FB-MULTIPIER vs ADINA VALIDATION MODELING

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2 FB-MULTIPIER vs ADINA VALIDATION MODELING 1. INTRODUCTION 1.1 Purpose of FB-MultiPier Validation testing Performing validation of structural analysis software delineates the capabilities and limitations that a given structural analysis program possesses. 1.2 Other FEA software employed (ADINA) The validation process was carried out by modeling given finite element models in both FB-MultiPier and ADINA, and comparing the results of these models under various load cases. 1.3 Modeling Goal (Dynamic Validation Model) The objective of this investigation was to develop and document a dynamic validation model of somewhat realistic complexity and scale. Accordingly, a multiple pier model, with piers replicating the structural characteristics of a physical bridge structure, were investigated. This model validation was performed using linear analysis, while ignoring the extensive soil features available in the FB-MultiPier program. Validation of the soil modeling features is presented in a separate report. 1.4 Validation Approach However, before a dynamic validation model of significant complexity was built, other simpler models were created and tested in order to simplify certain anticipated structural interactions under a given loading. More specifically, the validation process was conducted so that certain individual structural characteristics of the models within FB-MultiPier were isolated; this approach minimized any uncertainty regarding which structural responses were significantly contributing to computed response quantities. Hence, the validation process consisted of constructing and testing structural models of increasing complexity. The separate models listed below constitute the structural models tested during this validation process, and are discussed in detail later in this report. A single pile model was created and tested first, followed by the creation and testing of a four-pile with pile cap model. Next, a pier model was created and tested. Finally, a multiple-pier model was developed and tested. The aforementioned models are discussed in order of increasing complexity below. 2. DESCRIPTION OF SPECIALTY MODELING COMPONENTS IN FB- MULTIPIER The following is a description of special provisions/elements that are automatically implemented into FB-MultiPier models in an attempt to either more realistically transfer load from one portion of a given structure to another, or to simulate stiffness found in physical structures that may not be present in certain other finite element analysis software when using standard element formulations. 1

3 2.1 Artificial Torsional Stiffness Introduced in Pile Cap Shell Element Corner Nodes of FB- MultiPier The pile caps in FB-MultiPier pier models consist of a grid of nine-node shell elements. However, a drilling degree-of-freedom stiffness is not present in the standard shell element formulation. Hence, shell elements FB-MutliPier are supplied with out-of-plane torsional stiffness to the corner nodes (see Figure 1). The intent of this extra stiffness provision is based on the extreme thickness of pile caps that typically occurs in real-world pier applications. Pile cap thicknesses can exceed 10 ft, which is more than thick enough than that required to develop out-of-plane torsinal stiffness in a structural member. Figure 1. Out-of-Plane Torsional Stiffness Added to Four Corner Nodes of Each Shell Element in Pile Cap 2.2 Quad-Pod Elements Four beam elements extend from each FB-MultiPier pier column bottom node to four adjacent pile cap nodes. The pier column end of these elements permits transfer of moments, whereas the pile cap end of these elements does not. These quad-pod elements in FB-MultiPier models form the sole structural connection that links the pier column to the underlying pile cap (see Figure 2). More specifically, the bottom node of a given pier column in FB-MultiPier is not structurally tied to the immediately underlying pile cap node. The purpose of the quad-pod elements is to more evenly distribute pier column loads to the pile cap, or alternatively stated, prevent stress concentrations. 2

