Simplified Frame Analysis - Simplified Design of Reinforced Concrete Buildings - page 32

The designer has the choice of multiplying the service loads by the load factors before computing the factored
load effects (moments, shears, etc.), or computing the effects from the service loads and then multiplying the
effects by the load factors. For example, in the computation of bending moment for dead and live loads
U = 1.2D + 1.6L, the designer may (1) determine w u = 1.2 w d + 1.6 w ˜ and then compute the factored moments
using w u ; or (2) compute the dead and live load moments using service loads and then determine the factored
moments as M u = 1.2 M d + 1.6 M ˜ . Both analysis procedures yield the same answer. It is important to note that
the second alternative is much more general than the first; thus, it is more suitable for computer analysis, espe-
cially when more than one load combination must be investigated.

2.3 FRAME ANALYSIS BY COEFFICIENTS

The ACI Code provides a simplified method of analysis for both one-way construction (ACI 8.3.3) and
two-way construction (ACI 13.6). Both simplified methods yield moments and shears based on coefficients.
Each method will give satisfactory results within the span and loading limitations stated in Chapter 1.
The direct design method for two-way slabs is discussed in Chapter 4.

2.3.1 Continuous Beams and One-Way Slabs

When beams and one-way slabs are part of a frame or continuous construction, ACI 8.3.3 provides approximate
moment and shear coefficients for gravity load analysis. The approximate coefficients may be used as long as
all of the conditions illustrated in Fig. 2-2 are satisfied: (1) There must be two or more spans, approximately
equal in length, with the longer of two adjacent spans not exceeding the shorter by more than 20 percent;
(2) loads must be uniformly distributed, with the service live load not more than 3 times the dead load
(L/D 3); and (3) members must have uniform cross section throughout the span. Also, no redistribution of

moments is permitted (ACI 8.4). The moment coefficients defined in ACI 8.3.3 are shown in Figs. 2-3 through
2-6. In all cases, the shear in end span members at the interior support is taken equal to 1.15w u ˜ n /2. The shear
at all other supports is w u /2 (see Fig. 2-7). w u ˜ n is the combined factored load for dead and live loads,
w u = 1.2w d + 1.6 w ˜ . For beams, w u is the uniformly distributed load per unit length of beam (plf), and the
coefficients yield total moments and shears on the beam. For one-way slabs, w u is the uniformly distributed load
per unit area of slab (psf), and the moments and shears are for slab strips one foot in width. The span length ˜ n
is defined as the clear span of the beam or slab. For negative moment at a support with unequal adjacent spans,
˜ n is the average of the adjacent clear spans. Support moments and shears are at the faces of supports.

″

( )

Uniformly Distributed Load L/D ≤ 3

Prismatic
Members

1.2 n

≤

n

Figure 2-2 Conditions for Analysis by Coefficients (ACI 8.3.3)