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From page 145... ... 145 6.1 Foundation Deformations, Service I: Lifetime The geotechnical limit states for serviceability of a bridge structure relate to foundation deformations. Within the context of foundation deformation, the geotechnical limit states can be broadly categorized into vertical and horizontal deformations for any foundation type (e.g., spread footings, driven piles, drilled shafts, micropiles) Read the entire page →
From page 146... ... 146 g = load factor; R = resistance; Rmean = mean resistance; ϕ = resistance factor; Qn = nominal load; lQ = bias factor for load; f = frequency; Rn = nominal resistance; and lR = bias factor for resistance. Details of the AASHTO LRFD framework can be found in Nowak and Collins (2013) Read the entire page →
From page 147... ... 147 dF = deformation at factored load effect [QF = g(Qn) Read the entire page →
From page 148... ... 148 the bias factor for deformations (ld) will vary over the full range of the Q-d curve. Read the entire page →
From page 149... ... 149 be selected on the basis of the acceptable value of the target reliability index (bT) Read the entire page →
From page 150... ... 150 4. Select the design value of probability of exceedance (PeT) Read the entire page →
From page 151... ... 151 bridges were single-span structures. Two two-span and three four-span bridges were also monitored, in addition to a single five-span structure. Read the entire page →
From page 152... ... 152 Figure 6.8. Comparison of measured and calculated (predicted) Read the entire page →
From page 153... ... 153 [or dP/dT] Read the entire page →
From page 159... ... 159 Table 6.7. Statistics of ln(X) Read the entire page →
From page 160... ... 160 respectively) for lognormal distributions are not equal. Read the entire page →
From page 161... ... 161 6.1.3.5 Step 5: Develop Reliability Analysis Procedure The estimation of load factor for settlement (gSE) in terms of probability of exceedance (Pe) Read the entire page →
From page 162... ... 162 Table 6.8. Values of b and Corresponding Pe Based on Normally Distributed Data b Pe (%) Read the entire page →
From page 163... ... 163 values are close to the value of 1.06 in. for a 30.85% probability of exceedance obtained here. Read the entire page →
From page 164... ... 164 Figure 6.21. Evaluation of gSE based on current and target reliability indices. Read the entire page →
From page 165... ... 165 by the analytical method of Schmertmann et al. Read the entire page →
From page 166... ... 166 6.1.5.1 d-0 Concept for Vertical Deformations (Settlements) Because of the inherent variability of geomaterials, the vertical deformations at the support elements of a given bridge (i.e., piers and abutments) Read the entire page →
From page 167... ... 167 • At the same time, the actual settlement of the adjacent support element could be zero instead of the value calculated by using the same given method. The concept outlined above is referred to as the d-0 concept, with a value of d representing full calculated settlement at one support of a span and a value of 0 representing zero settlement at an adjacent support. Read the entire page →
From page 168... ... 168 distortions (hatched-pattern zones) based on the construction point concept. Read the entire page →
From page 169... ... 169 settlements. For example, significant long-term settlements may occur if foundations are founded on saturated clay deposits or if a layer of saturated clay falls within the zone of stress influence below the foundation, even though the foundation itself is founded on competent soil. Read the entire page →
From page 170... ... 170 4. Compare the Adm value with owner-specified angular distortion criteria. Read the entire page →
From page 171... ... 171 6.2 Cracking of reinforced Concrete Components, Service I Limit State: annual probability Traditionally, reinforced concrete components are designed to satisfy the requirements of the strength limit state, after which they are checked for the Service I limit state load combination to ensure that the crack width under service conditions does not exceed a certain value. However, the specifications provisions are written in a form emphasizing reinforcement details (i.e., limiting bar spacing rather than crack width) Read the entire page →
