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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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Step 1

Given data:

The ultimate tensile strength of component is S_ut = 30 ksi.
The ultimate compression strength is S_uc = 90 ksi.
The induced stress in x direction is σ_x = 15 ksi.
The induced stress in y direction is σ_y = -15 ksi.

Step 2

The expression for the equation of factor of safety using Coulomb Mohr theory is given by,

$\frac{1}{F_{S}} = \frac{σ_{x}}{S_{u t}} - \frac{σ_{y}}{S_{u c}}$

Substitute all the known value in above equation,

$\begin{array}{rcl} \frac{1}{F_{S}} & = & \frac{15 ksi}{30 ksi} - \frac{(- 15 ksi)}{90 ksi} \\ \frac{1}{F_{S}} & = & 0.66 \\ F_{S} & = & 1.5 \end{array}$

Thus, the the component is safe.

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