ASCE 7-10 Section 12.8.1.1 sets forth the following minimum base shear equations:

1. C_s shall not be less than C_s = 0.044S_DSI_e ≥ 0.01  (Equation 12.8-5)

2. C_s shall not be less than (0.5S₁)/(R/I_e) when S₁ is equal to or greater than 0.6g   (Equation 12.8-6)

In order to better understand these required minimums, a little history about why they exist is helpful.

C_s ≥ 0.044S_DSI_e — Following the 1933 Long Beach earthquake, the California Riley Act required every building to be designed for a minimum service-level seismic force equal to 3 percent of its weight. This minimum requirement eventually became seismic zone-dependent in the Uniform Building Code (UBC). In the 1997 UBC, this minimum base shear was brought up to strength level and was made soil-dependent; it became 0.11C_aIW — where C_a was a function of Z, the Seismic Zone Factor, and of the soil characteristics at the site of the structure; I was the importance factor; and W was the effective seismic weight. In the 2000 NEHRP Provisions, this minimum base shear became 0.044S_DSIW, based on S_DS = 2.5C_a.

C_s ≥ 0.01 — This minimum is intended to provide a nominal level of structural integrity that will improve the performance of buildings in the event of a possible earthquake.

C_s ≥ (0.5S₁)/(R/I_e) when S₁ is equal to or greater than 0.6g — Following the 1994 Northridge Earthquake, a lower-bound on the design base shear, applicable in Seismic Zone 4 only, was added to the 1997 UBC. This minimum was specifically intended to account for the large displacement and velocity pulses that were observed in near-fault ground motion in the Northridge earthquake. A corresponding minimum was added to the 1997 NEHRP Provisions. This minimum was originally applicable to structures assigned to SDC E and F only. In the 2000 IBC, this equation was also made applicable to all structures located where the mapped MCE spectral response acceleration at 1-second period, S₁, equaled or exceeded 0.6g, which is roughly equivalent to Zone 4 of the 1997 UBC. The applicability of this minimum value is the same in ASCE 7-10 as it is in the 2000 IBC.

Q1.  Do these minimum base shear equations apply when determining drift?

A1. In accordance with ASCE 7-10 Section 12.8.6.1 shown below, Eq. 12.8-6 applies, but Eq. 12.8-5 need not apply.

12.8.6.1 Minimum Base Shear for Computing Drift

The elastic analysis of the seismic force-resisting system for computing drift shall be made using the prescribed seismic design forces of Section 12.8.

EXCEPTION: Eq. 12.8-5 need not be considered for computing drift.

Q2.  Why doesn’t Eq. 12.8-5 need to apply?

A2.  Again, a little history will help answer the question.

C_s ≥ 0.044S_DSI_e — The 1997 UBC exempted the minimum base shear of 0.044S_DSIW from drift computation, but not without a lot of controversy surrounding it. This exemption was not adopted by ASCE 7-02, ASCE 7-05, or the first four editions of the IBC. Now the exemption has been brought back in ASCE 7-10. This change is significant when it comes to the design of tall buildings. Tall buildings are drift-controlled, rather than strength-controlled. The design of many tall buildings prior to ASCE 7-10, irrespective of seismic design category, has likely been governed, in the absence of this exemption, by drift computed under the 0.044S_DSIW minimum. Many consider this to be unreasonable, since this minimum design base shear is essentially a minimum strength requirement, with its magnitude arbitrarily set.

C_s ≥ 0.01 — ASCE 7-05 required that the 0.01 minimum be used for drift determination if it governed. However, this seldom controlled because it is such a low value. With ASCE 7-10, this minimum was bundled with C_s ≥ 0.044S_DSI_e in Eq. 12.8-5, and therefore, it does not need to be applied for drift computation.

C_s ≥ (0.5S₁)/(R/I_e) when S₁ is equal to or greater than 0.6g —ASCE 7-10 requires that the 0.5S₁/(R/I_e)W minimum be used for drift determination if it governs. This minimum is not exempt and should not be exempt from use in drift determination because it has a physical basis.