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Problem 5.15
Given: For the hanger shown, determine the
vertical deflection of point A, assuming that
bending effects dominate.
Express the
results in terms of P, E, I, L, and R.
Solution:
z
P
V
M
L
P
θ
M
V
N
R
R cos
θ
For 0 < z < L
V
1
P
=
M
1
Pz
⋅
=
For 0 <
θ
<
π
/2
V
2
P sin
θ
()
⋅
=
N
2
P cos
θ
⋅
=
M
2
P L
R 1
cos
θ
−
⋅
+
[]
⋅
=
q
A
P
U
d
d
=
0
L
z
M
1
EI
⋅
P
M
1
d
d
⎛
⎝
⎞
⎠
⋅
⌠
⎮
⎮
⌡
d
0
π
2
θ
M
2
⋅
P
M
2
d
d
⎛
⎝
⎞
⎠
⋅
R
⋅
⌠
⎮
⎮
⎮
⌡
d
+
=
q
A
0
L
z
⋅
⋅
z
⋅
⌠
⎮
⎮
⌡
d
0
π
2
θ
P L
R 1
cos
θ
−
⋅
+
⋅
⋅
L
R 1
cos
θ
−
⋅
+
⋅
R
⋅
⌠
⎮
⎮
⌡
d
+
=
Integration gives:
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This note was uploaded on 01/11/2011 for the course MAE 3040 taught by Professor Mechanicsofsolids during the Spring '10 term at Utah State University.
 Spring '10
 MechanicsofSolids

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