This document presents the seismic design project of a 12-story steel frame building in Stockton, California. The objectives are to analyze the building using equivalent lateral force (ELF), modal response spectrum, and modal time history analyses in SAP2000, and to compare the results to FEMA 451 examples. The building is irregular in plan and elevation, posing modeling challenges. The analyses determine member forces and drifts. ELF analysis results in story drifts up to 3.58 inches, within code allowables. Modal and time history analyses will provide more accurate force and deformation estimates for design.

1. Presented to Dr.Ganesh Thiagarajan for CIV-ENGR 5501B Seismic Design of Structures
Date: April 25,2011
Jury : Mr. Shivaji Jagtap P.E.
Mr. Shakeel
Seismic Design of Structures
Project
BY
Anirudha Vasudevan
Gunjan Shetye
Harsh Shah

2. The Problem
Earthquakes don’t kill people ……but bad buildings do!!!!
-- The Infrastructurist
Courtesy: Melissa Lafsky ,
http://www.infrastructurist.com/2010/01/20/earthquakes-dont-kill-
peoplebad-buildings-do-more-on-haitis-building-codes/

3. OBJECTIVES
 To analyze a 12 story steel frame building in Stockton, California using
three methods of analysis in SAP 2000 :
 Equivalent lateral force (ELF) procedure.
 Three-dimensional, modal-response-spectrum analysis.
 Three-dimensional, modal time-history analysis.
 To report the results obtained from the above three methods and compare
them with the FEMA 451 design example.

4. Why This Building??
 Highly irregular structure both in plan and elevation.
 Numerous Modeling challenges .
 Plenty of scope to learn the capabilities of SAP 2000.
Courtesy: Robot
Structural Analysis
Package

5. Description of The Structure
Special Moment Girders range from W30X108
Frame of Structural at roof to W30X132 at Level G
Steel as Lateral
Load Resisting
System
25 ft.
wide
bays in Y-
direction
Columns
range from
W24X146
at roof to
W24X229
One-story
at Level G
basement
18ft below
30 ft. wide bays in X-direction grade

6. Ground Motion Parameters for Stockton
,CA
Provisions Maps 3.3.1 and 3.3.2 NEHRP- (FEMA-450)
Spectral Response Accelerations: Ss = 1.25 S1 = 0.40
Site Class: C (Assumption )
Site co-efficients: Fa = 1.0 Fv = 1.4
Adjusted Spectral response SMS = 1.25 SM1 = 0.56
Accelerations:
Design spectral acceleration SDS = 0.833 SD1 = 0.373
parameters:
Ts=SD1/SDS = 0.373/0.833 = 0.45sec
Maximum Considered Earthquake Ground Motion for the
conterminous of United States of 0.2 sec Spectral
Response Acceleration (5% of Critical Damping) –
NEHRP2003 Fig. 3.3.1

7. Dynamic Properties
 Period of Vibration
Ta =1.59 sec
Cu = 1.4
Cu * Ta = 2.23 seconds
Courtesy: comp.uark.edu
 Damping
For steel structures damping ratio of 0.05 is appropriate.
Courtesy: edes.bris.ac.uk

8. Mass Distribution
Area masses on floor diaphragms (FEMA-451 Example 3.1)
Line masses on floor diaphragms (FEMA-451 Example 3.1)
 Applied as Gravity Dead Load using Uniform
to Frame option in SAP.
Applied as Uniformly Distributed Loads in the
Diagram for computation of floor mass (FEMA-451 Example)
gravity direction.

9. Equivalent Lateral Force Analysis
WHY ELF??
 For preliminary design purposes.
To asses the three dimensional response characteristics of the structure.
Most commonly used design procedure since the 1960s.

10. ELF Parameters
Seismic base shear
V = CsW (NEHRP Provisions Eq 5.2.1)
Maximum spectral acceleration
Csmax = SDS/(R/I) = 0.833/(8/1) = 0.104 (NEHRP Provisions Eq 5.2.2)
R = 8 and I = 1
Cs = SD1/T(R/I) = 0.373/2.23 (8/1) = 0.021. (NEHRP Provisions Eq 5.2.3)
And Cs shall not exceed 0.01.
Also, Csmin = 0.044ISDS = 0.037 (NEHRP Provisions Eq 5.4.1.1-2)

