Page 198 - Civil Engineering Formulas

134 CHAPTER FIVE

kd distance from extreme compression surface to neutral axis, in (mm)
d distance from extreme compression to centroid of reinforcement, in
(mm)

When the steel ratio A /bd, where A area of tension reinforcement,
s
s
2
2
in (mm ); and b beam width, in (mm), is known, k can be computed from
k 2 2n (n ) n (5.57)
2
Wherever positive-moment steel is required, should be at least 200/f , where
y
f is the steel yield stress. The distance jd between the centroid of compression
y
and the centroid of tension, in (mm), can be obtained from
k
j 1 (5.58)
3
Allowable Bending Moment
The moment resistance of the concrete, in kip (k Nm) is
2
1
M c 2 f c kjbd K c bd 2 (5.59)
1
c
c
where K 2 f kj. The moment resistance of the steel is
2
M s f s A s jd f s jbd K s bd 2 (5.60)
where K f j.
s
s
Allowable Shear
The nominal unit shear stress, v acting on a section with shear V is
V
v (5.61)
bd
Allowable shear stresses are 55 percent of those for ultimate-strength design.
Otherwise, designs for shear by the working-stress and ultimate-strength
methods are the same. Except for brackets and other short cantilevers, the
section for maximum shear may be taken at a distance d from the face of the
support. In working-stress design, the shear stress v carried by the concrete
c
alone should not exceed 1.1 f c . (As an alternative, the maximum for v c
may be taken as f c 1300 Vd/M , with a maximum of 1.9 f c ; f c is the
2
28-day compressive strength of the concrete, lb/in (MPa); and M is the bend-
ing moment at the section but should not be less than Vd.)
At cross sections where the torsional stress v exceeds 0.825 f c , v should
t c
not exceed
1.1 2 c
f
v c (5.62)
2 1 (v t /1.2v) 2