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Longitudinal Stress

One end of a ...

Question

One end of a uniform bar of weight $w_{1}$ is suspended from the roof and a weight $w_{2}$ is suspended from the other end, the area of cross-section is A. What is the stress at the mid point of the rod?

\frac{w_{1} + w_{2}}{A}

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\frac{w_{1} - w_{2}}{A}

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\frac{(w_{1} / 2) + w_{2}}{A}

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\frac{w_{2} / 2 + w_{1}}{A}

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Solution

The correct option is C $\frac{(w_{1} / 2) + w_{2}}{A}$
The downward tension at mid-point of the bar is due to weight of lower half of the bar and the hanging weight.

The downward tension at mid-point is, $(w_{1}) / 2 + w_{2}$
As, $s t r e s s = f o r c e / a r e a = \frac{(w_{1}) / 2 + w_{2}}{A}$

Option C is correct.

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