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From page 6... ... Most have a limitation on effective width based on span length. Given that a span length parameter is present, the notion of "effective span length" was invented to enable such criteria originally developed for positive moment regions to be co-opted for application in negative moment regions. Read the entire page →
From page 7... ... . As one might expect, there is a tradeoff between simplicity and accuracy -- especially when the full spectrum of possibilities must be accommodated even within the context of line-girder analysis (e.g., interior and exterior girders, positive and negative moment regions, linear and nonlinear realms of behavior, box and I-girders, and absence or presence of axial load, the latter being the case for cable-stayed and tied-arch structures) Read the entire page →
From page 8... ... of the slab such that the conditions of total force and resultant location are similar to those obtained from finite element analysis. Step 5: Computation of "effective slab width" After the value of σmin is obtained from Step 4, calculate the equivalent compressive block (area of the trapezoid) Read the entire page →
From page 9... ... σmax, , ˚ ˚ BeamTheory FEM top BeamTheory M S = Stop, Beam Theory = elastic section modulus for the extreme compression fiber This procedure can require an iterative process, unless the values of the maximum compressive stress at the extreme compression fiber obtained from the simple beam theory (Equation 3) are comparatively close to the extreme fiber stresses resulting from the finite element analysis. Read the entire page →
From page 10... ... The JOINTC elements that represent the stud shear connectors consist of three nonlinear springs in each of the translational coordinate directions. Figure 6 shows the finite element modeling scheme employed. Read the entire page →
From page 11... ... , which proposed a simple mathematical formulation that incorporates the beneficial effects of friction. The shear connection is modeled using two orthogonal spring elements to simulate the shear stiffness of stud shear connectors between the steel-concrete interface and the stiffness normal to the interface. Read the entire page →
From page 12... ... Furthermore, very little presentation of composite behavior is not explicitly intentional (i.e., composite behavior in the negative moment region due to friction and interface bond or due to longitudinal deck rebar anchored at the ends but without shear connectors along the length) Read the entire page →
From page 13... ... 18300mm (720in) Top Flange 24mm (0.9in) Read the entire page →
From page 14... ... The geometric parameters of the composite specimen are shown in Figures 12 and 13. The specimen was designed to enable study of the behavior within the positive and negative moment regions of continuous span bridge girders. Read the entire page →
From page 15... ... Two experimental loading cases were the focus of the results presented herein for the experiments conducted on the four-girder, quarterscale, two-span continuous slab-on-girder bridge specimen: • The "Positive Service Yield Case," loading one span to just reach yield of the bottom flanges in the positive moment region, and • The "Negative Strength Case," loading both spans to maximize negative moment at the support and form a plastic collapse mechanism in the specimen. Positive Service Yield Case Results. Read the entire page →
From page 16... ... The Negative Strength Case showed significant cracking in the negative moment region, as was to be expected with the continuous specimen. Although the results between the FEM and experimental specimen differed slightly, the results were generally consistent and thus verified FEM results for the positive moment region. Read the entire page →
From page 17... ... Many of the gages in the negative moment region on the concrete deck were lost because of severe cracking as shown in Figure 22. 2.3.3.4 Half-Scale Specimens and Instrumentation Two half-scale bridge specimens were produced based on the negative moment region of the prototype bridge described in Section 2.3.3.1. Read the entire page →
From page 18... ... Many states use shear connectors in the negative moment region of composite bridges while for others it is less common. Effective width criteria are based on composite behavior. Read the entire page →
From page 19... ... The ‘noncomposite' specimen, 4GHFNON, has clusters of shear studs in the vicinity of the permanent load inflection point to develop longitudinal rebar as The Code specifies. Instrumentation was placed not only for the reasons listed above but also to generate data that might be useful in comparing the intentionally composite behavior of specimen 4GHFCOM with the behavior of specimen 4GHFCOM, which was noncomposite but had longitudinal rebar anchored at the ends. Read the entire page →
From page 20... ... Strain gages on the girders and on the concrete deck girder line were positioned to give information about the strain profile within a section. These gages corresponded to the rebar gages mentioned earlier for the same purpose. Read the entire page →
