0 18.0S ) (18 65d ) Lever Rule ( 18.0S ) One-track-loaded 1.009 1.752 994.728 12.0 S d L Two-track-loaded 0.367 0.117 12.511 12.0 S d L (80 140L ) (6.0 10.0S ) (33 65d ) Steel Plate a One lane 0.25 36.0 S Two or more lanes 0.2 3512 2.0 SS ( 0.165.3 S ) ( 24020 L ) ( 0.125.4 st ) One-track-loaded 4.185 0.021 11.699 11.624 S S Two-track-loaded 1.761 0.161 6.285 11.343 S S ( 104 S ) ( 16080 L ) ( 10st ) Type of superstructure Applicable cross section in AASHTO LRFD AASHTO LRFD Proposed ( 4bN ) ( 3bN ) RC e One lane 0.25 36.0 S Two or more lanes 0.2 3512 2.0 SS ( 0.165.3 S ) ( 24020 L ) ( 0.125.4 st ) ( 4bN ) One-track-loaded 0.233 23.792 S Two-track-loaded 0.557 0.417 8.268 15.799 S S ( 104 S ) ( 7030 L ) ( 10st ) ( 3bN ) Table 3.25. Live load distribution calibrated for light rail loading (interior shear).

research program 67 PC I L = 80 ft L = 100 ft L = 140 ft Bending Shear Bending Shear Bending Shear Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int LRT 1 0.06 0.34 0.00 0.57 0.07 0.32 0.00 0.52 0.09 0.27 0.00 0.47 LRT 2 0.11 0.44 0.00 0.61 0.12 0.43 0.00 0.60 0.14 0.40 0.00 0.58 Case 1 0.28 0.54 0.14 0.79 0.29 0.52 0.15 0.77 0.31 0.47 0.17 0.74 Case 2 0.81 0.70 1.05 0.81 0.79 0.68 1.04 0.80 0.76 0.66 1.04 0.75 Case 3 0.86 0.75 1.08 0.83 0.85 0.74 1.08 0.82 0.83 0.72 1.07 0.78 Case 4 0.91 0.80 1.10 0.84 0.90 0.80 1.08 0.84 0.89 0.78 1.08 0.78 Case 5 0.32 0.60 0.15 0.82 0.34 0.58 0.16 0.81 0.37 0.55 0.18 0.78 Case 6 0.32 0.62 0.14 0.77 0.33 0.61 0.14 0.76 0.36 0.58 0.16 0.76 Case 7 0.36 0.69 0.14 0.81 0.38 0.69 0.15 0.81 0.42 0.68 0.17 0.81 Case 8 0.83 0.73 1.00 0.79 0.81 0.72 0.99 0.80 0.79 0.71 0.99 0.79 Case 9 0.88 0.78 1.03 0.82 0.87 0.78 1.03 0.83 0.86 0.78 1.02 0.82 Case 10 0.93 0.84 1.05 0.83 0.93 0.84 1.05 0.84 0.92 0.84 1.03 0.83 Case 11 0.84 0.67 1.08 0.83 0.82 0.65 1.08 0.83 0.79 0.61 1.07 0.78 Table 3.26. Summary of controlling live load distribution factors for prestressed concrete I bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case). PC Box L = 80 ft L = 100 ft L = 140 ft Bending Shear Bending Shear Bending Shear Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int LRT 1 0.14 0.26 0.03 0.49 0.16 0.25 0.05 0.45 0.16 0.22 0.06 0.41 LRT 2 0.22 0.44 0.05 0.70 0.23 0.43 0.07 0.68 0.26 0.40 0.08 0.66 Case 1 0.38 0.50 0.22 0.79 0.36 0.46 0.23 0.73 0.34 0.41 0.23 0.67 Case 2 0.74 0.77 0.84 0.96 0.67 0.70 0.79 0.91 0.57 0.62 0.72 0.84 Case 3 0.80 0.86 0.83 0.98 0.75 0.82 0.81 0.95 0.68 0.77 0.75 0.91 Case 4 0.85 0.94 0.86 1.03 0.82 0.92 0.84 1.00 0.78 0.90 0.79 0.99 Case 5 0.44 0.60 0.23 0.84 0.45 0.58 0.24 0.81 0.45 0.56 0.27 0.76 Case 6 0.46 0.63 0.23 0.88 0.46 0.61 0.24 0.85 0.46 0.57 0.26 0.80 Case 7 0.52 0.75 0.24 0.93 0.54 0.74 0.26 0.92 0.57 0.72 0.30 0.89 Case 8 0.82 0.89 0.81 1.01 0.76 0.84 0.79 0.98 0.69 0.78 0.73 0.94 Case 9 0.88 0.98 0.82 1.05 0.84 0.96 0.80 1.04 0.80 0.92 0.77 1.03 Case 10 0.92 1.06 0.85 1.10 0.91 1.06 0.83 1.11 0.90 1.06 0.81 1.12 Case 11 0.74 0.77 0.81 0.91 0.70 0.75 0.78 0.89 0.65 0.73 0.72 0.86 Table 3.27. Summary of controlling live load distribution factors for prestressed concrete box bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case). Steel Box L = 80 ft L = 100 ft L = 140 ft Bending Shear Bending Shear Bending Shear Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int LRT 1 0.08 0.31 0.00 0.47 0.10 0.29 0.00 0.45 0.11 0.26 0.00 0.44 LRT 2 0.12 0.48 0.00 0.61 0.13 0.46 0.00 0.60 0.17 0.42 0.01 0.59 Case 1 0.30 0.51 0.19 0.73 0.35 0.50 0.20 0.71 0.40 0.48 0.24 0.67 Case 2 0.77 0.74 1.02 0.77 0.84 0.75 1.03 0.75 0.91 0.74 1.12 0.76 Case 3 0.80 0.79 1.04 0.78 0.86 0.79 1.06 0.77 0.92 0.77 1.13 0.77 Case 4 0.86 0.84 1.05 0.79 0.89 0.82 1.07 0.78 0.93 0.79 1.13 0.77 Case 5 0.35 0.58 0.19 0.76 0.38 0.56 0.20 0.74 0.42 0.52 0.24 0.69 Case 6 0.33 0.62 0.18 0.76 0.37 0.61 0.19 0.75 0.44 0.58 0.23 0.73 Case 7 0.37 0.69 0.19 0.79 0.40 0.67 0.20 0.78 0.46 0.64 0.24 0.74 Case 8 0.77 0.77 0.98 0.80 0.84 0.79 0.99 0.79 0.94 0.80 1.10 0.76 Case 9 0.81 0.82 1.00 0.81 0.87 0.83 1.02 0.80 0.95 0.83 1.12 0.76 Case 10 0.87 0.88 1.02 0.83 0.89 0.86 1.03 0.82 0.95 0.85 1.12 0.76 Case 11 0.75 0.65 1.04 0.77 0.79 0.61 1.05 0.76 0.84 0.55 1.13 0.68 Table 3.28. Summary of controlling live load distribution factors for steel box bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case).

68 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads ST Plate L = 80 ft L = 100 ft L = 140 ft L = 160 ft Bending Shear Bending Shear Bending Shear Bending Shear Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int LRT 1 0.07 0.31 0.00 0.49 0.07 0.30 0.00 0.48 0.09 0.27 0.00 0.47 0.09 0.26 0.00 0.46 LRT 2 0.11 0.49 0.00 0.61 0.12 0.47 0.00 0.60 0.14 0.45 0.00 0.59 0.15 0.44 0.00 0.59 Case 1 0.28 0.52 0.17 0.75 0.29 0.50 0.17 0.74 0.31 0.46 0.17 0.73 0.30 0.46 0.16 0.73 Case 2 0.77 0.71 1.05 0.78 0.77 0.70 1.05 0.77 0.76 0.66 1.04 0.75 0.74 0.66 0.98 0.78 Case 3 0.82 0.76 1.08 0.80 0.82 0.74 1.05 0.77 0.83 0.72 1.05 0.76 0.83 0.71 1.05 0.76 Case 4 0.87 0.82 1.09 0.80 0.88 0.80 1.09 0.80 0.89 0.78 1.08 0.78 0.89 0.78 1.06 0.77 Case 5 0.33 0.58 0.18 0.78 0.35 0.57 0.18 0.77 0.37 0.54 0.19 0.76 0.37 0.54 0.22 0.77 Case 6 0.32 0.62 0.16 0.76 0.33 0.60 0.16 0.76 0.36 0.58 0.15 0.76 0.37 0.58 0.15 0.77 Case 7 0.36 0.70 0.17 0.81 0.39 0.69 0.17 0.81 0.42 0.68 0.18 0.81 0.44 0.67 0.21 0.81 Case 8 0.78 0.74 1.01 0.79 0.78 0.73 1.01 0.79 0.78 0.71 1.00 0.78 0.77 0.71 0.94 0.80 Case 9 0.83 0.79 1.03 0.83 0.84 0.78 1.04 0.83 0.86 0.78 1.03 0.82 0.88 0.78 0.97 0.83 Case 10 0.89 0.85 1.05 0.85 0.91 0.85 1.05 0.84 0.93 0.85 1.04 0.83 0.95 0.85 1.06 0.83 Case 11 0.78 0.65 1.08 0.79 0.79 0.64 1.08 0.79 0.79 0.61 1.07 0.77 0.81 0.61 1.06 0.77 Table 3.29. Summary of controlling live load distribution factors for steel plate bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case). RC L = 30 ft L = 50 ft L = 70 ft Bending Shear Bending Shear Bending Shear Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int LRT 1 0.04 0.57 0.00 0.76 0.08 0.39 0.01 0.66 0.10 0.31 0.02 0.58 LRT 2 0.06 0.69 0.00 0.77 0.11 0.57 0.01 0.7 0.16 0.43 0.02 0.66 Case 1 0.21 0.79 0.15 0.86 0.27 0.60 0.17 0.84 0.31 0.50 0.17 0.77 Case 2 0.76 0.94 1.11 0.85 0.77 0.93 0.96 0.85 0.85 0.74 0.95 0.81 Case 3 1.06 0.84 1.05 0.85 0.91 0.82 1.01 0.83 0.91 0.79 0.99 0.82 Case 4 0.90 0.97 1.06 0.87 0.86 0.88 1.00 0.87 0.86 0.79 0.98 0.85 Case 5 0.22 0.87 0.15 0.86 0.31 0.70 0.18 0.86 0.36 0.58 0.18 0.79 Case 6 0.28 0.89 0.17 0.84 0.33 0.75 0.19 0.84 0.36 0.60 0.20 0.78 Case 7 0.24 0.98 0.15 0.86 0.32 0.70 0.21 0.76 0.34 0.69 0.23 0.75 Case 8 0.89 1.02 1.04 0.86 0.87 0.80 1.01 0.82 0.87 0.79 0.95 0.81 Case 9 0.79 1.12 1.11 0.85 0.92 0.85 1.01 0.82 0.92 0.84 1.00 0.81 Case 10 0.81 1.20 1.06 0.91 0.86 0.99 1.05 0.91 0.93 0.86 1.00 0.86 Case 11 0.84 0.89 1.01 0.81 0.80 0.78 0.98 0.78 0.75 0.67 0.95 0.77 Table 3.30. Summary of controlling live load distribution factors for reinforced concrete bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case). PC I L = 80 ft L = 100 ft L = 140 ft Bending Shear Bending Shear Bending Shear Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int LRT 1 0.04 0.33 0.00 0.59 0.05 0.30 0.00 0.56 0.05 0.25 0.00 0.51 LRT 2 0.08 0.49 0.00 0.64 0.15 0.46 0.00 0.63 0.17 0.41 0.00 0.59 Case 1 0.12 0.50 0.00 0.77 0.13 0.48 0.00 0.76 0.14 0.43 0.01 0.72 Case 2 0.34 0.65 0.15 0.83 0.35 0.63 0.16 0.81 0.37 0.59 0.19 0.80 Case 3 0.85 0.82 1.07 0.88 0.84 0.79 1.07 0.85 0.81 0.75 1.07 0.81 Case 4 0.88 0.85 1.08 0.89 0.88 0.83 1.08 0.87 0.86 0.79 1.09 0.86 Case 5 0.91 0.88 1.10 0.90 0.91 0.86 1.10 0.88 0.89 0.83 1.11 0.87 Case 6 0.94 0.92 1.10 0.90 0.94 0.89 1.10 0.88 0.94 0.88 1.11 0.87 Case 7 0.26 0.55 0.01 0.80 0.26 0.53 0.01 0.79 0.26 0.50 0.01 0.76 Case 8 0.15 0.58 0.00 0.76 0.16 0.56 0.01 0.76 0.18 0.54 0.01 0.75 Case 9 0.36 0.67 0.14 0.80 0.38 0.66 0.15 0.81 0.40 0.63 0.18 0.82 Case 10 0.87 0.84 1.02 0.87 0.85 0.81 1.02 0.84 0.82 0.77 1.02 0.83 Case 11 0.90 0.87 1.03 0.85 0.89 0.85 1.01 0.81 0.88 0.82 1.01 0.81 Case 12 0.93 0.88 1.06 0.87 0.92 0.88 1.04 0.87 0.92 0.86 1.03 0.87 Case 13 0.96 0.94 1.07 0.88 0.96 0.92 1.05 0.87 0.97 0.91 1.05 0.87 Case 14 0.18 0.64 0.01 0.79 0.20 0.63 0.01 0.79 0.23 0.62 0.01 0.79 Table 3.31. Summary of controlling live load distribution factors for prestressed concrete I bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case).

