Handbook of Civil Engineering Calculations

Table 1. Values of Design Parameters at Balanced Design

fc and n fc ^ AT A: y p

2500 112 5 20,00 0 17 8 0.36 0 0.88 0 0.010 1

10

3000 135 0 20,00 0 22 3 0.37 8 0.87 4 0.012 8

9

4000 180 0 20,00 0 32 4 0.41 9 0.85 3 0.018 8

8

5000 225 0 20,00 0 42 3 0.44 1 0.85 3 0.024 8

7

In Fig. 12, AB represents the stress

line of the transformed section for a

beam in balanced design. If the area of

reinforcement is increased while the

width and depth remain constant, the

neutral axis is depressed to O'', and

A'O'B represents the stress line under

the allowable load. But if the width is

increased while the depth and area of re-

inforcement remain constant, the neutral

axis is elevated to 0", and AO'B' repre-

sents the stress line under the allowable

load. This analysis leads to these con-

clusions: If the reinforcement is in ex-

cess of that needed for balanced design,

the concrete is the first material to reach

its limiting stress under a gradually in-

creasing load. If the beam size is in ex-

FIGURE 12 cess °^ ^at nee(e( f°r balanced design,
the steel is the first material to reach its
limiting stress.

STRESSES IN A RECTANGULAR BEAM

A beam of 2500-lb/in^2 (17,237.5-kPa) concrete has a width of 12 in (304.8 mm) and an
effective depth of 19.5 in (495.3 mm). It is reinforced with one no. 9 and two no. 7 bars.
Determine the flexural stresses caused by a bending moment of 62 ft-kips (84.1 kN-m) (a)
without applying the basic equations of reinforced-concrete beam design; (b) by applying
the basic equations.

balanced design

Allowable fc

Allowable f$/n