OVERVIEW
The Seismic Load Analysis Procedure has 16 processes and it is largely divided into 2 parts : Series 1 (Including Series 2 , 3 & 4) and Series 5 (Modal Response Spectrum (RS) Analysis.
The part we will look over today is Series 5 : Modal Response Spectrum (RS) Analysis.
Modal Response Spectrum(RS) Analysis
Where
⋅ SDS = the design spectral response acceleration parameter at short periods
⋅ SD1 = the design spectral response acceleration parameter at a 1-sec period
⋅ T = the fundamental period of the structure, sec
⋅ T0 = 0.2(SD1/SDS )
⋅ TL = long-period transition period(s) shown in Figs. 22-14 through 22-17
Basic Steps in RS Analysis
1. Compute modal properties for each mode
> Frequency (period), Shape, Modal participation factor, Effective modal mass
2. Determine number of modes to use in analysis
> Use a sufficient number of modes to capture at least 90% of total mass in each direction.
3. Compute spectral accelerations for each contributing mode
> Use a general spectrum.
4. Compute modified spectral accelerations
> Multiply spectral accelerations by modal participation factor and by (I/R).
5. Compute modal displacements for each mode
6. Compute element forces in each mode
7. Statistically combine modal displacements to determine system displacements
> SRSS or CQC
8. Statistically combine component forces to determine system displacements
> SRSS or CQC
9. Scale-up seismic load of RS
> If the design base shear based on modal analysis is less than 85% of the base shear(Equivalent Lateral force) computed using T=TaCu.
→ combination of modes must be scaled such that the base shear equals
0.85 times the equivalent lateral force.
10. Add accidental torsion
> As a static loading and amplify if necessary
11. Check story drift
> multiply the results of the modal analysis
(including the I/R scaling but not the 85% scaling) by Cd/I.
2. Select "Response Spectrum" in analysis type.
3. Select modal combination method. (use CQC generally).
4. Click "Method" button in damping control.
5. Modify damping ratio if necessary.
: Specify whether to restore the signs deleted during the mode combination and specify the restoration method.
Along the Major Mode Direction: Restore the signs according to the signs(+, -) of the principal mode for every loading direction.
Along the Absolute Maximum Value: Restore the signs according to the signs of the absolute maximum values of the modal results.
• Use 3D analysis
• For concrete structures, include the effect of cracking (consider a stiffness for cracked section).
• For steel structures, include panel zone deformations.
• Include flexibility of foundation if well enough defined
• Include actual flexibility of diaphragm if well enough defined
• Include P-delta effects in the analysis if the program has the capability
• Do not try to include accidental torsion by the movement of the center of mass
• Include orthogonal load effects by running the fill 100% spectrum in each direction, and then SRSSing the results.
Generation of RS
Base shear(x-dir) for example model
𝑇=0.35574sec
So, Sa = SDS*Ie/R = 0.01728
(red dotted line)
⇓
V= W * Sa * Mass(%)
= 36817.5 * 0.01728 * 0.7089
= 451.01kN (just for 1st mode)