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Shear Stresses in Circular Beams
Problem 5.91
A wood pole of solid circular cross section (
d
5
diameter) is subjected to a horizontal force
P
5
450 lb (see figure). The
length of the pole is
L
5
6 ft, and the allowable stresses in the wood are
1900 psi in bending and 120 psi in shear.
Determine the minimum required diameter of the pole based upon (a)
the allowable bending stress, and (b) the allowable shear stress.
Solution 5.91
Wood pole of circular cross section
338
CHAPTER 5
Stresses in Beams
L
P
d
d
P
5
450 lb
L
5
6 ft
5
72 in.
s
allow
5
1900 psi
t
allow
5
120 psi
Find diameter
d
(a)
Based upon bending stress
M
max
5
PL
5
(450 lb)(72 in.)
5
32,400 lbin.
d
min
5
5.58 in.
(b)
Based upon shear stress
V
max
5
450 lb
d
min
5
2.52 in.
(Bending stress governs.)
t
5
4
V
3
A
5
16
V
3
p
d
2
Ê
d
2
5
16
V
max
3
p
t
allow
5
6.366 in.
2
s
5
M
S
5
32
M
p
d
3
Ê
d
3
5
32
M
max
p
s
allow
5
173.7 in.
3
L
P
d
d
Problem 5.92
A simple log bridge in a remote area consists of two
parallel logs with planks across them (see figure). The logs are Douglas
fir with average diameter 300 mm. A truck moves slowly across the
bridge, which spans 2.5 m. Assume that the weight of the truck is equally
distributed between the two logs.
Because the wheelbase of the truck is greater than 2.5 m, only one set
of wheels is on the bridge at a time. Thus, the wheel load on one log is
equivalent to a concentrated load
W
acting at any position along the span.
In addition, the weight of one log and the planks it supports is equivalent
to a uniform load of 850 N/m acting on the log.
Determine the maximum permissible wheel load
W
based upon (a) an
allowable bending stress of 7.0 MPa, and (b) an allowable shear stress of
0.75 MPa.
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View Full Document Problem 5.102
Dimensions of cross section:
b
5
180 mm,
t
5
12 mm,
h
5
420 mm,
h
1
5
380 mm, and
V
5
125 kN.
Solution 5.102
Wideflange beam
SECTION 5.10
Shear Stresses in Circular Beams with Flanges
343
b
5
180 mm
t
5
12 mm
h
5
420 mm
h
1
5
380 mm
V
5
125 kN
M
OMENT OF INERTIA
(Eq. 547)
(a) M
AXIMUM SHEAR STRESS IN THE WEB
(Eq. 548a)
t
max
5
V
8
It
(
bh
2
2
bh
1
2
1
th
1
2
)
5
28.43 MPa
I
5
1
12
(
bh
3
2
bh
1
3
1
th
1
3
)
5
343.1
3
10
6
mm
4
(b) M
INIMUM SHEAR STRESS IN THE WEB
(Eq. 548b)
(c) A
VERAGE SHEAR STRESS IN THE WEB
(Eq. 550)
(d) S
HEAR FORCE IN THE WEB
(Eq. 549)
V
web
V
5
0.957
V
web
5
th
1
3
(2
t
max
1
t
min
)
5
119.7 kN
t
max
t
aver
5
1.037
t
aver
5
V
th
1
5
27.41 MPa
t
min
5
Vb
8
It
(
h
2
2
h
1
2
)
5
21.86 MPa
t
h
1
b
h
Problem 5.103
Wideflange shape,
W
8
3
28 (see Table E1, Appendix
E);
V
5
10 k.
Solution 5.103
Wideflange beam
W
8
3
28
b
5
6.535 in.
t
5
0.285 in.
h
5
8.06 in.
h
1
5
7.13 in.
V
5
10 k
M
OMENT OF INERTIA
(Eq. 547)
(a) M
AXIMUM SHEAR STRESS IN THE WEB
(Eq. 548a)
(b) M
INIMUM SHEAR STRESS IN THE WEB
(Eq. 548b)
t
min
5
Vb
8
It
(
h
2
2
h
2
1
)
5
4202 psi
t
max
5
V
8
It
(
bh
2
2
bh
2
1
1
th
1
2
)
5
4861 psi
I
5
1
12
(
bh
3
2
bh
3
1
1
th
3
1
)
5
96.36 in.
4
(c) A
VERAGE SHEAR STRESS IN THE WEB
(Eq. 550)
(d) Shear force in the web (Eq. 549)
V
web
V
5
0.943
V
web
5
th
1
3
t
max
1
t
min
)
5
9.432 k
t
max
t
aver
5
0.988
t
aver
5
V
th
1
5
4921 psi
t
h
1
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This note was uploaded on 10/01/2009 for the course MEGR 2144 taught by Professor Sharpe during the Fall '08 term at UNC Charlotte.
 Fall '08
 Sharpe

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