Abutment Modeling SAP2000

G. Pekcan, A. Itani & E. Monzon 1

Title: Seismic Design Recommendations for Steel Girder Bridges with Integral Abutments 1 2 3

Authors: 4 5

Gokhan Pekcan, Ph.D. (CORRESPONDING AUTHOR) 6 Assistant Professor 7 Department of Civil and Environmental Engineering 8 University of Nevada, Reno / 258 9 Reno, NV 89557 10 Ph: 775-784-4512 11 Fx: 775-784-1390 12 E-mail: [email protected] 13 14 Ahmad M. Itani, Ph.D., P.E., S.E., F.ASCE 15 Professor-Steel Structures 16 Department of Civil and Environmental Engineering 17 University of Nevada, Reno / 258 18 Reno, NV 89557 19 Ph: 775-784-4379 20 Fx: 775-784-1390 21 E-mail: [email protected] 22

23 Eric V. Monzon 24 Graduate Research Assistant 25 Department of Civil and Environmental Engineering 26 University of Nevada, Reno 27 Ph: 775-354-6003 28 E-mail: [email protected] 29

30 31 32 33

Word Count: 4920 TEXT + (8)x250 =2000 FIGURES + (2)x250 = 500 TABLES = 7,420 34 35

TRB 2010 Annual Meeting CD-ROM Original paper submittal - not revised by author.


Seismic Design Recommendations for 1

Steel Girder Bridges with Integral Abutments 2 3 4

Gokhan Pekcan1, Ahmad M. Itani2, and Eric Monzon3 5 6 ABSTRACT 7 This paper discusses the results of the longitudinal seismic behavior of straight bridges with integral 8 abutments. Detailed nonlinear finite element (FE) models were utilized to establish the flexibility 9 (translational and rotational) of the steel plate girders and the abutment connections. These connection 10 springs were incorporated in a three dimensional global model of an integral abutment bridge to study the 11 structural dynamics characteristics, as well as the seismic load path and distribution to piles, soil, girder 12 elements. A procedure was demonstrated to determine embedment length of steel girders in the abutment 13 to ensure the connection rigidity and more importantly to ensure that the piles will develop their ultimate 14 flexural capacity. 15 16 INTRODUCTION 17 Integral abutment bridges (IABs) are jointless bridges where the deck is continuous and connected 18 monolithically to abutment wall with a moment-resisting connection. One line (row) of vertical piles 19 under the abutment wall is often used to carry vertical bridge loads. The rationale for integral abutments is 20 clear as presented by Wasserman (2007) and Wasserman and Walker (1996). Throughout the United 21 States, IABs are becoming a design choice for mostly short to moderate spans (Civjan, et al., 2007; 22 Maruri and Petro, 2005). IABs designed and constructed for a variety of configurations have typically 23 performed well when subjected to dead, live and thermal induced cyclic loading. (e.g. Soltani and 24 Kukreti, 1992; Burke, 1993; Kunin and Alampalli, 2000; Arockiasamy et al., 2004; Conboy and 25 Stoothoff, 2005). However, there is a lack of information on the seismic system response of steel bridges 26 with integral abutments. 27 28 Seismic Response Characteristics: Experimental and Analytical Studies 29 The benefits of IABs with respect to their seismic performance compared with conventional simply 30 supported bridges are: increased redundancy, larger damping due to nonlinear cyclic soil-pile-structure 31 interaction (pile support and abutment backfill), smaller displacements, and elimination of unseating 32 potential. Because of the presumed rigid connections between the bridge deck and the abutments, integral 33 bridges are expected to have improved seismic resistance compared to jointed bridges (Hoppe and 34 Gomez, 1996). 35