4 The exact connectivity (the exact designation of the beginning and end nodes) of the quadpods and the corresponding stiffness of the three member axes varies from model to model. Hence, a user wishing to perform validation must examine the output file generated by FB-MultiPier upon running analysis of a given model and search for SUBSTRUCTURE MEMBER CONNECTIVITY. The quad pod elements are designated element numbers 1-n where n is four times the number of pier columns. The quad-pod elements always occur in groups of four. The user may then return to the interface and visibly verify the geometric configuration of the quad-pod elements. Regarding the stiffness of the quad-pod elements, a user wishing to perform validation using accurate stiffness values may search the aforementioned output file using the query PROPERTIES FOR CONNECTOR ELEMENTS. This particular section of the output file describes the assigned moments of inertia, modulus of elasticity, etc. of the quad-pod elements. In general, the stiffness values of these elements are amplified relative to that of other ordinary elements in typical pier structures. Finally, the mass of these elements is assigned as zero so as to minimize dynamic effects due to mass contributions from specialized members, while still providing stiffness similar to real-world pier structures. Figure 2. Quad-Pod Elements Connectivity - Pier Columns to the Underlying Pile Caps. 2.3 Rigid Horizontal Link Elements along Pier Cap Beam For every bearing defined in a given FB-MultiPier model, a rigid link (of beam element type) spans from the pier cap beam centerline to the center-bottom of the bearing pad, as shown in Figure 3. The horizontal rigid links are used to realistically place the base of the pad elements (bridge bearing pads) within the model, with respect to the geometry found in real bridge structures. The stiffness of the horizontal rigid links is assigned such that any load coming from the superstructure (or described more locally, the bearing pads) will be transferred to the pier cap beam 3

5 with out contributing any additional displacement, and vice versa. The mass of the horizontal rigid links is assigned as zero so as to minimize dynamic effects due to mass contributions from specialized members, while still transferring any conceivable real-world loading to the other portions of a given pier structure. Figure 3. Pier Cap Beam Showing Horizontal Rigid Link Connectivity Pier Cap Beam to Bearing Pad Element 2.4 Bearing Pad Elements Bearing pad elements act to transfer forces between the superstructure and substructure of a given model, and vice versa (see Figure 4). More specifically, the bearing pad elements span between the respective horizontal rigid link outer node and the respective, vertically aligned transfer beam node (transfer beams are described in Section 2.5, below). Individual bearing pads may either be fixed, released, or custom-defined with respect to any or all of the three translational and any or all of the three rotational degrees of freedom. Additionally, because of the aforementioned horizontal rigid link elements, up to two rows of separately configured bearings may be placed (at realistic distances from the pier cap beam centerline) on a single pier cap beam; it is implied here that such a structure contains three or more piers. For purposes of validation, these elements were modeled as constraints in ADINA. For example, for a bearing set consisting of translationally fixed and rotationally released bearings in FB-MultiPier; a set of geometrically equivalent bearings would be created in ADINA constraining the top node of the bearing elements to match the translations of the respective bottom node. Furthermore, because the bearings were 4

6 modeled using a system of constraints, no actual elements are defined between the top and bottom bearing pad nodes in ADINA. Figure 4. Pier Cap Beam Denoting Bearing Pad Element Connectivity Horizontal Rigid Link to Transfer Beam 2.5 Transfer Beam Elements The transfer beam (see Figure 5) consists of beam elements that act to transfer forces to each of the bearing pad elements from the superstructure. Conversely, the transfer beam may accumulate all of the bearing pad element forces and transfer these forces to the superstructure. Regarding connectivity, the transfer beam of a given FB-MultiPier model connects all of the bearing pad elements in a given single row to a vertical link, which is described below. The stiffness of a given transfer beam may be further delineated as a combination of the cross-sectional area, moments of inertia, and modulus of elasticity. Alternatively, the transfer beam properties can be custom-defined to promote modeling of the desired span-end (e.g., diaphragm) rigidity. The mass of these elements is assigned as zero so as to minimize dynamic effects due to mass contributions from specialized members while still transferring any conceivable real-world loading to the other portions of a given pier structure. 5

7 Figure 5. Pier Cap Beam Denoting Transfer Beam Connectivity Bearing Pad Element to Vertical Link 2.6 Vertical Link Elements The vertical link consists of a beam element and acts to transfer forces from the superstructure beam to the transfer beam (see Figure 6). The main purpose of the vertical link is to transfer load from the center of the transfer beam up to the mid-height of the superstructure, where it connects to the spine model of the superstructure. The moments of inertia of the vertical link are assigned as the same values as those of the superstructure beam. However, the orientations of the local material axes differ between these two members, as shown in Figure 7. The mass of this element is assigned as zero so as to minimize dynamic effects due to mass contributions from specialized members while still transferring any conceivable real-world loading to the other portions of a given pier structure. 6

