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(a) Write the structural motion equation under earthquake excitation, and then determine the corresponding mass, stiffness and damping matrix. (b) Use the modal decomposition-based method to carry out the structural design. Please calculate the designed base shear and the inter-story drift ratio of the 1" story. The circular frequencies and mode shape vectors of the structure are given as following. (The corresponding tables from the Seismic Design Code is given in the Appendix) (c) Explain why the structural seismic responses are dominated the 1ª modal response.

(a) Write the structural motion equation under earthquake excitation, and then determine the corresponding mass, stiffness and damping matrix. (b) Use the modal decomposition-based method to carry out the structural design. Please calculate the designed base shear and the inter-story drift ratio of the 1" story. The circular frequencies and mode shape vectors of the structure are given as following. (The corresponding tables from the Seismic Design Code is given in the Appendix) (c) Explain why the structural seismic responses are dominated the 1ª modal response.

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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Table 2. Characteristics period (s) I 0.25 Soil type 1 group 2nd group 3rd group 0.45a 0.30 0.35 where a=yna ++ 0 0.1 T II 0.35 0.40 0.45 Note: when the earthquake intensity is equal to 8 or 9, the characteristics period should add 0.05s. 7=0.9+ 0.45 0.55 0.65 ST, IV 0.65 0.75 0.90 a=[n₂0.2²-n (T-5T) T(s) 0.05-5 0.3+65 Figure 2. Earthquake effect coefficient curve 77₁=0.02 + 6.0 0.05-5 4+325 7₂ = 1+ 0.05-5 0.08 +1.65
Transcribed Image Text:Table 2. Characteristics period (s) I 0.25 Soil type 1 group 2nd group 3rd group 0.45a 0.30 0.35 where a=yna ++ 0 0.1 T II 0.35 0.40 0.45 Note: when the earthquake intensity is equal to 8 or 9, the characteristics period should add 0.05s. 7=0.9+ 0.45 0.55 0.65 ST, IV 0.65 0.75 0.90 a=[n₂0.2²-n (T-5T) T(s) 0.05-5 0.3+65 Figure 2. Earthquake effect coefficient curve 77₁=0.02 + 6.0 0.05-5 4+325 7₂ = 1+ 0.05-5 0.08 +1.65
Figure 1 shows a two-story one-by building. The structural story stiffness are ki-k=12x106 N/m, the floor masses are m₁-m-10000 kg, the story damping coefficient c₁=c=1.5x10¹ N/(m/s), the story height is 3 m both stories. This building located in a zone of site category of II, and the damping ratio of the two modes are 0.025 and 0.065 respectively, the fortification intensity is 7 (basis acceleration value equals to 0.15g), belongs to the 2nd group. Answer the following questions. (a) Write the structural motion equation under earthquake excitation, and then determine the corresponding mass, stiffness and damping matrix. (b) Use the modal decomposition-based method to carry out the structural design. Please calculate the designed base shear and the inter-story drift ratio of the 1st story. The circular frequencies and mode shape vectors of the structure are given as following. (The corresponding tables from the Seismic Design Code is given in the Appendix) (c) Explain why the structural seismic responses are dominated the 1st modal response. w₁ = 6.77 rad/sec; w₂ = 17.72rad/sec $1 = (-0.0027 (0.0027; 2= 0.0017 Appendix: M2 üle ka,ca ki,ci Figure 1. Two-story one-bay building Table 1. Earthquake effect coefficient amax (damping ratio 0.05) Intensity 6 0.04 8 7 0.08(0.12) 0.16(0.24) 9 0.32 Frequent EQ Note: the values in brackets are used for the regions which Design Basis Earthquake acceleration values are 0.15g or 0.30g.
Transcribed Image Text:Figure 1 shows a two-story one-by building. The structural story stiffness are ki-k=12x106 N/m, the floor masses are m₁-m-10000 kg, the story damping coefficient c₁=c=1.5x10¹ N/(m/s), the story height is 3 m both stories. This building located in a zone of site category of II, and the damping ratio of the two modes are 0.025 and 0.065 respectively, the fortification intensity is 7 (basis acceleration value equals to 0.15g), belongs to the 2nd group. Answer the following questions. (a) Write the structural motion equation under earthquake excitation, and then determine the corresponding mass, stiffness and damping matrix. (b) Use the modal decomposition-based method to carry out the structural design. Please calculate the designed base shear and the inter-story drift ratio of the 1st story. The circular frequencies and mode shape vectors of the structure are given as following. (The corresponding tables from the Seismic Design Code is given in the Appendix) (c) Explain why the structural seismic responses are dominated the 1st modal response. w₁ = 6.77 rad/sec; w₂ = 17.72rad/sec $1 = (-0.0027 (0.0027; 2= 0.0017 Appendix: M2 üle ka,ca ki,ci Figure 1. Two-story one-bay building Table 1. Earthquake effect coefficient amax (damping ratio 0.05) Intensity 6 0.04 8 7 0.08(0.12) 0.16(0.24) 9 0.32 Frequent EQ Note: the values in brackets are used for the regions which Design Basis Earthquake acceleration values are 0.15g or 0.30g.
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