Seismic Design of Structures Project

BY

Anirudha Vasudevan

Gunjan Shetye

Harsh Shah

Presented to Dr.Ganesh Thiagarajan for CIV-ENGR 5501B Seismic Design of StructuresDate: April 25,2011Jury : Mr. Shivaji Jagtap P.E. Mr. Shakeel

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/

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.

OBJECTIVES

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

Why This Building??

Description of The Structure

Special Moment Frame of Structural Steel as Lateral Load Resisting System

30 ft. wide bays in X-direction

25 ft. wide bays in Y-direction

One-story basement 18ft below grade

Columns range from W24X146 at roof to W24X229 at Level G

Girders range from W30X108 at roof to W30X132 at Level G

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 = 0.56Accelerations:

Design spectral acceleration SDS = 0.833 SD1 = 0.373parameters:

Ts=SD1/SDS = 0.373/0.833 = 0.45sec

Ground Motion Parameters for Stockton ,CA

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

Dynamic Properties

Period of Vibration

Ta =1.59 secCu = 1.4 Cu * Ta = 2.23 seconds

Damping

For steel structures damping ratio of 0.05 is appropriate.

Courtesy: comp.uark.edu

Courtesy: edes.bris.ac.uk

Mass Distribution

Diagram for computation of floor mass (FEMA-451 Example)

Area masses on floor diaphragms (FEMA-451 Example 3.1)

Line masses on floor diaphragms (FEMA-451 Example 3.1)

Area Mass Applied as Gravity Dead Load using Uniform

to Frame option in SAP.

Line Mass Applied as Uniformly Distributed Loads in

the gravity direction.

Equivalent Lateral Force Analysis

For preliminary design purposes.

To asses the three dimensional response characteristics of the structure.

Most commonly used design procedure since the 1960s.

WHY ELF??

Elastic Linear Static

Analysis

Design Seismic Forces

Time varying Inertial Forces

Equivalent Static Forces

ELF Parameters

Seismic base shearV = CsW (NEHRP Provisions Eq 5.2.1)

Maximum spectral accelerationCsmax = 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)

Equivalent Lateral Forces

Fx = Cvx V

Level Wx hx k wxhx^k Cvx V Fx Vxx kips ft kips kips kips

Roof 1656.5 155.5 1.86 19761048 0.16671 1124.5 187.5 187.46412 1595.67 143 1.86 16288013 0.13741 1124.5 154.5 341.98111 1595.67 130.5 1.86 13739744 0.11591 1124.5 130.3 472.32410 1595.67 118 1.86 11393145 0.09612 1124.5 108.1 580.4069 3401 105.5 1.86 19717698 0.16634 1124.5 187.1 767.4598 2232.6 93 1.86 10237389 0.08637 1124.5 97.1 864.5777 2232.6 80.5 1.86 7826926.5 0.06603 1124.5 74.3 938.8276 2232.6 68 1.86 5718439.1 0.04824 1124.5 54.2 993.0765 4325.8 55.5 1.86 7593664.1 0.06406 1124.5 72.0 1065.114 3350.4 43 1.86 3658878.5 0.03087 1124.5 34.7 1099.823 3350.4 30.5 1.86 1931498.4 0.01629 1124.5 18.3 1118.152 3098 18 1.86 669712.3 0.00565 1124.5 6.4 1124.5

Totals 30666.9 118536155 1

Equivalent lateral Forces for buildings responding in X and Y directions based on NEHRP 2003

ELF

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

Torsional Irregularity in X direction

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 IrregularityR 6.03 6.19 6.11 6.19 1.01 none

12 5.83 6.01 5.92 6.01 1.02 none11 5.5 5.72 5.61 5.72 1.02 none10 5.04 5.33 5.185 5.33 1.03 none9 4.54 4.8 4.67 4.8 1.03 none8 4.11 4.34 4.225 4.34 1.03 none7 3.61 3.81 3.71 3.81 1.03 none6 3.07 3.24 3.155 3.24 1.03 none5 2.55 2.7 2.625 2.7 1.03 none4 2.14 2.25 2.195 2.25 1.03 none3 1.71 1.79 1.75 1.79 1.02 none2 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.

