Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis ProcedureExample: Dynamic Analysis Procedure (Response Spectrum Analysis)

The dynamic analysis procedure using hand calculations for buildings taller than, say, two or three stories becomes unwieldy. Therefore, in the following example, a planar frame of a two-story building is selected. To keep the explanation simple, a “shear building” model is assumed so that the problem will be a two DOF system.

Given. A two-story, 30 ft tall concrete building with a floor-to-floor height of 15 ft. Structural System: special moment frame system (SMRF)Icr = cracked moment of inertia of columns = 12,000 in4 each columnW = seismic dead load = 580 kips/floor = 2 × 580 = 1160 kips for the entire buildingE = modules of elasticity of concrete = 4000 ksi

Dynamic Analysis Procedure

The procedure consists of determining• Modal periods, T1 and T2

• Mode shapes corresponding to T1 and T2

• Modal mass and participation factors for each mode• Modal base shears

To help us understand how static base shear is used to scale dynamic shear, the remainder of this solution consists of determining

• Static base shear using equivalent lateral force procedure• Scaling of dynamic results• Distribution of modal base shear in each mode

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

The modal base shear may be combined by taking the square root of the sum of the squares (SRSS) of each of the modal values or by the complete quadratic combination (CQC) technique. The SRSS method is used here.

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis ProcedureFor higher modes, computer programs are used to perform the calculations.

SUMMARY - The general procedure is summarized as follows:

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure

Dynamic Analysis Procedure