Page 234 - Handbook of Civil Engineering Calculations, Second Edition

REINFORCED CONCRETE 2.19

The following symbols, shown in Fig. 11,
are to be added to the notational system given
earlier: kd distance from extreme compres-
sion fiber to neutral axis, in. (mm); jd dis-
tance between action lines of C and T, in.
(mm); z distance from extreme compression
fiber to action line of C, in. (mm).
The basic equations for the working-stress
design of a rectangular beam reinforced solely
in tension are

f c
k (21)
f c f s /n FIGURE 11. Stress and resultant forces.
k
j 1 (22)
3
M Cjd /2f c kjbd 2 (23)
1
M /6f c k(3 k)bd 2 (24)
1
M Tjd f s A s jd (25)
M f s pjbd 2 (26)
2
f s k (3 k)bd 2
M (27)
6n(1 k)
f c k
p (28)
2f s
k 2
p (29)
2n(1
k)
2 0.5
k [2pn (pn) ] pn (30)
For a given set of values of f c , f s , and n, M is directly proportional to the beam proper-
2
ty bd . Let K denote the constant of proportionality. Then
M Kbd 2 (31)
where
K /2f c kj f s pj (32)
1
The allowable flexural stress in the concrete and the value of n, which are functions of
the ultimate strength f c
, are given in the ACI Code, as is the allowable flexural stress in the
steel. In all instances in the following procedures, the assumption is that the reinforcement
is intermediate-grade steel having an allowable stress of 20,000 lb/sq.in. (137,900 kPa).
Consider that the load on a beam is gradually increased until a limiting stress is induced. A
beam that is so proportioned that the steel and concrete simultaneously attain their limiting