δmax

δmin

Torsional Irregularity in Y direction

Computation for Torsional Irregularity with ELF Loads Acting in Y Direction (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 none12 5.6 5.79 5.695 5.79 1.02 none11 5.37 5.56 5.465 5.56 1.02 none10 5.06 5.24 5.15 5.24 1.02 none9 4.3 4.74 4.52 4.74 1.05 none8 3.96 4.27 4.115 4.27 1.04 none7 3.57 3.75 3.66 3.75 1.02 none6 3.14 3.18 3.16 3.18 1.01 none5 2.23 2.6 2.415 2.6 1.08 none4 1.78 2.09 1.935 2.09 1.08 none3 1.33 1.56 1.445 1.56 1.08 none2 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.

δmax δmin

No Torsional Amplification Required

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

Total Drift Story DriftInelastic

StoryInealastic

Drift Allowable

from SAP

2000from SAP

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 1.41 311 5.95 0.56 3.08 1.75 310 5.39 5.39 3.38 1.92 39 4.77 0.59 3.22 1.83 38 4.19 0.64 3.52 2 37 3.55 0.65 3.58 2.03 36 2.9 0.63 3.44 1.95 35 2.27 0.55 3 1.7 34 1.73 0.55 3 1.7 33 1.18 0.54 2.94 1.67 32 0.65 0.65 3.55 2.02 4.32

ELF Drift for Building Responding in X Direction from SAP 2000

Level 1 2 3 4 5 Total Drift Story Drift Inelastic Story Inealastic Drift Allowable

from SAP

2000from SAP

2000 Drift Times 0.568 Drift (in.) (in.) (in.) (in.) (in.)R 6.11 0.19 1.045 0.59 3

12 5.92 0.31 1.705 0.97 311 5.61 0.43 2.365 1.34 310 5.185 0.52 2.86 1.62 39 4.67 0.45 2.475 1.41 38 4.225 0.52 2.86 1.62 37 3.71 0.56 3.08 1.75 36 3.155 0.53 2.915 1.66 35 2.625 0.43 2.365 1.34 34 2.195 0.45 2.475 1.41 33 1.75 0.48 2.64 1.50 32 1.275 1.275 7.0125 3.98 4.32

ELF Drifts in Y DirectionELF Drift for Building Responding in X Direction (FEMA-451 Design Examples Table3.1-7)

Level 1 2 3 4 5

Total Drift Story DriftInelastic

StoryInealastic

Drift Allowable

from SAP

2000from SAP

2000 Drift Times 0.568 Drift (in.) (in.) (in.) (in.) (in.)R 6.01 0.22 1.21 0.687 3

12 5.79 0.36 1.98 1.12 311 5.43 0.45 2.48 1.41 310 4.98 0.67 3.66 2.08 39 4.32 0.49 2.7 1.53 38 3.83 0.57 3.11 1.77 37 3.26 0.58 3.19 1.81 36 2.68 0.64 3.49 1.98 35 2.05 0.46 2.53 1.43 34 1.59 0.49 2.67 1.52 33 1.1 0.49 2.7 1.53 32 0.61 0.61 3.36 1.91 4.32

ELF Drift for Building Responding in Y Direction from SAP 2000

Level 1 2 3 4 5

Total Drift Story DriftInelastic

Story Inealastic Drift Allowable

from SAP

2000 from SAP 2000 Drift Times 0.568 Drift (in.) (in.) (in.) (in.) (in.)R 5.825 0.13 0.715 0.41 3

12 5.695 0.23 1.265 0.72 311 5.465 0.32 1.76 1.00 310 5.15 0.63 3.465 1.97 39 4.52 0.41 2.255 1.28 38 4.115 0.46 2.53 1.44 37 3.66 0.5 2.75 1.56 36 3.16 0.75 4.125 2.34 35 2.415 0.48 2.64 1.50 34 1.935 0.49 2.695 1.53 33 1.445 0.51 2.805 1.59 32 0.94 0.94 5.17 2.94 4.32

