Page 185 - Civil Engineering Formulas

122 CHAPTER FIVE

where f , f , f actual unit stresses in extreme fiber of concrete, in compressive
s
sc
c
reinforcing steel, and in tensile reinforcing steel, respectively,
2
lb/in (MPa)
c , c , c distances from neutral axis to face of concrete, to compressive
sc
c
s
reinforcing steel, and to tensile reinforcing steel, respectively,
in (mm)
4
4
I moment of inertia of transformed beam section, in (mm )
b beam width, in (mm)
and A , A , M, and n are as defined earlier in this chapter.
sc
s
Shear and Diagonal Tension in Beams The shearing unit stress, as a measure
of diagonal tension, in a reinforced concrete beam is
V
v (5.12)
bd
2
where v shearing unit stress, lb/in (MPa)
V total shear, lb (N)
b width of beam (for T-beam use width of stem), in (mm)
d effective depth of beam
If the value of the shearing stress as computed earlier exceeds the allowable
shearing unit stress as specified by the ACI Code, web reinforcement should be
provided. Such reinforcement usually consists of stirrups. The cross-sectional area
required for a stirrup placed perpendicular to the longitudinal reinforcement is
(V V )s
A v (5.13)
f i d
where A cross-sectional area of web reinforcement in distance s (measured
v
2
2
parallel to longitudinal reinforcement), in (mm )
2
f allowable unit stress in web reinforcement, lb/in (MPa)
v
V total shear, lb (N)
V shear that concrete alone could carry ( v bd), lb (N)
c
s spacing of stirrups in direction parallel to that of longitudinal rein-
forcing, in (mm)
d effective depth, in (mm)
Stirrups should be so spaced that every 45° line extending from the mid-
depth of the beam to the longitudinal tension bars is crossed by at least one stir-
2
rup. If the total shearing unit stress is in excess of 3 f c lb/in (MPa), every
such line should be crossed by at least two stirrups. The shear stress at any section
2
should not exceed 5 f c lb/in (MPa).
Bond and Anchorage for Reinforcing Bars In beams in which the tensile
reinforcing is parallel to the compression face, the bond stress on the bars is
V
u (5.14)
jd
0