Question

A bar with a cross section is loaded with 2000 lbs. If Maximum allowed stress is 20000lb, then what is the minimum dimension of the bar in inches?

Answer 1

We know that $Stress _{Max.}= \frac{Load}{Area}$

where

• Stress (Max) = 2e4 psi (NOT lb)
• Load = 2e3 lb

Thus, $Stress = \frac{Load}{Area}=>Area=\frac{Load}{Stress}=\frac{2e3}{2e4}=0.1\: in^{2}$

Also, the shape of the cross-section is not given, but below are the recommended shapes based on this Area.

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If the shape of the cross-section is SQUARE-

Area = Side x Side = 0.1 => Side = 0.3162 in

If the shape of the cross-section is CIRCLE-

$Area=\frac{\prod dia^{2}}{4}=0.1=>\mathbf{Dia=0.3568 \: in}$

If the shape of the cross-section is EQUILATERAL TRIANGLE-

.$Area=\frac{\sqrt{3}}{4}side^{2}=0.1=>\mathbf{Side=0.4805\: in}$

These are the minimum dimensions of the bar in inches.

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