Accurate period using Rayleigh Analysis

Rayleigh analysis for X-direction Period of Vibration

Level

Drift, δ Force, F Weight, W δF δ2W/g

(in.) (kips) (kips) (in.-kips) (in.-kips-sec2)R 6.11 186.9 1656 1141.959 159.99

12 5.92 154 1598 911.68 144.9411 5.61 129.9 1598 728.739 130.1610 5.185 107.6 1598 557.906 111.189 4.67 186.3 3403 870.021 192.078 4.225 100.8 2330 425.88 107.647 3.71 77 2330 285.67 83.006 3.155 56.2 2330 177.311 60.025 2.625 71.4 4323 187.425 77.094 2.195 31.5 3066 69.1425 38.233 1.75 16.6 3066 29.05 24.302 1.275 6.3 3097 8.0325 13.03 5392.816 1141.65

ω=(5392/1141)^0.5=2.17rad/sec. T=2π/ω=2.89sec 1.0in.=25.4mm , 1.0kip=4.45kN

ω =

Rayleigh analysis for Y-direction Period of Vibration

Level Drift, δ Force, F Weight, W δF δ2W/g (in.) (kips) (kips) (in.-kips) (in.-kips-sec2)R 5.825 186.9 1656 1088.7 145.42

12 5.695 154 1598 877.0 134.1311 5.465 129.9 1598 709.9 123.5210 5.15 107.6 1598 554.1 109.699 4.52 186.3 3403 842.1 179.938 4.115 100.8 2330 414.8 102.117 3.66 77 2330 281.8 80.786 3.16 56.2 2330 177.6 60.215 2.415 71.4 4323 172.4 65.254 1.935 31.5 3066 61.0 29.713 1.445 16.6 3066 24.0 16.572 0.94 6.3 3097 5.9 7.08 5209.34 1054.39

ω=(5209/1054)^0.5=2.22rad/sec. T=2π/ω=2.83 sec 1.0in.=25.4mm , 1.0kip=4.45kN

P-Delta Effects

Computation of P-Delta Effects for X-Direction Response FEMA 451 Design Example

Level hsx Δ PD PL PT PX VX θX

(in.) (in.) (kips) (kips) (kips) (kips) (kips) R 150 1.73 1656.5 315 1971.5 1971.5 186.9 0.022

12 150 2.48 1595.8 315 1910.8 3882.3 340.9 0.03411 150 3.08 1595.8 315 1910.8 5793.1 470.8 0.04610 150 3.38 1595.8 315 1910.8 7703.9 578.4 0.055

9 150 3.22 3403 465 386811571.

9 764.7 0.059

8 150 3.52 2330.8 465 2795.814367.

7 865.8 0.071

7 150 3.58 2330.8 465 2795.817163.

5 942.5 0.079

6 150 3.44 2330.8 465 2795.819959.

3 998.8 0.083

5 150 3 4323.8 615 4938.824898.

1 1070.2 0.085

4 150 3 3066.1 615 3681.128579.

2 1101.7 0.094

3 150 2.94 3066.1 615 3681.132260.

3 1118.2 0.103

2 216 3.55 3097 615 371235972.

3 1124.5 0.096

Computation of P-Delta Effects for X-Direction Response from SAP 2000

Level hsx Δ PD PL PT PX VX θX

(in.) (in.) (kips) (kips) (kips) (kips) (kips) R 150 1.045 1656.5 315 1971.5 1971.5 186.9 0.013

12 150 1.705 1595.8 315 1910.8 3882.3 340.9 0.02411 150 2.365 1595.8 315 1910.8 5793.1 470.8 0.03510 150 2.86 1595.8 315 1910.8 7703.9 578.4 0.046

9 150 2.475 3403 465 3868 11571.9 764.7 0.045

8 150 2.86 2330.8 465 2795.8 14367.7 865.8 0.058

7 150 3.08 2330.8 465 2795.8 17163.5 942.5 0.068

6 150 2.915 2330.8 465 2795.8 19959.3 998.8 0.071

5 150 2.365 4323.8 615 4938.8 24898.1 1070.2 0.067

4 150 2.475 3066.1 615 3681.1 28579.2 1101.7 0.078

3 150 2.64 3066.1 615 3681.1 32260.3 1118.2 0.092

2 216 7.0125 3097 615 3712 35972.3 1124.5 0.189

ASCE 7 ELF Load CombinationsFinal Design Load Combinations

1.37D + 0.5L + E0.73D+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.

