FB-PIER VALIDATION SET

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FB-PIER VALIDATION SET Dynamics February 2004 FB-Pier Dynamics Validation Manual 1

Example 1 Single Pile Subject to a Pulse Load at the Pile Head Problem: The single 24 square prestressed concrete pile is subject to a pulse load applied at the pile head. Load Load Lumped Mass Node 1 Load 30 ft 10 kips Time Node 17 Physical Model FE Model Solution Parameters: Newmark Average Acceleration t = 0.02 seconds Undamped solution Pile lumped mass = 0.0467 kip-sec 2 / in File: sp_pulse.in FB-Pier Dynamics Validation Manual 2

Results: The plot of pile head displacement versus time matches the exact solution. The peak amplitude of displacement is twice the static response. Displacement (in) 3.0 2.5 2.0 1.5 1.0 0.5 0.0 FB-Pier Exact Static -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Verified by: Exact solution FB-Pier Dynamics Validation Manual 3

Example 2 Single Pile Subject to a Pulse Load at the Pile Head with Damping Problem: The single 24 square prestressed concrete pile is subject to a pulse load applied at the pile head. Load Load Lumped Mass Node 1 Load 30 ft 10 kips Time Node 17 Physical Model FE Model Solution Parameters: Newmark Average Acceleration t = 0.02 seconds Pile lumped mass = 0.0467 kip-sec 2 / in Lumped damper 0, 1, 2, and 5% damping File: sp_pulsedamping.in FB-Pier Dynamics Validation Manual 4

Results: The plot of pile head displacement versus time matches the exact solution. The peak amplitude of displacement is twice the static response and the amplitudes decay with damping. Displacement (in) 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0% 1% 2% 5% Static -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Verified by: Exact solution FB-Pier Dynamics Validation Manual 5

Example 3 Single Pile Subject to a Ramp Load at the Pile Head Problem: The single 24 square prestressed concrete pile is subject to a pulse load applied at the pile head. Load Load Lumped Mass Node 1 Load 30 ft 10 kips Node 17 10 sec Time Physical Model FE Model Solution Parameters: Newmark Average Acceleration t = 0.1 seconds Undamped solution Pile lumped mass = 0.0467 kip-sec 2 / in File: sp_ramp.in FB-Pier Dynamics Validation Manual 6

Results: The plot of pile head displacement versus time matches the static solution after 10 seconds. Displacement (in) 1.4 1.2 1.0 0.8 0.6 0.4 0.2 FB-Pier Static 0.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 Verified by: Static solution FB-Pier Dynamics Validation Manual 7

Example 4 Single Pile Subject to a Blast Load at the Pile Head Problem: The single 24 square prestressed concrete pile is subject to a pulse load applied at the pile head. Load Load Lumped Mass Node 1 Load 12.85 ft 120 kips Time Node 17 0.02 sec 0.04 sec 0.06 sec Physical Model FE Model Solution Parameters: Newmark Average Acceleration t = 0.02 seconds Undamped solution Pile lumped mass = 0.1 kip-sec 2 / in File: sp_blast.in FB-Pier Dynamics Validation Manual 8

Results: The plot of pile head displacement versus time is close to the Paz solution. The Paz solution is approximate due to the coarseness in the solution to Duhamel s Integral. Displacement (in) 2.0 1.5 1.0 0.5 0.0-0.5-1.0 FB-Pier Paz -1.5 0.0 0.1 0.1 0.2 0.2 0.3 Verified by: Paz. Structural Dynamics. p. 73 FB-Pier Dynamics Validation Manual 9

Example 5 Single Pile Subject to a Constant Acceleration Problem: The single 24 square prestressed concrete pile is subject to a constant acceleration. u g Node 1 Acceleration 100 ft 0.1g Time Node 17 Physical Model FE Model Solution Parameters: Newmark Average Acceleration t = 0.02 seconds Undamped solution Pile mass density (using consistent mass matrix) = 2.25e-7 kip-sec 2 / in 4 File: sp_constgroundaccel.in FB-Pier Dynamics Validation Manual 10

Results: The plot of pile head displacement matches the ADINA solution. Displacement (in) 0.00-5.00-10.00-15.00-20.00 FB-Pier ADINA -25.00 0.0 0.5 1.0 1.5 2.0 Verified by: ADINA FB-Pier Dynamics Validation Manual 11