11. Equivalent Lateral Forces
ELF
Fx = Cvx V
Equivalent lateral Forces for buildings responding in X and Y directions based on NEHRP 2003
Level Wx hx k wxhx^k Cvx V Fx Vx
x kips ft kips kips kips
Roof 1656.5 155.5 1.86 19761048 0.16671 1124.5 187.5 187.464
12 1595.67 143 1.86 16288013 0.13741 1124.5 154.5 341.981
11 1595.67 130.5 1.86 13739744 0.11591 1124.5 130.3 472.324
10 1595.67 118 1.86 11393145 0.09612 1124.5 108.1 580.406
9 3401 105.5 1.86 19717698 0.16634 1124.5 187.1 767.459
8 2232.6 93 1.86 10237389 0.08637 1124.5 97.1 864.577
7 2232.6 80.5 1.86 7826926.5 0.06603 1124.5 74.3 938.827
6 2232.6 68 1.86 5718439.1 0.04824 1124.5 54.2 993.076
5 4325.8 55.5 1.86 7593664.1 0.06406 1124.5 72.0 1065.11
4 3350.4 43 1.86 3658878.5 0.03087 1124.5 34.7 1099.82
3 3350.4 30.5 1.86 1931498.4 0.01629 1124.5 18.3 1118.15
2 3098 18 1.86 669712.3 0.00565 1124.5 6.4 1124.5
Totals 30666.9 118536155 1

12. Accidental Torsion
Floor Diaphragms were modeled as infinitely rigid in-plane.
4 ksi concrete shell elements were used to represent diaphragm mass.
ELF
5 % eccentricity

13. Torsional Irregularity in X direction
δmax
Computation for Torsional Irregularity with ELF Loads Acting in X Direction
(SAP 2000 Analysis Output)
Level δ1 (in.) δ2 (in.) δavg (in.) δmax (in.) δmax/δavg Irregularity
R 6.03 6.19 6.11 6.19 1.01 none
12 5.83 6.01 5.92 6.01 1.02 none
11 5.5 5.72 5.61 5.72 1.02 none
10 5.04 5.33 5.185 5.33 1.03 none
9 4.54 4.8 4.67 4.8 1.03 none
8 4.11 4.34 4.225 4.34 1.03 none
7 3.61 3.81 3.71 3.81 1.03 none
6 3.07 3.24 3.155 3.24 1.03 none
5 2.55 2.7 2.625 2.7 1.03 none
4 2.14 2.25 2.195 2.25 1.03 none
3 1.71 1.79 1.75 1.79 1.02 none
2 1.25 1.3 1.275 1.3 1.02 none
Tabulated displacements are not amplified by Cd. Analysis includes accidental torsion.
1 in. = 25.4mm.
δmin

14. Torsional Irregularity in Y direction
Computation for Torsional Irregularity with ELF Loads Acting in Y Direction δmax δmin
(SAP 2000 Analysis Output)
Level δ1 (in.) δ2 (in.) δavg (in.) δmax (in.) δmax/δavg Irregularity
R 5.73 5.92 5.825 5.92 1.02 none
12 5.6 5.79 5.695 5.79 1.02 none
11 5.37 5.56 5.465 5.56 1.02 none
10 5.06 5.24 5.15 5.24 1.02 none
9 4.3 4.74 4.52 4.74 1.05 none
8 3.96 4.27 4.115 4.27 1.04 none
7 3.57 3.75 3.66 3.75 1.02 none
6 3.14 3.18 3.16 3.18 1.01 none
5 2.23 2.6 2.415 2.6 1.08 none
4 1.78 2.09 1.935 2.09 1.08 none
3 1.33 1.56 1.445 1.56 1.08 none
2 0.86 1.02 0.94 1.02 1.09 none
Tabulated displacements are not amplified by Cd. Analysis includes accidental torsion.
1 in. =25.4mm.
No Torsional Amplification Required

15. ELF Drifts in X Direction
ELF Drift for Building Responding in X Direction
(FEMA-451 Design Examples Table3.1-7)
Level 1 2 3 4 5
Inelastic Inealastic
Total Drift Story Drift Story Drift Allowable
from SAP from SAP
2000 2000 Drift Times 0.568 Drift
(in.) (in.) (in.) (in.) (in.)
R 6.71 0.32 1.73 0.982 3
12 6.4 0.45 2.48 1.41 3
11 5.95 0.56 3.08 1.75 3 ELF Drift for Building Responding in X Direction from
10 5.39 5.39 3.38 1.92 3 SAP 2000
9 4.77 0.59 3.22 1.83 3
8 4.19 0.64 3.52 2 3 Level 1 2 3 4 5
7 3.55 0.65 3.58 2.03 3
Total Drift Story Drift Inelastic Story Inealastic Drift Allowable
6 2.9 0.63 3.44 1.95 3
from SAP from SAP
5 2.27 0.55 3 1.7 3 2000 2000 Drift Times 0.568 Drift
4 1.73 0.55 3 1.7 3
(in.) (in.) (in.) (in.) (in.)
3 1.18 0.54 2.94 1.67 3
R 6.11 0.19 1.045 0.59 3
2 0.65 0.65 3.55 2.02 4.32
12 5.92 0.31 1.705 0.97 3
11 5.61 0.43 2.365 1.34 3
10 5.185 0.52 2.86 1.62 3
9 4.67 0.45 2.475 1.41 3
8 4.225 0.52 2.86 1.62 3
7 3.71 0.56 3.08 1.75 3
6 3.155 0.53 2.915 1.66 3
5 2.625 0.43 2.365 1.34 3
4 2.195 0.45 2.475 1.41 3
3 1.75 0.48 2.64 1.50 3
2 1.275 1.275 7.0125 3.98 4.32