ELF Member forces

Earthquake shears were obtained from SAP 2000 from gridline 1

Comparison of maximum Seismic Girder Shears

Girder Location

SAP 2000 FEMA 451 Design Example

R-12 6.83 9.5412-11 12.77 17.611-10 19.73 26.910-9 24.86 32.99-8 24.34 32.78-7 28.28 367-6 28.75 39.26-5 30.23 40.45-4 28.39 34.34-3 29.55 33.63-2 28.66 332-G 30.66 33

Modal-Response-Spectrum Analysis

I. Modal Analysis in SAP 2000• Mode Shapes• Period of vibration

ModeFEMA-451 Example

PeriodSAP2000 Analysis

Period

(sec) (sec)

1 2.867 2.96

2 2.745 2.86

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

MODESHAPESFEMA-451EXAMPLE

Mode Shapes from Modal Analysis in SAP2000

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5T=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 10T=0.78 sec T=0.67 sec T=0.64 sec T=0.47 sec T=0.43 sec

Response Spectrum Co-ordinates

SDS = 0.833 SD1 = 0.373To = 0.089sec Ts = 0.447sec

_I__ = _1_ R 8Modification

Analysis using Response Spectrum Co-ordinates in SAP 2000.

Combination of Seismic motion in X and Y direction is used.

Dynamic Base ShearStory Shears from Modal-Response-Spectrum AnalysisFrom FEMA-451 Example

Story X Directn Y Directn

(SF =2.18) (SF = 2.1) Unscaled Scaled Unscaled Scaled Shear Shear Shear Shear (kips) (kips) (kips) (kips)

R-12 82.5 180 79.2 16712 to 11 131 286 127.6 26811 to 10 163.7 358 163.5 34410 to 9 191.1 417 195 4109 t0 8 239.6 523 247.6 5218 to 7 268.4 586 277.2 5837 to 6 292.5 638 302.1 6356 to 5 315.2 688 326 6865 to 4 358.6 783 371.8 7824 to 3 383.9 838 400.5 8433 to 2 409.4 894 426.2 8972 to G 437.7 956 454.6 956

Story Shears from Modal-Response-Spectrum AnalysisFrom SAP 2000 analysis

Story X Directn Y Directn

(SF =2.14) (SF = 2.1) Unscaled Scaled Unscaled Scaled Shear Shear Shear Shear (kips) (kips) (kips) (kips)

R-12 72.11 154.3154 64.86 136.20612 to 11 125.5 268.57 119.6 251.1611 to 10 160.5 343.47 162.45 341.14510 to 9 113.64 243.1896 173.97 365.3379 t0 8 185.78 397.5692 212.65 446.5658 to 7 91.72 196.2808 181.65 381.4657 to 6 300.03 642.0642 308.2 647.226 to 5 323.375 692.0225 333.97 701.3375 to 4 372.93 798.0702 368.53 773.9134 to 3 403.291 863.0427 401.18 842.4783 to 2 425.94 911.5116 436.82 917.3222 to G 446.67 955.8738 458.12 962.052

Response spectrum analysis in SAP 2000 for Time Period 2.87 sec gives following shears:

ELF Base shear = 1124 kips for fundamental period of T=2.23 sec

Factors for scaling Response Spectrum base shear to 85% base shear computed in ELF

Response Spectrum Drifts in X-Direction

Response Spectrum Drift for Building Responding in X 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 1.96 4.28 0.18 0.99 3

12 1.88 4.1 0.26 1.43 311 1.76 3.84 0.3 1.65 310 1.62 3.54 0.33 1.82 39 1.47 3.21 0.34 1.87 38 1.32 2.87 0.36 1.98 37 1.15 2.51 0.4 2.2 36 0.968 2.11 0.39 2.14 35 0.789 1.72 0.38 2.09 34 0.615 1.34 0.38 2.09 33 0.439 0.958 0.42 2.31 32 0.245 0.534 0.53 2.91 4.32

1 in. = 25.4 mm

Response Spectrum Drift for Building Responding in X Direction from SAP 2000

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 2.14] (in.) (in.) (in.)R 1.93 4.1302 0.11 0.605 3

