Answered: A cylindrical rod has initial…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A cylindrical rod has initial dimensions of length ? = 4 m and
radius ? = 1 cm. When the rod is pulled in tension axially with
an external force of ? = 200 kN, the rod deforms to new
dimensions of length ?′ = 4.024 m and radius ?′ = 0.998 cm.
Determine the modulus of elasticity of the rod and its Poisson’s
ratio. Assume the rod deforms in the elastic range.

Expert Solution

Step 1

Given data:

The external force, P = 200 kN.
The change in length, $L^{'} = 4.024 m$ .
The change in radius, $r' = 0.998 cm$ .
The length of the rod, $L = 4 m$ .
The radius of the rod, $r = 1 cm$ .

Calculate the lateral strain as follows:

$\begin{array}{rcl} ε_{d} & = & \frac{r - r'}{r} \\ = & \frac{1 cm - 0.998 cm}{1 cm} \\ = & 2 \times 10^{- 3} \end{array}$

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