470_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

464
CHAPTER 5 Stresses in Beams (Basic Topics)
Solution 5.10-11 Square box beam
M
INIMUM SHEAR STRESS IN THE WEB
(
AT LEVEL
A.A )
; 1.03 ksi
t
min
VQ
It
(28,000 lb)(66.0 in.
3
)
(894.67 in
4
)(2.0 in.)
1033 psi
Q
(12 in.)
8
[(12 in.)
2
(10 in.)
2
] 66.0 in.
3
t
1
b b
1
2
Q
b
8
( b
2
b
1
2
)
Q Ay ( bt
1
) a
b
2
t
1
2
b a
bt
1
2
b ( b t
1
)
; 1.42 ksi
t
max
VQ
It
(28,000 lb)(91.0 in.
3
)
(894.67 in.
4
)(2.0 in.)
1424 psi
1
8
( b
3
b
1
3
) 91.0 in.
3
Q a
b
2
2
b a
b
4
b a
b
1
2
2
b a
b
1
4
b
.
.
.
.
M
OMENT OF INERTIA
M
AXIMUM SHEAR STRESS IN THE WEB
(
AT NEUTRAL AXIS
)
y
1
1
2
a
b
2
b
b
4
y
2
1
2
a
b
1
2
b
b
1
4
A
2
b
1
a
b
1
2
b
b
1
2
2
Q A
1
y
1
A
2
y
2
A
1
b a
b
2
b
b
2
2
I
1
12
( b
4
b
1
4
) 894.67 in.
4
t
VQ
It
t 2 t
1
2.0 in
b
1
10 in
b 12 in
t
1
1.0 in
V 28 k 28,000 lb
Problem 5.10-12 The T-beam shown in the figure has cross-sectional dimensions
as follows: , and . The beam