PC Box L = 80 ft L = 100 ft L = 140 ft Bending Shear Bending Shear Bending Shear Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int LRT 1 0.07 0.24 0.01 0.58 0.09 0.23 0.03 0.53 0.10 0.19 0.03 0.49 LRT 2 0.12 0.39 0.01 0.68 0.14 0.38 0.04 0.67 0.16 0.33 0.05 0.64 Case 1 0.21 0.43 0.04 0.72 0.22 0.38 0.09 0.66 0.26 0.37 0.11 0.63 Case 2 0.43 0.65 0.18 0.91 0.42 0.59 0.26 0.86 0.38 0.51 0.29 0.83 Case 3 0.77 0.92 0.70 1.19 0.70 0.83 0.73 1.14 0.60 0.71 0.78 1.10 Case 4 0.80 0.97 0.70 1.18 0.75 0.9 0.73 1.14 0.65 0.80 0.79 1.11 Case 5 0.82 1.01 0.70 1.18 0.78 0.95 0.73 1.15 0.70 0.90 0.79 1.11 Case 6 0.84 1.04 0.72 1.21 0.80 1.00 0.75 1.18 0.78 0.97 0.81 1.13 Case 7 0.24 0.50 0.04 0.76 0.26 0.49 0.10 0.70 0.29 0.45 0.12 0.68 Case 8 0.25 0.56 0.05 0.82 0.29 0.55 0.10 0.78 0.32 0.48 0.12 0.77 Case 9 0.47 0.72 0.19 0.91 0.55 0.77 0.26 0.87 0.47 0.67 0.30 0.86 Case 10 0.81 0.99 0.69 1.18 0.76 0.92 0.73 1.14 0.67 0.82 0.78 1.11 Case 11 0.84 1.04 0.69 1.18 0.80 1.11 0.73 1.15 0.74 1.02 0.78 1.11 Case 12 0.87 1.08 0.69 1.18 0.84 1.04 0.73 1.15 0.80 1.00 0.79 1.12 Case 13 0.88 1.11 0.71 1.21 0.85 1.11 0.75 1.18 0.82 1.08 0.80 1.14 Case 14 0.28 0.65 0.05 0.86 0.30 0.64 0.11 0.84 0.35 0.59 0.12 0.82 Table 3.32. Summary of controlling live load distribution factors for prestressed concrete box bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case). PC Box L = 80 ft L = 100 ft L = 140 ft Bending Shear Bending Shear Bending Shear Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int LRT 1 0.04 0.29 0.00 0.52 0.05 0.27 0.00 0.50 0.06 0.24 0.00 0.47 LRT 2 0.07 0.46 0.00 0.60 0.07 0.43 0.00 0.60 0.09 0.40 0.00 0.61 Case 1 0.13 0.47 0.01 0.71 0.18 0.45 0.02 0.68 0.21 0.43 0.03 0.66 Case 2 0.36 0.66 0.20 0.83 0.46 0.65 0.25 0.82 0.49 0.62 0.27 0.81 Case 3 0.80 0.84 1.03 0.89 0.88 0.83 1.04 0.85 0.88 0.79 1.06 0.85 Case 4 0.82 0.86 1.04 0.89 0.90 0.85 1.08 0.89 0.91 0.82 1.10 0.89 Case 5 0.85 0.89 1.05 0.90 0.92 0.88 1.09 0.89 0.94 0.85 1.12 0.89 Case 6 0.88 0.93 1.06 0.91 0.96 0.91 1.15 0.89 0.97 0.88 1.15 0.89 Case 7 0.16 0.52 0.01 0.74 0.19 0.49 0.02 0.69 0.22 0.47 0.04 0.67 Case 8 0.16 0.57 0.01 0.73 0.20 0.56 0.08 0.69 0.23 0.53 0.09 0.67 Case 9 0.38 0.70 0.19 0.80 0.45 0.69 0.25 0.78 0.51 0.68 0.28 0.76 Case 10 0.80 0.84 0.99 0.86 0.90 0.86 1.05 0.86 0.99 0.89 1.12 0.87 Case 11 0.84 0.88 1.00 0.86 0.93 0.89 1.13 0.87 1.00 0.91 1.13 0.88 Case 12 0.85 0.90 1.02 0.88 0.95 0.91 1.14 0.88 1.01 0.92 1.14 0.88 Case 13 0.89 0.94 1.03 0.89 0.98 0.94 1.11 0.91 1.01 0.92 1.13 0.91 Case 14 0.18 0.63 0.01 0.77 0.21 0.60 0.02 0.75 0.24 0.59 0.03 0.73 Table 3.33. Summary of controlling live load distribution factors for steel box bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case). ST Plate L = 80 ft L = 100 ft L = 140 ft L = 160 ft Bending Shear Bending Shear Bending Shear Bending Shear Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int LRT 1 0.04 0.29 0.00 0.53 0.04 0.28 0.00 0.53 0.05 0.25 0.00 0.51 0.05 0.24 0.00 0.50 LRT 2 0.07 0.46 0.00 0.61 0.08 0.44 0.00 0.60 0.09 0.41 0.00 0.58 0.10 0.40 0.00 0.57 Case 1 0.12 0.47 0.00 0.73 0.13 0.46 0.00 0.73 0.15 0.43 0.01 0.72 0.15 0.42 0.01 0.72 Case 2 0.34 0.64 0.18 0.82 0.35 0.62 0.19 0.82 0.36 0.59 0.20 0.81 0.36 0.58 0.20 0.81 Case 3 0.80 0.83 1.07 0.84 0.81 0.80 1.07 0.84 0.81 0.75 1.08 0.84 0.78 0.73 1.08 0.85 Case 4 0.84 0.86 1.08 0.86 0.85 0.83 1.09 0.85 0.86 0.79 1.09 0.85 0.82 0.78 1.13 0.85 Case 5 0.86 0.89 1.09 0.87 0.88 0.86 1.11 0.87 0.88 0.83 1.11 0.87 0.88 0.83 1.14 0.88 Case 6 0.90 0.93 1.09 0.86 0.92 0.91 1.11 0.86 0.94 0.88 1.11 0.87 0.96 0.87 1.11 0.87 Case 7 0.15 0.52 0.00 0.76 0.16 0.52 0.00 0.76 0.19 0.49 0.01 0.75 0.19 0.49 0.02 0.76 Case 8 0.15 0.56 0.00 0.75 0.16 0.56 0.00 0.76 0.19 0.53 0.01 0.75 0.19 0.52 0.01 0.76 Case 9 0.36 0.68 0.17 0.80 0.38 0.66 0.18 0.81 0.40 0.63 0.19 0.81 0.44 0.63 0.22 0.82 Case 10 0.81 0.84 1.03 0.82 0.82 0.80 1.03 0.82 0.83 0.77 1.03 0.82 0.80 0.76 0.97 0.85 Case 11 0.85 0.87 1.04 0.83 0.86 0.84 1.05 0.84 0.88 0.82 1.05 0.84 0.85 0.81 1.06 0.87 Case 12 0.88 0.90 1.06 0.86 0.90 0.88 1.06 0.86 0.92 0.86 1.07 0.86 0.93 0.85 1.07 0.87 Case 13 0.92 0.95 1.07 0.86 0.94 0.93 1.08 0.86 0.97 0.91 1.08 0.88 1.00 0.91 1.15 0.88 Case 14 0.18 0.63 0.00 0.80 0.20 0.63 0.00 0.80 0.23 0.61 0.01 0.80 0.24 0.60 0.02 0.80 Table 3.34. Summary of controlling live load distribution factors for steel plate bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case).

70 proposed aaShtO LrFD Bridge Design Specifications for Light rail transit Loads RC L = 30 ft L = 50 ft L = 70 ft Bending Shear Bending Shear Bending Shear Ext Int Ext Int Ext Int Ext Int Ext Int Ext Int LRT 1 0.03 0.55 0.00 0.76 0.05 0.37 0.00 0.68 0.06 0.29 0.00 0.62 LRT 2 0.04 0.66 0.00 0.77 0.07 0.54 0.00 0.66 0.10 0.40 0.00 0.56 Case 1 0.10 0.74 0.00 0.86 0.14 0.56 0.04 0.83 0.17 0.46 0.04 0.77 Case 2 0.28 0.82 0.17 0.91 0.31 0.72 0.20 0.82 0.38 0.59 0.21 0.82 Case 3 0.81 0.93 1.12 0.97 0.80 0.98 1.07 0.93 0.87 0.86 1.04 0.92 Case 4 0.88 0.93 1.06 1.01 0.78 0.84 1.05 0.96 0.77 0.84 1.05 0.93 Case 5 0.82 1.02 1.12 0.98 0.84 0.97 1.12 0.96 0.86 0.86 1.06 0.93 Case 6 0.84 1.07 1.12 0.97 0.87 1.06 1.11 0.97 0.90 0.90 1.06 0.93 Case 7 0.11 0.79 0.01 0.87 0.16 0.64 0.04 0.85 0.20 0.53 0.05 0.79 Case 8 0.11 0.85 0.01 0.86 0.15 0.61 0.01 0.86 0.16 0.61 0.01 0.79 Case 9 0.29 0.94 0.17 0.90 0.36 0.82 0.23 0.81 0.41 0.66 0.27 0.77 Case 10 0.82 1.04 1.11 0.97 0.86 0.95 0.97 0.89 0.9 0.82 0.96 0.84 Case 11 0.83 1.10 1.12 0.98 0.84 0.94 1.12 0.98 0.86 0.86 1.03 0.90 Case 12 0.86 1.13 1.05 0.97 0.87 1.01 0.99 0.93 0.94 0.92 0.58 0.51 Case 13 0.85 1.19 1.12 0.97 0.92 1.03 1.03 0.95 0.92 0.93 1.03 0.91 Case 14 0.13 0.91 0.01 0.87 0.17 0.74 0.11 0.75 0.17 0.66 0.14 0.75 Table 3.35. Summary of controlling live load distribution factors for reinforced concrete bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case). Primary suspension (per axle) Secondary suspension (per axle) Stiffness 6,740 lb/in 3,030 lb/in Damping 220 lb-s/in 520 lb-s/in Table 3.36. Suspension properties for wheel-rail system dynamic analysis (Gu and Franklin 2010).

