Bridge Superstructure Tolerance to Total and Differential Foundation Movements (2018)

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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. To structure the results, data sets were segmented by (a) continuity of the structure, (b) limit state, (c) type of support movement (LD versus TD), and (d) location of the support movement (at the abutment versus at the pier). Controlling limit states were identified for each type and location of support movement, as were the locations within the superstructure where the tolerance controls. In addition to exploratory analysis, linear regression was employed to determine the predictor variables (influential parameters) and their interactions that affect tolerance to LD and TD support movements. Only the controlling limit states/movements are discussed in detail. When applicable, the results were evaluated against the empirical guidance for support movements of simple span and continuous span bridges given in AASHTO LRFD (see Section 2). 5.1 Tolerable Support Movement Influences Throughout the analysis results discussed in this section, the trends associated with levels of tolerable support movement will be identified and traced to their underlying mechanisms. In the following sections, a set of common mechanisms will be discussed so that they may be referred to throughout this

NCHRP Project 12-103 44 section. In most (but not all) cases these mechanisms lead to additional capacity and thus act to increase a bridge’s tolerance to support movement. 5.1.1 Live Load Distribution Factors One of the key sources of conservatism associated with bridge design using the SLG modeling approach is due to the assumed load sharing between girders. Specifically, there is a conservative bias associated with the moment live load distribution factors prescribed by AASHTO LRFD (Masceri 2015). For example, consider Figure 5-1 which gives the ratio of FE to SLG Strength I Flexure ratings for a large suite of two-span continuous bridges. Based on this figure it is apparent that the level of conservatism varies greatly (from around 1.0 to 2.0) with the data approximately centered around 1.3 (i.e. the live load force effects computed from a SLG model will, on average, be approximately 1.3 times the live load force effects computed from an FE model). Importantly, the level of conservatism varied between interior and exterior girders and is influenced by both skew and the girder spacing-to-span length ratio. By overestimating the force effects during the design process, additional capacity is available in each girder to accommodate support movements. Figure 5-1 - Probability distribution for the ratio of FE-to-SLG Rating factor.

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). The reason for this load distribution is that when considering a perpendicular cross-section of the bridge, the section crosses the exterior girder on the obtuse side closer to the support than the adjacent (first interior) girder. As a result, along this perpendicular section the exterior girder is stiffer than the adjacent girder and thus it attracts additional forces. Since this mechanism is not explicitly considered by the SLG model, it can result in “under-sized” exterior girders, i.e., exterior girders designed for moment and shear force effects less than those computed by an FE model. As a result, this mechanism acts to reduce a bridge’s tolerance to support movements. Figure 5-2 - Schematic of skewed bridge with defining acute and obtuse side girder designation. This effect can influence both shear and moment force effects and is more prevalent for bridges that have skews greater than 20o. A skew of 20o corresponds to the limit of diaphragm configuration given by AASHTO LRFD (Article 6.7.4.2). These provisions specify that bridges with skews greater than 20o shall have diaphragms placed normal to the girder. Since diaphragms placed in this configuration provide an additional load path perpendicular to the girders, they act to exacerbate the distribution of forces towards exterior girders at an obtuse corner. To illustrate this mechanism, consider the dead load shear and moment diagrams of a highly-skewed bridge shown in Figure 5-3. As is apparent from this figure, there is a clear increase in shear and moment demands to exterior girders at an obtuse corner (which actually occurs on both sides of the bridge at interior supports). In the case of dead loads, the SLG girder model employs a tributary width assumption that ignores this phenomenon. In the case of live loads, the SLG model relies on live load distribution

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) the SLG model may under-estimate both dead load and live load force effects. Figure 5-3 - Dead load shear (left) and moment (right) diagrams for a highly-skewed bridge. Finally, it is important to point out that while increasing the transverse stiffness of a bridge (either through diaphragms perpendicular to the bridge or shorter girder spacing) makes the live load distribution factors more conservative, the opposite is true for this load distribution mechanism. That is, increasing the transverse stiffness of a bridge actually increases the distribution of “extra” shear and moment to exterior girders. This influence is most apparent for shear forces at the end of exterior girders adjacent to obtuse bearing locations. It follows that in the case of shear demands, an increase in girder spacing of skewed bridges is associated with an increased tolerance to support movements (exactly the opposite trend observed for flexure due to the live load distribution factors). 5.1.3 Elements Governed by the Fatigue Limit State For steel bridges, the Fatigue limit state generally controls the design of the steel cross-section in the positive moment region. Since this limit state is associated with cyclic loading, it is not influenced by tolerable support movements. As a result, elements that are governed by the Fatigue limit state have additional capacity for other limit states (such as Strength I Flexure and Service II). This additional capacity is predominately found in the positive moment region of steel bridges, and thus tolerable support movements that are generally governed by this region (namely, LD support movement of a pier) are quite large for steel bridges.

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. Stepwise linear regression was employed via Matlab’s statistical toolbox as an exploratory tool to determine a subset of predictor variables (bridge configuration parameters) and the combinations of those predictor variables that influence steel bridge superstructure tolerance to support movement. This technique fits a model to the data set by systematically adding (or removing) predictors based on the t-statistic of their coefficients. For each data set (movement type/location, limit state, etc.) a regression model was obtained and the influential parameters (and their interactions) were identified based on the p-value given for the t-statistic of each predictor in the regression model. For this study, a limiting p-value of 0.05 was chosen. The following sections discuss the results of the stepwise regression. Additional information for each regression model obtained is included in Appendix E. To verify the quality of fit for each regression model, values for the coefficient of determination (R2) are given in Table 5-1 and Table 5-2 for two- and three-span continuous steel multi-girder bridges, respectively. Table 5-1 - R2 value of each regression model used to determine the influential parameters and their interactions for two- span continuous steel multi-girder bridges. Movement Type/Location Strength I FlexureLinear Model R2 Strength I Shear Linear Model R2 Service II Linear Model R2 LD / Abutment 0.8325 0.8315 0.9302 TD / Abutment 0.7647 0.6960 0.8377 LD / Pier 0.9136 0.9343 0.9842 TD / Pier 0.7510 0.7699 0.8642 Table 5-2 - R2 value of each regression model used to determine the influential parameters and their interactions for three- span continuous steel multi-girder bridges. Movement Type/Location Strength I FlexureLinear Model R2 Strength I Shear Linear Model R2 Service II Linear Model R2 LD / Abutment 0.8227 0.8545 0.9519 TD / Abutment 0.7750 0.6993 0.8821 LD / Pier 0.8257 0.8532 0.9540 TD / Pier 0.8008 0.7411 0.9028

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. ride-ability) far before exceeding the Strength I Flexure and Service II limits. As a result, for all practical purposes it is concluded that these limit states are not influenced by support movements for simple span bridges. Only the Strength I limit state for shear exhibited non-negligible (i.e. relatively low) tolerance to TD support movements. These results are discussed in the following sections. 5.3.1 Strength I Shear Tolerance to TD Support Movements Significant scatter in results was observed when evaluating the current AASHTO LRFD criterion for shear based on Strength I limit state. Approximately 40% of the population exhibited tolerable support movements greater than 30 in. Approximately 6% of the population exhibited no tolerance at all to TD movements. Figure 5-4 gives the plot of span length versus tolerable TD support movement. The vertical scale of this plot was adjusted to focus on data points that fall below the current AASHTO LRFD guidance (e.g., less than 0.008L inches). Figure 5-4 – Tolerable TD support movements of the Strength I limit state for shear. Further investigation of the data found that the bridges with little or no tolerance to support movement were highly skewed (greater than 30⁰ on average), and generally had longer spans and/or smaller girder

