The figure illustrates a stepped torsion-bar spring OA with an actuating cantilever AB. Both parts are of carbon steel (Young's modulus is 207 GPa and shear modulus is 79.3 GPa). Use Castigliano's theorem to find the spring rate k corresponding to a force F acting at B. Hint: you need to consider the bending of member AB and torsion of member AO. 12 mm OC 18 mm 8 mm 0.2 m 0.4 m

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter3: Torsion
Section: Chapter Questions
Problem 3.4.17P: .17 A mountain-bike rider going uphill applies torque T = Fd(F = l5lb, d = 4 in.) to the end of the...
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For bar AO how come they do not include the bending caused by F ( internal reaction )?

The figure illustrates a stepped torsion-bar spring OA with an actuating cantilever AB. Both parts are of carbon
steel (Young's modulus is 207 GPa and shear modulus is 79.3 GPa). Use Castigliano's theorem to find the spring
rate k corresponding to a force F acting at B. Hint: you need to consider the bending of member AB and torsion
of member AO.
12 mm
0.2 m
18 mm
B
8 mm
0.2 m
0.4 m
Transcribed Image Text:The figure illustrates a stepped torsion-bar spring OA with an actuating cantilever AB. Both parts are of carbon steel (Young's modulus is 207 GPa and shear modulus is 79.3 GPa). Use Castigliano's theorem to find the spring rate k corresponding to a force F acting at B. Hint: you need to consider the bending of member AB and torsion of member AO. 12 mm 0.2 m 18 mm B 8 mm 0.2 m 0.4 m
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