## 1958 Load Combinations and Strength Requirements

Structures must be proportioned with adequate strength to resist the forces predicted by the lateral seismic analysis together with forces produced by response to vertical components of ground shaking as well as dead and live loads. Unless nonlinear response history analysis is performed using ground motion records that include a vertical component of motion, the effects of vertical earthquake shaking are accounted for by the equation

where QE are the element forces predicted by the lateral seismic analysis, SDS is the design spectral response acceleration at a 0.2 s response period, and D are the forces produced in the element by the structure's dead weight. The term 0.2SdsD represents the effect of vertical ground shaking response. For structures in zones of high seismicity, the term SDS has a value approximating 1.0g and, therefore, the vertical earthquake effects are taken as approximately 20% increase or decrease in the dead load stress demands on each element. In fact, there are very few cases on record where structural collapse has been ascribed to the vertical response of a structure. This is probably because design criteria for vertical load resistance incorporate substantial factors of safety and also because most structures carry only a small fraction of their rated design live loads when they are subjected to earthquake effects. Therefore, most structures inherently have substantial reserve capacity to resist additional loading induced by vertical ground motion components. In recognition of this, most earlier codes neglected vertical earthquake effects. However, during the formulation of ATC3.06, it was felt to be important to acknowledge that ground shaking includes three orthogonal components. The resulting expression, which was somewhat arbitrary, ties vertical seismic forces to the short period design spectral response acceleration, as most structures are stiff vertically and have very short periods of structural response for vertical modes.

The earthquake forces on structural elements derived from Equation 19.18 are combined with dead and live loads in accordance with the standard strength level load combinations of ASCE-7. The pertinent load combinations are

where D, L, and E are the dead, live, and earthquake forces, respectively. Elements must then be designed to have adequate strength to resist these combined forces. The reduction factor of 0.75 on the combination of earthquake and live loads accounts for the low likelihood that a structure will be supporting full live load at the same time that it experiences full design earthquake shaking. An alternative set of load combinations is also available for use with design specifications that utilize allowable stress design formulations. These are essentially the same as Equations 19.19 and 19.20, except that the earthquake loads are further reduced by a factor of 1.4.

The NEHRP Provisions recognize that it is undesirable to allow some elements to experience inelastic behavior as they may be subject to brittle failure and in doing so compromise the ability of the structure to develop its intended inelastic response. The connections of braces to braced frames are an example of such elements. The Provisions also recognize that inelastic behavior in some elements, such as columns supporting discontinuous shear walls, could trigger progressive collapse of the structure. For these elements, the earthquake force E that must be used in the load combination (Equations 19.19 and 19.20) is given by the formula:

where the term 0.2SDSD continues to represent the effects of vertical ground shaking response and the term Q0QE represents an estimate of the maximum force likely to be developed in the element as a result of lateral earthquake response, considering the inelastic response characteristics of the entire structural system. In Equation 19.20, the term Q0QE need never be taken larger than the predicted force on the element derived from a nonlinear analysis or plastic mechanism analysis.

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