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From page 43...
... NCHRP Project 12-103 43 Figure 4-6 - Example ECDF plot used to assess convergence. 5 Steel Multi-Girder Bridges This section presents the tolerable support movement results obtained from the analysis of steel bridges.
From page 44...
... NCHRP Project 12-103 44 section. In most (but not all)
From page 45...
... NCHRP Project 12-103 45 5.1.2 Load Distribution in Highly Skewed Bridges Skew can have a significant influence over the distribution of dead load and live load force effects, and these force effects are not always accurately captured by the SLG model. Of particular interest is the tendency for loads to be distributed from interior girders to the exterior girder adjacent to an obtuse corner (see Figure 5-2)
From page 46...
... NCHRP Project 12-103 46 factors, which has a skew correction factor, but it does not address this increase in force effects near obtuse corners. As a result of these, it is possible for certain bridge configurations (especially for skew angles greater than 20o)
From page 47...
... NCHRP Project 12-103 47 5.2 Methods for Identifying Tolerable Support Movement Influences The mechanisms discussed in Section 5.1 were identified though an exploratory examination of individual samples. This examination was driven by the parameters that were found to influence superstructure tolerance to LD and TD movements.
From page 48...
... NCHRP Project 12-103 48 5.3 Simple Span Steel Bridges For simple span steel bridges, Strength I Flexure and Service II tolerances to LD and TD support movements were found to be orders of magnitude greater than what would constitute an acceptable level of movement. Support movements of this magnitude would exceed other limits (e.g.
From page 49...
... NCHRP Project 12-103 49 spacing. The plot of skew and tolerable support movement (Figure 5-5)
From page 50...
... NCHRP Project 12-103 50 5.4 Two-Span Continuous Steel Bridges The following sections discuss the response of two-span continuous bridges to support movements as well as the influential parameters and their interactions that affect tolerance to LD and TD support movements. Due to the complexity of the results for continuous steel bridges, linear regression was employed in addition to exploratory analysis to determine the predictor variables (influential parameters)
From page 51...
... NCHRP Project 12-103 51 Figure 5-7 - Controlling limit state for a TD support movement occurring at the abutment of a two-span continuous steel multi-girder bridge. Figure 5-8 - Controlling limit state for a LD support movement occurring at the pier of a two-span continuous steel multigirder bridge.
From page 52...
... NCHRP Project 12-103 52 Figure 5-9 - Controlling limit state for a TD support movement occurring at the pier of a two-span continuous steel multigirder bridge. 5.4.2 Strength I Flexure Tolerance to LD Movements Occurring at the Abutment The Strength I Flexure limit controlled tolerance to LD movements occurring at the abutment for 95% of the population (See Figure 5-6)
From page 53...
... NCHRP Project 12-103 53 Figure 5-10 – Controlling location of Strength I Flexure tolerance to a LD support movement occurring at the abutment of a two-span continuous steel multi-girder bridge. Span length (L)
From page 54...
... NCHRP Project 12-103 54 Figure 5-11 – Effects plot for tolerance to LD movements occurring at the abutment of a two-span continuous steel multigirder bridge. The influence of span length on tolerable support movement is apparent in the plot of tolerance and span length (Figure 5-12)
From page 55...
... NCHRP Project 12-103 55 Figure 5-12 - Strength I Flexure tolerance to a LD support movement occurring at the abutment of a two-span continuous steel multi-girder bridge. The interaction plot (Figure 5-13)
From page 56...
... NCHRP Project 12-103 56 Figure 5-13 - Interaction plot of spacing and span length. The influence of girder spacing is likely because the distribution factors become less conservative (more accurate)
From page 57...
... NCHRP Project 12-103 57 5.4.3 Strength I Shear Tolerance to LD Movements Occurring at the Abutment Strength I Shear tolerance controlled for only 1% of all samples (see Figure 5-6)
From page 58...
... NCHRP Project 12-103 58 Figure 5-16 – Effects plot for tolerance to LD movements occurring at the abutment of a two-span continuous steel multigirder bridge. 5.4.4 Service II Tolerance to LD Movements Occurring at the Abutment Service II tolerance controlled for approximately 3% of the population (see Figure 5-6)
From page 59...