The highly nonlinear soil-structure and –pile interaction of integral abutment is stated as one of 36 the most complex issues as well as one of the main sources of uncertainty. This interaction is inherently 37 nonlinear and depends on the magnitude and nature of the abutment, soil and pile deformations 38 (translational, rotational). Limited experimental and analytical research has been conducted (e.g.: England 39 et al., 2000; Faraji et al., 2001; Burdette et al., 1999; 2004; Fennema et al., 2005; Khodair and Hassiotis, 40 2005; Hassiotis et al., 2006), however, only quasi-static loading conditions were considered in the 41 experimental studies. The most notable studies that involved field testing of large scale abutments were 42 by Burdette et al. (2000; 2004; 2007), and Hassiotis et al. (2006). In a two-phase experimental 43 investigation Burdette et al. (2000; 2007) investigated experimentally response behavior of H-piles 44 supporting [simulated] integral bridge abutments. Steel H-piles may be oriented for weak or strong-axis 45 bending. In the second phase, Burdette et al. conducted additional tests with H-piles along with precast, 46

1 Asst. Prof., Department of Civil and Environmental Engineering, University of Nevada, Reno, Reno, NV 89557 2 Professor, Department of Civil and Environmental Engineering, University of Nevada, Reno, Reno, NV 89557 3 Grad. Asst., Department of Civil and Environmental Engineering, University of Nevada, Reno, Reno, NV 89557



prestressed concrete piles. This study concluded that the current AASHTO and AISC column equations 1 for the design of steel H-piles had limited applicability and in most cases the equations were inappropriate 2 (Ingram et al, 2003). 3

There are limited analytical studies that considered explicitly the seismic response characteristics 4 of integral abutment bridges (e.g. Goel, 1997; Dehne and Hassiotis, 2003). The main objective of the 5 study by Goel (1997) was to measure the vibration properties of a two-span concrete bridge from its 6 motions recorded during actual earthquake events. Data was used in conjunction with an analytical model 7 to investigate how abutment participation affected the vibration properties of bridges with integral 8 abutments. It was noted that the abutment flexibility was an important element in seismic design of 9 bridges with integral abutments. In particular, a more flexible abutment would lead to higher deformation 10 demands on other lateral-load resisting elements. 11

In fact, modeling the contribution of bridge abutments to overall seismic response has been the 12 focus of significant research in the past decade. Many studies have shown how the abutment response 13 influences the response of short-and medium-length bridges. Realistic and accurate modeling of the 14 abutment-soil interaction becomes even more important in case of integral abutment bridges. One of the 15 major uncertainties in the design of IAB bridges are known to be the reaction of the soil behind the 16 abutments and next to the foundation piles, especially during thermal expansion and seismic loads. These 17 soil reactions along with the soil-pile interaction are inherently nonlinear. Tegos et al. (2005) noted that 18 the dynamic response of the structures in the longitudinal direction depends on the overall dynamic 19 stiffness of the deck-abutment-foundation system. More drastic reduction of seismic demand is generally 20 observed when the abutment stiffness is activated. The study by Dehne and Hassiotis (2003) concluded 21 that accurate soil-structure interaction modeling was required to evaluate the effects of longitudinal and 22 transverse earthquake excitation on the response of integral abutment bridges that will allow reliable 23 capacity and demand assessments. It is particularly noted that integral abutment design depends on the 24 connection of the superstructure to its abutment for the transfer of horizontal forces. The connection must 25 transfer such forces without damage to the piles or the soil behind the abutment. As such, the design (and 26 modeling) of the soil properties is of the utmost importance. Faraji et al. (2001) developed a three-27 dimensional finite-element model of an integral abutment bridge. The model consisted of a grillage model 28 of the deck, abutment, beam-column elements to model the piles and finally soil springs with nonlinear p-29 y properties to model the soil-pile-abutment-structure interaction. Although this study focused on loading 30 cases due to differential temperature, remarks were made regarding the impact of skew alignments on the 31 forces and moments at the abutment/superstructure joint, and the seismic response of long-span integral 32 abutment bridges. 33