NCHRP Project 12-103 49 spacing. The plot of skew and tolerable support movement (Figure 5-5) shows that bridges with higher skew exhibit lower levels of tolerable support movement. The influence of skew is due to the mechanism described in Section 5.1.2. As discussed in Section 5.1.2, a clear discontinuity exists between skew angles less than 20⁰ and skew angles greater than 20⁰. As apparent from Figure 5-5, simple span bridges with skew angles less than 20⁰ were found to have high levels of tolerance to TD support movements. This discontinuity coincides with the design threshold at which interior diaphragms (or cross frames) switch from being oriented parallel to the skew to being oriented perpendicular to the girders. Figure 5-5 – Tolerable TD support movements of the Strength I limit state for shear. The sensitivity of superstructure tolerance to TD support movements is explained by the under- estimation of dead load distribution in highly skewed bridges by the SLG model. A comparison of the demands calculated using the SLG model and those obtained using FE model confirms the under- estimation of dead load in highly skewed bridges made by the SLG model (see Figure 5-3 above). For the group of bridges that exhibited no tolerance, dead load and live load demands were compared between the SLG model and the FE model. For all cases, the dead load was underestimated by the SLG model. For some cases, the FE dead load was found to be nearly twice the SLG dead load. Live load demands were also found to be underestimated by the SLG model. For these cases, the controlling location for dead and live load shear was at the exterior girder at an obtuse corner.

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) and their interactions. This complexity was primarily the result of numerous parameters (e.g. span length, girder spacing, skew angle, bridge width) exerting influence over the level of tolerable support movements. 5.4.1 Controlling Limit States The figures in this section show the percentage of bridges that controlled for each limit state and for each type/location of support movement. The Strength I limits for flexure and shear were the primary controlling limit states for LD and TD movements occurring at either support location. Rigorous analysis was performed and is presented in the following sections for each of the controlling limit states. Figure 5-6 – Controlling limit state for a LD support movement occurring at the abutment of a two-span continuous steel multi-girder bridge.

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 multi- girder bridge.

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 multi- girder 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). The controlling location always occurred in the negative moment region. Tolerance controlled at an exterior girder for approximately 50% of the population (Figure 5-10).

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), girder spacing (S), skew, and span-to-depth (SD) were determined to be predictor variables of tolerance to a LD movement occurring at the abutment. The effects plot for these parameters is given by Figure 5-11. An effects plot shows the estimated effect on tolerance from increasing each parameter (from its lowest to its highest value), while keeping the remaining parameters at an average value. The horizontal axis gives the main effect on tolerance. The scale ranging from negative to positive, represents a decrease or increase in tolerable support movement, respectively. Each point represents a predictor variable (influential parameter). The location of each point along the horizontal axis indicates whether tolerance decreases or increases when the value of the variable is increased. The error bars indicate a 95% confidence bound on the effects of each variable. Thus, the effects plot below shows that increasing span length leads to higher tolerance, as does increasing SD but to a much lesser extent. In contrast, increasing girder spacing leads to lower tolerance, as does increasing the skew, but also to a much lesser extent. For this reason, span length and girder spacing were identified as the most influential parameters affecting Strength I Flexure tolerance to LD movements occurring at the abutment.

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 multi- girder bridge. The influence of span length on tolerable support movement is apparent in the plot of tolerance and span length (Figure 5-12). The current AASHTO LRFD guidance is roughly consistent (in terms of slope) with the observed tolerable support movement. Although this expression generally produces conservative estimates, the expression’s accuracy is highly variable. This variability is a consequence of using span length as the only explanatory variable, and results in predictions that may be overly conservative for many bridges. That is, bridges exhibit higher tolerance than what is predicted by this expression. This shortcoming is tempered however, since the magnitudes of support movements predicted by the current AASHTO LRFD guidance are still quite large and thus excessive tolerance observed in this study is not likely to be relevant in practice.

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) depicts the relationship between length and girder spacing. An interaction plot illustrates the interaction effects between two predictor variables in the fitted model. This plot provides way of showing the effect on tolerance due to the interaction of two influential parameters by assigning all other predictor variables their average value and evaluating the fitted model across the bounds of the two predictor variables considered to obtain the “Adjusted Tolerance”. Each line represents an upper, middle, and lower bound of the interacting parameter. The slope of this line indicates the rate at which tolerance increases or decreases (on average) as the parameter on the horizontal axis increases. Thus, the interaction plot of span length and girder spacing shows that the effect of girder spacing becomes more significant as span length increases. This appears to explain the variance in tolerance as span length increases, shown in Figure 5-12. Note: these interaction lines represent the mean of the data and therefore are only being used here as an exploratory tool for parameter interactions.

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) with larger spacing (see Section 5.1.1). The interaction of girder spacing and span length becomes evident when tolerance is plotted against the ratio of girder spacing to span length (Figure 5-14). The larger the ratio, the less tolerance to LD support movement the bridge will display. Figure 5-14 - Strength I Flexure tolerance to a LD support movement occurring at the abutment of a two-span continuous steel multi-girder bridge.

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). The levels of tolerable LD support movement for the Strength I limit state for shear were found to be much larger than those observed for the Strength I limit state for flexure. Figure 5-15 shows the plot of span length and tolerance. Based on these results it is concluded that two-span continuous bridges have the ability to tolerate large LD support movements under the Strength I limit state for shear. Given the high levels of tolerable support movement, rigorous analysis was not conducted. Figure 5-15 - Strength I Shear tolerance to a LD support movement occurring at the abutment of a two-span continuous steel multi-girder bridge. Span length (L), girder spacing (S), skew, and SD were determined to be predictor variables of tolerance to a LD movement occurring at the abutment. The effects plot for these parameters is given by Figure 5-16.

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 multi- girder 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). The levels of tolerable LD support movement for the Service II limit state were found to be much larger than those observed for the Strength I limit state for flexure. Figure 5-17 gives the plot of span length and tolerance, showing many of the bridges to have high Service II tolerance to LD movements occurring at the abutment. Given the high levels of tolerable support movement, rigorous analysis was not conducted. Only the parameters that influence Service II tolerance were identified. These parameters are span length and girder spacing. The effect of the influential parameters is described by the effects plot given by Figure 5-18.

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 multi- girder bridge. Figure 5-18 - Effects plot for tolerance to LD movements occurring at the abutment of a two-span continuous steel multi- girder bridge. 5.4.5 Strength I Flexure Tolerance to TD Movements Occurring at the Abutment The Strength I Flexure limit state controlled tolerance to TD support movements occurring at the abutment for over 75% of the population (see Figure 5-7). The controlling location always occurs in the negative moment region. Tolerance controlled at an exterior girder for 88% of the population (Figure

NCHRP Project 12-103 60 5-19). This is driven by the dead load distribution mechanism observed in highly-skewed bridges discussed in Section 5.1.2. The exterior girder controls when the TD movement takes place at the acute- side exterior girder. Further investigation found that for the small number of bridges where tolerance controls at an interior girder, these bridges were exposed to TD support movement that was maximum at the obtuse side of the bridge. Figure 5-19 - Controlling location of Strength I Flexure tolerance to a TD support movement occurring at the abutment of a two-span continuous steel multi-girder bridge. Span length (L), girder spacing (S), and skew were identified as the most influential parameters affecting superstructure tolerance to TD movements occurring at the abutment. The effects plot for the predictor variables is given by Figure 5-20. SD was again identified as a predictor variable but its effects on tolerance are far less than the effects of span length, girder spacing, or skew.