Example 6 Single Pile Subject to a Sinusoidal Ground Acceleration Problem: The single 24 square prestressed concrete pile is subject to a sinusoidal ground acceleration. u g Node 1 100 ft Acceleration (g) 1.50 1.00 0.50 0.00-0.50-1.00-1.50 0 1 2 3 4 5 Node 17 Physical Model FE Model Solution Parameters: Newmark Average Acceleration t = 0.02 seconds Undamped solution Pile mass density (using consistent mass matrix) = 2.25e-7 kip-sec 2 / in 4 File: sp_sinegroundaccel.in sp_sinegroundaccel_la.in sp_sinegroundaccel_wt.in FB-Pier Dynamics Validation Manual 12

Results: The plot of pile head displacement matches the ADINA solution. Displacement (in) 20.00 FB-Pier 15.00 ADINA 10.00 5.00 0.00-5.00-10.00-15.00-20.00 0.0 1.0 2.0 3.0 4.0 5.0 The plot of pile head displacement matches for solutions using Newmark s Average and Wilson Theta s method. Displacement (in) 20.00 FB-Pier 15.00 FB-Pier (WT) 10.00 5.00 0.00-5.00-10.00-15.00-20.00 0.0 1.0 2.0 3.0 4.0 5.0 Verified by: ADINA FB-Pier Dynamics Validation Manual 13

Example 7 Single Pile Subject to an El Centro Ground Acceleration Problem: The single 24 square prestressed concrete pile is subject to an El Centro Earthquake ground acceleration. u g Node 1 100 ft Acceleration (g) 0.4 0.3 0.2 0.1 0-0.1-0.2-0.3-0.4 0 5 10 15 20 25 30 Node 17 Physical Model FE Model Solution Parameters: Newmark Average Acceleration t = 0.02 seconds Undamped solution Pile mass density = 2.25e-7 kip-sec 2 / in 4 File: sp_elcentroaccel.in FB-Pier Dynamics Validation Manual 14

Results: The plot of pile head displacement matches the ADINA solution for both the lumped mass. The FB-Pier consistent mass solution is also very similar to the lumped mass solution. Note that the ADINA consistent mass solution is significantly different. The displaced shape is the same, but noticeably smaller in amplitude. ADINA uses a different consistent mass matrix (see ADINA Theory and Modeling Guide). Displacement (in) 30.00 20.00 10.00 0.00-10.00-20.00 FB-Pier (LM) ADINA (LM) FB-Pier (CM) ADINA (CM) -30.00 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Verified by: ADINA FB-Pier Dynamics Validation Manual 15

Example 8 Single Pile with Soil Subject to a Pulse Load Problem: The 72 concrete drilled shaft is subject to a pulse load. A single of layer of O Neill Sand is used. 100 kips Node 1 O Neill Sand γ = 110 pcf φ = 35 o k = 120 pci 100 ft Load 100 kips Node 17 Time Physical Model FE Model Solution Parameters: Newmark Average Acceleration t = 0.01 seconds Undamped solution Pile mass density = 2.25e-7 kip-sec 2 / in 4 File: sp_pulsewithsoil.in FB-Pier Dynamics Validation Manual 16

Results: The plot of pile head displacement is similar to the ADINA response. The results appear to converge when the time step is reduced from t = 0.02 sec to t = 0.01 sec. Both program are using Newmark s Average Acceleration Method, however, the results are still different. The slight difference in response frequencies in most likely due to the linear discretization of the O Neill soil curve in ADINA. The soil curve used in FB-Pier is hyperbolic and the ADINA nonlinear soil springs are composed of approximate linear segments. Both solutions oscillate about the static solution as expected. Displacement (in) 0.25 0.20 0.15 0.10 0.05 FB-Pier ADINA Static 0.00 0.0 0.3 0.5 0.8 1.0 Verified by: ADINA FB-Pier Dynamics Validation Manual 17

Example 9 Single Pile with Soil Subject to a Constant Ground Acceleration Problem: The 72 concrete drilled shaft is subject to a constant ground acceleration of 1g. A single of layer of O Neill Sand is used. u g Node 1 O Neill Sand γ = 110 pcf φ = 35 o k = 120 pci 100 ft Acceleration 1.0 g Node 17 Physical Model FE Model Solution Parameters: Newmark Average Acceleration t = 0.005 seconds Undamped solution Pile mass density = 2.25e-7 kip-sec 2 / in 4 File: sp_constaccelwithsoil.in FB-Pier Dynamics Validation Manual 18