16. ELF Drifts in Y Direction
ELF Drift for Building Responding in X Direction
(FEMA-451 Design Examples Table3.1-7)
Level 1 2 3 4 5
Inelastic Inealastic
Total Drift Story Drift Story Drift Allowable
from SAP from SAP
2000 2000 Drift Times 0.568 Drift
(in.) (in.) (in.) (in.) (in.)
R 6.01 0.22 1.21 0.687 3 ELF Drift for Building Responding in Y Direction
from SAP 2000
12 5.79 0.36 1.98 1.12 3
11 5.43 0.45 2.48 1.41 3
10 4.98 0.67 3.66 2.08 3 Level 1 2 3 4 5
9 4.32 0.49 2.7 1.53 3 Inelastic
Total Drift Story Drift Story Inealastic Drift Allowable
8 3.83 0.57 3.11 1.77 3
from SAP
7 3.26 0.58 3.19 1.81 3
2000 from SAP 2000 Drift Times 0.568 Drift
6 2.68 0.64 3.49 1.98 3
(in.) (in.) (in.) (in.) (in.)
5 2.05 0.46 2.53 1.43 3
R 5.825 0.13 0.715 0.41 3
4 1.59 0.49 2.67 1.52 3
12 5.695 0.23 1.265 0.72 3
3 1.1 0.49 2.7 1.53 3
11 5.465 0.32 1.76 1.00 3
2 0.61 0.61 3.36 1.91 4.32
10 5.15 0.63 3.465 1.97 3
9 4.52 0.41 2.255 1.28 3
8 4.115 0.46 2.53 1.44 3
7 3.66 0.5 2.75 1.56 3
6 3.16 0.75 4.125 2.34 3
5 2.415 0.48 2.64 1.50 3
4 1.935 0.49 2.695 1.53 3
3 1.445 0.51 2.805 1.59 3
2 0.94 0.94 5.17 2.94 4.32

17. Accurate period using Rayleigh Analysis
ω=
Rayleigh analysis for X-direction Period of Vibration Rayleigh analysis for Y-direction Period of Vibration
Lev Drift, Level Drift, δ Force, F Weight, W δF δ2W/g
el δ Force, F Weight, W δF δ2W/g (in.) (kips) (kips) (in.-kips) (in.-kips-sec2)
(in.) (kips) (kips) (in.-kips) (in.-kips-sec2) R 5.825 186.9 1656 1088.7 145.42
R 6.11 186.9 1656 1141.959 159.99 12 5.695 154 1598 877.0 134.13
12 5.92 154 1598 911.68 144.94 11 5.465 129.9 1598 709.9 123.52
11 5.61 129.9 1598 728.739 130.16 10 5.15 107.6 1598 554.1 109.69
10 5.185 107.6 1598 557.906 111.18 9 4.52 186.3 3403 842.1 179.93
9 4.67 186.3 3403 870.021 192.07 8 4.115 100.8 2330 414.8 102.11
8 4.225 100.8 2330 425.88 107.64 7 3.66 77 2330 281.8 80.78
7 3.71 77 2330 285.67 83.00 6 3.16 56.2 2330 177.6 60.21
6 3.155 56.2 2330 177.311 60.02
5 2.415 71.4 4323 172.4 65.25
5 2.625 71.4 4323 187.425 77.09
4 1.935 31.5 3066 61.0 29.71
4 2.195 31.5 3066 69.1425 38.23
3 1.445 16.6 3066 24.0 16.57
3 1.75 16.6 3066 29.05 24.30
2 1.275 6.3 3097 8.0325 13.03 2 0.94 6.3 3097 5.9 7.08
5392.816 1141.65 5209.34 1054.39
ω=(5392/1141)^0.5=2.17rad/sec. T=2π/ω=2.89sec 1.0in.=25.4mm , 1.0kip=4.45kN
ω=(5209/1054)^0.5=2.22rad/sec. T=2π/ω=2.83 sec 1.0in.=25.4mm , 1.0kip=4.45kN

