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. 18 mm 12 mm 0.2 m 0.4 m 8 mm 0.2 m

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. 18 mm 12 mm 0.2 m 0.4 m 8 mm 0.2 m

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

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.
18 mm,
12 mm
0.2 m
0.4 m
8 mm
0.2 m
B

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