12 1.88 4.0232 0.17 0.935 311 1.8 3.852 0.22 1.21 310 1.7 3.638 0.23 1.265 39 1.59 3.4026 0.29 1.595 38 1.45 3.103 0.28 1.54 37 1.32 2.8248 0.32 1.76 36 1.17 2.5038 0.36 1.98 35 1 2.14 0.3 1.65 34 0.86 1.8404 0.34 1.87 33 0.7 1.498 0.41 2.255 32 0.51 1.0914 1.09 5.995 4.32

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 1.1 311 1.69 3.55 0.24 1.32 310 1.58 3.31 0.37 2.04 39 1.4 2.94 0.29 1.6 38 1.26 2.65 0.33 1.82 37 1.1 2.32 0.35 1.93 36 0.938 1.97 0.38 2.09 35 0.757 1.59 0.32 1.76 34 0.605 1.27 0.36 2 33 0.432 0.908 0.39 2.14 32 0.247 0.518 0.52 2.86 4.32

1 in. = 25.4 mm

Response Spectrum Drift for Building Responding in Y Direction From SAP 2000

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 2.1] (in.) (in.) (in.)R 1.82 3.822 0.06 0.33 3

12 1.79 3.759 0.13 0.715 311 1.73 3.633 0.15 0.825 310 1.66 3.486 0.32 1.76 39 1.51 3.171 0.23 1.265 38 1.4 2.94 0.27 1.485 37 1.27 2.667 0.29 1.595 36 1.13 2.373 0.49 2.695 35 0.9 1.89 0.32 1.76 34 0.75 1.575 0.38 2.09 33 0.57 1.197 0.4 2.2 32 0.38 0.798 0.79 4.345 4.32

P-Delta Effects

Computation of P-Delta Effects for X-Direction Response from FEMA-451 Example

Level hsx Δ PD PL PT PX VX θX

(in.) (in.) (kips) (kips) (kips) (kips) (kips)

R 150 0.99 1656.5 315 1971.5 1971.5 180 0.013

12 150 1.43 1595.8 315 1910.8 3882.3 286 0.024

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

9 150 1.87 3403 465 3868 11571.9 523 0.05

8 150 1.98 2330.8 465 2795.8 14367.7 586 0.059

7 150 2.2 2330.8 465 2795.8 17163.5 638 0.072

6 150 2.14 2330.8 465 2795.8 19959.3 688 0.075

5 150 2.09 4323.8 615 4938.8 24898.1 783 0.081

4 150 2.09 3066.1 615 3681.1 28579.2 838 0.086

3 150 2.31 3066.1 615 3681.1 32260.3 894 0.101

2 216 2.91 3097 615 3712 35972.3 956 0.092

Computation of P-Delta Effects for X-Direction Response ffrom SAP 2000

Level hsx Δ PD PL PT PX VX θX

(in.) (in.) (kips) (kips) (kips) (kips) (kips)

R 150 0.605 1656.5 315 1971.5 1971.5 154.3154 0.01

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

10 150 1.265 1595.8 315 1910.8 7703.9 243.1896 0.05

9 150 1.595 3403 465 3868 11571.9 397.5692 0.06

8 150 1.54 2330.8 465 2795.8 14367.7 196.2808 0.14

7 150 1.76 2330.8 465 2795.8 17163.5 642.0642 0.06

6 150 1.98 2330.8 465 2795.8 19959.3 692.0225 0.07

5 150 1.65 4323.8 615 4938.8 24898.1 798.0702 0.06

4 150 1.87 3066.1 615 3681.1 28579.2 863.0427 0.08

3 150 2.255 3066.1 615 3681.1 32260.3 911.5116 0.10

2 216 5.995 3097 615 3712 35972.3 955.8738 0.19

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.

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.