8 Figure 6. Pier Cap Beam Denoting Vertical Link Connectivity Transfer Beam to Superstructure Beam 7

9 Figure 7. Material Axes Orientation of Vertical Link Relative to that of the Superstructure Beam 8

10 3. VALIDATION MODEL DESCRIPTIONS/RESULTS The following is a description of the various validation models that were tested during this study, as well as a comparison of the displacement output between ADINA and FB-MultiPier models. As aforementioned, the models are presented in order of increasing complexity. Wherever feasible, a comparison is also made between the software output and theoretical displacements. 9

11 3.1 V001 Series Models; Single Pile Models Model 1; Single Pile Model Static Load - Flexure Description: A single pile with fixed base; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Loading: A lateral load of 10 kips was statically applied to the top node to test pile flexure. Software Comparison: 0 20"x20" Prestressed Concrete Pile - X-Displacement Profile Depth (-20 ft = Point of fixity) (ft) Lateral Deflection (in) (a) (b) Figure 8(a). Physical Model Description and 8(b). Pile X-Displacement Profile Percent Difference Comparison: Table 1. Displacement Comparisons; Theoretical and Relative Data Source Max Displacement (in) Theoretical Percent Difference (%) ADINA Software Percent Difference (%) ADINA FB-MultiPier FB MultiPier Theory* *- Tip Deflection of a Cantilevered Bernoulli Beam ( = PL 3 /3EI); where is the tip displacement, P is the applied load, L is the length of the member, E is the modulus of elasticity, and I is the moment of inertia. 10

12 Model 2; Single Pile Model Static Load - Torsion Description: A single pile with fixed base; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Loading: A Z-Axis moment of 100 kip-ft was statically applied at the top node to test pile flexure. Software Comparison: Percent Difference Comparison: Figure 9. Physical Model Description Table 2. Displacement Comparisons; Theoretical and Relative Data Source Max Displacement (rad) Theoretical Percent Difference (%) Software Percent Difference (%) ADINA E FB-MultiPier E Theory* E *- Tip Deflection of a Pure Torsion Beam Member ( = TL/GJ); where is the tip rotation, T is the applied moment, L is the length of the member, G is the shear modulus, and J is the torsional moment of inertia. 11

13 3.1.3 Model 3; Single Pile Model Dynamic Load - Flexure Description: A single pile with fixed base; 30 length; 24 Diameter with 0.5 thickness; steel; ksi modulus of elasticity Loading: A lateral load of 10 kips was dynamically applied to the top node to test pile flexure dynamic behavior. Software Comparison: 3 Pile 3 X-Displacement 2 Lateral Deflection (in) (a) 2 ADINA FB-MultiPier time (sec) (b) Figure 10(a). Physical Model Description and 10(b). Pile X-Displacement vs Time Percent Difference Comparison: Table 3. Displacement Comparisons; Relative Data Source X-Displacement at Time = 10 sec (in) Software Percent Difference (%) ADINA FB-MultiPier *- For software comparison, the value of displacement with the smallest absolute value is taken is the denominator in the percent difference calculation. 12

14 3.2 V002 Series Models; Single Pile Cap with Four Piles Models Model 4; Single Pile Cap with Four Piles Model Static Load - Flexure Description: Piles: A four-pile model with fixed bases; 30 length; 24 diameter pipe pile with 0.5 thickness; Steel; ksi modulus of elasticity Pile Cap: A 4 thick pile cap; concrete; 4442 modulus of elasticity; finite element mesh consisted of 6 x6 shell elements; torsional properties were enabled in the FB-MultiPier model (see Sec 2.1) Loading: A lateral load of 100 kips was statically applied at the pile cap mid-plane to test pile group behavior. Software Comparison: (a) (b) Figure 11(a). Physical Model Description and 11(b). Typical Pile X-Displacement Profile Percent Difference Comparison: Table 4. Displacement Comparisons; Relative Data Source Max X-Displacement (in) Software Percent Difference (%) ADINA FB-MultiPier *- For software comparison, the value of displacement with the smallest absolute value is taken is the denominator in the percent difference calculation. 13

