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 = Eh – Ev = ρQE – 0.2SDSD per ASCE 7-05 Section 12.4.2
In both the above equations, the horizontal earthquake effect, QE, can be positive or negative. In the first equation, the positive sign governs, in the second equation the negative sign governs. The vertical load effect, ±0.2SDSD, increases or decreases the dead load factor in the seismic strength design load combinations. In the additive load combination, the dead load factor is increased by considering vertically downward earthquake effect; in the counteractive load combination, the dead load factor is decreased by considering vertically upward earthquake effect. In each case, this is the conservative approach.
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.
Answers to FAQs:
Q: If designing an element that only resists seismic load (such as a diaphragm) using allowable stress design (ASD), do you design for E or (0.7)(E)? Is E always E/1.4 for ASD and 1.0E for LRFD?
A: Load combinations are always used in design, except that sometimes the effects of one or more loads may be zero. For instance, the horizontal shear in a shear wall or a diaphragm would often be caused by earthquake forces alone. It is not that gravity effects are disregarded. It is just that gravity simply does not contribute to the particular load effect being considered. Then, if ASD is used, the element is designed for 0.7E, and if LRFD is used, the element is designed for 1.0E. In these cases, E is ρQE because D is zero.
S.K. Ghosh Associates Inc., is a seismic and building code consulting firm located in Palatine, Ill., and Laguna Niguel, Calif. President S.K. Ghosh, Ph.D., and Susan Dowty, S.E., are active in the development and interpretation of national structural code provisions. They can be contacted at email@example.com and firstname.lastname@example.org, respectively, or at www.skghoshassociates.com.