From page 172... ... 172 truck. This practice required developing the statistical parameters of the axle loads of the trucks in the weigh-in-motion (WIM) Read the entire page →
From page 173... ... 173 exposure conditions and a second time assuming Class 2 exposure conditions. Table 6.14 presents the summary information of the 15 designed bridge decks. Read the entire page →
From page 174... ... 174 moment region of decks designed for the current AASHTO LRFD. The selected target reliability indices are 1.6 and 1.0 for Class 1 and Class 2, respectively, based on ADTT = 5,000. Read the entire page →
From page 175... ... 175 6.2.3.8 Step 8: Select Potential Load and Resistance Factors for Service I, Crack Control Through the Distribution of Reinforcement The load factors for dead loads and live loads for the Service I limit state in the AASHTO LRFD (2012) Read the entire page →
From page 176... ... 176 6.2.3.9 Step 9: Calculate Reliability Indices As shown in Figure 6.27 and Figure 6.29, the reliability index associated with cracking at the top of the deck appears to be very uniform across the range of girder spacings considered. It was concluded that there was no need to redesign the decks for different load or resistance factors to improve the uniformity of the results. Read the entire page →
From page 177... ... 177 satisfy" a need for minimum global stiffness, the live load deflection for 41 bridges chosen from the NCHRP Project 12-78 database (Mlynarski et al. Read the entire page →
From page 178... ... 178 calibration using a deterministic value of tolerable deformation, as presented in Section 6.1.2.3 and illustrated in Figure 6.6. 6.3.2 Calibration Results 6.3.2.1 Formulate Limit State Function The live load deflection limit state function is merely the sum of the factored loads and must be less than or equal to the factored resistance, as shown by Equation 6.8: (6.8) Read the entire page →
From page 179... ... 179 Table 5.8. The resistance was taken from the CHBDC curves, which were treated as deterministic (i.e., the bias was assumed to be 1.0, and the CV was assumed to be 0.0) Read the entire page →
From page 180... ... 180 if AASHTO chooses to adopt the more complete approach of combining frequency, displacement, and perception, a possible set of revisions to accomplish that change are proposed in Chapter 7. Other considerations could include basing the determination of deflection on the fatigue truck of Article 3.6.1.4.1, as its longer wheel base is more representative of actual traffic. Read the entire page →
From page 181... ... 181 Table 6.17. Bending Moment Exceedances per Year Site Ratio Truck/HL-93 ≥1.0 Ratio Truck/HL-93 ≥1.1 Ratio Truck/HL-93 ≥1.2 Ratio Truck/HL-93 ≥1.3 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft Arizona (SPS-1) Read the entire page →
From page 182... ... 182 Table 6.17. Bending Moment Exceedances per Year (continued) Read the entire page →
From page 183... ... 183 Figure 6.33. Annual average exceedances versus span. Read the entire page →
From page 184... ... 184 Table 6.18. Events per Year Scaled to ADTT  2,500 Site Ratio Truck/HL-93 ≥1.0 Ratio Truck/HL-93 ≥1.1 Ratio Truck/HL-93 ≥1.2 Ratio Truck/HL-93 ≥1.3 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft Arizona (SPS-1) Read the entire page →
From page 185... ... 185 Wisconsin (SPS-1) 24 12 20 16 8 4 0 12 12 4 0 0 4 4 0 0 0 0 0 0 California Antelope EB 0 10 20 24 20 0 1 0 0 5 0 0 0 0 0 0 0 0 0 0 California Antelope WB 0 20 48 68 57 0 5 4 13 27 0 0 0 1 9 0 0 0 0 1 California Bowman 0 1 1 4 8 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 California LA-710 NB 2 20 31 31 17 0 7 11 11 3 0 1 5 4 0 0 0 1 0 0 California LA-710 SB 1 12 21 22 11 0 3 9 9 3 0 1 4 4 0 0 0 0 0 0 California Lodi 0 25 32 65 96 0 1 4 13 39 0 0 0 1 9 0 0 0 0 1 Florida I-10 151 76 86 142 82 44 22 26 42 21 12 9 8 9 3 6 3 2 3 1 Florida I-95 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Mississippi I-10 0 2 3 6 4 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 Mississippi I-55UI 0 2 3 6 4 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 Mississippi I-55R 93 66 167 229 58 13 21 33 40 22 5 5 11 14 13 1 2 3 5 6 Mississippi US-49 0 2 8 10 5 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 Mississippi US-61 0 6 23 40 29 0 0 6 11 6 0 0 6 6 0 0 0 0 0 0 Florida US-29 2,922 2,252 1,473 1,122 462 1,524 1,155 751 572 247 840 621 406 278 119 413 373 191 138 49 Annual Average 117.0 37.8 50.6 58.7 21.7 32.0 18.4 20.8 19.8 7.5 14.3 9.7 9.1 5.8 1.2 4.0 5.6 3.2 1.7 0.3 Table 6.18. Read the entire page →