15 3.3 V003 Series Models; Experimental Models Model 5; Experimental Model Static Loading Pile Torsion Description: Pile: A single pile with fixed base; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Pile Cap: A 4 thick pile cap; concrete; modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were enabled in the FB-MultiPier model (see Sec 2.1) Pier Column: A single column; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity; Quad-Pods were applied to the ADINA model (see Sec 2.2) Loading: A Z-Axis moment of 42 kip-ft was statically applied at the top node of the pile to test pile torsion behavior. Software Comparison: Percent Difference Comparison: Figure 12. Physical Model Description Table 5. Displacement Comparisons; Theoretical and Relative Data Source Pile Head Displacement (rad) Theoretical Percent Difference (%) Software Percent Difference (%) ADINA FB-MultiPier Theory* *- Tip Deflection of a Pure Torsion Beam Member ( = TL/GJ); where is the tip rotation, T is the applied moment, L is the length of the member, G is the shear modulus, and J is the torsional moment of inertia. 14

16 3.3.2 V003-2 Series Models; Experimental Models Pier Column Top Node Loading Model 6; Experimental Model Static Loading Axial on Pier Column Description: Pile: A single pile with fixed base; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Pile Cap: A 4 thick pile cap; concrete; 4442 modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were enabled in the FB-MultiPier model (see Sec 2.1) Pier Column: A single column; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity; Quad-Pods were applied to the ADINA model Loading: A Z-Axis load of 100 kips was statically applied at the top node of the pile to test proper load transfer in system flexure. Software Comparison: Percent Difference Comparison: Figure 13. Physical Model Description Table 6. Displacement Comparisons; Relative Data Source Pier Column Top Node Displacement (in) Software Percent Difference (%) ADINA FB-MultiPier *- For software comparison, the value of displacement with the smallest absolute value is taken is the denominator in the percent difference calculation. 15

17 Model 7; Experimental Model Static Loading Lateral on Pier Column Description: Pile: A single pile with fixed base; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Pile Cap: A 4 thick pile cap; concrete; 4442 modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were enabled in the FB-MultiPier model (see Sec 2.1) Pier Column: A single column; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity; Quad-Pods were applied to the ADINA model Loading: An X-Axis load of 1 kips was statically applied at the top node of the pile to test proper load transfer in system flexure. Software Comparison: Percent Difference Comparison: Figure 14. Physical Model Description Table 7. Displacement Comparisons; Relative Data Source Pier Column Top Node X- Displacement (in) Software Percent Difference (%) ADINA FB-MultiPier *- For software comparison, the value of displacement with the smallest absolute value is taken is the denominator in the percent difference calculation. 16

18 Model 8; Experimental Model Static Loading Longitudinal on Pier Column Description: Pile: A single pile with fixed base; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Pile Cap: A 4 thick pile cap; concrete; 4442 modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were enabled in the FB-MultiPier model (see Sec 2.1) Pier Column: A single column; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity; Quad-Pods were applied to the ADINA model Loading: A Y-Axis load of 100 kips was statically applied at the top node of the pile to test proper load transfer in system flexure. Software Comparison: Percent Difference Comparison: Figure 15. Physical Model Description Table 8. Displacement Comparisons; Relative Data Source Pier Column Top Node Displacement (in) Software Percent Difference (%) ADINA FB-MultiPier *- For software comparison, the value of displacement with the smallest absolute value is taken is the denominator in the percent difference calculation. 17