From page 21... ... The findings from the negative moment region subassemblage experiments may be summarized as follows: 21 1. There is a good correlation between the FEM and linegirder (LG) Read the entire page →
From page 22... ... But in doing so, it was overlooked that full (not 12t-limited) effective width would raise the neutral axis, thereby rendering the web noncompact. Read the entire page →
From page 23... ... This favorable outcome is believed to be due to the introduction of epoxy as the protective coating. The general unreliability of deck-related strain gages because of deck cracking makes it difficult, if not impossible, to extract effective width values directly from experimental results. Read the entire page →
From page 24... ... 2.4 FEM PARAMETRIC STUDY In the parametric study of the effective slab width project (NCHRP Project 12-58) , design of experiment (DOE) Read the entire page →
From page 25... ... The deck thickness depended on the girder spacing. The following thicknesses were used: Girder Deck Spacing Thickness S/t Design Method 2.4m 175mm 13.7 Empirical Design 3.6m 200mm 18.0 Empirical Design 4.8m 240mm 20.0 Conventional Overhang width was assumed as 0.4S for every bridge design based on an investigation of overhang width on several bridges to produce the same exterior girder as used for the interior girder, with similar structural efficiency, i.e., performance ratio. Read the entire page →
From page 26... ... Prestressed deck should be considered when S/t ≥ 20, which corresponds to the 4.8 m girder spacing. Prestressed deck was not considered as part of the basic parametric study but was considered as one of the special cases. Read the entire page →
From page 27... ... The bottom flange width was changed only in negative moment regions. • For positive moment regions, most of the girder sections were compact. Read the entire page →
From page 28... ... For short-span skewed bridges, the computed effective slab width ratios varied erratically along the span length. The effective slab width ratios at midspan of these short-span skewed bridges, the SS-19 and SS-21 bridges, were 0.90 and 0.93, respectively. Read the entire page →
From page 29... ... HL-93 truck configurations, simple span, interior girder, positive moment. Read the entire page →
From page 30... ... Each bridge analysis consisted of four subcases at the Service II limit state: • Positive Moment, Interior girder; • Positive Moment, Exterior girder; 30 • Negative Moment, Interior girder; and • Negative Moment, Exterior girder. For the positive moment loading, the truck middle axles were placed at 0.4L1 where L1 was the exterior span length, with the rear axle facing the closest abutment (see Figures 38 through 41) Read the entire page →
From page 31... ... For the negative moment loading, two truck middle axles were placed on the exterior span at 0.6L1 and the other two truck middle axles were placed at 1.4L2, where L1 and L2 were the exterior and interior span lengths, respectively. These locations were systematically chosen based on influence line concepts to maximize the negative bending moment at the interior support. Read the entire page →
From page 32... ... Interior Girder Exterior Girder Bridge ID 0.40L 0.45 L 0.50 L 0.55 L 0.60 L 0.40 L 0.45 L 0.50 L 0.55 L 0.60 L SS-01 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 SS-03 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 SS-07 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 SS-09 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 SS-14 1.00 1.00 1.00 1.00 1.00 0.98 0.97 0.95 0.97 0.98 SS-19 1.00 0.80 0.90 0.84 0.88 0.83 0.89 0.88 0.86 0.85 SS-21 0.85 0.80 0.93 0.81 0.81 0.80 0.75 0.80 0.78 0.78 SS-25 1.00 1.00 1.00 1.00 1.00 0.93 0.96 0.96 0.95 0.93 SS-27 0.95 0.92 0.94 0.94 0.94 0.80 0.81 0.92 0.83 0.80 TABLE 6 Effective slab width ratio (beff /b) for simple-span bridges Read the entire page →
From page 33... ... 33 Figure 36. beff /b and bending moment versus x/L, simple span, interior girder, positive moment. Read the entire page →
From page 34... ... Figure 37. beff /b and bending moment versus x/L, simple span, exterior girder, positive moment. Read the entire page →
From page 35... ... In this section, the main focus will be on the positive moment section where the maximum positive bending moments take place. The variations of effective slab width ratio were plotted along the normalized span length between 0L1 and 1.1L2 35 in Figures 46 and 47 for the interior girder of right and skewed bridges, respectively. Read the entire page →
From page 36... ... However, the effective slab width value associated with the maximum positive moment section was relatively close to 1.0. The exterior girders had more or less the same behavior as the interior girders in terms of effective slab width ratio (see Figures 48 and 49) Read the entire page →
From page 37... ... Figures 51 and 52 demonstrate how the effective slab width ratios of the interior girder varied in the region close to the interior pier, 1.0L1. Almost every right bridge experienced full width as 37 the effective slab width. Read the entire page →