18. P-Delta Effects
Computation of P-Delta Effects for X-Direction Response Computation of P-Delta Effects for X-Direction Response
FEMA 451 Design Example from SAP 2000
Level hsx Δ PD PL PT PX VX θX Level hsx Δ PD PL PT PX VX θX
(in.) (in.) (kips) (kips) (kips) (kips) (kips) (in.) (in.) (kips) (kips) (kips) (kips) (kips)
R 150 1.73 1656.5 315 1971.5 1971.5 186.9 0.022 R 150 1.045 1656.5 315 1971.5 1971.5 186.9 0.013
12 150 2.48 1595.8 315 1910.8 3882.3 340.9 0.034 12 150 1.705 1595.8 315 1910.8 3882.3 340.9 0.024
11 150 3.08 1595.8 315 1910.8 5793.1 470.8 0.046 11 150 2.365 1595.8 315 1910.8 5793.1 470.8 0.035
10 150 3.38 1595.8 315 1910.8 7703.9 578.4 0.055 10 150 2.86 1595.8 315 1910.8 7703.9 578.4 0.046
9 150 3.22 3403 465 3868 11571.9 764.7 0.059 9 150 2.475 3403 465 3868 11571.9 764.7 0.045
8 150 3.52 2330.8 465 2795.8 14367.7 865.8 0.071 8 150 2.86 2330.8 465 2795.8 14367.7 865.8 0.058
7 150 3.58 2330.8 465 2795.8 17163.5 942.5 0.079 7 150 3.08 2330.8 465 2795.8 17163.5 942.5 0.068
6 150 3.44 2330.8 465 2795.8 19959.3 998.8 0.083 6 150 2.915 2330.8 465 2795.8 19959.3 998.8 0.071
5 150 3 4323.8 615 4938.8 24898.1 1070.2 0.085 5 150 2.365 4323.8 615 4938.8 24898.1 1070.2 0.067
4 150 3 3066.1 615 3681.1 28579.2 1101.7 0.094 4 150 2.475 3066.1 615 3681.1 28579.2 1101.7 0.078
3 150 2.94 3066.1 615 3681.1 32260.3 1118.2 0.103 3 150 2.64 3066.1 615 3681.1 32260.3 1118.2 0.092
2 216 3.55 3097 615 3712 35972.3 1124.5 0.096 2 216 7.0125 3097 615 3712 35972.3 1124.5 0.189

19. ASCE 7 ELF Load Combinations
Final Design Load Combinations
1.37D + 0.5L + E
0.73D+E
Four directions of seismic forces
(+X,-X,+Y,-Y) were considered .
Total 8 possible combinations of direct
force plus accidental torsion were applied.
 X direction forces + 30% Y direction
forces are applied.
X direction 5% accidental
eccentricity
Y direction forces were applied without
eccentricity.

20. ELF Member forces
 Earthquake shears were obtained from SAP 2000 from gridline 1
Comparison of maximum Seismic Girder
Shears
Girder FEMA 451 Design
SAP 2000
Location Example
R-12 6.83 9.54
12-11 12.77 17.6
11-10 19.73 26.9
10-9 24.86 32.9
9-8 24.34 32.7
8-7 28.28 36
7-6 28.75 39.2
6-5 30.23 40.4
5-4 28.39 34.3
4-3 29.55 33.6
3-2 28.66 33
2-G 30.66 33

21. Modal-Response-Spectrum Analysis
I. Modal Analysis in SAP 2000
• Mode Shapes
• Period of vibration
FEMA-451 Example SAP2000 Analysis
Mode Period Period
MODE
(sec) (sec)
SHAPES
1 2.867 2.96 FEMA-451
2 2.745 2.86 EXAMPLE
3 1.565 1.79
4 1.149 1.15
5 1.074 1.08
6 0.724 0.78
7 0.697 0.67
8 0.631 0.64
9 0.434 0.47
10 0.427 0.43

22. Mode Shapes from Modal Analysis in SAP2000
Mode 1 Mode 2 Mode 3 Mode 4 Mode 5
T=2.96 sec T=2.86 sec T=1.79 sec T=1.15 sec T=1.08 sec
Mode 6 Mode 7 Mode 8 Mode 9 Mode 10
T=0.78 sec T=0.67 sec T=0.64 sec T=0.47 sec T=0.43 sec

23. Response Spectrum Co-ordinates
_I__ = _1_
SDS = 0.833 SD1 = 0.373 R 8
To = 0.089sec Ts = 0.447sec Modification
 Analysis using
Response Spectrum
Co-ordinates in SAP
2000.
 Combination of
Seismic motion in X
and Y direction is used.