19 Model 9; Experimental Model In-plane Pile Cap Shear without Torsional Provisions Description: Pile Cap: A 4 thick pile cap; concrete; 4442 modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were not enabled in the FB-MultiPier model (see Sec 2.1) Special Boundary Conditions: A line of supports was applied along Line I (as shown in Figure 18 below), fixing all degrees of freedom (DOF). A line of supports was applied along Line II fixing all DOF except for Y-Axis deflection. These boundary conditions were applied in an attempt to isolate shear within the pile cap. Loading: A Y-Axis line consisting of twenty-one 100 kip loads was statically applied at each node along the Line II support system. Software Comparison: Percent Difference Comparison: Figure 16. Physical Model Description Table 9. Displacement Comparisons; Relative and Theoretical Data Source Line II Average Displacement (in) Theoretical Percent Difference (%) Software Percent Difference (%) ADINA FB-MultiPier Theory* *- Pure shear deflection is calculated using = Vh/Gdw; where is the displacement, V is the applied shear, h is the span of the member between boundary conditions, G is the shear modulus, d is the depth of the member, and w is the width of the member. 18

20 Model 10; Experimental Model Pile Cap Through Cap Bending without Torsional Provisions Thin Cap Description: Pile Cap: A 6 thick pile cap; concrete; 4442 modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were not enabled in the FB-MultiPier model (see Sec 2.1) Special Boundary Conditions: A line of supports was applied along Line I (as shown in Figure 18 below), fixing all degrees of freedom (DOF). A line of supports was applied along Line II fixing all DOF except for Z-Axis deflection and Y-Axis rotation. These boundary conditions were applied in an attempt to isolate bending about the Y-axis within the pile cap. Loading: A Z-Axis line consisting of twenty-one 100 kip loads was statically applied at each node along the Line II support system. Software Comparison: Percent Difference Comparison: Figure 17. Physical Model Description Table 10. Displacement Comparisons; Relative and Theoretical Data Source Average Pile Cap Z Displacement (in) Theoretical Percent Difference (%) Software Percent Difference (%) ADINA FB-MultiPier Theory* *- Tip Deflection of a Cantilevered Bernoulli Beam ( = PL 3 /3EI); where is the tip displacement, P is the applied load, L is the length of the member, E is the modulus of elasticity, and I is the moment of inertia. 19

21 3.3.4 V004 Series Models; Old St. George Island Pier 3 Single Pier Models Model 11; Single Pier Model Static Lateral Load Description: Piles: Four piles per pier column with fixed bases for each pile; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Pile Cap: A 4 thick pile cap per pier column; 8 x10 X-Axis and Y-Axis dimensions, respectively; concrete; 4442 modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were disabled in the FB-MultiPier model (see Sec 2.1) Pier Column: Two pier columns spaced 20.5 center to center; 47.5 length; 50 x42 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; Quad-Pods were applied to the ADINA model Pier Cap Beam: 50 x48 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; connected pier columns Pier Strut: 48 x30 X-Axis and Z-Axis dimensions, respectively; Reinforced concrete; 4442 Modulus of Elasticity; placed 4 above pile cap midplane Loading: An X-Axis load of 500 kips was statically applied to the top pier column node to test pier lateral behavior. 20

22 Software Comparison: Pier Column Displacement Profile Distance Above Pile Cap Midplane (ft) Pile Displacement Profile ADINA FB-MultiPier Dist from Point of Fixity (ft) (a) (b) Figure 18(a). Physical Model Description and 18(b). Typical Pile and Pier Column X-Displacement Profiles Percent Difference Comparison: Table 11. Displacement Comparisons; Relative ADINA FB-MultiPier Lateral Deflection (in) Data Source Maximum X-Displacement (in) Software Percent Difference (%) ADINA FB-MultiPier *- For software comparison, the value of displacement with the smallest absolute value is taken is the denominator in the percent difference calculation. 21