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 multi- girder bridge. As was seen with LD movement, increasing span length leads to higher tolerance while increasing girder spacing and skew leads to lower tolerance. For TD movements, skew has a much greater influence on tolerance than what was observed for LD movements. The influence of skew is likely due to the increased stiffness displayed by skewed bridges. Figure 5-21 shows the plot of span length and tolerance to TD movements occurring at the abutment. Observations for samples with skew less than 20⁰ are highlighted. Samples with skew greater than 20⁰ have less tolerance to TD support movement than for samples with skew less than 20⁰. Such bridges have a higher stiffness and thus the resulting forces effects due to TD support movements are greater. Many of the samples with skew greater than 20⁰ fall below the current AASHTO LRFD criteria. This is no surprise since the expression given by current AASHTO LRFD guidance (0.004L) was not intended to cover this particular type of support movement.

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. Additional interactions exist between span length and skew as well as girder spacing and skew. These interactions are depicted in the interaction plots given by Figure 5-22 and Figure 5-23, respectively. The accompanying scatter plots of tolerance versus each of the interacting parameters are provided in Appendix C. In general, as skew increases, tolerance to TD support movement decreases. However, the effect of skew on tolerance is highly dependent on span length and girder spacing. The larger the span length and the smaller the girder spacing, the more influential skew becomes.

NCHRP Project 12-103 63 Figure 5-22 - Interaction plot of skew and span length. Figure 5-23 - Interaction plot of skew and spacing. 5.4.6 Strength I Shear Tolerance to TD Movements Occurring at the Abutment Strength I Shear tolerance to TD movements occurring at the abutment controlled for approximately 20% of the population (see Figure 5-7). The controlling location can occur over the pier or over the abutment when the obtuse-side exterior girder remains stationary. Tolerance controlled at an exterior girder for 94% of the population (Figure 5-24). The controlling tolerance occurs when the acute-side

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. This observation may be a consequence of the dead load distribution mechanism that exists for shear in highly skewed bridges (Section 5.1.2). Figure 5-24 - Controlling location of Strength I Flexure tolerance to a TD support movement occurring at the abutment of a two-span continuous steel multi-girder bridge. Span length (L), girder spacing (S), skew, width (W), and SD were all determined to be predictor variables of Strength I Shear tolerance to a TD movement occurring at the abutment. The effects plot for these parameters is given by Figure 5-25. From this plot, it is apparent that skew has the greatest influence on tolerance.

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 multi- girder bridge. The effect of skew is also evident in the plots of tolerance given by Figure 5-26 and Figure 5-27. In the plot of span length and tolerance (Figure 5-26), observations for bridges with skew less than 20⁰ are highlighted. These bridges display higher tolerance to TD movement compared to bridges with skew greater than 20⁰. In the plot of skew and tolerance (Figure 5-27), a clear discontinuity exists at a skew angle of 20⁰. This suggests that the provisions of AASHTO LRFD that specify the diaphragm orientation (parallel to the skew or normal to the girder) have a large influence on superstructure shear response to dead load, live load, and support movement (see Section 5.1.2).

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. Bridges with skew less than 20⁰ have far more tolerance than bridges with skew greater than 20⁰. For this reason, Strength I Shear tolerance was analyzed for bridges with skew greater than 20⁰. When examining only bridges with skew angles greater than 20⁰, width is no longer a predictor variable. The

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. It should be mentioned that there is considerable scatter in these trends, which is reflected by the relatively large error bars in Figure 5-28. Figure 5-28 - Effects plot for tolerance to TD movements occurring at the abutment of a two-span continuous steel multi- girder bridge. The interaction of skew and span length has an effect on Strength I Shear tolerance to TD movements occurring at the abutment. This interaction is shown in Figure 5-29. It appears that the tolerance shorter spans display is not affected by skew. As the span length gets larger, the effect of skew becomes more significant. This may have to do with the fact that in longer bridges the dead load force effects are more significant (in terms of a percentage of capacity) than their live load counterparts. As a result, the mechanism discussed in Section 5.1.2 is not nearly as important for shorter bridges that are more live load driven.

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). The levels of tolerable TD support movement for the Service II limit state were found to be much larger than those observed for the Strength I limit state for flexure. Figure 5-30 provides a plot of span length versus tolerable TD support movement. It shows that in most cases the Service II limit state is not very sensitive to TD support movements at the abutment. Given the high levels of tolerable support movement, rigorous analysis was not conducted. Only the parameters that influence Service II tolerance were identified. These parameters are span length (L), girder spacing (S), and skew. The effect of the influential parameters is described by the effects plot below (Figure 5-31).

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 multi- girder bridge. Figure 5-31 – Effects plot for tolerance to TD movements occurring at the abutment of a two-span continuous steel multi- girder bridge. 5.4.8 Strength I Flexure Tolerance to LD Movements Occurring at the Pier Strength I Flexure controlled the tolerable LD support movements at the pier for approximately 38% of the population (see Figure 5-8). The controlling location for this limit state was in the positive moment region of the span. The exterior girder controlled for 88% of the population (Figure 5-32).

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. This can be seen in the plot of span length versus tolerable LD support movement given by Figure 5-33. This plot shows many of the bridges to have high Strength I Flexure tolerance to LD movements occurring at the pier. Due to the design considerations of the Fatigue limit state, the cross-section within the positive moment region of steel bridges has excess capacity related to the Strength I limit state, and thus, this region never governs the level of tolerable support movement for steel bridges (see Section 5.1.3). For this reason, rigorous analysis was not conducted.

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) and girder spacing (S) were found to be the most influential parameters affecting Strength I Flexure tolerance to LD movements occurring at the pier. Figure 5-34 gives the effects plot for the influential parameters. Figure 5-34 Effects plot for tolerance to LD movements occurring at the pier of a two-span continuous steel multi-girder bridge.

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). Tolerance controlled at an exterior girder for this limit state across 94% of the population (Figure 5-35). The controlling location always occurs over the nearest abutment, particularly at an obtuse corner of the skew. Figure 5-35 - Controlling location of Strength I Shear tolerance to a LD support movement occurring at the pier of a two-span continuous steel multi-girder bridge. Span length (L), girder spacing (S), skew, and SD were determined to be predictor variables of the Strength I Shear tolerable to a LD movement occurring at the pier. The effects plot for these parameters is given by Figure 5-36. Skew clearly has the greatest influence on tolerance. Higher tolerance is associated with increased span length, girder spacing, and SD ratio. Lower tolerance is associated with increased skew. Figure 5-37 gives the plot of span length versus Strength I Shear tolerance to LD support movements.