... NCHRP Project 12-103 59 Figure 5-17 – Service II tolerance to a LD support movement occurring at the abutment of a two-span continuous steel multigirder bridge. Figure 5-18 - Effects plot for tolerance to LD movements occurring at the abutment of a two-span continuous steel multigirder bridge.
From page 60...
... NCHRP Project 12-103 60 5-19)
From page 61...
... NCHRP Project 12-103 61 Figure 5-20 - Effects plot for tolerance to LD movements occurring at the abutment of a two-span continuous steel multigirder bridge. As was seen with LD movement, increasing span length leads to higher tolerance while increasing girder spacing and skew leads to lower tolerance.
From page 62...
... NCHRP Project 12-103 62 Figure 5-21 - Strength I Flexure tolerance to a TD support movement occurring at the abutment of a two-span continuous steel multi-girder bridge. The same interaction between spacing and span length that was found with LD movements also exists with TD movements.
From page 63...
... NCHRP Project 12-103 63 Figure 5-22 - Interaction plot of skew and span length. Figure 5-23 - Interaction plot of skew and spacing.
From page 64...
... NCHRP Project 12-103 64 exterior girder is exposed to the maximum TD movement. For the few cases were tolerance controlled at an interior girder, further investigation found these cases to be associated with the obtuse-side exterior girder being exposed to the maximum TD movement.
From page 65...
... NCHRP Project 12-103 65 Figure 5-25 - Effects plot for tolerance to TD movements occurring at the abutment of a two-span continuous steel multigirder bridge. The effect of skew is also evident in the plots of tolerance given by Figure 5-26 and Figure 5-27.
From page 66...
... NCHRP Project 12-103 66 Figure 5-26 - Strength I Shear tolerance to a TD support movement occurring at the abutment of a two-span continuous steel multi-girder bridge. Figure 5-27 - Strength I Shear tolerance to a TD support movement occurring at the abutment of a two-span continuous steel multi-girder bridge.
From page 67...
... NCHRP Project 12-103 67 effects plot below shows the effect of each of the remaining parameters for bridges with skew angles greater than 20⁰. Higher tolerance is associated with increased spacing and SD ratio, while lower tolerance is associated with increased skew, and to a lesser extent, span length.
From page 68...
... NCHRP Project 12-103 68 Figure 5-29 - Interaction plot of skew and span length. 5.4.7 Service II Tolerance to TD Movements Occurring at the Abutment Service II tolerance controlled for approximately 3% of the population (see Figure 5-7)
From page 69...
... NCHRP Project 12-103 69 Figure 5-30 – Service II tolerance to a TD support movement occurring at the abutment of a two-span continuous steel multigirder bridge. Figure 5-31 – Effects plot for tolerance to TD movements occurring at the abutment of a two-span continuous steel multigirder bridge.
From page 70...
... NCHRP Project 12-103 70 Figure 5-32 - Controlling location for LD support movement at the pier of a two-span continuous bridge for the Strength I flexural limit state. The tolerable levels of LD support movement at the pier for the Strength I Flexure limit state were found to be much larger than those for LD movements occurring at the abutment.
From page 71...
... NCHRP Project 12-103 71 Figure 5-33 - Strength I Flexure tolerance to a LD support movement occurring at the pier of a two-span continuous steel multi-girder bridge. Span length (L)
From page 72...
... NCHRP Project 12-103 72 5.4.9 Strength I Shear Tolerance to LD Movements Occurring at the Pier Strength I Shear tolerance to LD movements occurring at the abutment controlled for approximately 57% of the population (see Figure 5-8)
From page 73...
... NCHRP Project 12-103 73 Figure 5-36 - Effects plot for tolerance to LD movements occurring at the pier of a two-span continuous steel multi-girder bridge. Figure 5-37 - Strength I Shear tolerance to a LD support movement occurring at the pier of a two-span continuous steel multigirder bridge.
From page 74...
