Question 5.13: Determine the bending stress in a cylinder fixed at one edge...
Determine the bending stress in a cylinder fixed at one edge (Figure 5.23a) due to a uniform rise in temperature of 200 °F, if
\alpha=605 \times 10^{-6} in./in.- °F
E=30 \times 10^{6} psi
\mu=0.3
The radial deflection of the cylinder if the ends are free is
w=(\alpha)(\Delta T)(r)=0.039in.
From Figure 5.23a and 5.23b, the rotation at the end is zero because the cylinder is fixed. Hence,
\frac{M_{0}}{\beta D}=\frac{Q_{0}}{2 \beta^{2} D}or
Q_{0}=2 \beta M_{0}In the second compatibility equation, the deflection due to temperature plus moment plus shear is equal to zero:
0.039+\frac{M_{0}}{2 \beta^{2} D}-\frac{Q_{0}}{2 \beta^{3} D}=0and
M_{0}=(0.039)\left(2 \beta^{2} D\right)= (0.039)(2)(0.4694)^{2}(42,930)
= 738in.-lb/in.
\sigma=\frac{6 M}{t^{2}}=70,800 psiRelated Answered Questions
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