Research Program 71 Parameter Variable F Technical interpretation Each F0.05 Bearing arrangement Two-span 0.33 4.26 Bridge responses are not different Three-span 0.12 3.49 Bridge responses are not different Centrifugal force (CE) Radius (PC Box) 14.99 3.19 Radius affects CE for PC Box bridges Radius (ST Box) 24.55 3.19 Radius affects CE for ST Box bridges Radius (ST I) 63.31 3.11 Radius affects CE for ST I bridges Girder spacing (PC Box) 0.07 3.19 Girder spacing does not affect CE Girder spacing (ST Box) 0.42 3.19 Girder spacing does not affect CE Girder spacing (ST I) 0.02 2.72 Girder spacing does not affect CE Span length (PC Box) 2.50 3.19 Span length does not affect CE Span length (ST Box) 0.20 3.19 Span length does not affect CE Span length (ST I) 1.67 2.72 Span length does not affect CE Curved bridge Radius (PC Box: moment, M) 0.00 3.19 Radius does not influence bending moment Radius (ST Box: M) 0.00 3.19 Radius does not influence bending moment Radius (ST I: M) 0.00 3.11 Radius does not influence bending moment Radius (PC Box: shear, V) 0.02 3.19 Radius does not influence shear force Radius (ST Box: V) 0.01 3.19 Radius does not influence shear force Radius (ST I: V) 0.00 3.11 Radius does not influence shear force Girder spacing (PC Box: M) 0.00 3.19 Girder spacing does not influence bending moment Girder spacing (ST Box: M) 0.00 3.19 Girder spacing does not influence bending moment Girder spacing (ST I: M) 0.00 3.11 Girder spacing does not influence bending moment Girder spacing (PC Box: V) 0.01 3.19 Girder spacing does not influence shear force Girder spacing (ST Box: V) 0.00 3.19 Girder spacing does not influence shear force Girder spacing (ST I: V) 0.00 3.11 Girder spacing does not influence shear force Span length (PC Box: M) 41.11 3.19 Span length affects moment of curved bridges Span length (ST Box: M) 40.04 3.19 Span length affects moment of curved bridges Span length (ST I: M) 52.85 3.11 Span length affects moment of curved bridges Span length (PC Box: V) 19.65 3.19 Span length affects shear of curved bridges Span length (ST Box: V) 18.42 3.19 Span length affects shear of curved bridges Span length (ST I: V) 23.88 3.11 Span length affects shear of curved bridges Dynamic load allowance (IM) Single-span 2.62 3.24 Single-span does not influence IM Multiple-span 0.91 3.49 Multiple-span does not influence IM Multiple presence factor (MPF) PC Box 0.53 3.19 PC Box type does not influence MPF PC I 0.90 3.14 PC I type does not influence MPF ST Box 1.63 3.19 ST Box type does not influence MPF ST Plate 0.03 3.11 ST Plate type does not influence MPF RC 0.00 3.14 RC type does not influence MPF Rail break 0, 1, 2, and 3 in gaps 59.17 2.60 Presence of rail break influences DLA Skewed bridge Girder spacing (PC Box: M) 0.01 3.14 Girder spacing does not influence bending moment Girder spacing (PC I: M) 0.00 2.72 Girder spacing does not influence bending moment Girder spacing (ST Box: M) 0.01 3.14 Girder spacing does not influence bending moment Girder spacing (ST Plate: M) 0.00 2.60 Girder spacing does not influence bending moment Girder spacing (RC: M) 0.12 2.72 Girder spacing does not influence bending moment Girder spacing (PC Box: V) 0.19 3.14 Girder spacing does not influence shear force Girder spacing (PC I: V) 0.01 2.72 Girder spacing does not influence shear force Girder spacing (ST Box: V) 0.00 3.14 Girder spacing does not influence shear force Girder spacing (ST Plate: V) 0.00 2.60 Girder spacing does not influence shear force Girder spacing (RC: V) 0.03 2.72 Girder spacing does not influence shear force Span length (PC Box: M) 41.57 3.14 Span length influences moment of skewed bridges Span length (PC I: M) 63.65 3.11 Span length influences moment of skewed bridges Span length (ST Box: M) 48.87 3.14 Span length influences moment of skewed bridges Span length (ST Plate: M) 71.20 2.60 Span length influences moment of skewed bridges Span length (RC: M) 79.97 3.11 Span length influences moment of skewed bridges Span length (PC Box: V) 14.50 3.14 Span length influences shear of skewed bridges Span length (PC I: V) 17.60 3.11 Span length influences shear of skewed bridges Span length (ST Box: V) 11.43 3.14 Span length influences shear of skewed bridges Span length (ST Plate: V) 20.32 2.60 Span length influences shear of skewed bridges Span length (RC: V) 28.61 3.11 Span length influences shear of skewed bridges Table 3.37. Analysis of Variance for design parameters at a 95% confidence interval.

Parameter Category F Technical interpretation Each F0.05 Braking force (BR) AASHTO LRFD 5.02 2.353 AASHTO BR is different from model data Proposed 1.03 2.353 Proposed BR is not different from model data Centrifugal force (CE) AASHTO LRFD (R = 500 ft) 0.70 1.943 AASHTO CE is not different from model data (upper envelopment for design) Proposed (R = 500 ft) 0.70 1.943 Proposed CE is not different from model data (upper envelopment for design) AREMA (R = 500 ft) 2.14 1.943 AREMA CE is different from model data (upper envelopment for design) AASHTO LRFD (R = 1000 ft) 0.68 1.860 AASHTO CE is not different from model data (upper envelopment for design) Proposed (R = 1000 ft) 0.68 1.860 Proposed CE is not different from model data (upper envelopment for design) AREMA (R = 1000 ft) 2.58 1.860 AREMA CE is different from model data (upper envelopment for design) AASHTO LRFD (R = 1500 ft) 0.45 1.860 AASHTO CE is not different from model data (upper envelopment for design) Proposed (R = 1500 ft) 0.45 1.860 Proposed CE is not different from model data (upper envelopment for design) AREMA (R = 1500 ft) 3.99 1.860 AREMA CE is different from model data (upper envelopment for design) Dynamic load allowance (IM) AASHTO LRFD (one-span) 5.59 2.132 AASHTO IM is different from model data (upper envelopment) Proposed (one-span) 3.51 2.132 Proposed IM is different from model data (upper envelopment) AASHTO LRFD (multiple-span) 5.74 2.132 AASHTO IM is different from model data (upper envelopment) Proposed (multiple-span) 3.01 2.132 Proposed IM is different from model data (upper envelopment) Multiple presence factor (MPF) AASHTO LRFD (PC Box)  1.706 AASHTO MPF is different from model data Proposed (PC Box) 0 1.706 Proposed MPF is not different from model data AASHTO LRFD (PC I)  1.645 AASHTO MPF is different from model data Proposed (PC I) 0 1.645 Proposed MPF is not different from model data AASHTO LRFD (ST Box)  1.706 AASHTO MPF is different from model data Proposed (ST Box) 0 1.706 Proposed MPF is not different from model data AASHTO LRFD (ST Plate)  1.645 AASHTO MPF is different from model data Proposed (ST Plate) 0 1.645 Proposed MPF is not different from model data AASHTO LRFD (RC)  1.645 AASHTO MPF is different from model data Proposed (RC) 0 1.645 Proposed MPF is not different from model data Skew correction factor (SK) AASHTO LRFD (PC Box: M, θ = 0o) 0 1.740 AASHTO SK is not different from model data Proposed (PC Box: M, θ = 0o) 0 1.740 Proposed SK is not different from model data AASHTO LRFD (PC I: M, θ = 0o) 0 1.714 AASHTO SK is not different from model data Proposed (PC I: M, θ = 0o) 0 1.714 Proposed SK is not different from model data AASHTO LRFD (ST Box: M, θ = 0o) 0 1.714 AASHTO SK is not different from model data Proposed (ST Box: M, θ = 0o) 0 1.714 Proposed SK is not different from model data AASHTO LRFD (ST Plate: M, θ = 0o) 0 1.645 AASHTO SK is not different from model data Proposed (ST Plate: M, θ = 0o) 0 1.645 Proposed SK is not different from model data AASHTO LRFD (RC: M, θ = 0o) 0 1.714 AASHTO SK is not different from model data Proposed (RC: M, θ = 0o) 0 1.714 Proposed SK is not different from model data AASHTO LRFD (PC Box: V, θ = 0o) 0 1.740 AASHTO SK is not different from model data Proposed (PC Box: V, θ = 0o) 0 1.740 Proposed SK is not different from model data AASHTO LRFD (PC I: V, θ = 0o) 0 1.714 AASHTO SK is not different from model data Proposed (PC I: V, θ = 0o) 0 1.714 Proposed SK is not different from model data AASHTO LRFD (ST Box: V, θ = 0o) 0 1.740 AASHTO SK is not different from model data Table 3.38. t-test for design parameters at a 95% confidence interval.

Parameter Category F Technical interpretation Each F0.05 Proposed (ST Box: V, θ = 0o) 0 1.740 Proposed SK is not different from model data AASHTO LRFD (ST Plate: V, θ = 0o) 0 1.645 AASHTO SK is not different from model data Proposed (ST Plate: V, θ = 0o) 0 1.645 Proposed SK is not different from model data AASHTO LRFD (RC: V, θ = 0o) 0 1.714 AASHTO SK is not different from model data Proposed (RC: V, θ = 0o) 0 1.714 Proposed SK is not different from model data AASHTO LRFD (PC Box: M, θ = 20o) 6.73 1.740 AASHTO SK is different from model data Proposed (PC Box: M, θ = 20o) 1.08 1.740 Proposed SK is not different from model data AASHTO LRFD (PC I: M, θ = 20o) 6.46 1.714 AASHTO SK is different from model data Proposed (PC I: M, θ = 20o) 0.09 1.714 Proposed SK is not different from model data AASHTO LRFD (ST Box: M, θ = 20o) 0.93 1.74 AASHTO SK is not different from model data Proposed (ST Box: M, θ = 20o) 1.00 1.74 Proposed SK is not different from model data AASHTO LRFD (ST Plate: M, θ = 20o) 6.79 1.645 AASHTO SK is different from model data Proposed (ST Plate: M, θ = 20o) 0.62 1.645 Proposed SK is not different from model data AASHTO LRFD (RC: M, θ = 20o) 1.60 1.714 AASHTO SK is not different from model data Proposed (RC: M, θ = 20o) 1.60 1.714 Proposed SK is not different from model data AASHTO LRFD (PC Box: V, θ = 20o) 19.7 1.740 AASHTO SK is different from model data Proposed (PC Box: V, θ = 20o) 1.45 1.74 Proposed SK is not different from model data AASHTO LRFD (PC I: V, θ = 20o) 3.09 1.714 AASHTO SK is different from model data Proposed (PC I: V, θ = 20o) 0.13 1.714 Proposed SK is not different from model data AASHTO LRFD (ST Box: V, θ = 20o) 8.46 1.740 AASHTO SK is different from model data Proposed (ST Box: V, θ = 20o) 0.46 1.740 Proposed SK is not different from model data AASHTO LRFD (ST Plate: V, θ = 20o) 2.12 1.645 AASHTO SK is different from model data Proposed (ST Plate: V, θ = 20o) 0.42 1.645 Proposed SK is not different from model data AASHTO LRFD (RC: V, θ = 4.92 1.714 AASHTO SK is different from model data 20o) Proposed (RC: V, θ = 20o) 0.02 1.714 Proposed SK is not different from model data AASHTO LRFD (PC Box: M, θ = 40o) 6.06 1.740 AASHTO SK is different from model data Proposed (PC Box: M, θ = 40o) 0.75 1.740 Proposed SK is not different from model data AASHTO LRFD (PC I: M, θ = 40o) 1.01 1.714 AASHTO SK is not different from model data Proposed (PC I: M, θ = 40o) 0.03 1.714 Proposed SK is not different from model data AASHTO LRFD (ST Box: M, θ = 40o) 9.35 1.740 AASHTO SK is different from model data Proposed (ST Box: M, θ = 40o) 1.09 1.740 Proposed SK is not different from model data AASHTO LRFD (ST Plate: M, θ = 40o) 2.16 1.645 AASHTO SK is different from model data Proposed (ST Plate: M, θ = 40o) 0.31 1.645 Proposed SK is not different from model data AASHTO LRFD (RC: M, θ = 40o) 0.63 1.714 AASHTO SK is not different from model data Proposed (RC: M, θ = 40o) 0.63 1.714 Proposed SK is not different from model data AASHTO LRFD (PC Box: V, θ = 40o) 1.30 1.74 AASHTO SK is not different from model data Proposed (PC Box: V, θ = 40o) 1.62 1.74 Proposed SK is not different from model data AASHTO LRFD (PC I: V, θ = 40o) 2.56 1.714 AASHTO SK is different from model data Proposed (PC I: V, θ = 40o) 0.27 1.714 Proposed SK is not different from model data AASHTO LRFD (ST Box: V, θ = 40o) 4.63 1.740 AASHTO SK is different from model data Proposed (ST Box: V, θ = 40o) 0.34 1.740 Proposed SK is not different from model data AASHTO LRFD (ST Plate: V, θ = 40o) 2.39 1.645 AASHTO SK is different from model data Proposed (ST Plate: V, θ = 40o) 0.59 1.645 Proposed SK is not different from model data Table 3.38. (Continued). (continued on next page)