23 Model 12; Single Pier Model Static Longitudinal Load Description: Piles: Four piles per pier column with fixed bases for each pile; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Pile Cap: A 4 thick pile cap per pier column; 8 x10 X-Axis and Y-Axis dimensions, respectively; concrete; 4442 modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were disabled in the FB-MultiPier model (see Sec 2.1) Pier Column: Two pier columns spaced 20.5 center to center; 47.5 length; 50 x42 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; Quad-Pods were applied to the ADINA model Pier Cap Beam: 50 x48 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; connected pier columns Pier Strut: 48 x30 X-Axis and Z-Axis dimensions, respectively; Reinforced concrete; 4442 Modulus of Elasticity; placed 4 above pile cap midplane Loading: A Y-Axis load of 500 kips was statically applied to the top pier column node of each column to test pier longitudinal behavior. 22

24 Software Comparison: Pier Column Displacement Profile Height above Pile Cap midplane (ft) FBMultiPier ADINA Pile Displacement Profile (a) (b) Figure 19(a). Physical Model Description and 19(b). Typical Pile and Pier Column X-Displacement Profiles Percent Difference Comparison: Height above Pile Point of Fixity (ft) Table 12. Displacement Comparisons; Relative Data Source Maximum X-Displacement (in) Software Percent Difference (%) ADINA FB-MultiPier *- For software comparison, the value of displacement with the smallest absolute value is taken is the denominator in the percent difference calculation. 5 Displacement (in) FB-MultiPier ADINA 23

25 Model 13; Single Pier Model Static Longitudinal Twist Load Description: Piles: Four piles per pier column with fixed bases for each pile; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Pile Cap: A 4 thick pile cap per pier column; 8 x10 X-Axis and Y-Axis dimensions, respectively; concrete; 4442 modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were disabled in the FB-MultiPier model (see Sec 2.1) Pier Column: Two pier columns spaced 20.5 center to center; 47.5 length; 50 x42 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; Quad-Pods were applied to the ADINA model Pier Cap Beam: 50 x48 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; connected pier columns Pier Strut: 48 x30 X-Axis and Z-Axis dimensions, respectively; Reinforced concrete; 4442 Modulus of Elasticity; placed 4 above pile cap midplane Loading: Two Y-Axis loads, oppositely directed, with a magnitude of 500 kips each were statically applied to the top pier column node of each column to test pier longitudinal twist behavior. 24

26 Software Comparison: Pier Column Displacement Profile Height above Pile Cap midplane (ft) FBMultiPier ADINA Pile Displacement Profile (a) (b) Figure 20(a). Physical Model Description and 20(b). Typical Pile and Pier Column X-Displacement Profiles Percent Difference Comparison: Height above Pile Point of Fixity (ft) Table 13. Displacement Comparisons; Relative FB-MultiPier ADINA Data Source Maximum X-Displacement (in) Software Percent Difference (%) ADINA FB-MultiPier *- For software comparison, the value of displacement with the smallest absolute value is taken is the denominator in the percent difference calculation Displacement (in) 25

27 Model 14; Single Pier Model Dynamic Lateral Load Description: Piles: Four piles per pier column with fixed bases for each pile; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Pile Cap: A 4 thick pile cap per pier column; 8 x10 X-Axis and Y-Axis dimensions, respectively; concrete; 4442 modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were disabled in the FB-MultiPier model (see Sec 2.1) Pier Column: Two pier columns spaced 20.5 center to center; 47.5 length; 50 x42 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; Quad-Pods were applied to the ADINA model Pier Cap Beam: 50 x48 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; connected pier columns Pier Strut: 48 x30 X-Axis and Z-Axis dimensions, respectively; Reinforced concrete; 4442 Modulus of Elasticity; placed 4 above pile cap midplane Loading: An X-Axis load of 500 kips was dynamically applied and suddenly released at the top pier column node to test pier lateral dynamic behavior. 26

