Introduction to the Mechanics of Deformable Solids by David H. Allen

Author:David H. Allen
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

Required 1.Using torsion bar theory, derive an expression for each of the following:(a)

(b)

(c)

(d)

2.Plot the results of (a)–(d) on four different graphs: , and

3.Suppose the bar is 10 m long, with and is made of A36 steel (), and the maximum allowable shear stress in the bar is , determine the minimum allowable radius, R, of the bar

Solution 1.(a) Since , it follows that, from (4.5)

(E.4.1.1)

Now consider the torque, , applied at the right end of the bar. Newton’s third law may be used to deduce that the boundary condition at the right end is . Applying this boundary condition to (E.4.1.1) results in

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