This paper presents the preliminary findings recommendations of an on-going study that 34 investigates the longitudinal and transverse seismic response behavior of straight and skew steel bridges 35 with integral abutments. In order to establish realistic guidelines for the modeling of steel girder to 36 abutment connection, first, detailed finite element (FE) models of a benchmark bridge (Wasserman and 37 Walker, 1996) were developed. The connection models were incorporated in a three dimensional global 38 model of an integral abutment bridge to study the structural dynamics characteristics, as well as the load 39 path and distribution to piles, soil, girder elements. A procedure was demonstrated to determine 40 embedment length of steel girders in the abutment to ensure the connection rigidity and more importantly 41 to ensure that the piles develop their flexural capacity. 42

43 FINITE ELEMENT (FE) MODELING OF AN INTEGRAL ABUTMENT CONNECTION 44 The benchmark bridge is a three-span steel-girder that was based on the example presented by 45 Wasserman and Walker (1996). The total deck width is 44 ft and total length is 426 ft. The end spans are 46 105 ft long and the main span is 216 ft long. The superstructure is composed of four composite steel plate 47 girders spaced at 11.75 ft and 9 in. thick deck slab. The piers are single column with diameter of 60 in. 48 and clear height of 25 ft. The cap beams are 75 in. deep and 85 in. wide. Cross-frame spacing at end spans 49 is 24 ft and at main span is 22 ft. The intermediate cross-frames are L5x5x5/8 while the support cross-50 frames are 2L5x5x5/8. The basic geometry of the bridge is shown in Figure 1. A typical detail at the 51



integral abutment was selected as shown in Figure 2. A detailed continuum model of concrete deck and 1 steel girder along with the abutment is modeled using ADINA (2008) as shown in Figure 3. The 2 flexibility of the girder-to-abutment connection detail is determined in terms of six (three translational, 3 three rotational) springs lumped at the abutment face. For this purpose, twelve monotonic loading cases 4 were conducted and the results of these cases are summarized. 5

6

7

8 Figure 1 Plan and cross-sectional view of the benchmark bridge Wasserman and Walker (1996) 9

Assumptions for the FE Analysis 10 Two models were developed; the first model is referred to as “fixed,” which essentially means that the 11 connection of the embedded girder and abutment is rigid. The second model is called “flexible” model. 12 in which the embedded girder has compression only springs at every point of contact with the concrete 13 material inside the abutment. The displacements and rotations were applied at the tip of the girder (where 14 an inflection point is assumed approximately) at the centeroid of deck and girder. The reactions and 15 displacements were measure at this location. Then the reactions and displacements of the flexible model 16 were subtracted from those of fixed model. This removes the flexibility of the cantilever part of the 17 girder and deck, therefore provides the springs properties at the end of the girder. These spring elements 18 can therefore be used to represent the stiffness of girder-to-abutment connection. It is noted that the 19 following were assumed in the development of the FE model: 20 1. The interfaces between the concrete deck-abutment, and between the embedded steel girder-abutment 21

are located at the intersection of nodes between the elements of deck and abutment. It is assumed that 22 there is no concrete crushing and tension resistance is neglected. Since during an earthquake the gap 23 can open and close, no shear resistance is assumed at this interface. Interface of the concrete deck 24 and the abutment is defined with plastic material. Nonlinear truss (compression-only) elements are 25 used at common nodes of deck and abutment. 26

2. Fix boundaries were used for the abutment boundaries associated with the pile and abutment soil 27 (Figure 2). Soil and pile stiffnesses will be accounted for explicitly in the global system model. 28



3. Steel girder is modeled with linear elastic material properties. However, the stresses in the steel girder 1 are monitored and the first yield of the steel as well as the subsequent ones is recorded. 2

4. The maximum compressive strength of concrete is assumed to be 4 ksi with a modulus of elasticity of 3 3,600 ksi. The modulus of elasticity of steel is 29,000 ksi. The yield stress of steel is 50 ksi. Although 4 the steel girder is modeled elastically, the yield stress is needed to monitor the sequence of yielding in 5 steel girder. 6

