055
a f is permitted to be linearly increased to 0.90 as the tensile strain in the extreme steel increases from the compressioncontrolled strain of 0.005. Note: Under seismic conditions strength reduction factors may require modifications.
a f is permitted to be linearly increased to 0.90 as the tensile strain in the extreme steel increases from the compressioncontrolled strain of 0.005. Note: Under seismic conditions strength reduction factors may require modifications.
TABLE 7.5 ACI Load Factors
Load case Structurals demand SD or (required strength U)
Note: D is the dead load, or related internal moments and forces, E is the seismic load, F is the weight and pressure of welldefined fluids, H is the weight and pressure of soils, water in soil, or other materials, L is the live load, Lr is the roof live load, R is the rain load, S is the snow load, T is the timedependent load (temperature, creep, shrinkage, differential settlement, etc.), and W is the wind load.
7.12.2 Beam Design
The main design steps for beam design and the formulas for determining beam capacity are outlined in the following.
7.12.2.1 Estimate Beam Size and Cover
Table 7.6 may be referenced for selecting a beam thickness. For practical construction, the minimum width of a beam is about 12 in. Economical designs are generally provided when the beam width to thickness ratio falls in the range of  to 1. Minimum concrete covers are listed in Table 7.7 and typically should not be less than 1.5 in.
7.12.2.2 Moment Capacity
Taking a beam segment, flexural bending induces a force couple (see Figure 7.4). Internal tension NT is carried by the reinforcement (the tensile strength of concrete is low and its tension carrying capacity is neglected). Reinforcement at the ultimate state is required to yield, hence
At the opposite side of the beam, internal compression force NC is carried by the concrete. Assuming a simplified rectangular stress block for concrete (uniform stress of 0.85fc),
To satisfy equilibrium, internal tension must be equal to internal compression, NC = NT. Hence, the depth of the rectangular concrete stress block a can be expressed as
0.85f'b
Compression
Crosssection Stain distribution
FIGURE 7.4 Mechanics of reinforced concrete beam under flexure.
Actual stress distribution
Equivalent rectangular stress distribution
Copyright 2005 by CRC Press

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