28 Software Comparison: 6 Pier 3 - Lateral Dynamic Load Response 4 Displacement (in) (a) (b) Figure 21(a). Physical Model Description and 21(b). Pier Column Top Node Displacement vs Time Percent Difference Comparison: Table 14. Displacement Comparisons; Relative ADINA FB-MultiPier Time (sec) Data Source Peak X-Displacement at 2 sec (in) Software Percent Difference (%) ADINA FB-MultiPier *- For software comparison, the value of displacement with the smallest absolute value is taken is the denominator in the percent difference calculation. 27

29 Model 15; Single Pier Model Dynamic Longitudinal Twist Load Description: Piles: Four piles per pier column with fixed bases for each pile; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Pile Cap: A 4 thick pile cap per pier column; 8 x10 X-Axis and Y-Axis dimensions, respectively; concrete; 4442 modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were disabled in the FB-MultiPier model (see Sec 2.1) Pier Column: Two pier columns spaced 20.5 center to center; 47.5 length; 50 x42 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; Quad-Pods were applied to the ADINA model Pier Cap Beam: 50 x48 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; connected pier columns Pier Strut: 48 x30 X-Axis and Z-Axis dimensions, respectively; Reinforced concrete; 4442 Modulus of Elasticity; placed 4 above pile cap midplane Loading: Two Y-Axis loads, oppositely directed, with a magnitude of 500 kips each were dynamically applied and suddenly released at the top pier column node of each column to test pier longitudinal twist behavior. 28

30 Software Comparison: 6 Pier 3 - Longitudinal Twist Dynamic Response 4 Displacement (in) (a) (b) Figure 22(a). Physical Model Description and 22(b). Pier Column Top Node Displacement vs Time Percent Difference Comparison: Table 15. Displacement Comparisons; Relative ADINA FB-MultiPier Time (sec) Data Source Peak Y-Displacement at 2 sec (in) Software Percent Difference (%) ADINA FB-MultiPier *- For software comparison, the value of displacement with the smallest absolute value is taken is the denominator in the percent difference calculation. 29

31 3.3.5 V005 Series Models; Old St. George Island Pier 3 Two Pier Models Model 16; Two Pier Model Static Lateral Load Description: Piles: Four piles per pier column with fixed bases for each pile; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Pile Cap: A 4 thick pile cap per pier column; 8 x10 X-Axis and Y-Axis dimensions, respectively; concrete; 4442 modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were enabled in the FB-MultiPier model (see Sec 2.1) Pier Strut: 48 x30 X-Axis and Z-Axis dimensions, respectively; Reinforced concrete; 4442 Modulus of Elasticity; placed 4 above pile cap midplane Pier Column: Two pier columns spaced 20.5 center to center; 47.5 length; 50 x42 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; Quad-Pods were not applied to the ADINA model Pier Cap Beam: 50 x48 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; connected pier columns Pier Superstructure Beam: Modeled using moments of inertia representative of the gross moments of inertia of the actual Old St. George Island Bridge superstructure; Reinforced concrete; 4442 ksi modulus of elasticity; all of the special elements described in Sect were applied to the ADINA model in order to emulate the superstructure to substructure interactions that occur in FB- MultiPier Loading: Two X-Axis loads with a magnitude of 500 kips each were statically applied at the top pier column node of one pier column of each pier to test multiple pier lateral static behavior. 30

32 Software Comparison: 20 Pier 1 Pile X-Displacement 15 Depth (ft) 10 5 (a) (b) Figure 23(a). Physical Model Description and 23(b). Pier 1 Typical Pile Displacement Percent Difference Comparison: Table 16. Displacement Comparisons; Relative ADINA FB-MultiPier Lateral Deflection (in) Data Source Peak X-Displacement (in) Software Percent Difference (%) ADINA FB-MultiPier *- For software comparison, the value of displacement with the smallest absolute value is taken is the denominator in the percent difference calculation. 31