7

8 9

10 Figure 2 Plan and elevation view at the integral abutment 11



1 Figure 3 Isometric view of the FE model and girder detail inside the abutment 2

Summary of FE Analysis Results 3 The FE models were subjected to six monotonic loading conditions; the displacements and rotations were 4 applied at the center-of-geometry of the free end of the deck-girder assembly. The reactions and 5 displacements were measured at this location. The reaction-displacement of the “flexible model” was 6 subtracted from those of “fixed model.” Therefore, the flexibility of the cantilever portion of the assembly 7 was excluded, hence providing the “spring” properties at the girder-to-abutment connection. The action-8 deformation curves so-obtained for the rotation about the transverse axis (parallel to the abutment wall) 9 along with the associated Von Mises stress distributions at the first yield of the embedded steel girder are 10 shown in Figure 4. There is a total of six (6) unsymmetrical nonlinear springs that will account for the 11 variation of location of neutral axis in an equivalent sense. Because of asymmetry and nonlinearity in the 12 force-deformation curves the location of neutral axis changes as the strain increases. 13

The nonlinearity of the concrete interface is modeled as explained earlier, and during the 14 pushover loading, the Von Mises stresses in the embedded steel girder were monitored also to capture the 15 sequence and propagation of yielding in steel. The percentage of yielded [finite] elements is used as an 16 indicator of the distribution of plasticity in steel. On the action-deformation relations of the equivalent 17 springs in the embedded region, the dashed line is used to represent the force-displacement of the entire 18 system, including girder and slab, whereas the solid line is the force-displacement in the embedded region 19 only. This was obtained by subtracting the flexibilities of the flexible and fixed models as explained 20 earlier. Also, the first yield of steel girder and the deformation at which 20% of the embedded steel girder 21 yielded, are marked in Figure 4. 22 23 THREE-DIMENSIONAL (3D) GLOBAL MODELS 24 Detailed 3D models of bridges with integral abutments shown in Figure 1 are developed to facilitate the 25 investigation of general structural dynamics characteristics. Several boundary conditions have been 26 identified to establish the effects on the modal response of the bridges in comparison to the most realistic 27 condition that incorporates the springs presented earlier. 28 29 Deck slab, girders, cap beams and columns 30 The bridge model geometry and components were defined using the Bridge Modeler (BrIM) option in 31 SAP2000 (CSI, 2008). The deck slab was modeled as shell elements while girders, cap beams and 32 columns were modeled as beam elements. The shell elements were located at the center of gravity of deck 33 slab. In Figure 5, the girders are shown to be located at the center of top flange. This was due to internal 34 automation in SAP2000 when BrIM is used in modeling the bridge superstructure but the properties are 35 actually transformed to the center of gravity of girder. Note that the center of gravity of the plate girder 36 may vary along the span. Locating the girder beam element at the center of top flange makes the 37

Web stiffener



modeling easier since the center of top flange will not vary along the span. The cap beams were defined 1 with gross section properties. Effective section properties were assigned to the columns. 2

3

4 Rotation about yneg Rotation about ypos 5 6 Figure 4 Moment-rotation response at the integral abutment and correspond stress distribution on 7 the girder inside the embedded section 8



1

2

3

4

Figure 5 3D view and details of the SAP2000 models 5

6 7 8

Table 1 Effective stiffnesses at first yield of girder-abutment connection 9

DOF Unit Description Kpos Kneg Kmod U1 kip/in vertical action 496 219 219 U2 kip/in longitudinal action 13,465 20,068 13,465 U3 kip/in transverse action 181 181 181 R1 kip-in/rad rotation about vertical axis 1.08E+08 1.08E+08 1.08E+08 R2 kip-in/rad rotation about longitudinal axis 1.94E+06 1.94E+06 1.94E+06 R3 kip-in/rad rotation about transverse axis 1.68E+08 3.14E+08 1.68E+08

