CIVIL ENGINEERING FORMULAS

CONCRETE FORMULAS 139

an I- or T-beam may be designed by the following formulas, which ignore the
compression in the stem, as is customary:

(5.82)

wherekddistance from extreme compression surface to neutral axis, in (mm)
ddistance from extreme compression surface to centroid of tensile
steel, in (mm)
fsstress in tensile steel, ksi (MPa)
fcstress in concrete at extreme compression surface, ksi (MPa)
nmodular ratioEs/Ec

Because the total compressive force Cequals the total tension T,

(5.83)

(5.84)

whereAsarea of tensile steel, in^2 (mm^2 ); and tflange thickness, in (mm).
The distance between the centroid of the area in compression and the cen-
troid of the tensile steel is

(5.85)

The moment resistance of the steel is

(5.86)

The moment resistance of the concrete is

(5.87)

In design, MsandMccan be approximated by

(5.88)

(5.89)

derived by substituting dt/ 2 for jdandfc/ 2 for fc(1t/2kd), the average
compressive stress on the section.

Mc

1

2

fcbtd

t

2 

MsAsfsd

t

2 

McCjd

fcbtjd

2 kd

(2kdt)

MsTjdAsfsjd

jddz z

t (3kd 2 t)

3(2kdt)

kd

2 ndAsbt^2

2 nAs 2 bt

C

1

2

fc(2kdt)

bt

kd

TAsfs

k

I

1 fs /nfc