Question

A shaft is formed by laminating very thin cylinders as shown in Fig P.14.68. The inside diameter (i.e., of the smallest cylinder) is 1 in. and the outside diameter is 3 in . We shall assume that the shear moduli of the larninae are different and can be expressed as a function of $r$ as follows: $$ G=G_1(1+2 r) $$ Determine the maximum shear stress and the twist at the end of the shaft for $G_1=15 \times 10^6 \mathrm{psi}$. Figure P.14.68.

   A shaft is formed by laminating very thin cylinders as shown in Fig P.14.68. The inside diameter (i.e., of the smallest cylinder) is 1 in. and the outside diameter is 3 in . We shall assume that the shear moduli of the larninae are different and can be expressed as a function of $r$ as follows:
$$
G=G_1(1+2 r)
$$

Determine the maximum shear stress and the twist at the end of the shaft for $G_1=15 \times 10^6 \mathrm{psi}$.
Figure P.14.68.

Introduction to Solid Mechanics

Irving H. Shames,… 3rd Edition

Chapter 13, Problem 68

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Step 1

The inside diameter of the smallest cylinder is $ d_i = 1 \, \text{in} $ and the outside diameter of the largest cylinder is $ d_o = 3 \, \text{in} $. The radius of the smallest cylinder is $ r_i = \frac{d_i}{2} = 0.5 \, \text{in} $ and the radius of the Show more…

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A shaft is formed by laminating very thin cylinders as shown in Fig P.14.68. The inside diameter (i.e., of the smallest cylinder) is 1 in. and the outside diameter is 3 in . We shall assume that the shear moduli of the larninae are different and can be expressed as a function of $r$ as follows: $$ G=G_1(1+2 r) $$ Determine the maximum shear stress and the twist at the end of the shaft for $G_1=15 \times 10^6 \mathrm{psi}$. Figure P.14.68.

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