Answered: How can the engineers transform the…

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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Question

How can the engineers transform the strains in order to obtain their values in
other directions?

Expert Solution

Step 1

Given

Strain

To find

How to calculate multi dimension strain

Step 2

Strain

It a mathematical procedure to understand the geometrical deformation.

The deformation is mathematically termed as the ratio of change in parameter to the original parameter. The parameter can be the length, radius, area, volume etc. In other words parameter is the geometrical relationship of the body.

So let us consider a cylinder of radius R and diameter L

Therefore mathematically we can write

$S t r a i n (ε) = \frac{C h a n g e i n p a r a m e t e r}{O r i g i n a l P a r a m e t e r} F o r X a x i s S t r a i n (ε) = \frac{|L_{O r i g i n a l} - L_{d e f r m e d}|}{L_{O r i g i n a l}} S t r a i n (ε) = \frac{|∆ L|}{L_{O r i g i n a l}} F o r Y a x i s S t r a i n (ε) = \frac{|R_{O r i g i n a l} - R_{d e f r m e d}|}{R_{O r i g i n a l}} S t r a i n (ε) = \frac{|∆ R|}{R_{O r i g i n a l}}$

Strain magnitude are constant at any direction and any parameter because during strain neither matter is added nor extracted. The matter distribution remains constant perhaps the matter distribution pattern can differ with respect to the axis or parameter but the magnitude remains same.

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