Kpos = effective stiffness at positive region of backbone curve at first yield Kpos = effective stiffness at negative region of backbone curve at first yield Kmod = effective stiffness used for modal analysis

10

Soil-pile springs

Pin supports (representing the location of pile inflection point)

Rigid frame elements

HP10x42 pile

Girder-Abutment Springs

Soil springs



Girder-abutment connection 1 The girder-abutment connection is represented by a 6-DOF spring with 3 nonlinear translational 2 properties and 3 nonlinear rotational properties. The spring properties were obtained from the FE analyses 3 of the girder-abutment connection as presented earlier. For the purpose of modal analysis, the elastic 4 stiffnesses used were the effective stiffness at first yield as summarized in Table 1. For DOFs where the 5 backbone curve is asymmetric (U1, U2 and R3), the smaller stifnesses were used in modal analysis. 6 7 Abutment soil passive resistance 8 The stiffness property of the soil behind the abutment was obtained from Caltrans’ Seismic Design 9 Criteria (SDC, Caltrans 2006). It assumes a uniform soil passive pressure distribution along the abutment. 10 The initial abutment stiffness is given by 11

5.5

/20

hw

ft

inkipKabut (1) 12

where, w is the abutment width and h is the abutment height. The initial stiffness of 20 kip/in/ft was 13 assumed based on the results of large-scale abutment testing at University of California, Davis (UC 14 Davis). This stiffness is scaled by the ratio (h/5.5) because the height of the abutment tested at UC Davis 15 was 5.5 ft. The maximum soil passive pressure that can be developed behind the abutment is 5.0 ksf. 16 Thus, the total static passive force is given by 17

5.50.5

hksfAP e (2) 18

where, Ae is the effective abutment area. Similar to initial stiffness, the maximum soil passive force is 19 scaled by (h/5.5). The soil resistance is distributed to the four girders, the stiffnesses of the soil springs 20 connected to exterior and interior girders are 400 kip/in and 460 kip/in respectively with yield 21 deformation at 2.69 in. The difference between the soil properties at exterior and interior girder is due to 22 difference in tributary area. The ultimate soil displacement in the figure is 12.9 in. which is 10% of the 23 abutment height. This is the code recommended displacement for cohesive soils. 24

In AASHTO Guide Specification (2007), the soil passive resistance is dependent on the type of 25 backfill used. For cohesionless, non-plastic backfill with fines content < 30%, the soil passive pressure is 26 pp = 2Hw/3 ksf per foot of wall length. However, for cohesive backfill with clay fraction > 15% and 27 estimated undrained shear strength > 4 ksf, the soil passive pressure is pp = 5 ksf. If the stress and strength 28 parameters (c and ) are known, the passive force may be computed using accepted analysis procedures. 29 The above parameters were not readily available thus the Caltrans’ SDC provisions were used in defining 30 the soil stiffness properties. For modal analysis, only half of the initial stiffnesses was assigned to the 31 abutment soil springs. This is due to the fact that the soil springs are compression only springs. 32 33 Soil-pile interaction 34 The soil-pile properties used in this study were also adopted from Wasserman and Walker (1996). Each 35 abutment is supported on seven HP10x42 steel piles. In the analytical model, beam elements with lengths 36 equal to 12.4 ft were used to represent these piles. The 12.4-ft length was based on the location of zero 37 moment in the pile which was measured from the pile head. The soil-pile interaction was represented by 38 2-DOF springs located at 0 ft, 5 ft, and 10 ft below the pile head. Figure 6 shows the p-y curves that 39 defines these springs. In modal analysis, the elastic stiffnesses used are 24 kip/in, 105 kip/in, and 145 40 kip/in for springs located at 0 ft, 5 ft, and 10 ft, respectively. Due to lack of data, it was assumed that the 41 p-y curves in the transverse direction are the same as that in the longitudinal direction. 42