SAP 2000 output for Shear forcesFEMA-451 Example

Story level

Shear Forces from Response

Spectrum Combinaton

Scaled Earth quake shear forces

Accidental Torsion

Shear Force

Scaled Accidental

torsion Shear force

Total earthquak

e shear force

Member forces

(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 17.811 to 10 7.58 16.221 1.35 1.15 17.37 2610 to 9 7.22 15.451 1.87 1.59 17.04 29.89 to 8 8.03 17.184 1.83 1.56 18.74 26.68 to 7 8.93 19.110 1.36 1.16 20.27 287 to 6 9.68 20.715 1.51 1.28 22.00 30.96 to5 8.69 18.597 1.78 1.51 20.11 32.35 to 4 9.46 20.244 1.43 1.22 21.46 27.94 to 3 10.1 21.614 1.1 0.94 22.55 28.83 to 2 12.02 25.723 1.14 0.97 26.69 29.72 to G 12.23 26.172 1.3 1.11 27.28 31.5

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

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

Ground Motions Used for Analysis

Modal Time History Analysis

Result Maxima from Time-History Analysis (Unscaled) from SAP 2000

Analysis Maximum Base Time of Max. Max. Roof Time of Max. shear Shear Displacement Displacement (S.F. = 0.115) (S.F. = 0.115) (kips) (sec) (in.) (sec.)

A 00-X 372.77 11.4 1.94 12.75A 00-Y 354.87 11.4 1.61 12.64A 90-X 819.3 12.8 5.02 11.4A 90-Y 714.95 12.78 4.34 11.34B 00-X 269.7 4.96 1.3 5.96B 00-Y 350.7 8.45 1 7.37B 90-X 307.4 8.64 1.01 7.4B 90-Y 350.63 8.5 0.98 7.3C 00-X 875 13.32 4.16 21.3C 00-Y 816.3 13.4 3.47 11.92C 90-X 817.53 12.85 4.8 14.2C 90-Y 823.63 13.02 4.1 14.1

• Twelve individual time-history analysis performed in SAP 2000• 5% Damping considered• Maximum scaled base shears computed

Result Maxima from Time-History Analysis (Scaled)

Analysis Maximum Base Required Adjusted Adjusted shear Additional Max. Roof Max. Roof (S.F. = 0.115) Scale Factor Displacement Displacement for V=1124 (S.F. = 0.115) X Cd (kips) kips (in.) (in.)

A 00-X 372.77 3.02 5.85 32.17A 00-Y 354.87 3.17 5.10 28.05A 90-X 819.3 1.37 6.89 37.88A 90-Y 714.95 1.57 6.82 37.53B 00-X 269.7 4.17 5.42 29.80B 00-Y 350.7 3.21 3.21 17.63B 90-X 307.4 3.66 3.69 20.31B 90-Y 350.63 3.21 3.14 17.28C 00-X 875 1.28 5.34 29.39C 00-Y 816.3 1.38 4.78 26.28C 90-X 817.53 1.37 6.60 36.30C 90-Y 823.63 1.36 5.60 30.77

ELF Base shear = 1124 kips for fundamental period of T=2.23 sec

Factors for scaling Modal Time History base shear to 100 % base shear computed in ELF

Drift

Drift and P-delta checked only for Motion A00 acting in X-direction

Time-History Drift for building responding in X Direction to Motion A 00X

Level 1 2 3 4 Elastic Total Elastic Story Inelastic Story Allowable Drift Drift Drift Drift (in.) (in.) (in.) (in.)R 5.849612362 0.22 1.21 3

12 5.638543874 0.27 1.485 311 5.367170105 0.38 2.09 310 4.975185771 0.39 2.145 39 4.522896156 0.51 2.805 38 4.010301258 0.7 3.85 37 3.316790514 0.3 1.65 36 3.015264104 0.39 2.145 35 2.62327977 0.33 1.815 34 2.291600719 0.42 2.31 33 1.869463744 0.48 2.64 32 1.387021488 1.39 7.645 4.32

Scaled Inertial Force and story shear envelopes from Analysis A00X

At Time of Max. Roof At Time of Max. BaseLevel Displacement Shear (T = 12.75 sec) (T = 11.4 sec)

Story Inertial force Story Inertial force Shear (k) (kips) Shear (k) (kips)

R 49.2085 49.21 35.57065 35.5712 92.08855 42.88 66.9185 34.3511 132.2868 40.2 68.402 1.48210 102.8882 -29.4 89.2239 20.829 175.099 72.12 146.625 57.418 83.6165 -91.39 74.3475 -72.287 256.3868 172.77 214.1381 139.796 272.7685 16.38 178.4478 -35.695 290.582 17.81 220.0859 41.564 317.86 27.28 234.9565 212.953 336.5705 18.71 324.1816 89.222 352.7625 16.19 349.7587 25.58

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.