24. Dynamic Base Shear
Story Shears from Modal-Response-Spectrum Analysis Story Shears from Modal-Response-Spectrum Analysis
From FEMA-451 Example From SAP 2000 analysis
Story X Directn Y Directn Story X Directn Y Directn
(SF =2.18) (SF = 2.1) (SF =2.14) (SF = 2.1)
Response spectrum Unscaled Scaled Unscaled Scaled Unscaled Scaled Unscaled Scaled
Shear Shear Shear Shear Shear Shear Shear Shear
analysis in SAP (kips) (kips) (kips) (kips) (kips) (kips) (kips) (kips)
2000 for Time R-12 82.5 180 79.2 167 R-12 72.11 154.3154 64.86 136.206
12 to 11 131 286 127.6 268 12 to 11 125.5 268.57 119.6 251.16
Period 2.87 sec 11 to 10 163.7 358 163.5 344 11 to 10 160.5 343.47 162.45 341.145
gives following 10 to 9 191.1 417 195 410 10 to 9 113.64 243.1896 173.97 365.337
9 t0 8 239.6 523 247.6 521 9 t0 8 185.78 397.5692 212.65 446.565
shears: 8 to 7 91.72 196.2808 181.65 381.465
8 to 7 268.4 586 277.2 583
7 to 6 292.5 638 302.1 635 7 to 6 300.03 642.0642 308.2 647.22
6 to 5 315.2 688 326 686 6 to 5 323.375 692.0225 333.97 701.337
5 to 4 358.6 783 371.8 782 5 to 4 372.93 798.0702 368.53 773.913
4 to 3 383.9 838 400.5 843 4 to 3 403.291 863.0427 401.18 842.478
3 to 2 409.4 894 426.2 897 3 to 2 425.94 911.5116 436.82 917.322
2 to G 437.7 956 454.6 956 2 to G 446.67 955.8738 458.12 962.052
ELF Base shear = 1124 Factors for scaling Response Spectrum
kips for fundamental base shear to 85% base shear computed
period of T=2.23 sec in ELF

25. Response Spectrum Drifts in
X-Direction
Response Spectrum Drift for Building Responding in X Direction
From FEMA-451 Example
Scaled
Level Total Drift from Scaled Total Drift Scaled Story Allowable
R.S. Analysis Drift (in.) Drift X Cd Story Drift
(in.) [Col-1 X 2.18] (in.) (in.) (in.)
R 1.96 4.28 0.18 0.99 3
12 1.88 4.1 0.26 1.43 3
11 1.76 3.84 0.3 1.65 3
10 1.62 3.54 0.33 1.82 3
9 1.47 3.21 0.34 1.87 3
8 1.32 2.87 0.36 1.98 3 Response Spectrum Drift for Building Responding in X Direction
from SAP 2000
7 1.15 2.51 0.4 2.2 3
6 0.968 2.11 0.39 2.14 3
5 0.789 1.72 0.38 2.09 3
4 0.615 1.34 0.38 2.09 3 Level Total Drift from Scaled Total Scaled Drift Scaled Story Allowable
3 0.439 0.958 0.42 2.31 3 R.S. Analysis Drift (in.) Drift X Cd Story Drift
2 0.245 0.534 0.53 2.91 4.32 (in.) [Col-1 X 2.14] (in.) (in.) (in.)
1 in. = 25.4 mm R 1.93 4.1302 0.11 0.605 3
12 1.88 4.0232 0.17 0.935 3
11 1.8 3.852 0.22 1.21 3
10 1.7 3.638 0.23 1.265 3
9 1.59 3.4026 0.29 1.595 3
8 1.45 3.103 0.28 1.54 3
7 1.32 2.8248 0.32 1.76 3
6 1.17 2.5038 0.36 1.98 3
5 1 2.14 0.3 1.65 3
4 0.86 1.8404 0.34 1.87 3
3 0.7 1.498 0.41 2.255 3
2 0.51 1.0914 1.09 5.995 4.32

26. Response Spectrum Drifts in
Y-Direction
Response Spectrum Drift for Building Responding in Y Direction
From FEMA-451 Example
Level Total Drift from Scaled Total Scaled Drift Scaled Story Allowable
R.S. Analysis Drift (in.) Drift X Cd Story Drift
(in.) [Col-1 X 2.18] (in.) (in.) (in.)
R 1.84 3.87 0.12 0.66 3
12 1.79 3.75 0.2 1.1 3
11 1.69 3.55 0.24 1.32 3
10 1.58 3.31 0.37 2.04 3
Response Spectrum Drift for Building Responding in Y Direction
9 1.4 2.94 0.29 1.6 3
From SAP 2000
8 1.26 2.65 0.33 1.82 3
7 1.1 2.32 0.35 1.93 3 Level Total Drift from Scaled Total Scaled Drift Scaled Story Allowable
6 0.938 1.97 0.38 2.09 3 R.S. Analysis Drift (in.) Drift X Cd Story Drift
5 0.757 1.59 0.32 1.76 3 (in.) [Col-1 X 2.1] (in.) (in.) (in.)
4 0.605 1.27 0.36 2 3 R 1.82 3.822 0.06 0.33 3
3 0.432 0.908 0.39 2.14 3 12 1.79 3.759 0.13 0.715 3
2 0.247 0.518 0.52 2.86 4.32 11 1.73 3.633 0.15 0.825 3
1 in. = 25.4 mm 10 1.66 3.486 0.32 1.76 3
9 1.51 3.171 0.23 1.265 3
8 1.4 2.94 0.27 1.485 3
7 1.27 2.667 0.29 1.595 3
6 1.13 2.373 0.49 2.695 3
5 0.9 1.89 0.32 1.76 3
4 0.75 1.575 0.38 2.09 3
3 0.57 1.197 0.4 2.2 3
2 0.38 0.798 0.79 4.345 4.32

