Illustration of 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 shown in Fig. 2.47 is selected. To keep the explanation simple, infinitely large values are assumed for the flexural stiffness of the beams and the axial stiffness of the columns. Thus, lateral deflection of the frame results from column flexure only.
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 in.4 each column
W = seismic dead load = 580 kips/floor
= 2 x 580 = 1160 kips for the entire building E = modules of elasticity of concrete = 4000 ksi
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
Seismic design data. The maximum considered earthquake spectral response acceleration at short period,
Seismic Use Group = I (standard occupancy)
Seismic importance factor, I = 1.0
Soil type = SD
Site coefficient Fa = 1.0
Site coefficient Fv = 1.5
Modified short period response, SMS = FaSs = 1 x 1.5 = 1.5 Modified 1-second period response, SM1 = FVS1 = 1.5 x 0.6 = 0.9 Design spectral response acceleration parameters at 5% damping:
At short period: At 1-second period:
SDS = 2/3Sms = 2/3 x 1.5 = 1.0 SD1 = 2/3SM1 = 2/3 x 0.9 = 0.6
For a special moment frame system (SMRF), R = 8, Cd = 6.5, where R and Cd are response modification and deflection factor, respectively.
Seismic Design Category based on both SDs and SD is D for the example building. Determine Mass Matrix [m].
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