1 Figure 6 p-y Curves for Soil-Pile Interaction 2

MODAL ANALYSES 3 Various models were developed to study the effect of connection flexibility at the integral abutment on 4 the global system behavior in relation to the flexibilities associated with the surrounding soil and 5 supporting piles. For this purpose, a total of seven different cases were identified (Table 2). In the table, 6 “rigid” implies that the component was assigned a large stiffness, “free” means zero stiffness, and 7 “flexible” means actual (realistic) stiffness values were used for the components listed. It is noted that, for 8 Case 6 and 7, steel piles are modeled such that they are in strong axis bending with respect to the 9 longitudinal direction of the bridge. The mode shapes were identified and modal participating mass ratios 10 for each mode in all of the cases were recorded. 11

Among the seven cases, Case 1 and 2, Case 3 and 4, and Case 6 and 7 are to isolate the effect of 12 the connection flexibility on the overall system dynamics. Particularly the second pair establishes those 13 effects in the absence of abutment soil passive resistance, and the first pair assumes infinite resistance 14 from the abutment back soil. It is important to note that in Case 1 and Case 3 where infinitely rigid 15 connection is assumed, the first modes of vibration were in fact not significant modes both occurring with 16 T = 0.623 sec. When the connection flexibility is introduced, however, Case 2 and Case 4 result in 17 remarkably similar modal response. Further comparison of modal responses between Case 2 and Case 5 18 confirm the fact that the abutment back soil contribution to the overall global response of integral 19 abutment bridges is negligible. In other words, among the cases where abutment back soil resistance is 20 considered as rigid, free, or flexible where other conditions were kept the same, the modal response did 21 not change significantly. However, comparisons between Case 1 – Case 2, and Case 3 – Case 4 clearly 22 indicate the significant effect of the consideration of connection flexibilities on the global response 23 behavior, however when no soil-pile interaction is modeled. 24



The most striking observation is the change in the global system dynamics due to soil-pile 1 interaction compared to all other cases. Significant modal coupling occurs in Mode #1 at a much longer 2 period, which involves predominantly transverse displacements and deck rotations. While the longitudinal 3 mode occurs at a very small period in Case 5 (no soil-pile interaction, Mode #17 with 0.098 sec), it takes 4 place at a significantly longer period of vibration when soil-pile interaction is considered in Case 6 (Mode 5 #5 with 0.35 sec). Finally, the comparison of Case 6 and 7 show that there is essentially no difference 6 between modal periods and participation ratios due to connection flexibility. Therefore, the effect of soil-7 pile interaction on the overall system response characteristics clearly is the most significant and governs 8 over the effect of connection flexibility. 9

10 Table 2 Various boundary conditions investigated 11

Case Abutment-Soil Girder-Abutment Connection Soil-Pile Interaction 1 rigid rigid rigid 2 rigid flexible rigid 3 free rigid rigid 4 free flexible rigid 5 flexible flexible rigid 6 flexible flexible flexible 7 flexible rigid flexible