From page 186... ... 186 0 20 40 60 80 100 120 30 ft 60 ft 90 ft 120 ft 200 ft An nu al A ve ra ge Span (ft.) >= 1.0HL93 >= 1.1HL93 >= 1.2HL93 >= 1.3HL93 Figure 6.35. Read the entire page →
From page 187... ... 187 Judgment and experience are still necessary. This issue is also clouded by the issues in Questions 6 and 7, "Should this requirement be applied to multilane loading? Read the entire page →
From page 188... ... 188 limit states. Use of the Monte Carlo analysis is presented in Section 3.2.3. Read the entire page →
From page 189... ... 189 deflection control in buried metal structures, tunnel liner plate, and thermoplastic pipe; to control crack width in reinforced concrete structures; and for transverse analysis relating to tension in concrete segmental girders. This load combination should also be used for the investigation of slope stability. Read the entire page →
From page 190... ... 190 the time-dependent losses. Before 2005, the specifications included a simpler approximate method termed approximate lump-sum estimate of time-dependent losses. Read the entire page →
From page 191... ... 191 index calculations were determined by analyzing the girder using the above assumptions. For bridges designed using the pre-2005 prestressing loss method, • The time-dependent prestressing loss method used is the method designated in the pre-2005 AASHTO LRFD editions as the Refined Estimates of Time-Dependent Losses. Read the entire page →
From page 192... ... 192 Table 6.21. Random Variables and the Value of Their Statistical Parameters Variable Distribution Mean () Read the entire page →
From page 193... ... 193 random during the performance of the reliability analyses. These variables represent a summary of the information from research studies by Siriaksorn and Naaman (1980) Read the entire page →
From page 194... ... 194 Table 6.23. Summary of Reliability Indices of Simulated Bridges Designed Using AASHTO Girders with ADTT  5,000 and ft  0.0948 fc′ Case Section Type Span Length (ft) Read the entire page →
From page 195... ... 195 Table 6.24. Summary of Reliability Indices of Simulated Bridges Designed Using AASHTO Girders with ADTT  5,000 and ft  0.19 fc′ Case Section Type Span Length (ft) Read the entire page →
From page 196... ... 196 Bridges designed for Case 1 and Case 3 are also thought to be similar to those designed using AASHTO Standard Specifications for the two environmental conditions. The reliability indices calculated for Case 1 and Case 3 represent the inherent reliability of bridges currently on the system, as most of them were designed before 2005. Read the entire page →
From page 197... ... 197 derived by setting the crack width to zero in the general equation for crack width. The majority of the equations for the prediction of the maximum crack width are given in terms of the stress in the steel. Read the entire page →
From page 198... ... 198 step 8a: seLect potentiaL Load and resistance factors for service iii: Bridges designed for MaxiMUM concrete tensiLe stress of ft = 0.0948 ′fc The calibration for a selected bridge database (shown in Table 6.26) was performed assuming an ADTT of 5,000 and a maximum concrete design tensile stress of ft = 0.0948 fc′. Read the entire page →
From page 199... ... 199 26 FIB-96 160 8 6.426 42 27 FIB-96 160 10 7.344 48 28 FIB-96 160 12 -- -- 29 FIB-96 180 6 7.344 48 30 Mod. Read the entire page →
From page 200... ... 200 Table 6.27. Summary Information of Bridges Designed with gLL  1.0 and ft  0.0948 fc′ Case Section Type Span Length (ft) Read the entire page →
From page 201... ... 201 R el ia bi lit y In de x Span Length (ft.) Figure 6.40. Read the entire page →
From page 202... ... 202 fc′. Similar to the case of bridges designed for a maximum concrete tensile stress of ft = 0.0948 fc′, the reliability level of bridges became more uniform than the case of using a live load factor of 0.8, particularly for the decompression and maximum tensile stress limit states. Read the entire page →