74 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Parameter Category F Technical interpretation Each F0.05 AASHTO LRFD (RC: V, θ = 40o) 8.82 1.714 AASHTO SK is different from model data Proposed (RC: V, θ = 40o) 0.01 1.714 Proposed SK is not different from model data AASHTO LRFD (PC Box: M, θ = 60o) 6.98 1.740 AASHTO SK is different from model data Proposed (PC Box: M, θ = 60o) 0.12 1.740 Proposed SK is not different from model data AASHTO LRFD (PC I: M, θ = 60o) 1.80 1.714 AASHTO SK is different from model data Proposed (PC I: M, θ = 60o) 0.00 1.714 Proposed SK is not different from model data AASHTO LRFD (ST Box: M, θ = 60o) 22.45 1.740 AASHTO SK is different from model data Proposed (ST Box: M, θ = 60o) 0.41 1.740 Proposed SK is not different from model data AASHTO LRFD (ST Plate: M, θ = 60o) 1.32 1.645 AASHTO SK is not different from model data Proposed (ST Plate: M, θ = 60o) 0.00 1.645 Proposed SK is not different from model data AASHTO LRFD (RC: M, θ = 60o) 0.88 1.714 AASHTO SK is not different from model data Proposed (RC: M, θ = 60o) 0.88 1.714 Proposed SK is not different from model data AASHTO LRFD (PC Box: V, θ = 60o) 11.26 1.740 AASHTO SK is different from model data Proposed (PC Box: V, θ = 60o) 0.10 1.740 Proposed SK is not different from model data AASHTO LRFD (PC I: V, θ = 60o) 0.69 1.714 AASHTO SK is not different from model data Proposed (PC I: V, θ = 60o) 0.01 1.714 Proposed SK is not different from model data AASHTO LRFD (ST Box: V, θ = 60o) 2.89 1.740 AASHTO SK is different from model data Proposed (ST Box: V, θ = 60o) 0.03 1.740 Proposed SK is not different from model data AASHTO LRFD (ST Plate: V, θ = 60o) 0.13 1.645 AASHTO SK is not different from model data Proposed (ST Plate: V, θ = 60o) 0.12 1.645 Proposed SK is not different from model data AASHTO LRFD (RC: V, θ = 60o) 5.35 1.714 AASHTO SK is different from model data Proposed (RC: V, θ = 60o) 0.00 1.714 Proposed SK is not different from model data Load distribution factor (LDF) PC Box (Lever rule: M- Ext) 20.87 1.740 Lever rule LDF is different from model data PC Box (Proposed: M- Ext) 0.01 1.740 Proposed LDF is not different from model data PC I (Lever rule: M- Ext) 20.07 1.714 Lever rule LDF is different from model data PC I (Proposed: M- Ext) 0.40 1.714 Proposed LDF is not different from model data ST Box (Lever rule: M- Ext) 15.23 1.740 Lever rule LDF is different from model data ST Box (Proposed: M- Ext) 0.01 1.740 Proposed LDF is not different from model data ST I (Lever rule: M- Ext) 22.37 1.645 Lever rule LDF is different from model data ST I (Proposed: M- Ext) 0.25 1.645 Proposed LDF is not different from model data RC (Lever rule: M- Ext) 19.12 1.714 Lever rule LDF is different from model data RC (Proposed: M- Ext) 1.06 1.714 Proposed LDF is not different from model data PC Box (Lever rule: M- Int) 18.10 1.740 Lever rule LDF is different from model data PC Box (Proposed: M- Int) 0.05 1.740 Proposed LDF is not different from model data PC I (Lever rule: M- Int) 24.95 1.714 Lever rule LDF is different from model data PC I (Proposed: M- Int) 0.00 1.714 Proposed LDF is not different from model data ST Box (Lever rule: M- Int) 24.70 1.740 Lever rule LDF is different from model data ST Box (Proposed: M- Int) 0.00 1.740 Proposed LDF is not different from model data ST I (Lever rule: M- Int) 29.52 1.645 Lever rule LDF is different from model data ST I (Proposed: M- Int) 0.00 1.645 Proposed LDF is not different from model data RC (Lever rule: M- Int) 11.17 1.714 Lever rule LDF is different from model data RC (Proposed: M- Int) 0.00 1.714 Proposed LDF is not different from model data PC Box (Lever rule: V- Ext) 17.04 1.740 Lever rule LDF is different from model data Table 3.38. (Continued).

Parameter Category F Technical interpretation Each F0.05 PC Box (Proposed: V- Ext) 0.02 1.740 Proposed LDF is not different from model data PC I (Lever rule: V- Ext) 19.03 1.714 Lever rule LDF is different from model data PC I (Proposed: V- Ext) 0.36 1.714 Proposed LDF is not different from model data ST Box (Lever rule: V- Ext) 12.0 1.740 Lever rule LDF is different from model data ST Box (Proposed: V- Ext) 0.00 1.740 Proposed LDF is not different from model data ST I (Lever rule: V- Ext) 17.20 1.645 Lever rule LDF is different from model data ST I (Proposed: V- Ext) 0.20 1.645 Proposed LDF is not different from model data RC (Lever rule: V- Ext) 19.12 1.714 Lever rule LDF is different from model data RC (Proposed: V- Ext) 0.11 1.714 Proposed LDF is not different from model data PC Box (Lever rule: V- Int) 22.18 1.740 Lever rule LDF is different from model data PC Box (Proposed: V- Int) 0.00 1.740 Proposed LDF is not different from model data PC I (Lever rule: V- Int) 24.71 1.714 Lever rule LDF is different from model data PC I (Proposed: V- Int) 0.00 1.714 Proposed LDF is not different from model data ST Box (Lever rule: V- Int) 28.98 1.740 Lever rule LDF is different from model data ST Box (Proposed: V- Int) 0.01 1.740 Proposed LDF is not different from model data ST I (Lever rule: V- Int) 33.18 1.645 Lever rule LDF is different from model data ST I (Proposed: V- Int) 0.00 1.645 Proposed LDF is not different from model data RC (Lever rule: V- Int) 17.27 1.714 Lever rule LDF is different from model data RC (Proposed: V- Int) 0.01 1.714 Proposed LDF is not different from model data Table 3.38. (Continued). Type of superstructure AASHTO LRFD Proposed M om en t PC Box tan25.005.1 tan21.0046.1 PC I 5.1 1 tan1 c 5.025.0 31 0.12 25.0 L S Lt K c s g 616.1 1 tan988.0 c 131.0442.0 31 617.9 32.0 L S Lt K c s g ST Box tan25.005.1 tan15.0023.1 ST Plate 5.1 1 tan1 c 5.025.0 31 0.12 25.0 L S Lt K c s g 456.2 1 tan982.0 c 121.0306.0 31 766.0 093.0 L S Lt K c s g RC 5.1 1 tan1 c 5.025.0 31 0.12 25.0 L S Lt K c s g Same as AASHTO LRFD Sh ea r PC Box tan70 0.1225.01 d L 015.0tan 70 12034.19653.17 dS L PC I tan0.1220.01 3.03 g s K Lt 168.0 036.03 tan 0.12086.1142.0 g s K Lt ST Box tan 6 0.120.1 S Ld 447.1 361.0 tan 209.15 9.85035.1 S Ld ST Plate tan0.1220.01 3.03 g s K Lt 677.0 156.03 tan 0.12303.0912.0 g s K Lt RC tan0.1220.01 3.03 g s K Lt 723.1 004.03 tan 587.1994305.0993.0 g s K Lt Table 3.39. Skew correction factors for light rail bridges.

76 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Parameter Category F Technical interpretation Each F0.05 Bearing arrangement Two-span (Case a) N/A N/A Reference case for other bridges Two-span (Case b) 0.24 2.353 Response is not different from reference case Two-span (Case c) 1.17 2.353 Response is not different from reference case Three-span (Case a) 0.37 2.353 Response is not different from reference case Three-span (Case b) 0.13 2.353 Response is not different from reference case Three-span (Case c) 0.50 2.353 Response is not different from reference case Three-span (Case d) 0.09 2.353 Response is not different from reference case Braking force (BR) PC Box N/A N/A Reference case for other bridges PC-I 1.51 2.920 BR is not different from reference case ST Box 1.68 2.353 BR is not different from reference case ST Plate 18.13 2.353 BR is different from reference case RC 3.09 2.353 BR is different from reference case Centrifugal force (CE) PC Box N/A N/A Reference case for other bridges ST Box 0.49 1.645 CE is not different from reference case ST Plate 1.55 1.645 CE is not different from reference case Load distribution factor (LDF) PC Box (M: Ext) N/A N/A Reference case for other bridges PC-I (M: Ext) 0.66 1.714 LDF is not different from reference case ST Box (M: Ext) 0.36 1.740 LDF is not different from reference case ST Plate (M: Ext) 0.91 1.645 LDF is not different from reference case RC (M: Ext) 1.23 1.714 LDF is not different from reference case PC Box (M: Int) N/A N/A Reference case for other bridges PC-I (M: Int) 5.36 1.714 LDF is different from reference case ST Box (M: Int) 6.06 1.645 LDF is different from reference case ST Plate (M: Int) 3.63 1.740 LDF is different from reference case RC (M: Int) 0.70 1.714 LDF is not different from reference case PC Box (V: Ext) N/A N/A Reference case for other bridges PC-I (V: Ext) 0.87 1.714 LDF is not different from reference case ST Box (V: Ext) 1.75 1.645 LDF is different from reference case ST Plate (V: Ext) 1.72 1.740 LDF is not different from reference case RC (V: Ext) 4.66 1.714 LDF is different from reference case PC Box (V: Int) N/A N/A Reference case for other bridges PC-I (V: Int) 3.42 1.714 LDF is different from reference case ST Box (V: Int) 2.80 1.645 LDF is different from reference case ST Plate (V: Int) 0.29 1.740 LDF is not different from reference case RC (V: Int) 2.83 1.714 LDF is different from reference case Curved bridge PC Box (M: R = 500 ft) N/A N/A Reference case for other bridges ST Box (M: R = 500 ft) 0.01 1.740 Response is not different from reference case ST Plate (M: R = 500 ft) 1.97 1.645 Response is different from reference case PC Box (V: R = 500 ft) N/A N/A Reference case for other bridges ST Box (V: R = 500 ft) 0.04 1.740 Response is not different from reference case ST Plate (V: R = 500 ft) 1.65 1.645 Response is different from reference case PC Box (M: R = 1000 ft) N/A N/A Reference case for other bridges ST Box (M: R = 1000 ft) 0.02 1.740 Response is not different from reference case ST Plate (M: R = 1000 ft) 1.99 1.645 Response is different from reference case PC Box (V: R = 1000 ft) N/A N/A Reference case for other bridges ST Box (V: R = 1000 ft) 0.19 1.740 Response is not different from reference case ST Plate (V: R = 1000 ft) 1.78 1.645 Response is different from reference case PC Box (M: R = 1500 ft) N/A N/A Reference case for other bridges ST Box (M: R = 1500 ft) 0.03 1.740 Response is not different from reference case ST Plate (M: R = 1500 ft) 1.98 1.645 Response is different from reference case PC Box (V: R = 1500 ft) N/A N/A Reference case for other bridges ST Box (V: R = 1500 ft) 0.10 1.740 Response is not different from reference case ST Plate (V: R = 1500 ft) 1.67 1.645 Response is different from reference case Multiple presence factor (MPF) PC Box N/A N/A Reference case for other bridges PC I 0 1.645 Response is not different from reference case ST Box 0 1.645 Response is not different from reference case ST Plate 0 1.645 Response is not different from reference case RC 0 1.645 Response is not different from reference case Rail break Span length (L = 30 ft) 2.19 1.753 Response is different from reference case Span length (L = 50 ft) 1.54 1.753 Response is not different from reference case Span length (L = 70 ft) 1.54 1.753 Response is not different from reference case Span length (L = 80 ft) N/A N/A Reference case for other bridges Span length (L = 100 ft) 3.48 1.645 Response is different from reference case Span length (L = 140 ft) 3.47 1.645 Response is different from reference case Span length (L = 160 ft) 5.17 1.753 Response is different from reference case Table 3.40. t-test for bridge responses against a reference bridge.

Research Program 77 Parameter Category F Technical interpretation Each F0.05 Skewed bridge Moment (θ = 0o) N/A N/A Reference case for other bridges Moment (θ = 20o) 0.29 1.645 Response is not different from reference case Moment (θ = 40o) 0.89 1.645 Response is not different from reference case Moment (θ = 60o) 2.71 1.645 Response is different from reference case Shear ( θ = 0o) N/A N/A Reference case for other bridges Shear ( θ = 20o) 1.52 1.645 Response is not different from reference case Shear ( θ = 40o) 4.57 1.645 Response is different from reference case Shear ( θ = 60o) 7.94 1.645 Response is different from reference case Table 3.40. (Continued). Bridge type Coefficient of variation Prestressed concrete box girder 0.075 Prestressed concrete I girder 0.075 Steel box girder 0.100 Steel I girder 0.100 Reinforced concrete girder 0.13 Table 3.41. Coefficient of variation of the resistance for bridge structures (NCHRP Project 12-33). Relevant limit state Description Relevance to NCHRP Project 12-92 Load factor Strength I (unless noted) Basic load combination relating to the normal vehicular use of the bridge without wind Relevant because this limit state covers most possible cases in design. Load factors will be proposed based on the standard live load model 1.65 Service I Load combination relating to the normal operational use of the bridge with a 55 mph wind and all loads taken at their nominal values. Relevant because this limit state covers most possible service cases 1.00 Fatigue I Fatigue and fracture load combination related to infinite load-induced fatigue life Relevant because light rail bridges should not experience fatigue cracking in any loading conditions 1.40 Fatigue II Fatigue and fracture load combination related to finite load-induced fatigue life Relevant because light rail bridges experience finite load- induced fatigue 0.85 Table 3.42. Summary of proposed load factors for light rail loading. Strength I Service I Fatigue I Fatigue II Load factor 1.75 1.00 1.75/1.40* 0.85 *: 1.75 for highway loading and 1.40 for light rail loading. Table 3.43. Proposed load factors for bridges carrying both light rail and highway traffic loadings.

