SM3_2_2004_Solutions notes

SM3_2_2004_Solutions notes - ASSIGNMENT 2 TIME-HISTORY...

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ASSIGNMENT 2 – TIME-HISTORY ANALYSIS, RESPONSE SPECTRUM CALCULATION NOTES ON SOLUTION Stiffness calculation Various assumptions were made about the trussed frame structure: Assumption Resulting Stiffness Period Analysis Method Accurate 19,200kN/m 0.7854s (stiffness method, 2m deep beam-col. connection) 6m portal 18,640kN/m 0.7971s (moment distribution or stiffness method) 5m portal 31,405kN/m 0.6141s (moment distribution or stiffness method) 7m portal 11,960kN/m 0.9951s (moment distribution or stiffness method) 6m, rigid beam 22,222kN/m 0.73s (moment-area or similar) The 6m simple portal, with the mass also assumed to act at a height of 6m, had an agreeable cancellation of errors leading to a good result. The resulting maximum displacement, max u , was then obtained using the step-by-step integration algorithm, as implemented in spreadsheet or Matlab. Maximum base shear could then be deduced as stiffness x maximum displacement, max u k ; or alternatively, as mass x maximum absolute acceleration
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