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 multi- girder bridge. Again, bridges with skew less than 20⁰ have far more tolerance than bridges with skew greater than 20⁰. For this reason, Strength I Shear tolerance is analyzed for bridges with skew greater than 20⁰. Span length (L), girder spacing (S), skew, width (W), and SD were all determined to be predictor variables of tolerance to a LD movement occurring at the pier. The effects plot below shows the effect of each of the

NCHRP Project 12-103 74 influential parameters. Higher tolerance is associated with increased span length, girder spacing, and SD ratio. Lower tolerance is associated with increased skew, and to a lesser extent, width. Figure 5-38 - Effects plot for tolerance to LD movements occurring at the pier of a two-span continuous steel multi-girder bridge. Several parameter interactions were found to affect tolerance to LD movements occurring at the pier. These interactions include: (1) girder spacing and span length, (2) skew and span length, and (3) width and span length, and (4) SD ratio and span length. Figure 5-39 and Figure 5-40 show the interaction plots of span length with girder spacing and skew, respectively. The accompanying scatter plot is given by Figure 5-37. At longer span lengths, lower tolerance was observed for bridges with smaller girder spacing. This behavior is opposite what was observed with tolerance of the Strength I Flexure limit state, but is consistent with the issue related to the distribution of dead loads within skewed bridges (see Section 5.1.2). Note that as the bridge length increases dead load accounts for a larger percentage of the bridge’s capacity and thus this influence would become more pronounced. At larger span lengths, lower tolerance is observed for bridges with larger skew, and becomes exceptionally high for skews less than 20⁰.

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. Figure 5-41 - Interaction plot of SD and span length. gives the interaction plot of SD ratio versus span length. The accompanying scatter plot is given by Figure 5-37. The effect of SD ratio becomes more significant as span length increases. Lower tolerance is associated with smaller SD ratio. This suggests that lower tolerance is associated with bridges that have deeper girders, which are characteristically stiffer than shallower girders.

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). The levels of tolerable LD support movement for the Service II limit state were found to be much larger than those observed for the Strength I Flexure limit state. Figure 5-42 gives the plot of span length versus tolerance, showing many of the samples to have high Service II tolerance to LD movements occurring at the pier. Given the high levels of tolerable support movement, rigorous analysis was not conducted. Only the parameters that influence Service II tolerance were identified. These parameters are span length (L), girder spacing (S), skew, and SD. The effect of the influential parameters is described by the effects plot below (Figure 5-43).

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. 5.4.11 Strength I Flexure Tolerance to TD Movements Occurring at the Pier The Strength I Flexure limit state controlled the tolerable TD support movements occurring at the pier for approximately 20% of the population (see Figure 5-9). For these movements, the controlling location

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 two- span continuous steel multi-girder bridge. For this limit state, an exterior girder controlled for 99% of the population, as shown in Figure 5-44. For bridges with skew angles less than 20o the controlling location was nearly always in one of the positive moment regions. However, for bridges with skew angles greater than 20o a considerable number of bridges had the controlling member located over the pier at the exterior girder opposite of where the TD movement occurred (i.e. the exterior girder that remains stationary). This observation was investigated and it was found that for relatively large skew, this type of TD movement induces addition negative moment over the pier (along the opposite side of the bridge to where the settlement occurred). Figure 5-45 depicts this behavior.

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. Observations with skew less than 20⁰ are highlighted. These bridges generally exhibit higher tolerance to TD support movement occurring at the pier than bridges with higher skew. Figure 5-47 gives the plot of skew and Strength I Flexure tolerance. Figure 5-46 - Strength I Flexure tolerance to a TD support movement occurring at the pier of a two-span continuous steel multi-girder bridge. Location of TD Movement

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), girder spacing (S), and skew were identified as the most influential parameters affecting superstructure tolerance to TD movements occurring at the pier. The effects plot for the predictor variables is given by Figure 5-48. SD was again identified as a predictor variable, but its effects on tolerance are far less than the effects of span length, girder spacing, or skew. Figure 5-48 - Effects plot for tolerance to TD movements occurring at the pier of a two-span continuous steel multi-girder bridge.

NCHRP Project 12-103 81 Several parameter interactions were found to affect tolerance to TD movements occurring at the pier. These interactions include: (1) girder spacing and span length, (2) skew and span length, (3) skew and girder spacing, and (4) SD ratio and girder spacing. The interaction plot of span length and girder spacing (Figure 5-49) shows that the effect of girder spacing becomes more significant as span length increases. Lower tolerance is associated with bridges with larger girder spacing (which is consistent with the general influence of girder spacing on flexural limit states, see Section 5.1.1). Figure 5-49 - Interaction plot of span length and girder spacing. Figure 5-50 gives the interaction plot of skew and span length. Lower tolerance is associated with higher skew, and the effect of skew becomes more significant as span length increases. Figure 5-51 gives the interaction plot of skew and girder spacing. Tolerance decreases as skew becomes larger, and lower tolerance is associated with larger girder spacing. The effect of skew is more significant for bridges with smaller girder spacing.

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. The interaction of spacing and SD ratio is shown in Figure 5-52. Lower tolerance is associated with smaller SD ratio for bridges with smaller girder spacing. As girder spacing increases, the effect of SD ratio becomes less significant.

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). For this limit state an exterior girder controlled for 96% of the population (Figure 5-53). The controlling location is generally in the obtuse corner of the nearest abutment. For a small number of observations, the controlling location was found to be over the pier at the exterior girder opposite of where the TD movement occurred (the exterior girder that remains stationary). Further investigation suggested that this behavior may be a factor of skew and the ratio of span length to width, and it is consistent with the issue described in Section 5.1.2.

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. Bridges with skew less than 20⁰ clearly have much higher Strength I Shear tolerance to TD support movements than for bridges with higher skew. Figure 5-54 - Strength I Shear tolerance to a TD support movement occurring at the pier of a two-span continuous steel multi- girder bridge. Span length (L), girder spacing (S), skew, and SD were determined to be predictor variables of tolerance to a TD movement occurring at the pier. Again, bridges with skew angles less than 20⁰ have far more tolerance than bridges with skew greater than 20⁰. For this reason, Strength I Shear tolerance was analyzed for bridges with skew greater than 20⁰. The effects plot for these parameters is given by Figure

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. Figure 5-55 - Effects plot for tolerance to TD movements occurring at the pier of a two-span continuous steel multi-girder bridge. Several parameter interactions were found to affect tolerance to TD movements occurring at the pier. These interactions include: (1) girder spacing and span length, (2) skew and span length, (3) span length and SD, and (4) girder spacing ratio and Skew. Figure 5-56 and Figure 5-57 show the interaction plots of span length with girder spacing and skew, respectively. The accompanying scatter plot is given by Figure 5-54. Lower tolerance is associated with bridges that have smaller girder spacing, which is consistent with the discussion of the distribution of force effects in skew bridges presented in Section 5.1.2.

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. Figure 5-58 shows the interaction of span length and SD ratio. The accompanying scatter plot is given by Figure 5-54. The effect of SD ratio becomes more significant as span length increases. Lower tolerance is associated with smaller SD ratio. This suggests that lower tolerance is associated with bridges that have deeper girders, which are characteristically stiffer than shallower girders.

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. The accompanying scatter plot is provided in Appendix C. As skew increases, the effect of girder spacing becomes less significant. This is likely since for higher skewed bridges force effects are disproportionately distributed to edge girders regardless of girder spacing. Figure 5-59 - Interaction plot of skew and girder spacing.

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). The levels of tolerable TD support movement for the Service II limit state were found to be much larger than those observed for the Strength I limit state for flexure. Figure 5-60 gives the plot of span length and tolerance, showing many of the bridges to have high Service II tolerance to TD movements occurring at the pier. Given the high levels of tolerable support movement, rigorous analysis was not conducted. Only the parameters that influence Service II tolerance were identified. These parameters are span length (L), girder spacing (S), skew, and SD. The effect of the influential parameters is described by the effects plot below (Figure 5-61). Figure 5-60 – Service II tolerance to a TD support movement occurring at the pier of a two-span continuous steel multi-girder bridge.

