398
CHAPTER
6
Stresses
in
Beams
(Advanced
Topics)
Bending
Df
Unsymmetric
Beams
When solving the problems
for
Section
6.5,
be sure to draw a sketch
of
the
cross section showing the orientation
of
the neutral axis
and
the locations
of
the points where the stresses are being found.
Problem
6.51
A beam
of
channel section
is
subjected to a
M
bending moment
M
having its vector at an angle
0
to the
z
axis
(see figure).
Determine
the
orientati on
of
the neutral axis and calculate the
c
maximum tensile stress
u,
and maximum compressive stress
U
in
c
the beam.
Use the following data: C 8
X
11.5 section,
M
=
20 kin.,
tan
0
=
1/3.
(Note:
See Table
E3
of
Appendix
E
for the dimensions
and properties
of
the channel section.)
Probs.
6.51
and
6.52
Solution
6.51
Channel section
n
MAXIMUM
TENSILE STRESS (POINT
A)
(EQ.
638)
ZA
=
C
=
0.571 in.
Y
A
=
dl2
=
4.00
in.
(M
sin
O)ZA
(M
cos
ti)YA
U,
=
UA
=
1
y
I,
=
5060 psi

z
LL~R
MAXIMUM
COMPRESSIVE STRESS (POINT
B)
(EQ.
638)
ZB
=
(b

c)
=
(2.260

0.571)
=
1.689
in.
c+
Y,
=
dl2
=
4.00 in.
(M
sin
O)zs
(M
cos
O)Ys
1
A
n
U
c
=
Us
=
1
y
(
M
=
20 kin.
C
8
X
11.5
c
=
0.571 in.
d
=
8.00 in.
tan
0
=
1/3
1
=
1.32 in.
4
y
b
=
2.260 in.
(j
=
18.435°
t
=
32.6 in.
4
=
10,420
psi

NEUTRAL AXIS
nn
(EQ.
640)
tan
(3
=
1,

tan
0
=
1
y
32.6

(1/3)
1.32
=
8.2323
{3
=
83.07°

Problem
6.52
Solve the preceding problem for a C 6
X
13
channel
section with
M
=
5.0 kin. and
0
=
ISO.
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SECTION
6.5
Bending
of
Unsymmetric
Beams
399
Problem
6.53
An angle section with equal legs is subjected
to
2
a bending moment
M
having its vector directed along the
11
axis,
as shown
in
the figure.
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 Spring '11
 huckelbridge
 Trigraph, maximum tensile stress, Compressive stress, Tensile stress, iy

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