... NCHRP Project 12-103 74 influential parameters. Higher tolerance is associated with increased span length, girder spacing, and SD ratio.
From page 75...
... NCHRP Project 12-103 75 Figure 5-39 - Interaction plot of spacing and span length. Figure 5-40 - Interaction plot of skew and span length.
From page 76...
... NCHRP Project 12-103 76 Figure 5-41 - Interaction plot of SD and span length. 5.4.10 Service II Tolerance to LD Movements Occurring at the Pier Service II tolerance controlled for approximately 5% of the population (see Figure 5-8)
From page 77...
... NCHRP Project 12-103 77 Figure 5-42 – Service II tolerance to a LD support movement occurring at the pier of a two-span continuous steel multi-girder bridge. Figure 5-43 - Effects plot for tolerance to LD movements occurring at the pier of a two-span continuous steel multi-girder bridge.
From page 78...
... NCHRP Project 12-103 78 is dependent on the orientation of the TD movement as well as the geometric configuration of the bridge. Figure 5-44 - Controlling location of Strength I Flexure tolerance to a TD support movement occurring at the pier of a twospan continuous steel multi-girder bridge.
From page 79...
... NCHRP Project 12-103 79 Figure 5-45 - TD movement moment diagram for a highly-skewed bridge. Figure 5-46 gives the plot of span length versus Strength I Flexure tolerance.
From page 80...
... NCHRP Project 12-103 80 Figure 5-47 - Strength I Flexure tolerance to a TD support movement occurring at the pier of a two-span continuous steel multi-girder bridge. Span length (L)
From page 81...
... NCHRP Project 12-103 81 Several parameter interactions were found to affect tolerance to TD movements occurring at the pier. These interactions include: (1)
From page 82...
... NCHRP Project 12-103 82 Figure 5-50 - Interaction plot of skew and span length. Figure 5-51 - Interaction plot of skew and girder spacing.
From page 83...
... NCHRP Project 12-103 83 Figure 5-52 - Interaction plot of spacing and SD ratio. 5.4.12 Strength I Shear Tolerance to TD Movements Occurring at the Pier The Strength I limit state for shear controlled the tolerable TD support movement at the pier for 78% of the population (see Figure 5-9)
From page 84...
... NCHRP Project 12-103 84 Figure 5-53 - Controlling location of Strength I Shear tolerance to a TD support movement occurring at the pier of a two-span continuous steel multi-girder bridge. Figure 5-54 gives the plot of span length and tolerance.
From page 85...
... NCHRP Project 12-103 85 5-55. Higher tolerance is associated with increased span length, girder spacing, and SD ratio while lower tolerance is associated with increased skew.
From page 86...
... NCHRP Project 12-103 86 Figure 5-56 - Interaction plot for span length and girder spacing. Figure 5-57 - Interaction plot of skew and span length.
From page 87...
... NCHRP Project 12-103 87 Figure 5-58 - Interaction of span length and SD ratio. The interaction of skew and girder spacing is given by Figure 5-59.
From page 88...
... NCHRP Project 12-103 88 5.4.13 Service II Tolerance to TD Movements Occurring at the Pier Service II tolerance controlled for less than 1% of the population (see Figure 5-9)
From page 89...
... NCHRP Project 12-103 89 Figure 5-61 - Effect of increasing each parameter on tolerance to TD movements occurring at the pier of a two-span continuous steel multi-girder bridge. 5.5 Three-Span Continuous Steel Bridges The following sections discuss the response of three-span continuous bridges to support movements as well as the influential parameters and their interactions that affect tolerance to LD and TD support movements.
From page 90...
... NCHRP Project 12-103 90 Figure 5-62 - Controlling limit state for a LD support movement occurring at the abutment of a three-span continuous steel multi-girder bridge. Figure 5-63 - Controlling limit state for a TD support movement occurring at the abutment of a three-span continuous steel multi-girder bridge.
From page 91...
... NCHRP Project 12-103 91 Figure 5-64 - Controlling limit state for a LD support movement occurring at the pier of a three-span continuous steel multigirder bridge. Figure 5-65 - Controlling limit state for a TD support movement occurring at the pier of a three-span continuous steel multigirder bridge.