Member Forces

story levelMaximum Member Forces for each story (kips)

R to 12 18.6112 to 11 37.6511 to 10 54.8810 to 9 71.769 to 8 16.258 to 7 82.577 to 6 87.526 to 5 87.745 to 4 73.144 to 3 72.233 to 2 75.57

2 to G 73.34

Comparison of Methods for Various Methods of Analysis

ELF

Response-spectrum Analysis

Modal-time-history-analysis

Base Shears and Story shearsSummary of results from various Methods of Analysis: Story Shear From FEMA-451 Example

Story Shear (kips)Level ELF RS TH at Time of TH at time of

Max. Max. Displacement Base ShearR 187 180 307 40.2

12 341 286 530 44.311 471 358 664 45.710 578 417 731 95.69 765 523 788 3198 866 586 818 4687 943 638 844 5596 999 688 856 5965 1070 783 829 6634 1102 838 779 7863 1118 894 718 9722 1124 956 669 1124

Summary of results from various Methods of Analysis: Story Shear from SAP 2000

Story Shear (kips)Level ELF RS TH at Time of TH at time of

Max. Max. Displacement Base ShearR 186.9 154.3 49.21 35.57

12 340.9 268.6 42.88 34.3511 470.8 343.5 40.2 1.48210 578.4 243.2 -29.4 20.829 764.7 397.6 72.12 57.418 865.8 196.3 -91.39 -72.287 942.5 642.02 172.77 139.796 998.8 692.02 16.38 -35.695 1070.2 798.07 17.81 41.564 1102.7 863.04 27.28 212.953 1118.2 911.5 18.71 89.222 1124.5 955.9 16.19 25.58

DriftSummary of Results from Various Methods of Analysis: Story Drift from FEMA-451 Example

X- Direction Drift (in.)Level ELF RS TH

R 0.982 0.99 2.5712 1.41 1.43 3.6311 1.75 1.65 4.1410 1.92 1.82 4.129 1.83 1.87 3.48 2 1.98 3.347 2.03 2.2 3.26 1.95 2.14 2.955 1.7 2.09 2.324 1.7 2.09 2.123 1.67 2.31 1.892 2.02 2.91 2.13

Summary of Results from Various Methods of Analysis: Story Drift from SAP 2000

X- Direction Drift (in.)Level ELF RS TH

R 0.59356 0.605 1.2112 0.96844 0.935 1.48511 1.34332 1.21 2.0910 1.62448 1.265 2.1459 1.4058 1.595 2.8058 1.62448 1.54 3.857 1.74944 1.76 1.656 1.65572 1.98 2.1455 1.34332 1.65 1.8154 1.4058 1.87 2.313 1.49952 2.255 2.642 3.9831 5.995 7.645

Member ForcesSummary of Results from Various Methods of Analysis: Beam Shear from FEMA-451 Example

X- Direction Drift (in.)Level ELF RS TH

R 9.54 9.7 17.512 17.6 17.7 32.311 26.3 24.9 45.610 31 27.7 49.39 32.7 26.5 44.58 34.1 26.7 43.57 38.1 28.8 45.46 38.4 30.4 42.95 34.3 27.7 36.44 31 27 35.33 31.7 28.8 36.12 31.8 30.6 37.3

Summary of Results from Various Methods of Analysis: Beam Shear from SAP 2000

X- Direction Drift (in.)Level ELF RS TH

R 4.56 2 17.0512 9.75 4.08 35.911 14.94 5.8 52.1910 17.96 6.63 60.489 22.09 7.63 71.528 27.2 9.5 88.97 30.22 10.46 96.636 31.3 11.09 95.15 39.5 10.84 82.874 27.7 10.69 75.283 29.5 11.93 77.422 34 14.4 88.66

Conclusion

ELF Modal-Response-spectrum Analysis Modal-time-history-analysis

Useful for Preliminary Design

ELF Analysis results are necessary for application of accidental torsion

Modal analysis essential for Final Design

Beneficial in-• Nonlinear dynamic

time history analysis

• Non-proportionally damped Linear systems

Questions

Thank you!