Results: The plot of pile head displacement is similar to the ADINA response. The results appear to converge when the time step is reduced from t = 0.01 sec to t = 0.005 sec. Both program are using Newmark s Average Acceleration Method, however, the results are still different. The slight difference in response frequencies in most likely due to the linear discretization of the O Neill soil curve in ADINA. The soil curve used in FB-Pier is hyperbolic and the ADINA nonlinear soil springs are composed of approximate linear segments. Both solutions oscillate about the static solution as expected. Displacement (in) 0.000-0.025-0.050-0.075 FB-Pier ADINA -0.100 0.0 0.2 0.4 0.6 0.8 1.0 Verified by: ADINA FB-Pier Dynamics Validation Manual 19

Example 10 Single Column Pier Subject to an El Centro Ground Acceleration Problem: The single column pier with a 108 concrete drilled shaft is subject to an El Centro ground acceleration. A single of layer of O Neill Sand is used. 30 ft 0.4 0.3 O Neill Sand γ = 110 pcf φ = 35 o k = 120 pci 100 ft Node 1 Acceleration (g) 0.2 0.1 0-0.1-0.2-0.3-0.4 0 5 10 15 20 25 30 Physical Model u g FE Model Node 17 Solution Parameters: Newmark Average Acceleration t = 0.01 seconds Undamped solution Pile mass density = 2.25e-7 kip-sec 2 / in 4 File: single11_00dm.in FB-Pier Dynamics Validation Manual 20

Results: The plot of pile head displacement matches the ADINA solution very well until about 9 sec into the solution. The results appear to converge when the time step is reduced from t = 0.02 sec to t = 0.01 sec. 0.400 FB-Pier ADINA 0.200 Displacement (in) 0.000-0.200-0.400 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Verified by: ADINA FB-Pier Dynamics Validation Manual 21

Example 11 Two Column Pier Subject to an El Centro Ground Acceleration Problem: The single column pier with 72 concrete drilled shafts is subject to an El Centro ground acceleration. A single of layer of O Neill Sand is used. 30 ft 0.4 0.3 O Neill Sand γ = 110 pcf φ = 35 o k = 120 pci 100 ft Node 1 Acceleration (g) 0.2 0.1 0-0.1-0.2-0.3-0.4 0 5 10 15 20 25 30 Physical Model u g FE Model Node 17 Solution Parameters: Newmark Average Acceleration t = 0.01 seconds Undamped solution Pile mass density = 2.25e-7 kip-sec 2 / in 4 File: twocol11_00dm.in FB-Pier Dynamics Validation Manual 22

Results: The plot of pile head displacement matches the ADINA solution very well until about 9 sec into the solution. The results appear to converge when the time step is reduced from t = 0.02 sec to t = 0.01 sec. 0.800 0.600 FB-Pier ADINA 0.400 Displacement (in) 0.200 0.000-0.200-0.400-0.600-0.800 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 Verified by: ADINA FB-Pier Dynamics Validation Manual 23

Example 12 Multiple Piers Two Identical Piles Subject to a Pulse Load Problem: Two identical piles are subject to the same pulse load applied at the pile cap. The two piles are isolated. The displacement records should match. Load 10 kips Time Solution Parameters: Newmark Average Acceleration t = 0.02 seconds Undamped solution Pile and pier mass density = 2.25e-7 kip-sec 2 / in 4 File: two identical piles dyn pulse.in FB-Pier Dynamics Validation Manual 24

Results: The plot of pile head displacements for both piles match. 3.00 2.50 Pile 1 Pile 2 2.00 Displacement (in) 1.50 1.00 0.50 0.00-0.50 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Verified by: FB-Pier FB-Pier Dynamics Validation Manual 25

Example 13 Multiple Piers Two Identical Piers Subject to a Pulse Load Problem: Two identical piers are subject to the same pulse load applied at the pile cap. The two piers are isolated. The displacement records should match. Load 100 kips Time Solution Parameters: Newmark Average Acceleration t = 0.02 seconds Undamped solution Pile and pier mass density = 2.25e-7 kip-sec 2 / in 4 File: two piers_example 2_dyn pulse.in FB-Pier Dynamics Validation Manual 26

Results: The plot of pile head displacements for both piers match. 0.08 0.07 Pier 1 Pier 2 0.06 Displacement (in) 0.05 0.04 0.03 0.02 0.01 0.00-0.01 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Verified by: FB-Pier FB-Pier Dynamics Validation Manual 27

Example 14 Multiple Piers Two Different Piers Subject to a Pulse Load Problem: Two different piers are subject to the same pulse load applied at the pile cap. The two piers are isolated. The displacement records should match the single pier solutions. Load 10 kips Time (Pier 1) (Pier 2) Solution Parameters: Newmark Average Acceleration t = 0.02 seconds Undamped solution Pile and pier mass density = 2.25e-7 kip-sec 2 / in 4 File: two piers_pier1 and Pier2_dyn pulse.in FB-Pier Dynamics Validation Manual 28

