Civil Engineering Reference
In-Depth Information
Bending Stresses
My
I
(12)(70,000)(6.78)
4067
f
c
1400 psi
f
s
n
My
I
(9)
(12)(70,000)(10.22)
4067
18,998 psi
EXAMPLE 2.3
Determine the allowable resisting moment of the beam of Example 2.2 if the allowable stresses are
f
c
1350 psi and
f
s
20,000 psi.
M
c
f
c
I
(1350)(4067)
6.78
SOLUTION
809,800 in.- lb
67.5 ft- k
k
y
M
s
f
s
I
ny
(20,000)(4067)
884,323 in.- lb
73.7 ft- k
(9)(10.22)
Discussion
For a given beam, the concrete and steel will not usually reach their maximum allowable
stresses at exactly the same bending moments. Such is the case for this example beam,
where the concrete reaches its maximum permissible stress at 67.5 ft-k, while the steel
does not reach its maximum value until 73.7 ft-k is applied. The resisting moment of the
section is 67.5 ft-k because if that value is exceeded, the concrete becomes overstressed
even though the steel stress is less than its allowable stress.
EXAMPLE 2.4
Compute the bending stresses in the beam shown in Figure 2.9 by using the transformed-area
method;
n
8 and
M
110 ft-k.
SOLUTION
Locating Neutral Axis (Assuming Neutral Axis below Hole)
x
2
(18
x
)
(6)(6)(
x
3)
(8)(5.06)(23
x
)
9
x
2
36
x
108
931
40.48
x
9
x
2
4.48
x
823
x
2
0.50
x
91.44
(
x
0.25)(
x
0.25)
91
.44
(0.25)
2
91.50
x
0.25
91.50
9.57
x
9.32
6
N.A. below hole as
assumed
Moment of Inertia
I
(
3
)(6)(9.32)
3
(2)
(
3
)(6)(3.32)
3
(8)(5.06)(13.68)
2
10.887 in.
4
