Page 229 - Shigley's Mechanical Engineering Design

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204 Mechanical Engineering Design
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4–81 and The part shown is formed from a -in diameter steel wire, with R = 5 in and l = 4 in. A force is
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4–82 applied with P = 1 lbf. Use Castigliano’s method to estimate the horizontal deflection at point A.
Justify any components of strain energy that you choose to neglect.

C R
C
B B
R P
l l
P
A A
Problem 4–81 Problem 4–82

4–83 Repeat Prob. 4–81 for the vertical deflection at point A.

4–84 Repeat Prob. 4–82 for the vertical deflection at point A.
4–85 A hook is formed from a 2-mm-diameter steel wire and fixed firmly into the ceiling as shown. A
1-kg mass is hung from the hook at point D. Use Castigliano’s theorem to determine the vertical
deflection of point D.

A

8 cm 2-mm dia.

B
Problem 4–85
E C
4 cm
D

4–86 The figure shows a rectangular member OB, made from -in-thick aluminum plate, pinned to the
1
4
1
ground at one end, and supported by a -in-diameter round steel rod that is formed into an arc
2
and pinned to the ground at C. A load of 100 lbf is applied at B. Use Castigliano’s theorem to
determine the vertical deflection at point B. Justify any choices to neglect any components of
strain energy.

1 -in dia. C
2
100 lbf
1 -in thick
4 2 in 10 in
Problem 4–86
A
O B
10 in 10 in 10 in

4–87 Repeat Prob. 4–86 for the vertical deflection at point A.