78 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) (e)(d)(c) Figure 3.1. Light rail bridges monitored: (a) County Line Bridge; (b) 6th Avenue Bridge; (c) Broadway Bridge; (d) Santa Fe Bridge; and (e) Indiana Bridge. Support Perforated hollow sectionNut Threaded rod P 193015153019 128 Unit in inch 115 RE Strain gage (Not to scale) Bearing plate 4 Strain gages (rail side) Strain gages (rail bottom) (c)(b)(a) Figure 3.2. Test details for response calibration: (a) schematic (unit in inch); (b) experimental setup; and (c) strain gage configurations for the side and bottom of the rail. 3.9 Chapter 3 Figures

Research Program 79 Theory Load Test Empty train Full train Test Theory Empty train Full train Load (b)(a) Figure 3.3. Load-strain behavior at bottom of rail: (a) simply-supported case and (b) continuous case. Empty train Full train G1G2 G3G4 G1 G3 G2 G4 Figure 3.4. Load-strain behavior on the side of continuous rail. For laboratory use For site use (a) (b) Figure 3.5. Validation of portable data acquisition system using rail strain at bottom: (a) unportable and portable systems; and (b) comparison.

80 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Strain gages (a) Laboratory: empty train (b) Figure 3.6. Calibration of load-strain response at the Auraria West Station: (a) wheel positioning and (b) comparison between in situ test and laboratory test (front wheel load). (a) Temperature gage Monitored span (b) (c) (d) Figure 3.7. Monitoring of the Broadway Bridge: (a) elevation view and girder cross section; (b) light rail train operation on site and portable data acquisition system; (c) strain gages bonded to rail; and (d) strain gages bonded to girders at mid span.

Research Program 81 Monitored span (a) (b) (c) (d) Figure 3.8. Monitoring of the Indiana Bridge: (a) elevation view and typical cross section of girder; (b) rail gage bonding; (c) one-way train track; and (d) girder gages. Monitored span (a) (b) (c) (d) Figure 3.9. Monitoring of the Santa Fe Bridge: (a) elevation view and typical cross section of girder; (b) rail gage bonding; (c) trains approaching; and (d) girder gages.

Monitored span (a) (b) (c) (d) Figure 3.10. Monitoring of the County Line Bridge: (a) elevation view and typical cross section of girder; (b) rail gage bonding; (c) trains approaching; and (d) girder gages. Monitored span (a) (b) (c) (d) Figure 3.11. Monitoring of the 6th Avenue Bridge: (a) elevation view and typical cross section of girder; (b) rail gage bonding; (c) trains approaching; and (d) girder gages. Figure 3.12. Typical temperature variation of track rail measured in the Broadway Bridge.

Research Program 83 (a) (b) Figure 3.13. Measured strains for light rail train wheel load: (a) Broadway Bridge and (b) Indiana Bridge. (continued on next page)

84 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (c) (d) Figure 3.13. (Continued) Measured strains for light rail train wheel load: (c) Santa Fe Bridge; and (d) County Line Bridge. (continued)

Research Program 85 (e) Figure 3.13. (Continued) Measured strains for light rail train wheel load: (e) 6th Avenue Bridge. (14.869 k) (14.869 k)(9.913 k) Figure 3.14. Fully loaded design axle loads of the light rail train operated in Denver, CO (the six axles loads of the articulated empty train consist of 14.869 k + 14.869 k + 9.913 k + 9.913 k + 14.869 k + 14.869).

86 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) (c) (d) Load = 0.0207(Speed) + 5.6293 Design load (heavy wheel: full load) Design load (light wheel: empty train) μ = 6.3 kips COV = 0.31 S = 23.4 mph μ = 6.2 kips COV = 0.30 S = 40.4 mph μ = 6.9 kips COV = 0.25 S = 46.0 mph μ = 6.6 kips COV = 0.20 S = 49.0 mph μ = 6.2 kips COV = 0.21 S = 32.9 mph (e) (f) N um be r o f o bs er va tio ns N um be r o f o bs er va tio ns N um be r o f o bs er va tio ns N um be r o f o bs er va tio ns N um be r o f o bs er va tio ns Figure 3.15. Distribution of measured train wheel load (l = average; COV = coefficient of variation; S = average train speed): (a) Broadway Bridge; (b) Indiana Bridge; (c) Santa Fe Bridge; (d) County Line Bridge; (e) 6th Avenue Bridge; and (f) mean train load measured versus average train speed (heavy wheel = front and rear; light wheel = middle).

Figure 3.16. Normality test of the Broadway Bridge. (a) (b) (d)(c) (f)(e) Number of samples (log scale) Number of samples (log scale) Number of samples (log scale) Number of samples (log scale) Number of samples (log scale) Figure 3.17. Comparison between measured and predicted train wheel loads: (a) Broadway Bridge; (b) Indiana Bridge; (c) Santa Fe Bridge; (d) County Line Bridge; (e) 6th Avenue Bridge; and (f) mean train wheel load.

88 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) Figure 3.18. Flexural response of monitored bridges: (a) Broadway Bridge (exterior girder); and (b) Indiana Bridge (exterior box web). (continued)

Research Program 89 (c) (d) (e) Figure 3.18. (Continued) Flexural response of monitored bridges: (c) Santa Fe Bridge (2nd interior box web); (d) County Line Bridge (interior girder); and (e) 6th Avenue Bridge (interior girder).

90 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) (c) (d) μ = 0.12 V = 0.30 μ = 0.31 V = 0.06 μ = 0.57 V = 0.06 μ = 0.73 V = 0.07 μ = 0.53 V = 0.03 μ = 0.74 V = 0.09 μ = 0.48 V = 0.07 μ = 0.34 V = 0.07 μ = 0.18 V = 0.20 μ = 0.40 V = 0.08 μ = 0.32 V = 0.13 μ = 0.29 V = 0.19 μ = 0.27 V = 0.14 μ = 0.31 V = 0.21 μ = 0.27 V = 0.09 μ = 0.15 V = 0.54 μ = 0.17 V = 0.47 μ = 0.25 V = 0.20 μ = 0.34 V = 0.12 μ = 0.25 V = 0.15 μ = 0.35 V = 0.13 μ = 0.37 V = 0.19 μ = 0.21 V = 0.14 μ = 0.07 V = 0.25 μ = 0.04 V = 0.27 μ = 0.16 V = 0.35 μ = 0.47 V = 0.08 μ = 0.33 V = 0.11 Figure 3.19. Live load distribution factors and statistical properties measured on site: (a) Broadway Bridge; (b) Indiana Bridge; (c) Santa Fe Bridge; and (d) County Line Bridge. (continued)

Research Program 91 (e) μ = 0.33 V = 0.47 μ = 0.26 V = 0.43 μ = 0.27 V = 0.53 μ = 0.27 V = 0.43 μ = 0.26 V = 0.61 μ = 0.20 V = 0.68 μ = 0.22 V = 0.01 μ = 0.27 V = 0.06 μ = 0.37 V = 0.26 μ = 0.41 V = 0.15 μ = 0.38 V = 0.22 μ = 0.35 V = 0.17 μ = 0.11 V = 0.01 μ = 0.14 V = 0.06 μ = 0.19 V = 0.26 μ = 0.21 V = 0.15 μ = 0.19 V = 0.22 μ = 0.17 V = 0.17 Figure 3.19. (Continued) Live load distribution factors and statistical properties measured on site: (e) 6th Avenue Bridge. (c) (a) (b) Figure 3.20. Comparison among mean live load distribution factors, lever rule, and AASHTO LRFD equations: (a) Broadway Bridge; (b) Indiana Bridge; and (c) Santa Fe Bridge. (continued on next page)

92 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (d) (e) Figure 3.20. (Continued) Comparison among mean live load distribution factors, lever rule, and AASHTO LRFD equations: (d) County Line Bridge and (e) 6th Avenue Bridge. (a) (b) (c) Reflector at midspan Figure 3.21. Non-contact interferometric radar technique for measuring dynamic behavior of the County Line Bridge: (a) installation of a reflector; (b) trains passing; and (c) IBIS setup for monitoring.

Research Program 93 Walkway Steel I girder Deck slab Bearing Direct fixation track Bearing Bearing Walkway Deck slab Pier cap Steel I girder (a) Modeled spans Bearing Direct fixation track Prestressed concrete box girder Bearing Pier Prestressed concrete box girder WalkwayWalkway Direct fixation track Pier (b) Modeled spans Bearing Prestressed concrete box girder Ballasted track Pier Bearing Prestressed concrete box girder Pier Ballasted track Prestressing strands Modeled spans (c) Figure 3.22. Bridge models developed: (a) Broadway Bridge (2 spans: 278 ft); (b) Indiana Bridge (5 spans: 628 ft); and (c) Santa Fe Bridge (2 spans: 334 ft). (continued on next page)

94 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (e) Modeled spans Bearing Prestressed concrete Pier cap Deck slab Walkway Bearing Prestressed concrete Deck slab Direct fixation track Prestressing strands Modeled spans Bearing Prestressed concrete Ballast track Precast element Prestressing strands Bearing Prestressed concrete Ballast track Ballast link (d) Figure 3.22. (Continued) Bridge models developed: (d) County Line Bridge (4 spans: 580 ft) and (e) 6th Ave Bridge (4 spans: 328 ft). Train 1 (6 axles) Train 2 (6 axles) (a) (c) (b) (d) Figure 3.23. Behavior of the Indiana Bridge subjected to two articulated light rail trains at a speed of 40.4 mph (scaled view): (a) maximum negative moment for the first pier; (b) maximum positive moment for the second span; (c) maximum negative moment for the second pier; and (d) maximum positive moment for the fourth span.

Research Program 95 Load case 1 Load case 2 Load case 3 (a) Load case 1 (b) Load case 1 Load case 2 (c) Figure 3.24. Comparison between field test and model prediction: (a) Broadway Bridge; (b) Indiana Bridge; (c) Santa Fe Bridge. (continued on next page)

96 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (e) Load case 1 Load case 2 Load case 3 Load case 2Load case 1 (d) Figure 3.24. (Continued) Comparison between field test and model prediction: (d) County Line Bridge and (e) 6th Avenue Bridge. (a) (b) Figure 3.25. Comparison between measured and predicted displacements at midspan: (a) Broadway Bridge (steel plate girder) and (b) Indiana Bridge (prestressed concrete box girder). (continued)

Research Program 97 (c) (d) (e) Figure 3.25. (Continued) Comparison between measured and predicted displacements at midspan: (c) Santa Fe Bridge (prestressed concrete box girder); (d) County Line Bridge (prestressed concrete I girder); and (e) 6th Avenue Bridge (prestressed concrete I girder). Acceptable Unacceptable Acceptable Unacceptable (a) (b) Figure 3.26. Evaluation of user comfort (pedestrian): (a) average test data with service train load and (b) model prediction with empty and fully loaded light rail train loads.

98 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads 4.719.254.71 9.254.71 4.71 4.714.71 9.25 32 9.254.71 4.71 6 4 44 4 4 4 6 32 32 32 4 6 6 6 6 4 4 8 8 8 6 10 10 6 (a) 4 6 6 66 4 4.71 9.25 4.71 4 4 9.254.71 4.71 32 6 4.714.71 9.25 8 8 8 10 10 6 3232 (b) 4.719.254.71 4.719.254.71 4.71 4.71 9.25 9.254.71 4.71 6444446 32 6101068884466664 4 32 32 32 (c) 4 32 84 88 4.714.71 9.25 32 6 1010 6 4.719.254.71 32 4 4 4.714.71 9.25 12 12 (e) (d) 4.714.71 9.25 4.719.254.71 4.71 9.254.71 9.254.71 4.71 6 4 4 4 4 4 6 32 4 6 6 6 6 4 4 8 8 8 6 10 10 6 32 32 32 4 Figure 3.27. Dimensional configurations of benchmark bridge models (unit in ft; not to scale): (a) steel plate girder; (b) steel box girder; (c) prestressed concrete I girder; (d) prestressed concrete box girder; and (e) reinforced concrete box girder.