From page 92...
... NCHRP Project 12-103 92 5.5.2 Strength I Flexure Tolerance to LD Movements Occurring at the Abutment Strength I Flexure tolerance controlled LD movements occurring at the abutment for approximately 81% of the population (see Figure 5-62)
From page 93...
... NCHRP Project 12-103 93 Figure 5-67 – Strength I Flexure tolerance to a LD support movement occurring at the abutment of a three-span continuous steel multi-girder bridge. Span length (L)
From page 94...
... NCHRP Project 12-103 94 Figure 5-68 - Effect of increasing each parameter on tolerance to LD movements occurring at the abutment of a three-span continuous steel multi-girder bridge. Several parameter interactions were found to affect tolerance to LD movements occurring at the abutment.
From page 95...
... NCHRP Project 12-103 95 Figure 5-69 - Interaction plot for span length and girder spacing. Figure 5-70 shows the interaction of girder spacing and skew.
From page 96...
... NCHRP Project 12-103 96 Figure 5-71 shows the interaction of girder spacing and width. The accompanying scatter plot is provided in Appendix C
From page 97...
... NCHRP Project 12-103 97 Similar behavior was observed for the interaction of girder spacing with SD ratio, as seen in the interaction plot (Figure 5-72)
From page 98...
... NCHRP Project 12-103 98 Figure 5-74- Controlling location of Strength I Shear tolerance to a LD support movement occurring at the abutment of a three-span continuous steel multi-girder bridge. Figure 5-75 gives the plot of span length versus LD tolerable support movement, and indicates that many bridges within the population can undergo relatively larger support movements before violating the Strength I Shear limit state.
From page 99...
... NCHRP Project 12-103 99 Figure 5-75 – Strength I Shear tolerance to a LD support movement occurring at the abutment of a three-span continuous steel multi-girder bridge. Span length (L)
From page 100...
... NCHRP Project 12-103 100 Figure 5-76 - Effect of increasing each parameter on tolerance to LD movements occurring at the abutment of a three-span continuous steel multi-girder bridge. 5.5.4 Service II Tolerance to LD Movements Occurring at the Abutment The Service II limit state controlled the level of LD tolerable support movement for 13% of the population (see Figure 5-62)
From page 101...
... NCHRP Project 12-103 101 Figure 5-77 – Service II tolerance to a LD support movement occurring at the abutment of a three-span continuous steel multi-girder bridge. Figure 5-78 - Effects plot for tolerance to LD movements occurring at the abutment of a three-span continuous steel multigirder bridge.
From page 102...
... NCHRP Project 12-103 102 underwent the largest support movement governed (Figure 5-79)
From page 103...
... NCHRP Project 12-103 103 Figure 5-80 - Effect of increasing each parameter on tolerance to TD movements occurring at the abutment of a three-span continuous steel multi-girder bridge. Figure 5-81 gives a plot of span length versus tolerable TD support movement (at an abutment)
From page 104...
... NCHRP Project 12-103 104 Figure 5-81 – Strength I Flexure tolerance to a TD support movement occurring at the abutment of a three-span continuous steel multi-girder bridge. Several parameter interactions were found to affect tolerance to TD movements occurring at the abutment.
From page 105...
... NCHRP Project 12-103 105 Figure 5-82 - Interaction plot for skew and span length. The effect of skew on tolerance appears to be less significant for bridges with shorter span length.
From page 106...
... NCHRP Project 12-103 106 Figure 5-83 - Interaction plot for girder spacing and skew. The interaction of skew and SD ratio can be seen in the plot below.
From page 107...
... NCHRP Project 12-103 107 5.5.6 Strength I Shear Tolerance to TD Movements Occurring at the Abutment The Strength I Shear limit state controlled the tolerable TD support movement for 20% of the population (see Figure 5-63)
From page 108...
... NCHRP Project 12-103 108 Figure 5-86 - Strength I Shear tolerance to a TD support movement occurring at the abutment of a three-span continuous steel multi-girder bridge. Figure 5-87 - Strength I Shear tolerance to a TD support movement occurring at the abutment of a three-span continuous steel multi-girder bridge.