From page 38... ... 2.4.4 Summary of FEM Parametric Study FEM results showed the following: Figure 41. HL-93 truck configurations of the multiple-span continuous cases (skewed bridges, exterior girder, positive moment) Read the entire page →
From page 39... ... HL-93 truck configurations of the multiple-span continuous cases (right bridges, interior girder, negative moment) Read the entire page →
From page 40... ... The solution obtained for the global model was used as input to the local model of the structure where a part of the bridge Figure 43. HL-93 truck configurations of the multiple-span continuous cases (skewed bridges, interior girder, negative moment) Read the entire page →
From page 41... ... Figure 44. HL-93 truck configurations of the multiple-span continuous cases (right bridges, exterior girder, negative moment) Read the entire page →
From page 42... ... , Figure 45. HL-93 truck configurations of the multiple-span continuous cases (skewed bridges, exterior girder, negative moment) Read the entire page →
From page 43... ... 43 Figure 46. beff /b and bending moment versus x/L for the multiple-span continuous cases (right bridges, interior girder, positive moment, Service II) Read the entire page →
From page 44... ... 44 Figure 47. beff /b and bending moment versus x/L for the multiple-span continuous cases (skewed bridges, interior girder, positive moment, Service II) Read the entire page →
From page 45... ... 45 Figure 48. beff /b and bending moment versus x/L for the multiple-span continuous cases (right bridges, exterior girder, positive moment, Service II) Read the entire page →
From page 46... ... 46 Figure 49. beff /b and bending moment versus x/L for the multiple-span continuous cases (skewed bridges, exterior girder, positive moment, Service II) Read the entire page →
From page 47... ... Further details on the validation cases appear in Appendix J Interior Girder Exterior Girder Bridge ID 0.3L1 0.35 L1 0.4 L1 0.45 L1 0.5 L1 0.3L1 0.35 L1 0.4 L1 0.45 L1 0.5 L1 CS-01 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 CS-03 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 CS-07 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 CS-09 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 CS-19 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 CS-21 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 CS-25 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 CS-27 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 CS-41 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 CS-55 0.95 0.95 0.96 0.96 0.96 1.00 1.00 1.00 1.00 1.00 CS-57 0.96 0.95 0.94 0.94 0.94 1.00 1.00 1.00 1.00 1.00 CS-61 0.85 0.92 0.98 0.95 0.92 1.00 1.00 1.00 1.00 1.00 CS-63 0.99 0.99 0.99 0.99 1.00 1.00 1.00 1.00 1.00 1.00 CS-73 0.86 0.89 0.92 0.95 0.97 1.00 1.00 1.00 1.00 1.00 CS-75 0.87 0.81 0.74 0.72 0.70 1.00 1.00 1.00 1.00 1.00 CS-79 0.94 0.95 0.96 0.95 0.98 1.00 1.00 1.00 1.00 1.00 CS-81 0.97 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 TABLE 8 Effective slab width ratio (beff /b) Read the entire page →
From page 48... ... 48 Figure 50. beff /b and bending moment versus x/L for the multiple-span continuous cases (Span 2 loading, interior girder, positive moment, Service II) Read the entire page →
From page 49... ... 49 Figure 51. beff /b and bending moment versus x/L for the multiple-span continuous cases (right bridges, interior girder, negative moment, Service II) Read the entire page →
From page 50... ... 50 Figure 52. beff /b and bending moment versus x/L for the multiple-span continuous cases (skewed bridges, interior girder, negative moment, Service II) Read the entire page →
From page 51... ... 51 Figure 53. beff /b and bending moment versus x/L for the multiple-span continuous cases (right bridges, exterior girder, negative moment, Service II) Read the entire page →
From page 52... ... 52 Figure 54. beff /b and bending moment versus x/L for the multiple-span continuous cases (skewed bridges, exterior girder, negative moment, Service II) Read the entire page →
From page 53... ... Deck Slab Thickness (mm) 8_8 495 255 16 250 8_15 735 375 30 250 12_8 495 255 16 250 12_15 735 375 30 250 Cooper River 867 471 38.4 240 TABLE 9 Effective slab width ratio (beff /b) Read the entire page →
From page 54... ... 54 Figure 56. Elements composing the global model; close-up of the area near the cable. Read the entire page →
From page 55... ... Transverse distribution of normal stresses in the negative moment region close to the support of Bridge 12_15 (3-D plot) Read the entire page →
From page 56... ... Transverse distribution of normal stresses in the positive moment region close to the support of the Cooper River Bridge (3-D plot) Read the entire page →
From page 57... ... Longitudinal distribution of the normalized effective width for Bridge 12_8 (Region III) Read the entire page →
From page 58... ... Longitudinal distribution of the normalized effective width for the main span of the Cooper River Bridge. Read the entire page →

From page 6...

... Most have a limitation on effective width based on span length. Given that a span length parameter is present, the notion of "effective span length" was invented to enable such criteria originally developed for positive moment regions to be co-opted for application in negative moment regions.