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(1) Figure 1 shows a two-story one-by building. The structural story stiffness are kı-k2-1x106 N/m, the floor masses are mi-m2-1000 kg, 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 all 0.05, the fortification intensity is 7 (basis acceleration value equals to 0.15g), belongs to the 2nd group. Answer the following questions. (a) 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) (b) Use the modal effective mass to explain why the design base shear of structure is dominated the 1st modal response.

(1) Figure 1 shows a two-story one-by building. The structural story stiffness are kı-k2-1x106 N/m, the floor masses are mi-m2-1000 kg, 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 all 0.05, the fortification intensity is 7 (basis acceleration value equals to 0.15g), belongs to the 2nd group. Answer the following questions. (a) 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) (b) Use the modal effective mass to explain why the design base shear of structure is dominated the 1st 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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Appendix: Table 1. Earthquake effect coefficient amax (damping ratio 0.05) Intensity Frequent EQ Rare EQ Note: the values in brackets are used for the regions which Design Basis Earthquake acceleration values are 0.15g or 0.30g. nama Table 2. Characteristics period (s) Soil type I II III 1st group 0.25 0.35 0.45 2nd group 0.30 0.40 0.55 3rd group 0.35 0.45 0.65 Note: when the earthquake intensity is equal to 8 or 9, the characteristics period should add 0.05s. 0.45a a 0 0.1 T₂ 6 0.04 where 7 8 9 0.08(0.12) 0.16(0.24) 0.32 0.50(0.72) 0.90(1.20) 1.40 a = √yna F₁ = nama ST, T(s) ≤0.35 0.35 0.55 > 0.55 0.05-5 0.3+65' 0.05-5. 7=0.9+ 4+325 Figure 3. Earthquake effect coefficient curve Table 3. Top additional earthquake force coefficients a=[1₂0.2"-n(T-5T₂)Ja n=0.02 + T>1.4T 0.087, +0.07 0.087, +0.01 0.087,-0.02 IV 0.65 0.75 0.90 6.0 -FEK (1-8) 1.4T 0 0 0 T(s) The earthquake load distribution formula in base shear method H,G, ΣH,G, k=1 7/₂=1+ 0.05-5 0.08+1.65
Transcribed Image Text:Appendix: Table 1. Earthquake effect coefficient amax (damping ratio 0.05) Intensity Frequent EQ Rare EQ Note: the values in brackets are used for the regions which Design Basis Earthquake acceleration values are 0.15g or 0.30g. nama Table 2. Characteristics period (s) Soil type I II III 1st group 0.25 0.35 0.45 2nd group 0.30 0.40 0.55 3rd group 0.35 0.45 0.65 Note: when the earthquake intensity is equal to 8 or 9, the characteristics period should add 0.05s. 0.45a a 0 0.1 T₂ 6 0.04 where 7 8 9 0.08(0.12) 0.16(0.24) 0.32 0.50(0.72) 0.90(1.20) 1.40 a = √yna F₁ = nama ST, T(s) ≤0.35 0.35 0.55 > 0.55 0.05-5 0.3+65' 0.05-5. 7=0.9+ 4+325 Figure 3. Earthquake effect coefficient curve Table 3. Top additional earthquake force coefficients a=[1₂0.2"-n(T-5T₂)Ja n=0.02 + T>1.4T 0.087, +0.07 0.087, +0.01 0.087,-0.02 IV 0.65 0.75 0.90 6.0 -FEK (1-8) 1.4T 0 0 0 T(s) The earthquake load distribution formula in base shear method H,G, ΣH,G, k=1 7/₂=1+ 0.05-5 0.08+1.65
(1) Figure 1 shows a two-story one-by building. The structural story stiffness are kı-k₂-1x106 N/m, the floor masses are m₁= m2-1000 kg, 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 all 0.05, the fortification intensity is 7 (basis acceleration value equals to 0.15g), belongs to the 2nd group. Answer the following questions. (a) 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) (b) Use the modal effective mass to explain why the design base shear of structure is dominated the 1st modal response. W₁ = 6.8 rad/sec; w₂ = 17.7rad/sec = {-1.618 Φι = {0.618; 2 = { = 992 195.2 üz k2,c2 (2) For the same structure shown in Figure 2: (a) Use the base shear method to conduct the structural seismic resistant design ki,ci Figure 1. Two-story one-bay building (b) Use contra-flexural point method to draw the designed moment diagram of the structure. It is assumed that the stiffness of two columns in the same story are the same.
Transcribed Image Text:(1) Figure 1 shows a two-story one-by building. The structural story stiffness are kı-k₂-1x106 N/m, the floor masses are m₁= m2-1000 kg, 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 all 0.05, the fortification intensity is 7 (basis acceleration value equals to 0.15g), belongs to the 2nd group. Answer the following questions. (a) 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) (b) Use the modal effective mass to explain why the design base shear of structure is dominated the 1st modal response. W₁ = 6.8 rad/sec; w₂ = 17.7rad/sec = {-1.618 Φι = {0.618; 2 = { = 992 195.2 üz k2,c2 (2) For the same structure shown in Figure 2: (a) Use the base shear method to conduct the structural seismic resistant design ki,ci Figure 1. Two-story one-bay building (b) Use contra-flexural point method to draw the designed moment diagram of the structure. It is assumed that the stiffness of two columns in the same story are the same.
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