From page 109...
... NCHRP Project 12-103 109 below shows the effect of each of the influential parameters. Higher tolerance is associated with increasing girder spacing, width, and SD ratio.
From page 110...
... NCHRP Project 12-103 110 Figure 5-89 - Interaction plot of skew and span length. The interaction plot for width and girder spacing is in Figure 5-90.
From page 111...
... NCHRP Project 12-103 111 5.5.7 Service II Tolerance to TD Movements Occurring at the Abutment The Service II limit state controlled the tolerable TD support movement at an abutment for approximately 13% of the population (see Figure 5-63)
From page 112...
... NCHRP Project 12-103 112 Figure 5-92 - Effects plot for tolerance to TD movements occurring at the abutment of a three-span continuous steel multigirder bridge. 5.5.8 Strength I Flexure Tolerance to LD Movements Occurring at the Pier The Strength I Flexure limit state controlled the tolerable LD support movement occurring at a pier for over 75% of the population (see Figure 5-64)
From page 113...
... NCHRP Project 12-103 113 Figure 5-93 - Controlling location of Strength I Flexure tolerance to a LD support movement occurring at the pier of a threespan continuous steel multi-girder bridge. Figure 5-94 gives the plot of span length versus tolerable LD support movement at the pier.
From page 114...
... NCHRP Project 12-103 114 Figure 5-94 – Strength I Flexure tolerance to a LD support movement occurring at the pier of a three-span continuous steel multi-girder bridge. All five parameters were determined to affect tolerance, however, span length (L)
From page 115...
... NCHRP Project 12-103 115 Several parameter interactions were found to affect tolerance to LD movements occurring at the pier. These interactions include: (1)
From page 116...
... NCHRP Project 12-103 116 support movements was actually the dead load distribution mechanism discussed in Section 5.1.2. For these bridges, the dead load shear demands of the FE model were 20-50% higher than the SLG demands.
From page 117...
... NCHRP Project 12-103 117 Figure 5-98 - Effects plot for tolerance to LD movements occurring at the pier of a three-span continuous steel multi-girder bridge. Several parameter interactions were identified to influence the Strength I Shear tolerance to LD movements occurring at the pier.
From page 118...
... NCHRP Project 12-103 118 Figure 5-99 - Interaction plot of span length and girder spacing. The interaction of skew and span length is shown in Figure 5-100.
From page 119...
... NCHRP Project 12-103 119 Similar interaction behavior exists between span-depth and span length (Figure 5-101)
From page 120...
... NCHRP Project 12-103 120 The interaction of width and girder spacing is shown in Figure 5-103. The accompanying scatter plot is provided in Appendix C
From page 121...
... NCHRP Project 12-103 121 Figure 5-104 – Service II tolerance to a LD support movement occurring at the pier of a three-span continuous steel multigirder bridge. Figure 5-105 - Effect of increasing each parameter on tolerance to LD movements occurring at the pier of a three-span continuous steel multi-girder bridge.
From page 122...
... NCHRP Project 12-103 122 Figure 5-106 - Controlling location of Strength I Flexure tolerance to a TD support movement occurring at the pier of a threespan continuous steel multi-girder bridge. For flexure, the location of the controlling member was primarily over the pier that underwent the TD settlement, at the exterior girder opposite of where the TD movement occurred (the exterior girder that remains stationary)
From page 123...
... NCHRP Project 12-103 123 less than 20⁰ generally have more tolerance to TD support movement than for samples with skew greater than 20⁰. The current AASHTO LRFD expression is clearly unconservative for approximately 35% of the population studied.
From page 124...
... NCHRP Project 12-103 124 Figure 5-109 - Effects plot for tolerance to TD movements occurring at the pier of a three-span continuous steel multi-girder bridge. The following parameter interactions were identified to influence tolerance to TD movement occurring at the pier: (1)
From page 125...
