Page 186 - Civil Engineering Formulas

CONCRETE FORMULAS 123

2
where u bond stress on surface of bar, lb/in (MPa)
V total shear, lb (N)
d effective depth of beam, in (mm)

sum of perimeters of tensile reinforcing bars, in (mm)
0
For preliminary design, the ratio j may be assumed to be 7/8. Bond stresses
may not exceed the values shown in Table 5.3.

Columns

The principal columns in a structure should have a minimum diameter of 10 in
(255 mm) or, for rectangular columns, a minimum thickness of 8 in(203 mm) and
2
2
a minimum gross cross-sectional area of 96 in (61,935 mm ).
Short columns with closely spaced spiral reinforcing enclosing a circular
concrete core reinforced with vertical bars have a maximum allowable load of
P A g (0.25f c f s p g ) (5.15)
where P total allowable axial load, lb (N)
2
2
A gross cross-sectional area of column, in (mm )
g
2
f compressive strength of concrete, lb/in (MPa)
c
2
f allowable stress in vertical concrete reinforcing, lb/in (MPa), equal to
s
40 percent of the minimum yield strength, but not to exceed 30,000 lb/
2
in (207 MPa)
p ratio of cross-sectional area of vertical reinforcing steel to gross area
g
of column A g
The ratio p should not be less than 0.01 or more than 0.08. The minimum num-
g
ber of bars to be used is six, and the minimum size is No. 5. The spiral reinforc-
ing to be used in a spirally reinforced column is
p s 0.45 A g 1 f c (5.16)
A c f y
where p ratio of spiral volume to concrete-core volume (out-to-out spiral)
s
2
2
A cross-sectional area of column core (out-to-out spiral), in (mm )
c
2
f yield strength of spiral reinforcement, lb/in (MPa), but not to
y
exceed 60,000 lb/in (413 MPa)
2
The center-to-center spacing of the spirals should not exceed one-sixth of the
core diameter. The clear spacing between spirals should not exceed one-sixth
the core diameter, or 3 in (76 mm), and should not be less than 1.375 in (35 mm),
or 1.5 times the maximum size of coarse aggregate used.
Short Columns with Ties The maximum allowable load on short columns
reinforced with longitudinal bars and separate lateral ties is 85 percent of that given