We have received some questions about the definition of E, the earthquake load, and what it is for each of the following three sets of load combinations:

• SD
• Basic ASD
• Alternative ASD

The answers are not all that straight forward because of some incompatibility between the IBC and ASCE 7.  Hopefully the below explanation provides some clarity about how E is defined for each of the three sets of load combinations

Definition of E

E is defined in 2012 IBC Section 1602 as the “Combined effect of horizontal and vertical earthquake induced forces as defined in Section 12.4.2 of ASCE 7.” This definition applies to all of Chapter 16. However, the E term appears only in Section 1605, Load Combinations.

ASCE 7-10 Section 12.4.2 requires: The seismic load effect, E, shall be determined in accordance with the following:

1. For use in load combination 5 in Section 2.3.2 or load combinations 5 and 6 in Section 2.4.1, E shall be determined in accordance with Eq. 12.4-1 as follows:

E = E_h + E_v                                                                                (12.4-1)

2. For use in load combination 7 in Section 2.3.2 or load combination 8 in Section 2.4.1, E shall be determined in accordance with Eq. 12.4-2 as follows:

E = E_h – E_v                                                                                (12.4-2)

ASCE 7-10 Section 12.4.2.1 defines E_h as ρQ_E , while Section 12.4.2.2 defines E_v as 0.2S_DSD.

Strength Design (SD/LRFD) Load Combinations

ASCE 7-10 Section 2.3.2 Load Combinations 5 and 7 are counterparts of 2012 IBC Equations 16-5 and 16-7, respectively. Those equations are:

1.2(D + F) + 1.0E + ƒ₁L + 1.6H + ƒ₂S                                     (Equation 16-5)

which can be rewritten by plugging in E_h = ρQ_E  and E_v = 0.2S_DSD as:

         (1.2 + 0.2S_DS)D + 1.2F + 1.0 ρQ_E + ƒ₁L + 1.6H + ƒ₂S

and                                        0.9(D + F) + 1.0E+ 1.6H                                                      (Equation 16-7)

which can be rewritten as:    (0.9 – 0.2S_DS)D + 0.9F + 1.0 ρQ_E + 1.6H

Basic ASD Load Combinations

ASCE 7-10 Section 2.4.1 Load Combinations 5, 6 (should be 6b), and 8 are counterparts of 2012 IBC Equations 16-12, 16-14 and 16-16, respectively. Those equations are:

                                                D + H + F + (0.6W or 0.7E)                                               (Equation 16-12)

which can be rewritten as:   (1 + 0.14S_DS)D + H + F + (0.6W or 0.7ρQ_E)

                                                D + H + F + 0.75 (0.7E) + 0.75L + 0.75S                           (Equation 16-14)

which can be rewritten as:     (1 + 0.105S_DS)D + H + F + 0.75 (0.7ρQ_E) + 0.75L + 0.75S

                                                0.6(D + F) + 0.7E + H                                                         (Equation 16-16)

which can be rewritten as:     (0.6 – 0.14S_DS)D + 0.6F + 0.7ρQ_E + H

Exceptions Applicable to SD/LRFD and Basic ASD Load Combinations

There are the following important exceptions to the definition for E_v in ASCE 7-10 Section 12.4.2.2:

The vertical seismic load effect, E_v, is permitted to be taken as zero for either of the following conditions:

1. In Eqs. 12.4-1, 12.4-2, . . .  where S_DS is equal to or less than 0.125.

2. In Eq. 12.4-2 where determining demands on the soil–structure interface of foundations.

Thus, in all the above seismic SD/LRFD or ASD load combinations, E_v can be taken as zero for any S_DS ≤ 1/8. Also, in Equations 16-7 and 16-16, when they are applied to determining demands on the soil-structure interface of foundations, E_v may be taken equal to zero.

Alternative Basic Load Combinations

The alternative basic load combinations in 2012 IBC Section 1605.3.2 are not and never have been part of ASCE 7. ASCE 7-10 Section 2.4.1 Load Combinations 6 (should be 6b), and 8 have direct counterparts in Equations 16-21 and 16-22, respectively. ASCE 7-10 Section 2.4.1 Load Combination 5 does not have a direct counterpart. But 2012 IBC Section 1605.1 requires that “Each load combination shall also be investigated with one or more of the variable loads set to zero.” If, in 2012 IBC Equation 16-21, L and S are both taken equal to zero, it becomes the direct counterpart of ASCE 7-10 Section 2.4.1 Combination 5.

The definition of E in ASCE 7-10 Section 12.4.2 must still be considered valid, because there is no definition of E in the 2012 IBC other than by reference to that ASCE 7-10 section. Thus,

                                                D + L + S + E/1.4                                                       (Equation 16-21)

can be rewritten as:                (1 + 0.14S_DS)D + L + S + ρQ_E/1.4

and                                          0.9D + E/1.4                                                                (Equation 16-22)

can be rewritten as:                (0.9 – 0.14S_DS)D + ρQ_E/1.4

Exceptions Applicable to Alternative Basic Load Combinations

Our advice would be not to apply the exceptions in ASCE 7-10 Section 12.4.2.2 to the alternative basic load combinations. This set has its own exceptions: in Section 1605.3.2, although they are presented in paragraph form rather than exceptions.

1. When using these alternative load combinations to evaluate sliding, overturning and soil bearing at the soil-structure interface, the reduction of foundation overturning from Section 12.13.4 in ASCE 7 shall not be used. This reduction is explained below. 

Overturning moment at foundation-soil interface, which would normally be ∑F_x(h_x + h_b-s), where h_b-s is the distance below the base to the foundation-soil interface is allowed to be reduced 25%, if the F_x forces are obtained from equivalent lateral force analysis or 10%, if the F_x forces are obtained from modal response spectral analysis. No reduction is allowed for cantilever column systems and inverted pendulum systems.

2. When using these alternative basic load combinations for proportioning foundations for loadings, which include seismic loads, the vertical seismic load effect, E_v, in Equation 12.4-4 of ASCE 7 is permitted to be taken equal to zero.