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. 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) and their interactions. 5.5.1 Controlling Limit States The figures in this section show the percentage of bridges that controlled for each limit state and for each type/location of support movement. The Strength I limits of flexure and shear were the primary controlling limit states for LD and TD movements occurring at either support location.

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.

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 multi- girder bridge. Figure 5-65 - Controlling limit state for a TD support movement occurring at the pier of a three-span continuous steel multi- girder bridge.

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). The controlling location always occurs in the negative moment region over the pier nearest to the abutment which displayed the movement, and was found to occur in both interior and exterior girders alike (Figure 5-66). Figure 5-66 - Controlling location of Strength I Flexure tolerance to a LD support movement occurring at the abutment of a three-span continuous steel multi-girder bridge. Figure 5-67 shows the plot of span length and Strength I Flexure tolerance to LD movements occurring at the abutment. AS is apparent in this plot, several observations fall below the current expression given by AASHTO LRFD guidance (0.004L), many of these occurring at span length lower than 1200 in (or 100 ft.). Given that in most case a three-span continuous bridge would have span length of at least 100 ft. (if not much greater) this will likely have negligible impact in practice.

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), girder spacing (S), skew, width (W), and SD were all determined to be predictor variables of tolerance to a LD movement occurring at the abutment for the Strength I limit flexural limit state. Span length and girder spacing were the most influential parameters. The effects plot for these parameters is given by Figure 5-68. The purpose of an effects plot is to illustrate the effect of each predictor variable (influential parameter) on the response variable (tolerable support movement). Effects plots are described in further detail in Section 5.4.2. Higher tolerance is associated with increased span length while lower tolerance is associated with increased spacing. Individually, skew, width, and SD ratio appear to have minimal influence on tolerable support movement.

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. These interactions include: (1) spacing and span length, (2) skew and spacing, (3) width and spacing, (4) SD and spacing, and (5) skew and SD. Figure 5-69 shows the interaction of girder spacing and span length. The accompanying scatter plot is given by Figure 5-67. For shorter spans, girder spacing has less of an effect on tolerance. Girder spacing appears to explain the variance in tolerance for longer span bridges. That is, for longer spans, bridges with larger girder spacing have lower tolerance than bridges with smaller girder spacing.

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. The accompanying scatter plot is provided in Appendix C. As girder spacing increases, tolerance to LD movements decreases. For bridges with smaller girder spacing, higher skew appears to be associated with lower tolerance. The inverse of this behavior occurs as girder spacing increases above 120 inches (10ft). Figure 5-70 - Interaction plot for girder spacing and skew.

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. Again, as girder spacing increases, tolerance to LD movements decreases. For bridges with smaller girder spacing, smaller width appears to be associated with lower tolerance. The inverse of this behavior occurs as girder spacing increases. For bridges with larger girder spacing, greater width is associated with lower tolerance to LD movements. Figure 5-71 - Interaction plot for girder spacing and width. Figure 5-72 - Interaction of girder spacing and SD ratio.

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). At shorter girder spacing, smaller SD ratio is associated with lower tolerance. As girder spacing increases, the effect of SD ratio appears to become less significant. The interaction plot below (Figure 5-73) describes the interaction between skew and SD ratio. At smaller values of skew, lower tolerance is associated with smaller SD ratio. The effect of SD ratio appears to become less significant as skew increases. The accompanying scatter plots for Figure 5-72 and Figure 5-73 are provided in Appendix C. Figure 5-73 - Interaction plot for skew and SD ratio. 5.5.3 Strength I Shear Tolerance to LD Movements Occurring at the Abutment The Strength I Shear limit state controlled the tolerable LD support movement at the abutment for only 5% of the population (see Figure 5-62). The controlling location of Strength I Shear occurs at interior and exterior girders alike (Figure 5-66), and always over the pier nearest to the abutment which displayed the movement.

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. Five samples (2.5 % of the population) were found to have little or no tolerance. These samples were investigated further to determine the cause. First the SLG rating factor was verified to be 1.0 or greater. This confirmed that the “design” of these bridges was in fact valid. When evaluating the rating factor for these bridges using finite element demands (often referred to as a refined load rating), the FE rating factor for shear was found to be less than 1.0. Additionally, all of these bridges were determined to have skew angles greater than 45⁰, and further investigation found that the dead load distribution mechanism described in Section 5.1.2 resulted in little or no tolerance to support movement. For these bridges, the dead load shear demands of the FE model were compared to the dead load shear calculated using the SLG model. The FE demands were determined to be 20-50% larger than the SLG demands, suggesting that the single line girder model underestimated the shear demands in the design of these bridges.

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), girder spacing (S), skew, width (W), and SD were all identified as influential parameters affecting Strength I Shear tolerance to LD movements occurring at the abutment. The effects plot below shows the effect of each parameter on tolerance. All parameters except for width were found to have significant influence on tolerance. Individually, width does not have a significant effect. However, width was found to interact with other parameters. The effects plot shows that higher tolerance is associated with increased span length, girder spacing, and SD ratio. Lower tolerance is associated with increasing skew. Given the fact that many of the bridges exhibited relatively large tolerance to LD movements occurring at the abutment (except for the highly-skewed bridges that exhibited no tolerance), rigorous analysis of parameter interaction was not conducted.

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). In general, the levels of tolerable LD support movement for the Service II limit state were found to be much larger than those observed for the Strength I limit state for flexure. Figure 5-77 gives the plot of span length versus tolerable support movement, and shows that in general bridges may undergo relatively large LD support movements without violating the Service II limit state. Given the high levels of tolerable support movement, rigorous analysis was not conducted. Only the parameters that influence Service II tolerance were identified. These parameters are span length (L), girder spacing (S), skew, and SD. The effect of the influential parameters is described by the effects plot below (Figure 5-78).

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 multi- girder bridge. 5.5.5 Strength I Flexure Tolerance to TD Movements Occurring at the Abutment The Strength I Flexure limit state controlled the level of tolerable support movement for over 65% of the population (see Figure 5-63). The location of the controlling member was always over the pier nearest to the abutment that displayed the movement. In over 70% of the population the exterior that

NCHRP Project 12-103 102 underwent the largest support movement governed (Figure 5-79). More specifically, the exterior girder controls over the pier when the TD movement takes place at the acute side of the abutment. Further investigation found that the bridges that were controlled by the first interior girder or middle girders, were exposed to TD support movement that occurred at the obtuse side of the abutment. Figure 5-79 - Controlling location of Strength I Flexure tolerance to a TD support movement occurring at the abutment of a three-span continuous steel multi-girder bridge. All five parameters were determined to affect tolerance, however, span length (L), girder spacing (S), and skew were the most influential. The effects plot for these parameters is given by Figure 5-80. Higher tolerance is associated with increased span length while lower tolerance is associated with increased girder spacing and skew. Individually, width and SD ratio appear to have minimal influence on tolerable support movement.

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) for the Strength I Flexure limit state. Observations for samples with skew less than 20⁰ are highlighted. Samples with skew angles greater than 20⁰ generally have less tolerance to TD support movement than for samples with skew less than 20⁰. This is likely due to the distribution of dead and live load forces in skew bridges as described in Section 5.1.2. The current AASHTO LRFD criterion (0.004L) is plotted in Figure 5-81 as a point of comparison. Approximately 10% of the population falls below the current criterion. For the bridges that display tolerable support movements below this expression, many have skew angles greater than 20o and the rest are for bridges with span lengths less than 1000 in. (~84 ft.) (which are very uncommon among three-span continuous bridges).

