Solution to Problem 226 Biaxial Deformation

Problem 226
A 2-in.-diameter steel tube with a wall thickness of 0.05 inch just fits in a rigid hole. Find the tangential stress if an axial compressive load of 3140 lb is applied. Assume ν = 0.30 and neglect the possibility of buckling.
 

Solution 226

 
Mohd Naseem Hashmi
Mohd Naseem Hashmi's picture

Answer seems to be wrong. I think there is some typo here.
The answer should 2998.5 psi.
Since $$\frac{3430}{\pi}=2998.5$$
However we can get more accurate answer by considering the area of cross-section as $$A= \frac{\pi}{4}(d_2^2-d_1^2)$$
Where $$d_2$$is outside diameter and $$d_1$$ is inner diameter.

Jhun Vert
Jhun Vert's picture

The formula for area used here is

$$A = \pi d t$$

Where d is supposed to be mean diameter and t is the thickness. We did not check the extent of the error. Sources of errors are (1) the formula itself is for very thin tube, (2) we use the inner diameter for d, instead of mean diameter.

Thank you for pointing it out.

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