# 2006 IBC Section 1605.2.1: Seismic Strength Design Load Combinations

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This "Code Simple" addresses a common question asked about the seismic load effect, E, used in the 2006 International Building Code (IBC) Section 1605 load combinations and defined in Section 12.4.2 of ASCE 7-05. The question is: How does one combine a horizontal component, due to the base shear, V, with a vertical component, due to the dead load?

In a literal sense, loads are never combined. Gravity loads (which act in a vertical direction) and wind forces (which act horizontally) are simply not combinable. What is combined through the so-called load combinations are load "effects." The word effects is very important. Gravity loads cause bending moments, shear forces, and axial forces at critical sections of structural members and these are the effects of gravity loads. Horizontal wind forces do exactly the same thing, the resulting bending moments and so on are the effects of wind forces. These bending moments, shear forces, and axial forces are combinable, as reflected in the building codes.

The earthquake effect, E, is more complicated in the sense that it has both a horizontal and a vertical component to it. First, a close look at the two equations that include seismic loads in the strength load combinations of the 2006 IBC Section 1605.2.1 will be helpful. They are Equations 16-5 and 16-7. For the purpose of discussion, let it be assumed that there is not an H load (load due to lateral earth pressure, ground water pressure, or pressure of bulk materials), f1 = 0.5 and f2 = 0.2.

Equation 16-5 can be rewritten as follows and is considered an additive load combination because gravity and seismic forces are causing bending moments, shear forces, and axial forces in the same direction:

= 1.2D + 0.5L + 0.2S + 1.0E,
= (1.2 + 0.2SDS)D + 0.5L + 0.2S + ρQE,
because in this case  E = Eh + Ev = ρQE + 0.2SDSD per ASCE 7-05 Section 12.4.2.

Equation 16-7 can be rewritten as follows and is considered a counteractive load combination because gravity and seismic forces cause bending moments, shear forces, and axial forces in opposite directions:

= 0.9D + 1.0E,
= (0.9—0.2SDS)D + ρQE,
because in this case E = EhEv = ρQE – 0.2SDSD per ASCE 7-05 Section 12.4.2

For example, consider a fully redundant structure (ρ = 1.0) located where SDS = 1.0; a bearing wall system consisting of reinforced concrete shear walls is used for the seismic force-resisting system. If the bending moments in a shear wall cross-section due to dead loads, live loads, snow loads, and horizontal earthquake forces are 200 foot-kips, 60 foot-kips, 0 foot-kips, and 150 foot-kips, respectively, the design moments (required flexural strengths) by the strength design load combinations (IBC Equations 16-5 and 16-7) are:

Mu = [(1.2) + (0.2)(1.0)]( 200) + (0.5)(60) + (1)(150) = 460 foot-kips
Mu = [(0.9)—(0.2)(1.0)](200)—(1)(150) = -10 foot-kips

The shear wall needs to be reinforced to carry these bending moments at the cross-section in question.