Results: Pile head displacement results for Pier 1. 8.00 7.00 Single Multiple 6.00 Displacement (in) 5.00 4.00 3.00 2.00 1.00 0.00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Pile head displacement results for Pier 2. 0.60 0.50 Single Mutliple 0.40 Displacement (in) 0.30 0.20 0.10 0.00-0.10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Verified by: FB-Pier FB-Pier Dynamics Validation Manual 29

Example 15 Response Spectrum Analysis Two Story Shear Building Problem: A two story frame is modeled as a shear building. The models are loaded using a response spectrum for a constant 0.1g acceleration and no damping. The objective is to compare the frequency results and the shear building floor displacements. The bottom floor is modeled with a pile and the top floor is modeled with a pier column (since the section properties are different between the two floors). Two modes are used in the modal combination. m=0.066 k-sec2/in W10x21 (k=30.7 k/in) m=0.136 k-sec2/in 10 ft W10x45 (k=44.3 k/in) 15 ft Thin Element Mode Thick Element Mode Frame Model File: 2 story col_modal.in FB-Pier Dynamics Validation Manual 30

Response Spectrum: 216.38 Accel. (in/sec 2 ) Freq. (rad/sec) Results: ω1 (rad/sec) ω2 (rad/sec) 1 st floor (in) 2 nd floor (in) FB-Pier 11.83 32.90 1.406 1.780 Paz Solution 11.83 32.89 1.426 1.789 Verified By: Paz, M. Structural Dynamics, 3 rd Ed. VNR, p 241 (Example 11.2). FB-Pier Dynamics Validation Manual 31

Example 16 Response Spectrum Analysis Five Story Shear Building versus Frame Problem: A five story frame is modeled as both a shear building and frame. The models are loaded using a response spectrum of the El Centro earthquake with 5% structural damping. The objective is to compare the column base shear and overturning moment results for both models. A time history analysis of the frame was also conducted for comparison to validate the modal analysis results. The modal contribution factors are checked to ensure that most of the modal response is captured in the first five vibration modes. Shear Building Frame File: 5 story col_modal.in, 5 story col_modal_frame.in, 5 story col_timehistory_frame.in FB-Pier Dynamics Validation Manual 32

Results: Model Col #1 Base Shear (kip) Col #2 Base Shear (kip) Total Base Shear (kip) Overturning Moment (kip-ft) Top Floor Disp. (in) Shear Building 67.3 n/a 67.3 n/a 6.89 Chopra Solution 66.5 n/a 66.5 2,572 6.79 Frame 33.2 33.2 66.4 2,229 6.77 Frame (Time history) 28.9 36.3 65.2 2,205 6.67 Time history results: 8.0 6.0 4.0 Top Story Disp. (in) 2.0 0.0-2.0-4.0-6.0-8.0 0 2 4 6 8 10 12 14 16 18 20 Modal contribution factors: Mode % Contribution 1 87.85 2 8.71 3 2.42 4 0.75 5 0.16 Total 99.89 Verified By: Chopa, A. Dynamics of Structures, 2 nd Ed. Prentice Hall, p 523 (Example 13.8.2). Chopa, A. Dynamics of Structures, 2 nd Ed. Prentice Hall, p 450 (Table 12.11.1 Modal Contribution Factors). FB-Pier Dynamics Validation Manual 33

Example 17 Response Spectrum Analysis Two Excitation Directions Problem: A single pile is subject to a constant 0.1g ground acceleration that is applied in both the x and y direction. Different factors are used to control the percentage application in each direction and the results are compared. Single Pile File: sp_2dspectrum_100x_0y.in, sp_2dspectrum_100x_50y.in, sp_2dspectrum_0x_100y.in, sp_2dspectrum_50x_100y.in, sp_2dspectrum_100x_100y.in FB-Pier Dynamics Validation Manual 34

Results: Pile Head Displacement: Case x % y % x-disp (in) y-disp (in) 1 100 0 0.1743 0.0000 2 100 50 0.1743 0.0774 3 0 100 0.0000 0.1549 4 50 100 0.0872 0.1549 5 100 100 0.1743 0.1549 The different load cases show the variation in displacement depending on the direction factor. When a 50% direction factor is used, the displacement is exactly half of the 100% direction factor displacement, as expected. FB-Pier Dynamics Validation Manual 35

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