... NCHRP Project 12-103 125 Figure 5-110 - Interaction of span length and skew. The interaction plot given by Figure 5-111 shows the interaction between skew and girder spacing.
From page 126...
... NCHRP Project 12-103 126 Figure 5-112 shows the interaction plot for width and girder spacing. The accompanying scatter plot is given in Appendix C
From page 127...
... NCHRP Project 12-103 127 Figure 5-113- Controlling location of Strength I Shear tolerance to a TD support movement occurring at the pier of a threespan continuous steel multi-girder bridge. Figure 5-114 shows the plot of span length and Strength I Shear tolerance to TD movements occurring at the pier.
From page 128...
... NCHRP Project 12-103 128 Figure 5-114 – Strength I Shear tolerance to a TD support movement occurring at the pier of a three-span continuous steel multi-girder bridge. All five parameters were all identified as influential parameters affecting Strength I Shear tolerance to TD movements occurring at the pier.
From page 129...
... NCHRP Project 12-103 129 Figure 5-115 - Effects plot for tolerance to TD movements occurring at the pier of a three-span continuous steel multi-girder bridge. Several parameter interactions were identified to influence the Strength I Shear tolerance to TD movements occurring at the pier.
From page 130...
... NCHRP Project 12-103 130 Figure 5-116 - Interaction plot of span length and girder spacing. The interaction of skew and span length is shown by Figure 5-117.
From page 131...
... NCHRP Project 12-103 131 smaller SD ratio. In fact, as span length increases, the effect of SD ratio becomes more significant, and tolerance decreases for bridges with lower SD ratio.
From page 132...
... NCHRP Project 12-103 132 5.5.13 Service II Tolerance to TD Movements Occurring at the Pier The Service II limit state controlled the tolerable TD movement at a pier in less than 10% of the population studied (see Figure 5-65)
From page 133...
... NCHRP Project 12-103 133 Figure 5-121 - Effects plot for tolerance to TD movements occurring at the pier of a three-span continuous steel multi-girder bridge. 5.6 Summary of Results Superstructure tolerance to LD and TD support movements is a complex problem that depends not only on bridge configuration but on the level of conservativism inherent in a specific bridge design, the type and location of support movement, and the limit state being evaluated.
From page 134...
... NCHRP Project 12-103 134 found to be associated with bridges that have larger girder spacing. In contrast, for the Strength I Flexure limit, higher tolerance was found to be associated with smaller girder spacing.
From page 135...
... NCHRP Project 12-103 135 Table 5-3 compares the results of this study to the current AASHTO LRFD guidance for all bridges, and for bridges with skew less than 20⁰. The percentage of the sample population of bridges that exhibited tolerance less than what is suggested by AASHTO LRFD is given.
From page 136...
... NCHRP Project 12-103 136 Strength I Shear 1% 0% - Service II 1% 0% - TD Support Movement at Abutment*
From page 137...
... NCHRP Project 12-103 137 Three-Span Continuous LD Support Movement at Abutment Strength I Flexure 19% 20% 0.003L for bridges with less than 20o skew and spans longer than 100 ft Strength I Shear 3% 0% - Service II 0% 0% - TD Support Movement at Abutment*
From page 138...
... NCHRP Project 12-103 138 account for dead load distribution of highlyskewed bridges Strength I Shear 17% 0% Due to stiffness effects of highly-skewed bridges and inability of SLG model to properly account for dead load distribution of skewed bridges Service II 4% 0% - * The percentage given is that of the subset of bridges that have skew less than 20⁰.
From page 139...
... NCHRP Project 12-103 139 Figure 5-122 - Scatter plot of S/L Ratio versus Tolerance for the Strength I and Service II Limit States (Note: the vertical axis of this plot has been scaled to encompass the data within a reasonable range, essentially hiding many of the data points observed for Strength I Shear greater than 40 inches)
From page 140...
... NCHRP Project 12-103 140 Figure 5-123 – Scatter plot of tolerance for Strength I and Service II limit states with the expression developed for estimating maximum tolerable support movement. Table 5-4 – Expression for estimating maximum tolerable support movements of steel multi-girder bridges.

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