12 ANALYSIS OF ABUTMENT FORCES 13 Nonlinear pushover analyses were conducted to assess primarily the load path, hence the distribution of 14 abutment force to various components. For this purpose, the abutment-soil springs were modeled at four 15 locations along the abutment height. Previously, only one abutment-soil spring was used and it was 16 aligned with the girder beam element. Comparisons of the modal properties of these two models show 17 that the effect of the number of abutment-soil springs on global behavior is minimal but will have 18 considerable effect on local distribution of forces. The difference between modal periods and modal 19 participation ratios is in the order of 1% to 5%. The moment demand on the bridge superstructure, 20 however, was observed to be sensitive on the number of abutment-soil springs used. The four abutment-21 soil springs was deemed appropriate for the purpose of obtaining the accurate superstructure moments. 22 The Mode #5 (longitudinal translation) was used as the pushover load for both Case 6 and Case 7. Since 23 the models were pushed only in the longitudinal direction, full compression stiffness was assigned to the 24 abutment-soil springs in the direction of the push and zero stiffness was assigned at the other abutment. 25 The analyses suggest that the “weak link” in terms of longitudinal capacity are the piles. Therefore, a 26 procedure is demonstrated to determine the required embedment length of the steel girders in to the 27 abutment, calculated based on the corresponding bridge superstructure moments and that will ensure the 28 development of plastic moment capacity of the piles. 29 30 Girder-to-abutment embedment length 31 The embedment length of steel girders in to was calculated based on the mechanism (Figure 7) proposed 32 by Shama et al. (2002). This mechanism assumes a simplified stress mechanism and was developed for 33 steel-pile embedment in to concrete cap beam or abutment. The resistance to external moment M is to 34 come from the couple created by bearing stresses on concrete. The concrete stress block force Cm can be 35 evaluated as 36

embfcm lbfC '5.0 (3) 37

where, is a factor applied to f’c; is a factor for the depth of stress block; f’c is the concrete compressive 38 strength; bf is the flange width of the steel section (girder flange width in this case); and lemb is the 39 embedment length of steel section into the concrete. The couple lever arm is 40



5.01 embljd (4) 1

Assuming = 1, jd can be taken as 0.5lemb. The moment capacity of the connection is then 2

jdCM mc (5) 3

where is the strength reduction factor and is equal to 0.9. By substituting (3) and (4), (5) can be 4 rewritten as 5

2'25.0 embfcc lbfM (6) 6

To maintain integrity of the connection, the MM c criteria must be satisfied. Thus, the equation for 7

embedment length is given by 8

fcemb

bf

Ml

'2

(7) 9

For a maximum concrete strain cu of 0.003, the stress block factors and can be taken as both equal to 10 0.85. Applying the factor, (7) can be further simplified as 11

fcemb

bf

Ml

'48.2 (8) 12

13

Figure 7 Simplified mechanism for steel section embedded in concrete 14

Case 6 – Realistic girder-abutment connection stiffness 15 The total base shear was 2,103 kips as illustrated in Figure 8a. This base shear corresponds to instance 16 where the pile plastic moment was reached at Abutment 1. The plastic moment capacity of each HP10x42 17 pile is 1,738 kip-in. The maximum pile moments were observed at Abutment 1 but the maximum 18 superstructure moments were observed at Abutment 4. As shown in Figure 8a, 79% of the total base shear 19 is at the Abutment 4. Of this base shear, 86% is due to the abutment-soil passive resistance and 14% is 20 due to the soil-pile interaction. The bents are taking a small portion only of the total base shear which is 21 4% at each bent. The remaining 13% of the total base shear is taken by Abutment 1 which is primarily 22 due to the soil-pile resistance. The girder bending moments due to dead load and pushover along the 23 bridge length and on individual girders were recorded. At Abutment 1, the bending moment on the entire 24 bridge section was 41,031 kip-in (positive moment), on exterior girders it was 10,518 kip-in, and on 25 interior girders it was 9,998 kip-in. At Abutment 4, the bending moment on the entire bridge was 86,243 26

M

P

F

Cm

Cm

f'c

jd

lemb



kip-in (negative moment), on exterior and interior girders, it was 21,297 kip-in, and 21,824 kip-in, 1 respectively. Note that, as mentioned above, the pile plastic moment was reached at Abutment 1. 2 However, the design moments to be used for calculating the girder-to-abutment embedment lengths are 3 the moments at Abutment 4 as they are considerably larger than the moments at Abutment 1. The 4 maximum of exterior and interior girder moments is used to determine the embedment lengths. 5 6

7

(a) 275 kips (13%)

81 kips (4%)

2,103 kips 91 kips (4%)

1,656 kips (79%)