33 Model 17; Two Pier Model Dynamic Lateral Load Description: Piles: Four piles per pier column with fixed bases for each pile; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Pile Cap: A 4 thick pile cap per pier column; 8 x10 X-Axis and Y-Axis dimensions, respectively; concrete; 4442 modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were enabled in the FB-MultiPier model (see Sec 2.1) Pier Strut: 48 x30 X-Axis and Z-Axis dimensions, respectively; Reinforced concrete; 4442 Modulus of Elasticity; placed 4 above pile cap midplane Pier Column: Two pier columns spaced 20.5 center to center; 47.5 length; 50 x42 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; Quad-Pods were not applied to the ADINA model Pier Cap Beam: 50 x48 X-Axis and Y-Axis dimensions, respectively; Reinforced concrete; 4442 ksi modulus of elasticity; connected pier columns Pier Superstructure Beam: Modeled using moments of inertia representative of the gross moments of inertia of the actual Old St. George Island Bridge superstructure; Reinforced concrete; 4442 ksi modulus of elasticity; all of the special elements described in Sect were applied to the ADINA model in order to emulate the superstructure to substructure interactions that occur in FB- MultiPier Loading: Two X-Axis loads with a magnitude of 500 kips each were dynamically applied and suddenly released at the top pier column node of one pier column of each pier to test multiple pier lateral dynamic behavior. 32

34 Software Comparison: 2 Two Pier - Lateral Dynamic Response Lateral Displacement (in) (a) (b) Figure 24(a). Physical Model Description and 24(b). Pier 1 - Pile 8 Top Node Displacement vs Time Percent Difference Comparison: FB-MultiPier ADINA Table 17. Displacement Comparisons; Relative Time (sec) Data Source Peak X-Displacement at 8 sec (in) Software Percent Difference (%) ADINA FB-MultiPier *- For software comparison, the value of displacement with the smallest absolute value is taken is the denominator in the percent difference calculation. 33

35 3.3.6 V006 Series Models; Miscellaneous Models; Brick vs Shell Element Pile Caps Model 18; Pile Cap Models Static Lateral Load Description: The V005-5 Pile Cap Models consist of a comparison of 3 models within FB- MultiPier and ADINA, with varying aspect ratios with respect to cap length and depth. The specific aspect ratios and accompanying dimensions are described below. Piles: Four piles per pier column with fixed bases for each pile; 20 length; 20 x20 Prestressed Concrete; 4415 ksi modulus of elasticity Pile Cap: A 4 thick pile cap for each of three models in each program; with X-Axis and Y-Axis dimensions of 16 x8, 24 x8, and 40 x8 for aspect ratios of 4, 6, and 10, respectively; concrete; 4442 modulus of elasticity; finite element mesh consisted of 1 x1 shell elements; torsional properties were enabled in the FB-MultiPier model (see Sec 2.1) Loading: One X-Axis load with a magnitude of 100 kips was statically applied at the mid-plane of the pile cap to test lateral static behavior of brick and shell element pile caps. Software Comparison: (a) 34

36 Depth (in) Depth (in) Pile Displacements in the X-Direction for Aspect Ratio = X-Displacement (in) (b) (c) shell element aspect=4 brick element aspect=4 Pile Displacements in the X-Direction for Aspect Ratio = 6 shell element aspect=6 brick element aspect= X-Displacement (in) 35

37 Depth (in) Pile Displacements in the X-Direction for Aspect Ratio = shell element aspect=10 2 brick element aspect= (d) Figure 25(a). Physical Model Description (Shell Element Pile Cap with an Aspect Ratio of 6 is shown) and 25(b)-25(d). Typical Pile Displacements for Aspect Ratios 4, 6, and 10, respectively Percent Difference Comparison: X-Displacement (in) Table 18. Displacement Comparisons; Relative Peak X-Displacement (in) Software Percent Difference (%) Data Source Aspect 4 Aspect 6 Aspect 10 Aspect 4 Aspect 6 Aspect 10 ADINA FB-MultiPier *- For software comparison, the value of displacement with the smallest absolute value is taken is the denominator in the percent difference calculation. 36