Question

A shaft having a diameter $D$ of 3 in. (see Fig. P.14.52) is acted on by a torque $T$ of $300 \mathrm{ft}-\mathrm{lb}$ at one end, while at the other end is consected by a rubber material to a fixed rigid disk. The latter support gives a linear, elastic torsional spring constant $K_T$ to the end having the value of 700 ft -lbideg. What is the total twist $\phi$ at end $\boldsymbol{A}$ and the relative twist $\phi_{A B}$ between eads $A$ and $B$ ? The length $L$ is 10 ft and $G=10 \times 10^6 \mathrm{psi}$. Figure P.14.52.

   A shaft having a diameter $D$ of 3 in. (see Fig. P.14.52) is acted on by a torque $T$ of $300 \mathrm{ft}-\mathrm{lb}$ at one end, while at the other end is consected by a rubber material to a fixed rigid disk. The latter support gives a linear, elastic torsional spring constant $K_T$ to the end having the value of 700 ft -lbideg. What is the total twist $\phi$ at end $\boldsymbol{A}$ and the relative twist $\phi_{A B}$ between eads $A$ and $B$ ? The length $L$ is 10 ft and $G=10 \times 10^6 \mathrm{psi}$.
Figure P.14.52.

Introduction to Solid Mechanics

Irving H. Shames,… 3rd Edition

Chapter 13, Problem 52

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Step 1

We have: - Diameter of the shaft, $ D = 3 $ in. - Torque applied, $ T = 300 $ ft-lb. - Length of the shaft, $ L = 10 $ ft. - Torsional spring constant, $ K_T = 700 $ ft-lb/deg. - Shear modulus, $ G = 10 \times 10^6 $ psi. Show more…

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A shaft having a diameter $D$ of 3 in. (see Fig. P.14.52) is acted on by a torque $T$ of $300 \mathrm{ft}-\mathrm{lb}$ at one end, while at the other end is consected by a rubber material to a fixed rigid disk. The latter support gives a linear, elastic torsional spring constant $K_T$ to the end having the value of 700 ft -lbideg. What is the total twist $\phi$ at end $\boldsymbol{A}$ and the relative twist $\phi_{A B}$ between eads $A$ and $B$ ? The length $L$ is 10 ft and $G=10 \times 10^6 \mathrm{psi}$. Figure P.14.52.

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