In seismic design, a diaphragm must be designed for the larger of the following two different design forces that are specified in ASCE 7-10 Section 12.10.1.1:

• The seismic design forces, F_x at Level x, determined from elastic analysis of the structure; these forces are typically determined using either the Equivalent Lateral Force procedure of Section 12.8 or the Modal Response Spectrum Analysis procedure of Section 12.9.

• Inertia forces determined from Equation 12.10-1:

Equation 12.10-1 gives the diaphragm design forces as a function of story shear in the story below the diaphragm and the ratio of the weight tributary to the diaphragm to the sum of the weights tributary to all the diaphragms above and including the diaphragm. A (non-mandatory) upper-bound value and a (mandatory) lower-bound value are also given as 0.4S_DSI_ew_px and 0.2S_DSI_ew_px, respectively.

The inertia force given by Equation 12.10-1 is simply an approximation of the response acceleration at the level of the diaphragm times its distributed mass.

The detailing of diaphragms is generally independent of the type of seismic force-resisting system (SFRS) selected for a building; therefore the system R-value does not appear in the upper- and the lower-limit equations.

In addition to these diaphragm design forces, in multistory structures, there may be seismic design forces to be transferred from vertical  elements of the SFRS above the diaphragm to other vertical elements of the SFRS below the diaphragm. For structures assigned to SDC D, E, or F, the redundancy factor, ρ, as applicable to the whole structure, is to be applied to the transfer forces, but it need not apply to forces obtained from Equation 12.10-1.

Table 1 illustrates the determination of the diaphragm design forces for a 6-story structure. These calculations and the governing design forces are illustrated in Figure 1.

Q. There appear to be too many quantities that may be the diaphragm design force: F_x, F_px, F_px,max, F_px,min. Which one governs and when? Could you please comment on this?

A. The way Eq. 12.10-1 is set up, F_px = F_x at the top level of a building and is larger than F_x at every other level. In other words, F_x ≤ F_px

The requirement: F_px  ≥ F_px,_min = 0.2S_DSI_ew_px does not affect the above relationship.

If F_px (≥ F_x) ≥ F_px,max (= 0.4S_DSI_ew_px)  →  F_px,_max governs.

If F_x (≤ F_px) ≥ F_px,_max  →  F_x governs.