CIVIL ENGINEERING FORMULAS

CONCRETE FORMULAS 137

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

(5.71)

whereCtotal compression on beam cross section, kip (N)
Cctotal compression on concrete, kip (N) at section
Csforce acting on compressive steel, kip (N)
Tforce acting on tensile steel, kip (N)

(5.72)

whereAs/bdand.
For reviewing a design, the following formulas may be used:

(5.73)

(5.74)

wherejdis the distance between the centroid of compression and the centroid
of the tensile steel. The moment resistance of the tensile steel is

(5.75)

whereMis the bending moment at the section of beam under consideration.
The moment resistance in compression is

(5.76)

(5.77)

Computer software is available for the preceding calculations. Many design-
ers, however, prefer the following approximate formulas:

(5.78)

Ms MM 1  2 fsAs(dd) (5.79)

M 1 

1

2

fcbkdd

kd

3 

fc

2 M

jbd^2 {k 2 n[1(d/kd)] }

Mc

1

2

fcjbd^2 k 2 n 1 

d

kd

MsTjdAsfsjd fs

M

Asjd

z

(k^3 d /3) 4 nd[k(d/d)]

k^2  4 n[k(d/d)]

jddz

k

B

2 n

d

d

n^2 ()^2 n()

 As/bd

fs

fc



k

2[(kdd)/(dkd)]

CCcCsT

fs