From page 203... ... 203 index and whether they were uniform across the range of spans considered. If they were not, the load factors, resistance factors, and/or the concrete tensile stress limit used for design were changed, and Step 8 was repeated. Read the entire page →
From page 204... ... 204 was compared (see Table 6.31) Read the entire page →
From page 205... ... 205 Table 6.31. Comparison of Number of Strands Required for Different Design Assumptions Case Section Type Span Length (ft) Read the entire page →
From page 206... ... 206 reliability approximately equal to the target reliability index provided that the load factor is based on a reliability index calculated using the decompression criteria and assuming one lane of traffic. 6.5.6 Results for Adjacent Box Beams, Spread Box Beams, and American Segmental Box Institute Box Beams Work similar to that described above for I-beams was performed for adjacent box beams, spread box beams, and American Segmental Box Institute (ASBI) Read the entire page →
From page 207... ... 207 The results shown in Figure 6.55 to Figure 6.60 indicate that the reliability indices for each type of girder are reasonably uniform across the range of spans considered. With the exception of the adjacent box beams, the average reliability indices for other section types were very close to each other and to the target reliability index. Read the entire page →
From page 208... ... 208 6.6 Fatigue Limit States: Lifetime 6.6.1 Steel Members 6.6.1.1 Formulate Limit State Function Two limit states for load-induced fatigue of steel details are defined in AASHTO LRFD Article 3.4.1: Fatigue I, related to infinite load-induced fatigue life; and Fatigue II, related to finite load-induced fatigue life. For load-induced fatigue considerations, according to AASHTO LRFD Article 6.6.1.2.2, each steel detail should satisfy Equation 6.14: (6.14) Read the entire page →
From page 209... ... 209 6.6.1.3 Determine Load and Resistance Parameters for Selected Design Cases A comprehensive database containing constant and variable amplitude fatigue test results for various welded steel bridge detail types was developed by Keating and Fisher (1986) Read the entire page →
From page 210... ... 210 where (Sr) eff = effective constant amplitude stress range; gi = percentage of cycles at a particular stress range; and Sri = constant amplitude stress range for a group of cycles (ksi) Read the entire page →
From page 211... ... 211 Determination of Nominal Fatigue Parameter and Bias Values CV and the mean of the fatigue resistance data were determined as described in the previous subsection. These values, along with the nominal fatigue resistance, were needed to determine the bias of the data. Read the entire page →
From page 212... ... 212 resistance factors that would achieve reliability close to the target reliability index. The Monte Carlo technique samples load and resistance parameters from selected statistical distributions, such as a normal distribution. Read the entire page →
From page 213... ... 213 at b = 1.7. Similarly, two Fatigue II limit state reliability indices appear to be too large (detail Category D at b = 1.3 and detail Category E′ at b = 1.4) Read the entire page →
From page 214... ... 214 Equation 6.23, which is seen as a variation of Equation 6.14 applicable only to infinite life: f F (6.23) Read the entire page →
From page 215... ... 215 Figure 6.65. Normal probability plot of truncated fatigue resistance data with best-fit line for steel reinforcement in tension. Read the entire page →
From page 216... ... 216 of the current Fatigue I limit state for concrete in compression and the Fatigue I and II limit states for structural steel members. This proposed target reduces the reliability of steel reinforcement in tension to levels consistent with the three other calibrated fatigue limit states. Read the entire page →

From page 145...

... 145 6.1 Foundation Deformations, Service I: Lifetime The geotechnical limit states for serviceability of a bridge structure relate to foundation deformations. Within the context of foundation deformation, the geotechnical limit states can be broadly categorized into vertical and horizontal deformations for any foundation type (e.g., spread footings, driven piles, drilled shafts, micropiles)