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CHAPTER 5

RESPONSE HISTORY ANALYSIS

5.1 INTRODUCTION

This section provides details about the response history analysis of the building. Response history analysis is performed for upper bound properties in DE and upper and lower bound properties in MCE events. The selection and scaling of ground motions for response history analysis, RHA are described in sections 3.2 and 3.3 (section 3.3.2 is specifically applied in scaling ground motion histories). The resultant forces and displacements are then compared with that of equivalent lateral force method.

5.2 ANALYSIS KEY INPUT AND ASSUMPTIONS

The following points describe the important input data and assumptions for

response history analysis.

5.2.1 SCALING OF TIME HISTORIES

The time histories were scaled per ASCE 7-16, section 17.3.4 and described in section 3.3.2. The resultant scale factors are 1.35 for fault normal component applied on U1 direction and 0.675 for fault parallel component applied on U2 direction of the building, this order of scaling is referred as “Case A”. The order was reversed for another analysis, (1.35 for fault normal component applied on U2 direction and 0.675 for fault parallel component applied on U1 direction of the building). This order of scaling is referred as “Case B”. It was observed that the resultant responses were almost identical (except the axes were swapped) and therefore the results presented later applies only to “Case A” (Case A will not be mentioned explicitly) except for response history analysis for DE, where both cases are shown for verification of the above claim. The factors will be reduced by a factor of (2/3) to account of the design nature of earthquake loading in DE response history analysis with upper bound properties.

5.2.2 MODAL ANALYSIS

For modal analysis, Ritz method was used. The number of Ritz vectors were specified to be 240, the minimum number of Ritz vectors per [A. A. S. Sarlis and

M.C. Constantinou] is 3 time the number of isolator plus the rigid masses. The goal

was to take in to account modal mass participation of 99% at all 6 degrees of freedom. Figure below shows the base reaction for EQ4, it is clear from the

highlighted column that 240 modes are sufficient for taking the whole weight (33000 kip) in to account in the analysis (it is the same case for other EQs).

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Figure 5 1: Base Reaction (Vertical reaction in each time step is equal to weight of the

structure)

5.2.3 DAMPING

Constant Damping with Override procedure was used for specifying damping. Damping was set constant to 0.02 except for the first 6 modes, in these modes damping was override to 0.01. The periods for the first nine modes are shown below.

StepType Period Text Sec

Mode -1 4.89

Mode -2 4.88 Mode -3 4.48

Mode -4 0.34 Mode -5 0.33 Mode -6 0.29

Mode -7 0.20 Mode -8 0.18

Mode -9 0.17