(b) 275 kips (13%)

82 kips (4%)

2,136 kips 92 kips (4%)

1,687 kips (79%)

Figure 8 Distribution of total base shear; (a) Case 6, (b) Case 7 8

Case 7 – Infinitely rigid girder-abutment connection stiffness 9 The total base shear was 2,136 kips as illustrated in Figure 8b which implies that the effect of girder-10 abutment connection flexibility is insignificant as the difference in modal properties and base shears is 11 very small (in the order of 1% to 5%). The distribution of base shear among the abutments and bents is 12 similar to that in Case 6 where Abutment 4 is taking most of the applied loads. Also similar to Case 6, the 13 pile plastic moment was reached at Abutment 1 but the maximum superstructure moments were observed 14 at Abutment 4. At Abutment 1, the total bending moment on the entire bridge section was 41,087 kip-in 15 (positive moment), on exterior and interior girders it was 10,532 kip-in, and 10,011 kip-in, respectively. 16 At Abutment 4, the corresponding bending moments were 88,404 kip-in (negative moment), 21,841 kip-17 in, and 22.361 kip-in. 18 19 Calculated embedment lengths 20 The girder-to-abutment embedment length is determined based on the superstructure moments observed 21 at Abutment 4 which are negative moments. It is noted that these moments corresponds to the instance at 22 which the flexural capacity of piles are reached due to modal pushover in the critical longitudinal 23 direction. For the bridge considered in this study, the girder bottom flange width bf is 22 inches and the 24 concrete compressive strength f’c is 4 ksi. Thus, the required embedment length (equation (8) for Case 6 is 25 39 inches. For Case 7, the required embedment length is 40 inches. These are about 30% larger than the 26 provided embedment length of 30 inches which was also used in the finite element analysis of the girder-27 abutment connection. 28 29 SUMMARY, RECOMMENDATIONS AND FUTURE RESEARCH 30 This paper discusses the results of the longitudinal seismic behavior of straight bridges with integral 31 abutments. Detailed nonlinear finite element (FE) models were utilized to establish the flexibility 32 (translational and rotational) of the steel plate girders and the abutment connections. These connection 33 springs were incorporated in a three dimensional global model of an integral abutment bridge to study the 34 structural dynamics characteristics, as well as the seismic load path and distribution to piles, soil, girder 35 elements. A procedure was demonstrated to determine embedment length of steel girders in the abutment 36 to ensure the connection rigidity and more importantly to ensure that the piles will develop their ultimate 37 flexural capacity. Nonlinear pushover analyses were conducted to assess primarily the load path, hence 38 the distribution of abutment force to various components. The results of these analyses indicated that the 39 piles play a detrimental role in the longitudinal response of bridges with integral abutments. The piles 40

Abutment 1 Abutment 4



represent the “weak link.” Therefore, a procedure is demonstrated to determine the required embedment 1 length of the steel girders in to the abutment, calculated based on the corresponding bridge superstructure 2 moments and that will ensure the development of plastic moment capacity of the piles. Further analysis 3 will investigate the load path and the seismic response in the transverse direction of the bridge. The study 4 will also investigate the seismic behavior and response of straight and skew bridges and compare it to the 5 behavior of bridges using seat type abutments. 6

7 ACKNOWLEDGEMENTS 8 Partial funding for the study presented in this paper was provided by the Federal Highway Administration 9 (FHWA) through a contract (DTFH61-07-D-00004 – Task Order 003) with the HDR Engineering, Inc. 10 The authors would also like to acknowledge Mr. Edward Wasserman, and Mr. Vasant Mistry of FHWA, 11 and Mr. John Yadlosky of HDR Engineering, Inc. for their valuable comments and feedback. Any 12 opinions, findings, and conclusions expressed in this paper are those of the authors and do not necessarily 13 reflect the view of the sponsor. 14 15 REFERENCES 16

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Abutment Modeling SAP2000