CIVIL ENGINEERING FORMULAS

136 CHAPTER FIVE

where adepth of equivalent rectangular compressive stress distribution


bwidth of beam, in (mm)

ddistance from extreme compression surface to centroid of tensile

steel, in (mm)

distance from extreme compression surface to centroid of compres-

sive steel, in (mm)

Asarea of tensile steel, in^2 (mm^2 )

area of compressive steel, in^2 (mm^2 )

fyyield strength of steel, ksi (MPa)

28-day strength of concrete, ksi (MPa)

This is valid only when the compressive steel reaches fyand occurs when

(5.68)

where As/bd

 1 a constant

WORKING-STRESS DESIGN OF RECTANGULAR BEAMS
WITH COMPRESSION BARS

The following formulas, based on the linear variation of stress and strain with
distance from the neutral axis, may be used in design:

(5.69)

where fsstress in tensile steel, ksi (MPa)
fcstress in extreme compression surface, ksi (MPa)
nmodular ratio, Es/Ec

(5.70)

where fsstress in compressive steel, ksi (MPa)
ddistance from extreme compression surface to centroid of tensile
steel, in (mm)
ddistance from extreme compression surface to centroid of compres-
sive steel, in (mm)

The factor 2 is incorporated into the preceding equation in accordance with
ACI 318, “Building Code Requirements for Reinforced Concrete,” to account

fs

kdd

dkd

2 fs

k

1

1 fs/nfc

 As/bd

()0.85 1

fcd

fyd



87,000

87,000fy

fc

As

d

(AsAs)fy/fcb