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Earth 0205-response spectrum

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Earth 0205-response spectrum

  1. 1. EARTHQUAKE ENGINEERING2.5. Response Spectrum 2.5.1. Definition and Construction of Response Spectrum 2.5.2. Analysis Procedure Using Response Spectrum
  2. 2. 2.5.1. Definition and Construction of Response SpectrumDefinition Response Spectrum is a Plot of the Maximum Peak Response of Single Degree of Freedom System as a Function of its Natural Period (Frequency) For a Specific Dynamic Force (or Earthquake) Prof.Dr. Osman Shaalan 2 Earthquake Engineering Dr. Tharwat Sakr
  3. 3. 2.5.1. Definition and Construction of Response SpectrumExample NorthBridge Earthquake 3 Prof.Dr. Osman Shaalan Earthquake Engineering Dr. Tharwat Sakr
  4. 4. 2.5.1. Definition and Construction of Response SpectrumDamping Effects 4 Prof.Dr. Osman Shaalan Earthquake Engineering Dr. Tharwat Sakr
  5. 5. 2.5.1. Definition and Construction of Response SpectrumBenefits Characterization of Ground Motions Response Spectrum 15 20 9000 18 8000 16 7000 14 10 6000 Acceleration Acceleration 12 5000 10 4000 8 5 3000 6 2000 4 1000 2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 Period [sec] Prof.Dr. Osman Shaalan 5 Earthquake Engineering Dr. Tharwat Sakr
  6. 6. 2.5.1. Definition and Construction of Response SpectrumBenefits Earthquake Resistance Design Almost all Codes of Practice recommends the Response Spectrum as the Main Method for Earthquake Resistance Design Prof.Dr. Osman Shaalan 6 Earthquake Engineering Dr. Tharwat Sakr
  7. 7. 2.5.1. Definition and Construction of Response SpectrumGeneration of Response Spectrum Select the Required excitation & Damping Ration Choose SDOF System Change the Period of the System in the practical range For each Period make a Time History and Get the Maximum Required Response (Displacement – Velocity – Acceleration) Plot The Response Vs Period REFER TO THE MATLAB SEGMENT ATTACHED Prof.Dr. Osman Shaalan 7 Earthquake Engineering Dr. Tharwat Sakr
  8. 8. 2.5.2. Analysis Procedure Using Response SpectrumSDOF Structures (Procedure) Calculate the Structure dynamic parameters (K, M, ω, T) Select the Appropriate Value of Damping Ratio From the Response Spectrum Chart get the Spectral Value of the required response (Sa, Sv or Sd) Commonly Sa The Maximum Displacement umax = S a / ω 2 The Maximum Base Shear Vmax = S d × K = ( S a / g ) × W The Maximum Base Moment M max = Vmax × h Prof.Dr. Osman Shaalan 8 Earthquake Engineering Dr. Tharwat Sakr
  9. 9. 2.5.2. Analysis Procedure Using Response SpectrumSDOF Example Determine The Maximum Displacement, Base Shear and Overturning moment of the following Frame for 5% damping (Response Spectrum Chart is Given) Stiffness= 100000 kN.m2 - Mass = 100 t - Height = 4 m Response Spectrum 4.5 4 3.5 3 Acceleration 2.5 2 1.5 1 0.5 0 0 1 2 3 4 5 6 Period [sec] Prof.Dr. Osman Shaalan 9 Earthquake Engineering Dr. Tharwat Sakr
  10. 10. 2.5.2. Analysis Procedure Using Response SpectrumSDOF Example (Solution) ω = 31.6278 rad /s T = 0.1988 s From the Chart Sa = 0.25 m/s Umax = Sa/ω 2 =0.00025 m =0.25 mm Vmax = Sa×m =25.00 kN =2.50 t Mmax = Vmax ×h = 100 kN.m =10.0 t.m Prof.Dr. Osman Shaalan 10 Earthquake Engineering Dr. Tharwat Sakr
  11. 11. 2.5.2. Analysis Procedure Using Response SpectrumMDOF Structures (Procedure) Calculate the Structure dynamic parameters (φ I and ω I) Corresponding to each DOF For each degree of freedom (Mode) From the Response Spectrum Chart get the value of Sa corresponding to the mode i frequency ω i The Max. Displacement at DOF number u ji = Γiφ ji S ai / ωi 2 j The Max. Inter-Story Drift Story j ∆ ji = Γi (φ ji − φ( j −1) i ) S ai / ωi 2 The Max. Story Force at Story j F ji = Γi m jφ ji S ai Based on the Story Force, Story Shear, Moment and Base moment can be computed N Combine all modes by the SRSS formula R= ∑ Ri2 i =1 Prof.Dr. 11 Osman Shaalan Earthquake Engineering Dr. Tharwat Sakr
  12. 12. 2.5. Response SpectrumMDOF Example Investigate the inter-story drift and story shear for the given multistory building using the attached response spectrum chart No of Stories =2 Story Height =4m Story Mass = 60 t Story Stiffness = 240000 kN/m Damping Ratio = 5% Prof.Dr. Osman Shaalan 12 Earthquake Engineering Dr. Tharwat Sakr
  13. 13. 2.5. Response SpectrumMDOF Example 0.5 0.45 0.4 0.35 Acceleration [g] 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Period [sec] Prof.Dr. Osman Shaalan 13 Earthquake Engineering Dr. Tharwat Sakr
  14. 14. 2.5. Response SpectrumMDOF Example (Solution) ω = 39.09 T =0.1607 102.30 0.0614s φ= -0.0679 -0.1098 -0.1098 0.0679 From the Spectrum Participation Factor Sa1 = 0.45 Γ = -10.66 Sa2 = 0.315 -2.517 Displacements (Mode1 2 SRSS E-4 u1 = 2.1 0.0832 2.13 m U2 = 3.44 -0.0514 3.45 m Prof.Dr. Osman Shaalan 14 Earthquake Engineering Dr. Tharwat Sakr
  15. 15. 2.5. Response SpectrumMDOF Example (Solution) Inter-Story Drift (Mode1 2 SRSS) E-4 ∆1 = 2.1 0.0832 0.053%0 ∆2 = 1.31 -0.134 0.033%0 Forces (Mode1 2 SRSS) f1 = 19.54 5.22 20.23 kN f2 = 31.6 -3.23 31.77 kN Overturning Moment M = 335.05 kN.m Prof.Dr. Osman Shaalan 15 Earthquake Engineering Dr. Tharwat Sakr

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