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Required. 1. Modal analysis to determine base shears. 2. Story forces, overturning moments, accelerations, and displacements for eac mode. 3. Square-root-of-the-sum (SRSS) combinations.

Required. 1. Modal analysis to determine base shears. 2. Story forces, overturning moments, accelerations, and displacements for eac mode. 3. Square-root-of-the-sum (SRSS) combinations.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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T3 = 0.182 sec Spectral Acceleration. From the response spectrum of Fig. 2.51, the spectral ac- celerations are S₁₁ = 0.251 g for mode 1 S₁₂ = 0.41 g for mode 2 S = 0.41 g for mode 3 Required. 1. Modal analysis to determine base shears. 2. Story forces, overturning moments, accelerations, and displacements for each mode. 3. Square-root-of-the-sum (SRSS) combinations. Level Tm, sec R 3 2 Σ . PF Rm PF 30 20.45 3m PF 2m am Sa v=αmS₂W R1=0.3320 931 $21 Mass (k-sec²) 9x1 5.81 0.3320 7.32 0.2044 1.496 7.32 0.0860 0.630 0.964 ΣΜΦ Emo² 0.2044 0.086 Mode 1 (Emo)² Em(Emo²) 4.055 1.000 PR1= 1.346 0.829 0.349 = 0.8040 ** 0.251 g 132.7 kips -0.2201 -0.2075 R2=0.2384 0.356 $32 Mode 2 3 $22 Mode 2 momo -1.745 1.000 -0.416 0.384 0.362 0.149 Mode 1 mxx1 m,o 9x2 1.929 0.640 0.2384 1.385 0.330 0.0713 0.4143 0.030 0.306 -0.2201 -1.611 0.355-0.2154 -1.577 0.340 0.054 -0.2075 -1.519 0.315 0.2936 2.149 0.631 0.9863 1.001 0.41 g 40.2 kips m=1 9x3 0.182 R3=0.0713 $23 -0.2154 $33 0.2936 777777. Mode 3 Mode 3 m₂0x3 0.070 -0.212 0.289 0.048 Note that the sum of the modal participation factors PFxm=1.0 and the sum of modal base shear 3 participation factors Σm = 1.0. m=1 ** The mode shapes have been normalized by the computer program so that Σmo² = 1.0. Figure 2.52. Three-story building; modal analysis to determine base shears. 0.41 g 13.0 kips
Transcribed Image Text:T3 = 0.182 sec Spectral Acceleration. From the response spectrum of Fig. 2.51, the spectral ac- celerations are S₁₁ = 0.251 g for mode 1 S₁₂ = 0.41 g for mode 2 S = 0.41 g for mode 3 Required. 1. Modal analysis to determine base shears. 2. Story forces, overturning moments, accelerations, and displacements for each mode. 3. Square-root-of-the-sum (SRSS) combinations. Level Tm, sec R 3 2 Σ . PF Rm PF 30 20.45 3m PF 2m am Sa v=αmS₂W R1=0.3320 931 $21 Mass (k-sec²) 9x1 5.81 0.3320 7.32 0.2044 1.496 7.32 0.0860 0.630 0.964 ΣΜΦ Emo² 0.2044 0.086 Mode 1 (Emo)² Em(Emo²) 4.055 1.000 PR1= 1.346 0.829 0.349 = 0.8040 ** 0.251 g 132.7 kips -0.2201 -0.2075 R2=0.2384 0.356 $32 Mode 2 3 $22 Mode 2 momo -1.745 1.000 -0.416 0.384 0.362 0.149 Mode 1 mxx1 m,o 9x2 1.929 0.640 0.2384 1.385 0.330 0.0713 0.4143 0.030 0.306 -0.2201 -1.611 0.355-0.2154 -1.577 0.340 0.054 -0.2075 -1.519 0.315 0.2936 2.149 0.631 0.9863 1.001 0.41 g 40.2 kips m=1 9x3 0.182 R3=0.0713 $23 -0.2154 $33 0.2936 777777. Mode 3 Mode 3 m₂0x3 0.070 -0.212 0.289 0.048 Note that the sum of the modal participation factors PFxm=1.0 and the sum of modal base shear 3 participation factors Σm = 1.0. m=1 ** The mode shapes have been normalized by the computer program so that Σmo² = 1.0. Figure 2.52. Three-story building; modal analysis to determine base shears. 0.41 g 13.0 kips
Roof Third Given. The example is illustrated in Fig. 2.50. Weights and Masses WR = 187 kips mR = Second Sa.g 0.9 0.8 0.7 0.6 Figure 2.50. Three-story building example; dynamic analysis. 0.5 0.4 0.3 0.2 0.1 0.0 187 32.2 0.0 -= 5.81 kip sec²/ft 1.0 m₂ = m₂ = W = 187 kips W₂ = 256 kips W₂ = W3 = 236 kips W₂ = 256 kips 236 32.2 Periods. T₁ = 0.964 sec T₂ = 0.356 sec 2.0 Period, seconds Period 0.0 .586 80 1.0 1.5 2.0 3.0 4.0 Sa.g.14 .41 .300 .240.160.120 .080 .060 Figure 2.51. Three-story building; response spectrum. 3.0 4.0 7.33 kip-sec²/ft
Transcribed Image Text:Roof Third Given. The example is illustrated in Fig. 2.50. Weights and Masses WR = 187 kips mR = Second Sa.g 0.9 0.8 0.7 0.6 Figure 2.50. Three-story building example; dynamic analysis. 0.5 0.4 0.3 0.2 0.1 0.0 187 32.2 0.0 -= 5.81 kip sec²/ft 1.0 m₂ = m₂ = W = 187 kips W₂ = 256 kips W₂ = W3 = 236 kips W₂ = 256 kips 236 32.2 Periods. T₁ = 0.964 sec T₂ = 0.356 sec 2.0 Period, seconds Period 0.0 .586 80 1.0 1.5 2.0 3.0 4.0 Sa.g.14 .41 .300 .240.160.120 .080 .060 Figure 2.51. Three-story building; response spectrum. 3.0 4.0 7.33 kip-sec²/ft
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