ME
211 Homework Set #13 Solutions
12-5-2008
Problem #1 16.35
The A-36 steel beam has a depth of 10in. and is subjected to a constant moment M
o
which
causes the stress at the outer fibers to become
σ
y
=36ksi.
Determine the radius of curvature
of the beam and the maximum slope and deflection.
1.)
Moment – curvature relationship
in
Ec
EI
I
c
EI
M
y
y
o
78
.
4027
36
)
5
)(
10
(
0
.
29
1
1
1
3
=
=
=
⇒
=
=
σ
ρ
σ
ρ
ρ
2.) Slope and elastic curve
EI
d
2
v
dx
2
=
M
(
x
)
EI
d
2
v
dx
2
= −
M
o
EI
dv
dx
= −
M
o
x
+
C
1
EIv
=
−
M
o
x
2
2
+
C
1
x
+
C
2
3.) Boundary Conditions

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