055

a f is permitted to be linearly increased to 0.90 as the tensile strain in the extreme steel increases from the compression-controlled 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 compression-controlled 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 well-defined 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 time-dependent 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

Cross-section Stain distribution

FIGURE 7.4 Mechanics of reinforced concrete beam under flexure.

Neutral axis (axis of zero strain)

Actual stress distribution

Equivalent rectangular stress distribution

Copyright 2005 by CRC Press

TABLE 7.6 Minimum Depth of Beams
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