Research Program 99 (a) (b) (c) (d) Figure 3.28. Effect of gage length: (a) moment of County Line Bridge; (b) moment of 6th Avenue Bridge; (c) shear of County Line Bridge; and (d) shear of 6th Avenue Bridge. k 573 .42 5.9ft k 573 .42 k 5 .52 k 5 .52 k 5 .52 k 5 .71 k 5 .71 k 5 .52 6.3ft 6.3ft6.3ft16.8ft 16.8ft Massachusetts 5.9ft k 58 .22 k 58 .22 28.8ft 5.9ft 6.0ft5.9ft28.8ft Minnesota k 54 .03 k 54 .03 k 0 .72 k 58 .22 k 58 .22 k 0 .72 k 573 .42 k 052 .61 k 052 .61 k 573 .42 5.9ft19.6ft19.6ft 5.9ft Colorado 6.0ft28.0ft28.0ft 6.0ft Utah k 0 .72 k 0 .72 k 0 .72 k 0 .72 92ft (over coupler faces) 92ft (over coupler faces) 74ft (over coupler faces) 79ft (over coupler faces) Figure 3.29. Selected live load models representing light rail train design loads in the nation.

100 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads 8 ft spacing (4 webs) 12 ft spacing (3 webs)10 ft spacing (3 webs) 6 ft spacing (5 girders) 8 ft spacing (4 girders) 10 ft spacing (3 girders) 10 ft spacing (3 girders)4 ft spacing (6 girders) 6 ft spacing (5 girders) 8 ft spacing (4 girders) 4 ft spacing (6 girders) 6 ft spacing (5 girders) 10 ft spacing (3 girders)8 ft spacing (4 girders) 10 ft spacing (3 girders)4 ft spacing (6 girders) 6 ft spacing (5 girders) 8 ft spacing (4 girders) (a) (b) (c) (d) (e) Figure 3.30. Selected finite element models for parametric investigations: (a) steel plate girder bridge; (b) steel box girder bridge; (c) prestressed concrete I girder bridge; (d) prestressed concrete box girder bridge; and (e) reinforced concrete girder bridge.

Research Program 101 (d) (e) (f) (g) (h) (a) (b) (c) Figure 3.31. Curved and skewed bridge models: (a) prestressed concrete box (R = 500 ft); (b) steel box (R = 500 ft); (c) steel plate (R = 500 ft); (d) prestressed concrete box (40°); (e) steel box (40°); (f) prestressed concrete I (40°); (g) steel plate (40°); and (h) reinforced concrete (40°). Solid: 2-track loaded Hollow: 1-track loaded (a) Solid: 2-track loaded Hollow: 1-track loaded (b) Hollow: 1-track loaded Solid: 2-track loaded (c) Solid: 2-track loaded Hollow: 1-track loaded (d) Figure 3.32. Maximum static moment of simply supported steel plate girder bridges: (a) Colorado trains; (b) Utah trains; (c) Minnesota trains; and (d) Massachusetts trains.

102 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Hollow: 1-track loaded (c) Hollow: 1-track loaded (d) Solid: 2-track loaded Hollow: 1-track loaded (a) Solid: 2-track loaded Hollow: 1-track loaded (b) Solid: 2-track loaded Solid: 2-track loaded Figure 3.33. Maximum static moment of simply supported steel box girder bridges: (a) Colorado trains; (b) Utah trains; (c) Minnesota trains; and (d) Massachusetts trains.

Research Program 103 Hollow: 1-track loaded (c) Hollow: 1-track loaded (d) Solid: 2-track loaded Hollow: 1-track loaded (a) Solid: 2-track loaded Hollow: 1-track loaded (b) Solid: 2-track loaded Solid: 2-track loaded Figure 3.34. Maximum static moment of simply supported prestressed concrete I girder bridges: (a) Colorado trains; (b) Utah trains; (c) Minnesota trains; and (d) Massachusetts trains.

104 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Solid: 2-track loaded Hollow: 1-track loaded (a) Solid: 2-track loaded Hollow: 1-track loaded (b) Hollow: 1-track loaded Solid: 2-track loaded (c) Solid: 2-track loaded Hollow: 1-track loaded (d) Figure 3.35. Maximum static moment of simply supported prestressed concrete box girder bridges: (a) Colorado trains; (b) Utah trains; (c) Minnesota trains; and (d) Massachusetts trains.

Research Program 105 Solid: 2-track loaded Hollow: 1-track loaded (a) Solid: 2-track loaded Hollow: 1-track loaded (b) Hollow: 1-track loaded Solid: 2-track loaded (c) Solid: 2-track loaded Hollow: 1-track loaded (d) Figure 3.36. Maximum static moment of simply supported reinforced concrete girder bridges: (a) Colorado trains; (b) Utah trains; (c) Minnesota trains; and (d) Massachusetts trains.

106 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (d)(c) (f)(e) (b)(a) 93HL trainraillight M M 93HL trainraillight M M 93HL trainraillight M M 93HL trainraillight M M 93HL trainraillight M M 93HL trainraillight M M Reference line Reference line Reference line Reference line Reference line Reference line Figure 3.37. Comparison with HL-93 load: (a) steel plate girder (single-train loaded); (b) steel plate girder (multiple-train loaded); (c) steel box girder (single-train loaded); (d) steel box girder (multiple-train loaded); (e) prestressed concrete I girder (single-train loaded); and (f) prestressed concrete I girder (multiple-train loaded). (continued)

Research Program 107 93HL trainraillight M M 93HL trainraillight M M 93HL trainraillight M M 93HL trainraillight M M (j)(i) (h)(g) Reference line Reference line Reference line Reference line Figure 3.37. (Continued) Comparison with HL-93 load: (g) prestressed concrete box girder (single-train loaded); (h) prestressed concrete box girder (multiple-train loaded); (i) reinforced concrete girder (single-train loaded); and (j) reinforced concrete girder (multiple-train loaded).

108 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Solid: 2-track loaded Hollow: 1-track loaded (a) (b) (c) (d) Figure 3.38. Behavior of various span bridges subjected to Utah train loading: (a) steel plate girder; (b) steel box girder; (c) prestressed concrete box girder; and (d) reinforced concrete girder.

Research Program 109 (a) (b) (c) (d) (e) (f) Figure 3.39. Behavior of curved bridges: (a) prestressed concrete box (moment); (b) prestressed concrete box (shear); (c) steel box (moment); (d) steel box (shear); (e) steel plate (moment); and (f) steel plate (shear).

110 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) (c) (d) (e) (f) Figure 3.40. Behavior of skewed bridges: (a) prestressed concrete box (moment); (b) prestressed concrete box (shear); (c) prestressed concrete I (moment); (d) prestressed concrete I (shear); (e) steel box (moment); and (f) steel box (shear). (continued)

Research Program 111 (g) (h) (i) (j) Figure 3.40. (Continued) Behavior of skewed bridges: (g) steel plate (moment); (h) steel plate (shear); (i) reinforced concrete (moment); and (j) reinforced concrete (shear). (a) (b) Ratio = skewed response / straight response Ratio = skewed response / straight response Figure 3.41. Effect of skew angles on bridge behavior: (a) moment ratio and (b) shear ratio.

112 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) (c) Figure 3.42. Variation of fundamental frequency with span length for curved bridges: (a) prestressed concrete box; (b) steel box; and (c) steel plate. (a) (b) (c) (d) (e) Figure 3.43. Variation of fundamental frequency with span length for skewed bridges: (a) prestressed concrete box; (b) prestressed concrete I; (c) steel box; (d) steel plate; and (e) reinforced concrete. Deterministic analysis Probabilistic analysis Integration • Selection of existing load models • Numerical parametric study • Determination of equivalent live load model • Simulation for bridge responses with various live load effects • Identifying possible response ranges in bending and shear • Integrate the deterministic live load model and the probabilistic analysis results • Proposal of standard live load for light rail transit • Comparative assessment with existing load models Figure 3.44. Schematic of procedures for determining the standard live load model of light rail transit.

Research Program 113 (a) (b) (c) Figure 3.45. European live load model for train (European Railway Research Institute): (a) existing LM71; (b) newly developed LM 2000; and (c) candidate live load models considered. w Uniformly distributed load P P P Concentrated loads P P P Proposed live load model w (Magnitude to be determined) (Magnitude, spacing, and number of concentrated loads to be determined) Figure 3.46. Proposed standard live load format for light rail transit.

(a) (b) (d)(c) (f)(e) Truck-average = 0.59 Lane-average = 0.41 72 cases Truck-average = 0.55 Lane-average = 0.45 96 cases Truck-average = 0.56 Lane-average = 0.44 72 cases Truck-average = 0.52 Lane-average = 0.48 128 cases Truck-average = 0.64 Lane-average = 0.36 96 cases Truck-average = 0.57 of HL93 Lane-average = 0.43 of HL93 464 cases Lo ad e ffe ct : C om po ne nt /H L- 93 Lo ad e ffe ct : C om po ne nt /H L- 93 Lo ad e ffe ct : C om po ne nt /H L- 93 Lo ad e ffe ct : C om po ne nt /H L- 93 Lo ad e ffe ct : C om po ne nt /H L- 93 Lo ad e ffe ct : C om po ne nt /H L- 93 Figure 3.47. Decomposition of HL-93 load effect on the simply supported benchmark bridges: (a) prestressed concrete box girder; (b) prestressed concrete I girder; (c) steel box girder; (d) steel plate girder; (e) reinforced concrete girder; and (f) comparison of average load effects. PC Box (288 load cases) PC I (384 load cases) Steel Box (288 load cases) Steel Plate (512 load cases) RC (384 load cases) Figure 3.48. Comparison of equivalent lane load for various bridge types.

(c) (d) (a) (b) (e) 288 load cases 75-year 99.9% 90.0% 384 load cases 75-year 99.9% 90.0% 288 load cases 75-year 99.9% 90.0% 512 load cases 75-year 99.9% 90.0% 384 load cases 75-year 99.9% 90.0% Figure 3.49. Normality check for equivalent lane load of each bridge type: (a) prestressed concrete box girder; (b) prestressed concrete I girder; (c) steel box girder; (d) steel plate girder; and (e) reinforced concrete girder. Upper 20% load RC (384 load cases) PC Box (288 load cases) Steel Box (288 load cases) PC I (384 load cases) Steel Plate (512 load cases) Figure 3.50. Determination of upper 20% equivalent lane load.

116 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) 75-year (ave) = 0.96 k/ft 99.9% (ave) = 0.82 k/ft Upper 20% (ave) = 0.67 k/ft Average (ave) = 0.61 k/ft 1,856 load cases 75-year (ave) = 1.50 99.9% (ave) = 1.29 Upper 20% (ave) = 1.05 Average (ave) = 0.96 1,856 load cases Eq ui v. la ne lo ad /L an e of H L- 93 Figure 3.51. Equivalent lane load: (a) summary per bridge type and (b) comparison with lane load of HL-93. Figure 3.52. Possible moving load schemes depending upon span length. PC Box (7,200 load cases) PC I (9,600 load cases) Steel Box (7,200 load cases) Steel Plate (12,800 load cases) RC (9,600 load cases) Figure 3.53. Comparison of equivalent concentrated load (single axle load P) for various bridge girder types.

Research Program 117 (e) (d)(c) (b)(a) Based on 7,200 load cases Based on 9,600 load cases Based on 7,200 load cases Based on 12,800 load cases Based on 9,600 load cases Figure 3.54. Average equivalent concentrated load based on existing light rail train loads: (a) prestressed concrete box girder; (b) prestressed concrete I girder; (c) steel box girder; (d) steel plate girder; and (e) reinforced concrete girder.

118 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads 288 load cases 75-year 99.9% 90.0% 75-year 99.9% 90.0% 384 load cases 288 load cases 75-year 99.9% 90.0% 75-year 99.9% 90.0% 512 load cases 75-year 99.9% 90.0% 384 load cases (e) (d)(c) (b)(a) Figure 3.55. Normality check for equivalent concentrated single axle load P of each bridge type: (a) prestressed concrete box girder; (b) prestressed concrete I girder; (c) steel box girder; (d) steel plate girder; and (e) reinforced concrete girder.

Upper 20% load RC (9,600 load cases) Steel Box(7,200 load cases) PC Box (7,200 load cases) PC I (9,600 load cases) Steel Plate (12,800 load cases) Figure 3.56. Comparison of each bridge type at 14 ft spacing of single axle load P. (e) (d)(c) (b)(a) Figure 3.57. Equivalent concentrated load based on probability: (a) prestressed concrete box girder; (b) prestressed concrete I girder; (c) steel box girder; (d) steel plate girder; and (e) reinforced concrete girder.

120 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (c) (d) (a) (b) Figure 3.58. Comparison of single axle concentrated load per load level: (a) 75-year; (b) 99.9%; (c) upper 20%; and (d) average. (c)(a) (b) Proposed 14-ft spacing Proposed 14-ft spacing Proposed 14-ft spacing Eq ui v. la ne lo ad /H L- 93 (la ne ) Eq ui v. co n ce n tr. lo ad /H L- 93 (tr u ck ) To ta l e qu iv. lo ad /H L- 93 Figure 3.59. Comparison of equivalent light rail train load with HL-93: (a) lane load; (b) concentrated load (three axles); and (c) total load (concentrated load plus lane load multiplied by axle spacing).