27. P-Delta Effects
Computation of P-Delta Effects for X-Direction Computation of P-Delta Effects for X-Direction Response
Response from FEMA-451 Example ffrom SAP 2000
Level hsx Δ PD PL PT PX VX θX Level hsx Δ PD PL PT PX VX θX
(in.) (in.) (kips) (kips) (kips) (kips) (kips)
(in.) (in.) (kips) (kips) (kips) (kips) (kips)
R 150 0.99 1656.5 315 1971.5 1971.5 180 0.013 R 150 0.605 1656.5 315 1971.5 1971.5 154.3154 0.01
12 150 1.43 1595.8 315 1910.8 3882.3 286 0.024 12 150 0.935 1595.8 315 1910.8 3882.3 268.57 0.02
11 150 1.21 1595.8 315 1910.8 5793.1 343.47 0.02
11 150 1.65 1595.8 315 1910.8 5793.1 358 0.032
10 150 1.82 1595.8 315 1910.8 7703.9 417 0.041 10 150 1.265 1595.8 315 1910.8 7703.9 243.1896 0.05
9 150 1.87 3403 465 3868 11571.9 523 0.05 9 150 1.595 3403 465 3868 11571.9 397.5692 0.06
8 150 1.98 2330.8 465 2795.8 14367.7 586 0.059 8 150 1.54 2330.8 465 2795.8 14367.7 196.2808 0.14
7 150 2.2 2330.8 465 2795.8 17163.5 638 0.072 7 150 1.76 2330.8 465 2795.8 17163.5 642.0642 0.06
6 150 2.14 2330.8 465 2795.8 19959.3 688 0.075 6 150 1.98 2330.8 465 2795.8 19959.3 692.0225 0.07
5 150 2.09 4323.8 615 4938.8 24898.1 783 0.081 5 150 1.65 4323.8 615 4938.8 24898.1 798.0702 0.06
4 150 2.09 3066.1 615 3681.1 28579.2 838 0.086 4 150 1.87 3066.1 615 3681.1 28579.2 863.0427 0.08
3 150 2.31 3066.1 615 3681.1 32260.3 894 0.101 3 150 2.255 3066.1 615 3681.1 32260.3 911.5116 0.10
2 216 2.91 3097 615 3712 35972.3 956 0.092 2 216 5.995 3097 615 3712 35972.3 955.8738 0.19

28. Torsion, Orthogonal Loading and
Load Combinations
Response Spectrum Analysis including accidental torsion and orthogonal loading
Effects in SAP 2000 for determining member design forces
 100 percent of scaled X spectrum acting in one direction, concurrent with 30
percent of scaled Y spectrum in orthogonal direction.
 Similar analysis performed for larger loads in Y direction.

29. Member Design Forces
Design forces include 100 percent of the scaled X-direction spectrum added to 30
percent of scaled Y-direction spectrum and accidental torsion is added to combined
spectral loading.
FEMA-451
SAP 2000 output for Shear forces Example
Scaled
Shear Forces Earth Scaled Total
from Response quake Accidental Accidental earthquak Member
Story Spectrum shear Torsion torsion e shear forces
level Combinaton forces Shear Force Shear force force (kips)
R-12 2.03 4.344 0.43 0.37 4.71 9.9
12 to 11 2.23 4.772 0.88 0.75 5.52 17.8
11 to 10 7.58 16.221 1.35 1.15 17.37 26
10 to 9 7.22 15.451 1.87 1.59 17.04 29.8
9 to 8 8.03 17.184 1.83 1.56 18.74 26.6
8 to 7 8.93 19.110 1.36 1.16 20.27 28
7 to 6 9.68 20.715 1.51 1.28 22.00 30.9
6 to5 8.69 18.597 1.78 1.51 20.11 32.3
5 to 4 9.46 20.244 1.43 1.22 21.46 27.9
4 to 3 10.1 21.614 1.1 0.94 22.55 28.8
3 to 2 12.02 25.723 1.14 0.97 26.69 29.7
2 to G 12.23 26.172 1.3 1.11 27.28 31.5

