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# Scaling of Dynamic Base Shears

## Scaling of Dynamic Base Shears

(OP)
Below are my assumptions for doing a response spectrum analysis and design. Any comments would be appreciated.

1)    Perform modal analysis per section 12.9 of ASCE 7-05.
Response spectral ordinates Sa as defined in 11.4.5 are scaled by dividing them by (R/I).
2)    CQC method is used for combining modal response parameters.
3)    Compare the dynamic base shear (Vt) with the static base shear (V) obtained from equivalent lateral force procedure.
4)    If Vt < 0.85 V, scale the design forces by a factor 0.85*V/Vt, which basically scales up the dynamic base shear to 0.85V.
5)    If Vt > V, no further scaling is required.

Note that ASCE 7-98, required the dynamic base shears to be scaled to 1.0 V. I have not seen this requirement any more in ASCE 7-02 & ASCE 7-05.
Replies continue below

### RE: Scaling of Dynamic Base Shears

Per ASCE7-05 sections 12.9.2, 12.9.4 and 12.12.1, for drift calculation the only criteria need to follow are the requirements in section 12.9.2 and there is no need to match up any percentage of the calculated base shear using the equivalent lateral force procedure.  For force calculation, however, per section 12.9.4 engineers have to match up at least 85% of the base shear using the equivalent lateral force procedure.

In conclusion, let’s assume we already have a response spectra defined according to Section 11.4.5 or 21.2 and let’s assume the calculated base shear using the equivalent lateral force procedure is V and using a scale factor equal to I/R per section 12.9.2 we get a base shear Vt.

Case 1: Vt < 0.85V.

Drift Check - There is no need to increase the scale factor to increase the base shear Vt. However, per section 12.9.2 the drift value shall be multiplied by the quantity Cd/I and the result shall be smaller than the drift limits defined in Section 12.12.1.

Strength Check – The scale factor has to be multiplied by 0.85V/Vt to increase the base shear Vt to 0.85V per section 12.9.4.

Case 2: Vt > 0.85V.

Drift Check - There is no need to change the scale factor to change the base shear.  However, per section 12.9.2 the drift value shall be multiplied by the quantity Cd/I
and the result shall be smaller than the drift limits defined in Section 12.12.1.

Strength Check – There is no need to change the scale factor to change the base shear Vt per section 12.9.4.

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