Research Program 121 Existing design loadsCandidate design loads (with lane load along 28 ft only) Figure 3.60. Comparison of candidate standard live load models with representative design train loads (one articulated train). (a) (b) (c) (d) Figure 3.61. Assessment of candidate standard live load models for moment: (a) prestressed concrete box girder (one-track loaded); (b) prestressed concrete box girder (two-track loaded); (c) prestressed concrete I girder (one-track loaded); and (d) prestressed concrete I girder (two-track loaded). (continued on next page)

122 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (i) (j) (h)(g) (e) (f) Figure 3.61. (Continued) Assessment of candidate standard live load models for moment: (e) steel box girder (one-track loaded); (f) steel box girder (two-track loaded); (g) steel plate girder (one-track loaded); (h) steel plate girder (two-track loaded); (i) reinforced concrete girder (one-track loaded); and (j) reinforced concrete girder (two-track loaded).

Research Program 123 (a) (b) (c) (d) (e) (f) Figure 3.62. Assessment of candidate standard live load models for shear: (a) prestressed concrete box girder (one-track loaded); (b) prestressed concrete box girder (two-track loaded); (c) prestressed concrete I girder (one-track loaded); (d) prestressed concrete I girder (two-track loaded); (e) steel box girder (one-track loaded); and (f) steel box girder (two-track loaded). (continued on next page)

124 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (g) (i) (h) (j) Figure 3.62. (Continued) Assessment of candidate standard live load models for shear: (g) steel plate girder (one-track loaded); (h) steel plate girder (two-track loaded); (i) reinforced concrete girder (one-track loaded); and (j) reinforced concrete girder (two-track loaded).

Research Program 125 75-year 99.9% 90.0% 75-year 99.9% 90.0% 75-year 99.9% 90.0% 75-year 99.9% 90.0% 75-year 99.9% 90.0% Upper 20% moment (a) (b) (c) (d) (e) (f) Figure 3.63. Load inference based on site data: (a) Broadway Bridge; (b) County Line Bridge; (c) Santa Fe Bridge; (d) Indiana Bridge; (e) 6th Avenue Bridge; and (f) upper 20% moment.

126 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) (c) (d) Average site-based to candidate model ratio = 0.75 (99.9%) Average site-based to candidate model ratio = 0.75 (75-year) Average site-based to candidate model ratio = 0.78 (Average) Average site-based to candidate model ratio = 0.74 (Upper 20%) Figure 3.64. Assessment of candidate standard live load models for bending against site-based extreme moments. Figure 3.65. Proposed live load model for light rail transit (LRT-16).

Research Program 127 P1 P2 4PP3 a b c d Train 1 Four-axle trains Six-axle trains Eight-axle trains P 2P1 4P3 P P5 6P P8P7 9P 10P Ten-axle trains Train 2 P P P P1 2 3 4 a b c Train 1 Train 2 3PPP1 2 P4 PP5 6 a b c b a d a b bc a P PPP P P21 3 4 5 6 Train 1 Train 2 P P P P1 2 3 4 65 PP P7P 8 P21 PP P3P 4 65 P 87P P a b c d c b a e a cb d bc a P21 PP P3P 4 65 P 87P P P P9 10 a cb d c e c f a g a b c cd e fc a Train 1 Train 2 Figure 3.66. Dimensional configuration of light rail trains used for load-enveloping assessment. (c) (d) (a) (b) 330 load cases 330 load cases Standard load Standard load Maximum deviation = 6.8% Maximum deviation = 14.6% Figure 3.67. Load enveloping of proposed live load models against 33 light rail trains operated in the United States (29 trains) and Canada (four trains) with AW4 structural load (empty train weight + fully seated passengers + 205 standees): (a) moment; (b) shear; (c) moment ratio normalized by standard load effect; and (d) shear ratio normalized by standard load effect.

128 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (c) (d) (a) (b) 330 load cases 330 load cases Standard load Standard load Maximum deviation = 11.4% Maximum deviation = 18.7% Figure 3.68. Load enveloping of proposed live load models against 33 light rail trains operated in the United States (29 trains) and Canada (four trains) with AW4 structural load (empty train weight + fully seated passengers + 240 standees): (a) moment; (b) shear; (c) moment ratio normalized by standard load effect; and (d) shear ratio normalized by standard load effect.

Research Program 129 (b)(a) (e) (c) (d) 288 load cases AREMA (L/640) AASHTO LRFD (L/800) Light rail agencies (L/1000) AREMA (L/640) AASHTO LRFD (L/800) Light rail agencies (L/1000) 384 load cases 288 load cases AREMA (L/640) AASHTO LRFD (L/800) Light rail agencies (L/1000) AREMA (L/640) AASHTO LRFD (L/800) Light rail agencies (L/1000) 512 load cases AREMA (L/640) AASHTO LRFD (L/800) Light rail agencies (L/1000) 384 load cases Figure 3.69. Assessment of deflection requirements for simply supported bridges subjected to the four train loads: (a) prestressed concrete box; (b) prestressed concrete I; (c) steel box; (d) steel plate; and (e) reinforced concrete.

130 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads 216 load cases AREMA (L/640) AASHTO LRFD (L/800) Light rail agencies (L/1000) AREMA (L/640) AASHTO LRFD (L/800) Light rail Light rail agencies (L/1000) 216 load cases 384 load cases AREMA (L/640) AASHTO LRFD (L/800) agencies (L/1000) AREMA (L/640) AASHTO LRFD (L/800) Light rail agencies (L/1000) 288 load cases (b)(a) (c) (d) Figure 3.70. Assessment of deflection requirements for one- to three-span bridges subjected to the Utah train load: (a) prestressed concrete box; (b) steel box; (c) steel plate; and (d) reinforced concrete.

Research Program 131 (a) (b) (e) Acceptable Unacceptable 288 load cases No pedestrian Frequent pedestrian Occasional pedestrian Acceptable Unacceptable 288 load cases No pedestrian Frequent pedestrian Occasional pedestrian Acceptable Unacceptable 512 load cases No pedestrian Frequent pedestrian Occasional pedestrian Acceptable Unacceptable 384 load cases No pedestrian Frequent pedestrian Occasional pedestrian 384 load cases Acceptable Unacceptable Occasional pedestrian No pedestrian Frequent pedestrian (c) (d) Figure 3.71. Comfort criteria for simply-supported bridges subjected to the four train loads: (a) prestressed concrete box; (b) prestressed concrete I; (c) steel box; (d) steel plate; and (e) reinforced concrete.

132 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) (c) (d) Unacceptable Acceptable 216 load cases No pedestrian Frequent pedestrian Occasional pedestrian 384 load cases Unacceptable Acceptable No pedestrian Frequent pedestrian Occasional pedestrian Unacceptable Acceptable 288 load cases No pedestrian Frequent pedestrian Occasional pedestrian 216 load cases Unacceptable Acceptable No pedestrian Frequent pedestrian Occasional pedestrian Figure 3.72. Comfort criteria for one- to three-span bridges subjected to the Utah train load: (a) prestressed concrete box; (b) steel box; (c) steel plate; and (d) reinforced concrete.

(a) (b) (c) (d) (e) Figure 3.73. Predicted live load distribution of the bridges based on bending moment: (a) prestressed concrete box; (b) prestressed concrete I; (c) steel box; (d) steel plate; and (e) reinforced concrete. (a) (b) (c) (d) Moment Moment Moment Moment Figure 3.74. Assessment of existing methods for bending moment: (a) lever rule for exterior girders; (b) lever rule for interior girders; (c) AASHTO LRFD for exterior girders; and (d) AASHTO LRFD for interior girders.

134 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (c) (b) (d) ShearShear ShearShear Figure 3.75. Assessment of existing methods for shear: (a) lever rule for exterior girders; (b) lever rule for interior girders; (c) AASHTO LRFD for exterior girders; and (d) AASHTO LRFD for interior girders.

Research Program 135 (a) (b) (c) (d) (e) (f) Moment Moment Moment Moment Moment Moment Figure 3.76. Comparison of moment between the finite model prediction and proposed equation: (a) prestressed concrete box (interior); (b) prestressed concrete box (exterior); (c) prestressed concrete I (interior); (d) prestressed concrete I (exterior); (e) steel box (interior); and (f) steel box (exterior). (continued on next page)

136 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (g) (h) (i) (j) Moment Moment Moment Moment Figure 3.76. (Continued) Comparison of moment between the finite model prediction and proposed equation: (g) steel plate (interior); (h) steel plate (exterior); and (i) reinforced concrete (interior); (j) reinforced concrete (exterior).

Research Program 137 (a) (b) (c) (d) (e) (f) Shear Shear Shear Shear Shear Shear Figure 3.77. Comparison of shear between the finite model prediction and proposed equation: (a) prestressed concrete box (interior); (b) prestressed concrete box (exterior); (c) prestressed concrete I (interior); (d) prestressed concrete I (exterior); (e) steel box (interior); and (f) steel box (exterior). (continued on next page)

138 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (g) (h) (i) (j) Shear Shear Shear Shear Figure 3.77. (Continued) Comparison of shear between the finite model prediction and proposed equation: (g) steel plate (interior); (h) steel plate (exterior); (i) reinforced concrete (interior); and (j) reinforced concrete (exterior).

Research Program 139 (a) (c) (b) (d) Figure 3.78. Comprehensive comparison between the proposed and predicted distribution factors: (a) moment for exterior girders; (b) moment for interior girders; (c) shear for exterior girders; and (d) shear for interior girders.

(a) (b) (c) (d) (e) Figure 3.79. Application of the proposed live load distribution equations to the five bridges in Denver: (a) Broadway; (b) Indiana; (c) Santa Fe; (d) County Line; and (e) 6th Avenue.

Research Program 141 (a) (b) LRT-1 LRT-2 Load-1 Load-2 Load-3 Load-4 Load-5 Load-6 Load-7 Load-8 Load-9 Load-10 Load-11 (c) LRT-1 LRT-2 Load-1 Load-2 Load-3 Load-4 Load-5 Load-6 Load-9 Load-10 Load-14Load-13 Load-8Load-7 Load-12Load-11 (d) Figure 3.80. Load scenarios for combined loading: (a) 2+2+2 loading; (b) 3+2+3 loading; (c) load combination for 2+2+2 loading; and (d) load combination for 3+2+3 loading.

142 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Figure 3.81. Bending moment distribution of prestressed concrete I girder bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case).

Research Program 143 Figure 3.82. Shear force distribution of prestressed concrete I girder bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case).

144 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Figure 3.83. Bending moment distribution of prestressed concrete box girder bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case).

Research Program 145 Figure 3.84. Shear force distribution of prestressed concrete box girder bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case).

146 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Girder number: Steel Box (L = 100 ft) Girder number: Steel Box (L = 100 ft) Girder number: Steel Box (L = 100 ft) Girder number: Steel Box (L = 140 ft) Girder number: Steel Box (L = 140 ft) Girder number: Steel Box (L = 140 ft) Figure 3.85. Bending moment distribution of steel box girder bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case).

Research Program 147 Girder number: Steel Box (L = 100 ft) Girder number: Steel Box (L = 100 ft) Girder number: Steel Box (L = 100 ft) Girder number: Steel Box (L = 140 ft)Girder number: Steel Box (L = 140 ft)Girder number: Steel Box (L = 140 ft) Figure 3.86. Shear force distribution of steel box girder bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case).

148 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Figure 3.87. Bending moment distribution of steel plate girder bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case).

Research Program 149 Figure 3.88. Shear force distribution of steel plate girder bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case).

150 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Figure 3.89. Bending moment distribution of reinforced concrete girder bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case).

Research Program 151 Figure 3.90. Shear force distribution of reinforced concrete girder bridges subjected to a combination of light rail train and HL-93 loadings (2+2+2 loading case).

152 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Figure 3.91. Bending moment distribution of prestressed concrete I girder bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case).

Research Program 153 Figure 3.92. Shear force distribution of prestressed concrete I girder bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case).

154 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Figure 3.93. Bending moment distribution of prestressed concrete box girder bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case).

Research Program 155 Figure 3.94. Shear force distribution of prestressed concrete box girder bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case).

156 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Figure 3.95. Bending moment distribution of steel box girder bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case).

Research Program 157 Figure 3.96. Shear force distribution of steel box girder bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case).

158 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Figure 3.97. Bending moment distribution of steel plate girder bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case).

Research Program 159 Figure 3.98. Shear force distribution of steel plate girder bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case).

160 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads Figure 3.99. Bending moment distribution of reinforced concrete girder bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case).

Research Program 161 Figure 3.100. Shear force distribution of reinforced concrete girder bridges subjected to a combination of light rail train and HL-93 loadings (3+2+3 loading case).

