Maximum Load of a Member | Stress | Mechanics of Materials | 3rd Edition | Timothy Philpot | Problem P1.1

A stainless steel tube with an outside diameter of 60 mm and a wall thickness of 5 mm is used as a compression member. If the axial normal stress in the member must be limited to 200 MPa, determine the maximum load P that the member can support.

SOLUTION:

The cross-sectional area of the stainless steel tube is

\displaystyle A=\frac{\pi }{4}\left(D^2-d^2\right)

\displaystyle A=\frac{\pi }{4}\left[\left(60\:mm\right)^2-\left(50\:mm\right)^2\right]

\displaystyle A=863.938\:mm^2

The normal stress in the tube can be expressed as 

\displaystyle \sigma =\frac{P}{A}

The maximum normal stress in the tube must be limited to 200 MPa. Using 200 MPa as the allowable normal stress, rearrange this expression to solve for the maximum load P.

\displaystyle P_{max}=\sigma _{max}A

\displaystyle P_{max}=\left(200\:MPa\right)\left(863.938\:mm^2\right)

\displaystyle P_{max}=\left(200\:\frac{N}{mm^2}\right)\left(863.938\:mm^2\right)

\displaystyle P_{max}=172\:788\:N

\displaystyle P_{max}=172.8\:kN

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