30. Modal Time History Analysis
 Structure analyzed for three different pairs of ground motion time-histories
 The emphasis here was to implement and understand Time-History approach
Ground Motions Used for Analysis
Record Name Orientation Source Motion
RecordA00 N-S Lucern (Landers)
RecordA90 E-W Lucern (Landers)
RecordB00 N-S Corrolitos (Loma Prieta)
RecordB90 E-W Corrolitos (Loma Prieta)
RecordC00 N-S Dayhook (Tabas,Iran)
RecordC90 E-W Dayhook (Tabas,Iran)
Time History for Loma – Prieta used in SAP 2000
analysis

31. Modal Time History Analysis
• Twelve individual time-history analysis performed in SAP 2000
• 5% Damping considered
• Maximum scaled base shears computed
Result Maxima from Time-History Analysis (Unscaled) from Result Maxima from Time-History Analysis (Scaled)
SAP 2000
Analysis Maximum Base Required Adjusted Adjusted
Analysis Maximum Base Time of Max. Max. Roof Time of Max. shear Additional Max. Roof Max. Roof
shear Shear Displacement Displacement (S.F. = 0.115) Scale Factor Displacement Displacement
(S.F. = 0.115) (S.F. = 0.115) for V=1124 (S.F. = 0.115) X Cd
(kips) (sec) (in.) (sec.) (kips) kips (in.) (in.)
A 00-X 372.77 11.4 1.94 12.75 A 00-X 372.77 3.02 5.85 32.17
A 00-Y 354.87 11.4 1.61 12.64 A 00-Y 354.87 3.17 5.10 28.05
A 90-X 819.3 12.8 5.02 11.4 A 90-X 819.3 1.37 6.89 37.88
A 90-Y 714.95 12.78 4.34 11.34 A 90-Y 714.95 1.57 6.82 37.53
B 00-X 269.7 4.96 1.3 5.96 B 00-X 269.7 4.17 5.42 29.80
B 00-Y 350.7 8.45 1 7.37 B 00-Y 350.7 3.21 3.21 17.63
B 90-X 307.4 8.64 1.01 7.4 B 90-X 307.4 3.66 3.69 20.31
B 90-Y 350.63 8.5 0.98 7.3 B 90-Y 350.63 3.21 3.14 17.28
C 00-X 875 13.32 4.16 21.3 C 00-X 875 1.28 5.34 29.39
C 00-Y 816.3 13.4 3.47 11.92 C 00-Y 816.3 1.38 4.78 26.28
C 90-X 817.53 12.85 4.8 14.2 C 90-X 817.53 1.37 6.60 36.30
C 90-Y 823.63 13.02 4.1 14.1 C 90-Y 823.63 1.36 5.60 30.77
ELF Base shear = 1124 kips for Factors for scaling Modal Time
fundamental period of T=2.23 sec History base shear to 100 %
base shear computed in ELF

32. Drift
Drift and P-delta checked only for Motion A00 acting in X-direction
Scaled Inertial Force and story shear envelopes from Analysis A00X
Time-History Drift for building responding in X Direction to Motion A 00X
At Time of Max. Roof At Time of Max. Base
Level 1 2 3 4
Level Displacement Shear
Elastic Total Elastic Story Inelastic Story Allowable
(T = 12.75 sec) (T = 11.4 sec)
Drift Drift Drift Drift
(in.) (in.) (in.) (in.) Story Inertial force Story Inertial force
R 5.849612362 0.22 1.21 3 Shear (k) (kips) Shear (k) (kips)
12 5.638543874 0.27 1.485 3 R 49.2085 49.21 35.57065 35.57
11 5.367170105 0.38 2.09 3 12 92.08855 42.88 66.9185 34.35
10 4.975185771 0.39 2.145 3 11 132.2868 40.2 68.402 1.482
9 4.522896156 0.51 2.805 3 10 102.8882 -29.4 89.2239 20.82
8 4.010301258 0.7 3.85 3 9 175.099 72.12 146.625 57.41
7 3.316790514 0.3 1.65 3 8 83.6165 -91.39 74.3475 -72.28
6 3.015264104 0.39 2.145 3 7 256.3868 172.77 214.1381 139.79
5 2.62327977 0.33 1.815 3 6 272.7685 16.38 178.4478 -35.69
4 2.291600719 0.42 2.31 3 5 290.582 17.81 220.0859 41.56
3 1.869463744 0.48 2.64 3 4 317.86 27.28 234.9565 212.95
2 1.387021488 1.39 7.645 4.32 3 336.5705 18.71 324.1816 89.22
2 352.7625 16.19 349.7587 25.58

33. Torsion and Orthogonal Loading
Accidental Torsion applied without using 0.85 as the factor.
 Orthogonal loading accounted by concurrently running one ground
motion in one principle direction with 30 percent of companion motion
in orthogonal direction.