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. These interactions include: (1) spacing and span length, (2) skew and span length, (3) skew and spacing, (4) width and spacing, (5) SD and spacing, and (6) skew and SD. The interactions of spacing and span length (1), width and span length (4), and SD ratio and span length (5) that exist for LD movements were found to be the same for TD movements, and therefore discussion of those interactions is not repeated here. The plot below shows the interaction between skew and span length. The accompanying scatter plot is given by Figure 5-81.

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. As span length increases, lower tolerance is associated with bridges that have higher skew. It appears that highly-skewed bridges have a steady limit of tolerance regardless of the span length. Figure 5-83 describes the interaction between girder spacing and skew. The accompanying scatter plot is provided in Appendix C. The effect of skew on tolerance appears to be more significant with smaller girder spacing. For bridges with smaller girder spacing, lower tolerance is associated with bridges that have higher skew.

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. The accompanying scatter plot is provided in Appendix C. The effect of SD ratio on tolerance to TD movements appears to become less significant as skew increases. For bridges with less skew, lower tolerance is associated with bridges that have a smaller SD ratio. Smaller SD ratio corresponds to bridges with deeper girders which are characteristically stiffer than shallower girders. The effect of SD may become less significant at higher skew because another parameter interacting with skew becomes more significant. Figure 5-84 - Interaction plot for skew and SD ratio.

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). The controlling tolerance was located at an exterior girder for 86% of the population (Figure 5-85). The controlling Strength I Shear tolerance occurs at the exterior girder when the acute- side exterior girder is exposed to the TD movement. For the few cases where an interior girder controlled, further investigation found in these cases the obtuse-side of the abutment underwent the TD movement. Figure 5-85 - Controlling location of Strength I Shear tolerance to a TD support movement occurring at the abutment of a three-span continuous steel multi-girder bridge. The plot of span length versus tolerable TD support movement (provided in Figure 5-86), highlights the bridges with skew angles less than 20⁰. It is evident that there is an interaction between span length and skew (for skew angles less than 20⁰). In the plot of skew angle versus tolerable TD support movement (Figure 5-87), a discontinuity exists at a skew angle of 20o, similar to what was found for two-span continuous bridges. Again, several samples were found to have little or no tolerance. This behavior was again determined to be a factor of high skew and the dead load distribution mechanism described in Section 5.1.2.

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. Since bridges with skew less than 20⁰ have far more tolerance than bridges with skew greater than 20⁰, an analysis was carried out on only bridges with skew angles greater than 20⁰. For this sub-population, girder spacing (S), skew, width (W), and SD ratio were identified as the most influential parameters. Span length (L) was also identified however its effects were found to be less significant. The effects plot

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. Lower tolerance is associated with increasing skew. Figure 5-88 - Effects plot for tolerance to TD movements occurring at the abutment of a three-span continuous steel multi- girder bridge. The interactions of span length and skew, as well as girder spacing and skew were found to influence the tolerable TD support movements for this limit state. The interaction plot of span length and skew (see Figure 5-89) indicates that for highly skewed bridges the tolerable support movement decreases as the span length increases. This is consistent with the bridge becoming more governed by dead load (compared to live load) and thus the influence of skew on the distribution of force effects becomes more pronounced (see Section 5.1.2). The accompanying scatter plot for this interaction is given by Figure 5-86.

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. The accompanying scatter plot for this interaction is provided in Appendix C. As illustrated by this plot, as girder spacing increases, the effect of width becomes less significant. For bridges with smaller girder spacing, lower tolerance is associated with smaller width. It appears that tolerance is not affected for bridges with larger width, regardless of the girder spacing. Figure 5-90 - Interaction plot of width and girder spacing.

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). In general, however, the levels of tolerable TD support movement for the Service II limit state were found to be much larger than those observed for the Strength I Flexure limit state. Figure 5-91 gives the plot of span length versus tolerable TD support movement, and indicates that bridges may undergo relatively large TD movements without violating the Service II limit state. Also, nearly all observations are greater than the estimates given by current AASHTO LRFD criterion (0.004L). Given the relatively high levels of tolerable support movement, rigorous analysis was not conducted. Only the parameters that influence Service II tolerance were identified. These parameters are span length (L), girder spacing (S), skew, and SD. The effect of the influential parameters is described by the effects plot below (Figure 5-92). Figure 5-91 – Service II tolerance to a TD support movement occurring at the abutment of a three-span continuous steel multi-girder bridge.

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 multi- girder 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). The controlling location occurs in the negative moment regions at both interior and exterior girders depending on the specific bridge (Figure 5-93). The levels of tolerance to LD support movements occurring at the pier were found to be smaller overall compared to LD movements occurring at the abutment. This is opposite what was observed for two-span continuous bridges. The reason for this discrepancy is that in a three-span continuous bridge a LD support movement of a pier creates a large negative moment over the adjacent pier. In fact, due to the continuity over the pier undergoing the support movement, this negative moment is larger than the negative moment caused by a LD support movement at an abutment.

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 three- span continuous steel multi-girder bridge. Figure 5-94 gives the plot of span length versus tolerable LD support movement at the pier. As a result of the continuity discussed above, three-span continuous bridges exhibit a smaller tolerance to support movements than their two-span counterparts. In addition, approximately 30% of the observations were found to fall below the expression given by current AASHTO LRFD guidance (0.004L). If this criterion was modified to be 0.003L and limited to bridges with spans above 100 ft, the it would be conservative for 99% of the population studied.

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), girder spacing (S), and skew were the most influential. The effects plot for these parameters is given by Figure 5-95. Higher tolerance is associated with increased span length while lower tolerance is associated with increased spacing. Individually, skew, width, and SD ratio appear to have minimal influence on tolerable support movement. Figure 5-95 - Effects plot for tolerance to LD movements occurring at the pier of a three-span continuous steel multi-girder bridge.

NCHRP Project 12-103 115 Several parameter interactions were found to affect tolerance to LD movements occurring at the pier. These interactions include: (1) spacing and span length, (2) skew and span length, (3) skew and spacing, (4) width and spacing, (5) SD and spacing, and (6) skew and SD. The same interactions were found for LD movements occurring at the abutment (see Section 5.5.2). All interactions exhibited the same behavior as they did with LD movements occurring at the abutment of a two-span continuous bridge, therefore discussion of those interactions is not repeated here. 5.5.9 Strength I Shear Tolerance to LD Movements Occurring at the Pier The Strength I limit state for shear controlled the tolerable LD support movement occurring at the pier for only 12% of the population (see Figure 5-64). The controlling location of the Strength I Shear limit state included both interior and exterior girders, but was always over a support adjacent to the pier which underwent the LD support movement (Figure 5-96). Figure 5-96- Controlling location of Strength I Shear tolerance to a LD support movement occurring at the pier of a three-span continuous steel multi-girder bridge. Figure 5-97 gives the plot of span length versus tolerable LD support movement for the Strength I Shear limit state. Several samples (approximately 4% of the population) were found to have little or no tolerance. These samples were investigated to determine the cause. All of these bridges were determined to have a SLG rating factor of 1.0 or greater, however each had an FE rating less than 1.0 and skew greater than 45⁰. This suggests that the cause for the seemingly negligible tolerance to

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. Figure 5-97 – Strength I Shear tolerance to a LD 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 LD movements occurring at the pier. Individually, width does not have a significant effect. However, width was found to affect tolerance when it interacts with other parameters. The effects plot shows that higher tolerance is associated with increasing span length, girder spacing, and SD ratio. Lower tolerance is associated with increasing skew.

