Page 201 - Civil Engineering Formulas

CONCRETE FORMULAS 137

for the effects of creep and nonlinearity of the stress–strain diagram for con-
crete. However, f s should not exceed the allowable tensile stress for the steel.
Because total compressive force equals total tensile force on a section,

C C c C s T (5.71)

where C total compression on beam cross section, kip (N)
C total compression on concrete, kip (N) at section
c
C force acting on compressive steel, kip (N)
s
T force acting on tensile steel, kip (N)
k
f s
(5.72)
f c 2[ (kd d )/(d kd)]
where A /bd and A s /bd .
s
For reviewing a design, the following formulas may be used:

2
2
k 2n d n ( ) n( ) (5.73)
B d
3
(k d /3) 4n d [k (d /d)]
z jd d z (5.74)
2
k 4n [k (d /d)]
where jd is the distance between the centroid of compression and the centroid
of the tensile steel. The moment resistance of the tensile steel is
M
M s Tjd A s f s jd f s (5.75)
A s jd
where M is the bending moment at the section of beam under consideration.
The moment resistance in compression is

1 d
M c f c jbd k 2n 1 (5.76)
2
2 kd
2M
f c (5.77)
2
jbd {k 2n [1 (d /kd)]}
Computer software is available for the preceding calculations. Many design-
ers, however, prefer the following approximate formulas:

1 kd
M 1 f c bkd d (5.78)
2 3
M s M M 1 2 f s A s (d d ) (5.79)