Answered: What is the equation for the twisting…

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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What is the equation for the twisting moment of a bar?

Expert Solution

Step 1

Assuming a bar shown in figure having length L and radius R and which is twist at angle $θ$ along radius and $γ$ along length.

The angle γ in the bar is given as,

$\tan γ = \frac{A A}{L}$

The angle tanγ is nearly equal to γ,

Lγ = AA......(1)

The angle θ in the bar is given as,

$a r c (A A) = r θ A A = R θ$

Step 2

The expression of modulus of rigidity is given as,

$G = \frac{τ}{γ} γ = \frac{τ}{G}$

Here, $τ$ is the shear stress.

Substitute above values in equation (1),

$\begin{array}{rcl} L γ & = & A A \\ L \frac{τ}{G} & = & R θ \\ τ & = & \frac{G R θ}{L} \\ \frac{G θ}{L} & = & \frac{τ}{R} . . . . . . (2) \end{array}$

Force required to twist the bar is,

$d F = τ d A d F = \frac{G θ R}{L} d A$

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