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Mechanics of Materials | 7th Edition | ISBN: 9780073398235 | Authors: Ferdinand P. Beer; E. Russell Johnston Jr.; John T. DeWolf; David F. Mazurek
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The uniform rod BC has cross-sectional area A and is made

Chapter 2, Problem 2.135

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QUESTION:

The uniform rod BC has cross-sectional area A and is made of a mild steel that can be assumed to be elastoplastic with a modulus of elasticity E and a yield strength \(\sigma_{Y}\). Using the block-and-spring system shown, it is desired to simulate the deflection of end C of the rod as the axial force P is gradually applied and removed, that is, the deflection of points C and \(C^{\prime}\) should be the same for all values of P. Denoting by \(\mu\) the coefficient of friction between the block and the horizontal surface, derive an expression for (a) the required mass m of the block, (b) the required constant k of the spring.

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QUESTION:

The uniform rod BC has cross-sectional area A and is made of a mild steel that can be assumed to be elastoplastic with a modulus of elasticity E and a yield strength \(\sigma_{Y}\). Using the block-and-spring system shown, it is desired to simulate the deflection of end C of the rod as the axial force P is gradually applied and removed, that is, the deflection of points C and \(C^{\prime}\) should be the same for all values of P. Denoting by \(\mu\) the coefficient of friction between the block and the horizontal surface, derive an expression for (a) the required mass m of the block, (b) the required constant k of the spring.

ANSWER:

Step 1 of 7

Calculate Maximum Allowed force  in the rod

Stress in the rod is equal to force divided by area.

So force  when rod fails is:

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