Page 200 - Civil Engineering Formulas

136 CHAPTER FIVE

where a depth of equivalent rectangular compressive stress distribution
(A s A s )f y /f c b
b width of beam, in (mm)
d distance from extreme compression surface to centroid of tensile
steel, in (mm)
d distance from extreme compression surface to centroid of compres-
sive steel, in (mm)
2
2
A area of tensile steel, in (mm )
s
2
A s area of compressive steel, in (mm )
2
f yield strength of steel, ksi (MPa)
y
f c 28-day strength of concrete, ksi (MPa)
This is valid only when the compressive steel reaches f and occurs when
y
f c d 87,000
( ) 0.85 1 (5.68)
f y d 87,000 f y
where A /bd
s
A s /bd
a constant
1
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:
1
k (5.69)
1 f s /nf c
where f stress in tensile steel, ksi (MPa)
s
f stress in extreme compression surface, ksi (MPa)
c
n modular ratio, E /E c
s
kd d
f s 2f s (5.70)
d kd
where f stress in compressive steel, ksi (MPa)
s
d distance from extreme compression surface to centroid of tensile
steel, in (mm)
d distance 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