34. Member Forces
Maximum Member Forces for each story
story level (kips)
R to 12 18.61
12 to 11 37.65
11 to 10 54.88
10 to 9 71.76
9 to 8 16.25
8 to 7 82.57
7 to 6 87.52
6 to 5 87.74
5 to 4 73.14
4 to 3 72.23
3 to 2 75.57
2 to G 73.34

35. Comparison of Methods for
Various Methods of Analysis
ELF
Response-spectrum Analysis
Modal-time-history-analysis

36. Base Shears and Story shears
Summary of results from various Methods of Analysis: Story Shear Summary of results from various Methods of Analysis: Story Shear
From FEMA-451 Example from SAP 2000
Story Shear (kips) Story Shear (kips)
Level ELF RS TH at Time of TH at time of Level ELF RS TH at Time of TH at time of
Max. Max. Max. Max.
Displacement Base Shear Displacement Base Shear
R 187 180 307 40.2 R 186.9 154.3 49.21 35.57
12 341 286 530 44.3 12 340.9 268.6 42.88 34.35
11 471 358 664 45.7 11 470.8 343.5 40.2 1.482
10 578 417 731 95.6 10 578.4 243.2 -29.4 20.82
9 765 523 788 319 9 764.7 397.6 72.12 57.41
8 866 586 818 468 8 865.8 196.3 -91.39 -72.28
7 943 638 844 559 7 942.5 642.02 172.77 139.79
6 999 688 856 596 6 998.8 692.02 16.38 -35.69
5 1070 783 829 663 5 1070.2 798.07 17.81 41.56
4 1102 838 779 786 4 1102.7 863.04 27.28 212.95
3 1118 894 718 972 3 1118.2 911.5 18.71 89.22
2 1124 956 669 1124 2 1124.5 955.9 16.19 25.58

37. Drift
Summary of Results from Various Methods of Analysis: Story Drift Summary of Results from Various Methods of Analysis: Story Drift
from FEMA-451 Example from SAP 2000
X- Direction Drift (in.) X- Direction Drift (in.)
Level ELF RS TH Level ELF RS TH
R 0.982 0.99 2.57 R 0.59356 0.605 1.21
12 1.41 1.43 3.63 12 0.96844 0.935 1.485
11 1.75 1.65 4.14 11 1.34332 1.21 2.09
10 1.92 1.82 4.12 10 1.62448 1.265 2.145
9 1.83 1.87 3.4 9 1.4058 1.595 2.805
8 2 1.98 3.34 8 1.62448 1.54 3.85
7 2.03 2.2 3.2 7 1.74944 1.76 1.65
6 1.95 2.14 2.95 6 1.65572 1.98 2.145
5 1.7 2.09 2.32 5 1.34332 1.65 1.815
4 1.7 2.09 2.12 4 1.4058 1.87 2.31
3 1.67 2.31 1.89 3 1.49952 2.255 2.64
2 2.02 2.91 2.13 2 3.9831 5.995 7.645

38. Member Forces
Summary of Results from Various Methods of Analysis: Beam Shear from Summary of Results from Various Methods of Analysis: Beam Shear from
FEMA-451 Example SAP 2000
X- Direction Drift (in.) X- Direction Drift (in.)
Level ELF RS TH Level ELF RS TH
R 9.54 9.7 17.5 R 4.56 2 17.05
12 17.6 17.7 32.3 12 9.75 4.08 35.9
11 26.3 24.9 45.6 11 14.94 5.8 52.19
10 31 27.7 49.3 10 17.96 6.63 60.48
9 32.7 26.5 44.5 9 22.09 7.63 71.52
8 34.1 26.7 43.5 8 27.2 9.5 88.9
7 38.1 28.8 45.4 7 30.22 10.46 96.63
6 38.4 30.4 42.9 6 31.3 11.09 95.1
5 34.3 27.7 36.4 5 39.5 10.84 82.87
4 31 27 35.3 4 27.7 10.69 75.28
3 31.7 28.8 36.1 3 29.5 11.93 77.42
2 31.8 30.6 37.3 2 34 14.4 88.66

39. Conclusion
ELF Modal-Response-spectrum Analysis Modal-time-history-analysis
Useful for Preliminary Beneficial in-
Design •Nonlinear dynamic
Modal analysis essential time history analysis
ELF Analysis results for Final Design
are necessary for •Non-proportionally
application of damped Linear
accidental torsion systems

40. Questions

41. Thank you!