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Strength of Materials

Deformation of Bars due to Axial Load

The total elo...

Question

The total elongation of the structural element (fixed at one end, free at the other end, and of varying cross-section) as shown in the figure, when subjected to load 2P at the free end is

A

6.66 \frac{P l}{A E}

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B

5.55 \frac{P l}{A E}

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C

4.44 \frac{P l}{A E}

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D

3.33 \frac{P l}{A E}

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Solution

The correct option is A $6.66 \frac{P l}{A E}$

Total elongation $Δ$

$= Δ_{1} + Δ_{2} + Δ_{3}$

$= \frac{2 P I}{A E} + \frac{2 P l}{3 A E} + \frac{2 P l}{\frac{A}{2} E}$

$= \frac{2 P l}{A E} + \frac{2 P I}{3 A E} + \frac{4 P l}{A E} = 6.66 \frac{P l}{A E}$

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