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. These interactions include: (1) span length and girder spacing, (2) span length and skew, (3) span length and SD, (4) span length and width, and (5) girder spacing and width. The interaction of girder spacing and span length can be seen in Figure 5-99. The accompanying scatter plot is given by Figure 5-97. As span length increases the effect of girder spacing becomes more significant. Lower tolerance is associated with smaller girder spacing, which is consistent with the examination of the shear limit states for other types of support movement.

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. The accompanying scatter plot is given by Figure 5-97. For longer span bridges, lower tolerance is associated with higher skew. As span length increases, the effect of skew becomes more significant. Figure 5-100 - Interaction plot of skew and span length.

NCHRP Project 12-103 119 Similar interaction behavior exists between span-depth and span length (Figure 5-101). The accompanying scatter plot is given by Figure 5-97. Lower tolerance is associated with smaller SD ratio, and as span length increases, the effect of SD ratio becomes more significant. Figure 5-101 - Interaction plot of span length and SD ratio. The interaction of skew and girder spacing is shown in the figure below. The accompanying scatter plot is given by Figure 5-97. The effect of skew is more significant for bridges with smaller girder spacing, and lower tolerance is associated with higher skew. Figure 5-102 - Interaction plot of span length and width.

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. For bridges with smaller girder spacing, lower tolerance is associated with smaller bridge width. The inverse of this behavior occurs as girder spacing increases. For bridges with larger girder spacing, lower tolerance is associated with larger bridge width. Figure 5-103 - Interaction plot of width and girder spacing. 5.5.10 Service II Tolerance to LD Movements Occurring at the Pier The Service II limit state controlled the tolerable LD support movement at a pier for only 10% of the population (see Figure 5-64). The levels of tolerable LD support movement for the Service II limit state were found to be much larger than those observed for the Strength I limit state for flexure. Figure 5-104 gives the plot of span length versus tolerable LD support movement and shows that bridges may undergo relatively large support movements without violating the Service II limit state. Given the high levels of tolerable support movement, rigorous analysis was not conducted. Only the parameters that influence Service II tolerance were identified. These parameters are span length (L), girder spacing (S), skew, and SD. The effect of the influential parameters is described by the effects plot below (Figure 5-105).

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 multi- girder 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. 5.5.11 Strength I Flexure Tolerance to TD Movements Occurring at the Pier The Strength I Flexure limit state controlled the tolerable TD support movement at a pier for over 65% the population (see Figure 5-65). For these movements, the controlling location was dependent on the orientation of the TD movement as well as the geometric configuration of the bridge.

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 three- span 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). These observations were associated with higher skewed bridges where the TD pier movement towards one side of the bridge resulted in additional negative moment in the exterior girder on the opposite side. The figure below (same as Figure 5-45) depicts this behavior. Figure 5-107 - TD movement moment diagram for highly-skewed bridge. Figure 5-108 gives the plot of span length versus tolerable TD support movement occurring at the abutment. Observations for samples with skew angles less than 20⁰ are highlighted. Samples with skew Location of TD Movement

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. However, this is to be expected since the current criterion was never intended to reflect the tolerable level of this type of TD support movement. Figure 5-108 – Strength I Flexure tolerance to a TD 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), girder spacing (S), and skew were the most influential. The effects plot for these parameters is given by Figure 5-80. Higher tolerance is associated with increased span length while lower tolerance is associated with increased spacing and skew. Individually, width and SD ratio appear to have minimal influence on tolerable support movement.

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) girder spacing and span length, (2) skew and span length, (3) skew and girder spacing, (4) width and girder spacing, (5) girder spacing and SD ratio, and (6) skew and SD ratio. Interactions 1, 5, and 6 were also observed for TD movements occurring at the abutment and pier (see Sections 5.5.2 and 5.5.8). These interactions are not repeated here. The interaction of span length and skew is shown in Figure 5-110. The accompanying scatter plot is given by Figure 5-108. The effect of skew becomes more significant as span length increases. At larger span lengths, lower tolerance is associated with bridges that have higher skew. The same trend was observed for two-span continuous bridges and was traced to the dead load distribution mechanism described in Section 5.1.2.

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. The accompanying scatter plot is given in Appendix C. The effect of skew becomes more significant as girder spacing gets smaller. For bridges with smaller girder spacing, lower tolerance is associated with bridges that have higher skew. Figure 5-111 - Interaction between skew and girder spacing.

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. At smaller girder spacing, lower tolerance is associated with bridges that have a smaller width. As girder spacing increases, however, the inverse is true, and lower tolerance becomes associated with bridges that have a larger width. Figure 5-112 - Interaction plot for width and girder spacing. 5.5.12 Strength I Shear Tolerance to TD Movements Occurring at the Pier The Strength I Shear limit state controlled the tolerable TD movement at a pier for 26% of the population (see Figure 5-65). The controlling member was nearly always located at an exterior girder (Figure 5-113), and always over a support adjacent to the support which displayed the movement.

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 three- span 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. Again, several samples (approximately 5% of the population) were found to have little or no tolerance. All of these bridges were determined to have SLG ratings of 1.0 or greater, however each had an FE rating less than 1.0 and skew greater than 45⁰. This suggests that the dead load distribution mechanism may be the cause (see Section 5.1.2). For these bridges, the dead load shear demands of the FE model were 20-50% higher than the SLG demands.

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. Individually, width does not have a significant effect. However, width was found to affect tolerance when it interacts with other parameters. The effects plot below shows that higher tolerance is associated with increased span length, girder spacing, width, and SD ratio. Lower tolerance is associated with increasing skew.

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. These interactions include: (1) span length and girder spacing, (2) span length and skew, (3) span length and SD, and (4) girder spacing and width. The interaction of girder spacing and span length is shown in in Figure 5-116. The accompanying scatter plot is given by Figure 5-114. As span length increases the effect of girder spacing becomes more significant. Lower tolerance is associated with smaller girder spacing (which is consistent with all of the shear limit states examined for other bridge configurations as well).

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. The accompanying scatter plot is given by Figure 5-114. For longer span bridges, lower tolerance is associated with higher skew. As span length increases, the effect of skew becomes more significant. Figure 5-117 - Interaction plot of skew and span length. Similar interaction behavior exists between span-depth and span length (Figure 5-118), but to a lesser extent. The accompanying scatter plot is given by Figure 5-114. Lower tolerance is associated with

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. Figure 5-118 - Interaction plot of span length and SD ratio. The interaction of width and girder spacing is shown in Figure 5-119. The accompanying scatter plot is provided in Appendix C. For bridges with smaller girder spacing, lower tolerance is associated with smaller bridge width. The inverse of this behavior occurs as girder spacing increases. For bridges with larger girder spacing, lower tolerance is associated with larger bridge width. Figure 5-119 - Interaction plot of width and girder spacing.

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). The levels of tolerable TD support movement for the Service II limit state were found to be much larger than those observed for the Strength I limit state for flexure. Figure 5-120 gives the plot of span length versus tolerable TD support movement and shows that bridges may undergo relatively larger TD support movements without violating the Service II limit state. Given the high levels of tolerable support movement, rigorous analysis was not conducted. Only the parameters that influence Service II tolerance were identified. These parameters are span length (L), girder spacing (S), skew, and SD. The effect of the influential parameters is described by the effects plot below (Figure 5-121). Figure 5-120 - Service II tolerance to a TD support movement occurring at the pier of a three-span continuous steel multi- girder bridge.