162 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (c) (d) (a) (b) (e) (f) Figure 3.101. Increase in load effect due to combined 2+2+2 loading: (a) prestressed concrete box (moment); (b) prestressed concrete box (shear); (c) prestressed concrete I (moment); (d) prestressed concrete I (shear); (e) steel box (moment); and (f) steel box (shear). (continued)

Research Program 163 (g) (i) (j) (h) Figure 3.101. (Continued) Increase in load effect due to combined 3+2+3 loading: (g) steel plate (moment); (h) steel plate (shear); (i) reinforced concrete (moment); and (j) reinforced concrete (shear).

164 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (c) (d) (a) (b) (e) (f) Figure 3.102. Increase in load effect due to combined 3+2+3 loading: (a) prestressed concrete box (moment); (b) prestressed concrete box (shear); (c) prestressed concrete I (moment); (d) prestressed concrete I (shear); (e) steel box (moment); and (f) steel box (shear). (continued)

Research Program 165 (g) (h) (i) (j) Figure 3.102. (Continued) Increase in load effect due to combined 3+2+3 loading: (g) steel plate (moment); (h) steel plate (shear); (i) reinforced concrete (moment); and (j) reinforced concrete (shear).

166 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (c) (d) (a) (b) Figure 3.103. Comprehensive comparison of increase in load effect (moment): (a) 2+2+2 loading with one-track light rail train; (b) 2+2+2 loading with two-track light rail train; (c) 3+2+3 loading with one-track light rail train; and (d) 3+2+3 loading with two-track light rail train.

Research Program 167 (a) (b) (c) (d) Figure 3.104. Comprehensive comparison of increase in load effect (shear): (a) 2+2+2 loading with one-track light rail train; (b) 2+2+2 loading with two-track light rail train; (c) 3+2+3 loading with one-track light rail train; and (d) 3+2+3 loading with two-track light rail train.

168 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) (c) (d) 288 load cases 288 load cases 33% in AASHTO LRFD 33% in AASHTO LRFD 384 load cases 33% 512 load cases 33% in AASHTO LRFD (e) 384 load cases 33% in AASHTO LRFD Figure 3.105. Dynamic load allowance for simply supported bridges subjected to the four train loads: (a) prestressed concrete box; (b) prestressed concrete I; (c) steel box; (d) steel plate; and (e) reinforced concrete.

Research Program 169 (c) (d) (a) (b) 216 load cases 33% in AASHTO LRFD 216 load cases 33% in AASHTO LRFD 384 load cases 33% in AASHTO LRFD 288 load cases 33% in AASHTO LRFD Figure 3.106. Dynamic load allowance for one- to three-span bridges subjected to the Utah train load: (a) prestressed concrete box; (b) steel box; (c) steel plate; and (d) reinforced concrete.

170 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) (c) (d) (e) (f) Figure 3.107. Comparison of DLA between ACI-343 and NCHRP 12-92: (a) prestressed concrete box; (b) prestressed concrete I; (c) steel box; (d) steel plate; (e) reinforced concrete; and (f) comparison among bridges.

Research Program 171 75-year 99.9% 90.0% 288 load cases 75-year 99.9% 90.0% 384 load cases 75-year 99.9% 90.0% 512 load cases (e) (c) (d) (a) (b) 75-year 99.9% 90.0% 75-year 99.9% 90.0% 288 load cases 384 load cases Figure 3.108. Normal distribution of dynamic load allowance for simply-supported bridges subjected to the four train loads: (a) prestressed concrete box; (b) prestressed concrete I; (c) steel box; (d) steel plate; and (e) reinforced concrete.

172 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (c) (d) (a) (b) 75-year 99.9% 75-year 99.9% 75-year 99.9% 90.0% 75-year 99.9% 90.0% 90.0% 90.0% 216 load cases 216 load cases 384 load cases 288 load cases Figure 3.109. Normal distribution of dynamic load allowance for multiple-span bridges subjected to the Utah train load: (a) prestressed concrete box; (b) steel box; (c) steel plate; and (d) reinforced concrete. (a) (b) Figure 3.110. Summary of dynamic load allowance for light rail bridges: (a) simply supported span and (b) one to three span.

Research Program 173 Maximum + ve moment for interior span Six axle articulated train Figure 3.111. Simultaneous loading on a two-track steel plate girder bridge (L = 160 ft) subjected to one articulated Utah train per track. (c) (d) (a) (b) Figure 3.112. Multiple presence factor: (a) prestressed concrete box (one-track-loaded); (b) prestressed concrete box (two-track-loaded); (c) prestressed concrete I (one-track-loaded); and (d) prestressed concrete I (two-track-loaded). (continued on next page)

174 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (e) (f) (g) (h) (i) (j) Figure 3.112. (Continued) Multiple presence factor: (e) steel box (one-track-loaded); (f) steel box (two-track-loaded); (g) steel plate (one-track-loaded); (h) steel plate (two-track-loaded); (i) reinforced concrete (one-track-loaded); and (j) reinforced concrete (two-track-loaded).

Research Program 175 (a) (b) (c) One-track bridge One-track bridge One-track bridge O cc ur re nc e (% ) O cc ur re nc e (% ) O cc ur re nc e (% ) Figure 3.113. Frequency of multiple presence observed on site: (a) counting in 2014; (b) counting in 2015; and (c) average of 2014 and 2015 count data.

176 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads PC Box PC Box PC I PC I (a) (b) (c) (d) Steel Box Steel Box (e) (f) Skew correction factor (AASHTO LRFD) Skew correction factor (AASHTO LRFD) Skew correction factor (AASHTO LRFD) Skew correction factor (AASHTO LRFD) Skew correction factor (AASHTO LRFD) Skew correction factor (AASHTO LRFD) Figure 3.114. Assessment of skew correction factors in AASHTO LRFD for light rail bridges: (a) prestressed concrete box (moment); (b) prestressed concrete box (shear); (c) prestressed concrete I (moment); (d) prestressed concrete I (shear); (e) steel box (moment); and (f) steel box (shear). (continued)

Research Program 177 Reinforced Concrete Reinforced Concrete Steel Plate Steel Plate (g) (h) (i) (j) Skew correction factor (AASHTO LRFD) Skew correction factor (AASHTO LRFD) Skew correction factor (AASHTO LRFD) Skew correction factor (AASHTO LRFD) Figure 3.114. (Continued) Assessment of skew correction factors in AASHTO LRFD for light rail bridges: (g) steel plate (moment); (h) steel plate (shear); (i) reinforced concrete (moment); and (j) reinforced concrete (shear).

178 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) Figure 3.116. Comprehensive comparison of skew correction factors: (a) moment and (b) shear. (a) (b) (c) (d) (e) Figure 3.115. Comparison of skew correction factors between model predictions and proposed equations: (a) prestressed concrete box; (b) prestressed concrete I; (c) steel box; (d) steel plate; and (e) reinforced concrete.

Research Program 179 (a) (c) (e) (b) (d) (f) AASHTO LRFD with MPF AREMA AREMA AASHTO LRFD with MPF AASHTO LRFD with and without MPF AREMAAREMA AASHTO LRFD with MPF AREMA AASHTO LRFD with and without MPF AREMA AASHTO LRFD with and without MPF AASHTO LRFD without MPF AASHTO LRFD without MPF AASHTO LRFD without MPF Figure 3.117. Assessment of exiting centrifugal-force equations with variable superstructural radii based on one axle load: (a) prestressed concrete box (one-track-loaded); (b) prestressed concrete box (two-track-loaded); (c) steel box (one-track-loaded); (d) steel box (two-track- loaded); (e) steel plate (one-track-loaded); and (f) steel plate (two-track-loaded).

180 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (f) (a) (b) (c) (d) (e) Proposed Proposed Proposed Proposed Proposed Proposed Figure 3.118. Proposed expression for centrifugal force: (a) prestressed concrete box (one-track-loaded); (b) steel box (one-track-loaded); (c) steel plate (one-track-loaded); (d) prestressed concrete box (two-track- loaded); (e) steel box (two-track-loaded); and (f) steel plate (two-track-loaded). Figure 3.119. Validation of braking distance (H&D = Handoko and Dhanasekar 2006; Nankyo et al. 2006).

Research Program 181 TCRP 155 range TCRP 155 upper limit TCRP 155 lower limit TCRP 155 average (a) (b) Figure 3.120. Sensitivity analysis of braking distance: (a) variation of deceleration and (b) relation with operating speed. TCRP 155 upper limit TCRP 155 lower limit TCRP 155 average Figure 3.121. Variation of the longitudinal braking multiplier ` based on theory. RC All others (a) (b) Figure 3.122. Braking force predicted by finite element model: (a) variation with girder spacing and (b) theory versus model prediction.

Figure 3.123. Comparison of longitudinal braking force ratios between AASHTO LRFD and the proposed standard live load model. AASHTO LRFD thermal gradient loading Figure 3.124. Comparison of model prediction with theory for thermal gradient loading. (a) (b) (c) (d) (e) Figure 3.125. Thermal response of light rail bridges: (a) prestressed concrete box; (b) prestressed concrete I; (c) steel box; (d) steel plate; and (e) reinforced concrete.

Research Program 183 Temperature variation (steel) Moderate: 0°F to 120°F Cold: -30°F to 120°F Figure 3.126. Predicted maximum gap due to rail break induced by temperature. Rail Pier Girder Rail break Continuous steel plate girder bridge Rail break above Rail break (a) (b) Figure 3.127. Rail break model at piered location: (a) element view and (b) expanded 3-dimensional view.

184 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) (c) (d) D LA w ith ou t r ai l b re ak (% ) D LA w ith ra il br ea k, 2 in (% ) D LA w ith ra il br ea k, 3 in (% ) D LA w ith ra il br ea k, 1 in (% ) Figure 3.128. Effect of rail break at expansion-jointed piers: (a) DLA without rail break; (b) DLA with 1-inch rail break; (c) DLA with 2-inch rail break; and (d) DLA with 3-inch rail break. Figure 3.129. Comparison of average DLA induced by rail break at expansion-jointed piers.

Research Program 185 (a) Case a Train Train Case b Train Case c F E E E E E EF F Train Train Train Case a Case c Case b Case d Train F F FF E E E E E E E E E E E (b) Figure 3.130. Various bearing arrangement: (a) two-span bridge and (b) three-span bridge. Figure 3.131. Comparison between gravity loading of Utah train and horizontal bearing force. F Train Case a E E E Case b F E E Case c E F EEE EEE F F F Train Case c Case a EE E F EE Case d Case b E (a) (b) Figure 3.132. Effect of bearing arrangement on load transfer from super to substructure: (a) two-span bridges and (b) three-span bridges.

186 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) Figure 3.133. Details of wheel-rail system: (a) 115 RE rail and (b) AAR-1B wheel. Suspension-damping with train mass Connecting beam Suspension-damping with train lumped mass Hexahedral solid element Spring element Automatic surface-to-surface contact Tied surface-to-surface contact (a) (b) Figure 3.134. Wheel-rail model in LS-DYNA: (a) 115 RE rail and AAR-1B wheel system and (b) AAR-1B wheel coupled with discrete springs for suspension system.

Research Program 187 0.02 sec 0.04 sec 0.06 sec 0.10 sec0.08 sec Figure 3.135. Vertical stress contour of simulated wheel-rail system moving at 60 mph. At 50 mph and 60 mph Figure 3.136. Validation of the modeling approach. Proposed 75-year 99.9% 90.0% Average AASHTO LRFD BDS Proposed (a) (b) Figure 3.137. Predicted DLA based on wheel-rail interaction: (a) train type and (b) comparison with probability-based DLAs at a bridge level.

(a) (b) Average COV = 0.165 Number of samples (log scale) Figure 3.138. Monte-Carlo simulation of girder response: (a) normality test for girder response measured on site and (b) simulated coefficient of variation (COV). (a) (b) (d) (e) (c) Figure 3.139. Load effect of in situ bridges: (a) Broadway bridge; (b) County Line Bridge; (c) Santa Fe Bridge; (d) Indiana Bridge; and (e) 6th Avenue Bridge. (a) (b) Figure 3.140. Development of load factor for light rail train load (Strength I): (a) convergence and (b) average load factor.

Research Program 189 Figure 3.141. Evaluation of load factors (Strength I). (a) (b) Figure 3.142. Load factor calibration (Fatigue I): (a) individual response of bridges and (b) average. Figure 3.143. Comparison of bridge responses between mean and root mean cube.

190 Proposed AASHTO LRFD Bridge Design Specifications for Light Rail Transit Loads (a) (b) Figure 3.144. Load factor calibration (Fatigue II): (a) response comparison and (b) load factor. Figure 3.145. Comprehensive comparison of proposed load factors with AASHTO LRFD BDS.