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. As discussed throughout Section 5, the parameters that influence superstructure tolerance to support movements will vary depending on the type and location of support movement. In the study of steel multi-girder bridges, span length, girder spacing, skew, and SD ratio were identified as the most influential parameters. Skew has a significant effect on tolerance for both flexure and shear related limit states. Bridges with larger skew angle were found to be less tolerable to movements occurring at the abutment or at the pier. Specifically, little to no shear tolerance and lower flexure tolerance was observed for bridges with higher skew. Additionally, it was discovered that skew in conjunction with diaphragm configuration (particularly for skews greater than 20⁰) results in low levels of tolerable support movement. The effect of higher skew angle becomes even more unfavorable for TD movements. Span length was found to be most influential for the flexure related limit states, although the influence of span length on Strength I Shear tolerance rises for bridges with skew less than 20⁰. Higher Strength I Flexure and Service II tolerance was found to be associated with longer span bridges. Girder spacing affects both flexure and shear related limit states. For the Strength I Shear limit, higher tolerance was

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. SD ratio was found to have an influence on shear tolerance. Lower Strength I Shear tolerance was found to be associated with smaller SD ratio (i.e. deeper girders). The effects of each of the influential parameters can most likely be attributed to their contribution to the stiffness of the superstructure and its elements. Compared to structures that are more flexible, stiffer bridges will experience greater force effects to dead load, live load, and support movement, and therefore stiffer bridges will exhibit less tolerance to support movement. This was evident in the results of this study. For example, longer span bridges have less flexural stiffness than shorter spans, and thus they displayed higher levels of tolerable support movement. Another example is for girder spacing. Larger girder spacing leads to a larger (and therefore stiffer) girder in order to carry the additional flexure load. The lower flexural tolerance to support movement is further reinforced by the fact that live load distribution factors are less conservative (more accurate) for large girder spacing. Comparable relationships between the rest of the influential parameters, the stiffness of the superstructure, and ultimately the tolerance to support movements have been made. Further, tolerance can also be dependent on the ability of the superstructure to evenly distribute load to each of the girders. When loading is not evenly distributed, girders will exhibit less tolerance to LD and TD support movements. Throughout this section, the levels of tolerable support movement observed for the various different bridge configurations, under each of the limit states, were compared to current AASHTO guidance on what constitutes as a “tolerable” support movement. The current guidance listed in the AASHTO LRFD specifications (0.008L for simply supported bridges, 0.004L for continuous) was only intended for LD movements however it is used for comparison purposes when examining TD movements. The current guidance was found to be conservative for many bridges, however, there were a considerable number of bridges where the current guidance was found to be unconservative. This was especially true for bridges with skew greater than 20⁰ and for TD movements (although it is important to note that the current AASHTO LRFD guidance was not intended for these types of movements). Note: guidance was deemed conservative if the observed level of tolerable support movement was found to be greater than what is suggested by AASHTO LRFD. In contrast, the guidance was deemed unconservative if the observed level of tolerable support movement was found to be less than what is suggested by AASHTO LRFD.

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. Despite the current AASHTO LRFD guidance not being intended for TD movements, these movements are still considered. Note: due to the sampling approach employed for this study, roughly one third of the sample population of bridges have skew less than 20⁰. Thus, the percentage given is that of the subset of bridges that have skew less than 20⁰. Table 5-3 - Summary of results for steel-multi-girder bridges. Continuity Type of Support Movement Limit State Comparison with Current AASHTO Guidance (% Failing) Comparison with Current AASHTO Guidance for Bridges with Skew < 20o (% Failing*) Comments Simple- Span LD Support Movement at Abutment Strength I Flexure 0% 0% - Strength I Shear 0% 0% - Service II 0% 0% - TD Support Movement at Abutment** Strength I Flexure 0% 0% - Strength I Shear 37% 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 0% 0% - Two-Span Continuous LD Support Movement at Abutment Strength I Flexure 15% 7% Due to the stiffness effects of shorter spans and larger girder spacing

NCHRP Project 12-103 136 Strength I Shear 1% 0% - Service II 1% 0% - TD Support Movement at Abutment** Strength I Flexure 34% 3% Due to stiffness effects of shorter spans, higher skew, and larger girder spacing, and inability of SLG model to properly account for dead load distribution of highly- skewed 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 5% 0% - LD Support Movement at Pier Strength I Flexure 0% 0% - Strength I Shear 6% 0% - Service II 0% 0% - TD Support Movement at Pier** Strength I Flexure 5% 0% - Strength I Shear 25% 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 1% 0% -

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** Strength I Flexure 22% 13% Due to stiffness effects of shorter spans, higher skew, and larger girder spacing, and inability of SLG model to properly account for dead load distribution of highly- skewed bridges Strength I Shear 11% 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 1% 0% - LD Support Movement at Pier Strength I Flexure 36% 39% Due to stiffness effects of shorter spans and larger girder spacing, and inability of SLG model to properly account for dead load distribution of highly- skewed bridges Strength I Shear 7% 0% - Service II 3% 6% - TD Support Movement at Pier** Strength I Flexure 39% 30% Due to stiffness effects of shorter spans, higher skew, and larger girder spacing, and inability of SLG model to properly

NCHRP Project 12-103 138 account for dead load distribution of highly- skewed 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. ** Although current AASHTO LRFD guidance is not intended for TD movements, these movements are still considered for comparison purposes. Due to the unconservative nature of the current AASHTO LRFD guidance the Research Team proposed three different options for estimating tolerable support movements: 1. Retain the current model and specify range of applicability 2. Update the coefficients of the current model and specify range of applicability 3. Develop a new model for predicting tolerable support movements After discussion with the project panel, option #3 was chosen for estimating tolerable support movement as a function of the ratio of girder spacing (S) to span length (L) as defined in Table 5-4. The results of the regression analysis conducted in Phase II suggested this ratio (S/L) had a significant influence on tolerable support movements under the Strength I and Service II limit states for flexure. As observed from the scatter plot in Figure 5-122, the data shows far less variability when plotted in S/L space (for Strength I and Service II flexure only).

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). In developing the expression to estimate maximum tolerable support movement, a traditional line of best fit through the mean of the data was not desirable as this line would overestimate tolerable support movement for half of the dataset. Instead, what is desired is the lower bound envelope of the dataset. In mathematics, this is called a convex hull or convex envelope. To avoid additional conservatism in the already conservative estimates of maximum tolerable support movement, a curve was fit through the 5th percentile of the data. That is, this curve was fit as an envelope to 95% of the data. The curve and the developed expression are provided in Figure 5-123 below. This expression is valid for simple span and multiple-span continuous steel multi-girder bridges under the Strength I limits of flexure and shear, and Service II stress limits of the bottom flange, for the ranges of applicability noted in Table 5-4.

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. Type of Superstructure Applicable Cross-Section from Table 4.6.2.2.1-1 Tolerance Estimate Range of Applicability Concrete Deck, Reinforced Concrete Slab on Steel Beams a (also b and c, however this expression may provide more conservative estimates for these bridge types as these types are typically constructed outside the range of applicability) 40ft ≤ L ≤ 160ft 5ft ≤ S ≤ 12ft 0 ≤ Skew ≤ 45° 36ft ≤ Width ≤ 72ft 20 ≤ L/d ≤ 30 0.55 ܮܵ