Find maximum principal stress70 MPa50 MPa-40 MPа — х0, =-40 MPaa, = 70 MPa--50 MPa

Answered: Find maximum principal stress 70 MPu 50…

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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Find maximum principal stress
70 MPa
50 MPa
-40 MPа — х
0, =-40 MPa
a, = 70 MPa
--50 MPa

Expert Solution

Step 1

As given in question,

Normal stress in x direction = σ_x = -40 MPa

Normal stress in x direction = σ_y = 70 MPa

Shear stress in x-y plane = τ_xy = -50 MPa

Maximum principal stress is given by,

$\begin{array}{rcl} σ_{1} & = & (\frac{σ_{x} + σ_{y}}{2}) + \sqrt{{(\frac{σ_{x} - σ_{y}}{2})}^{2} + {(τ_{x y})}^{2}} \\ = & (\frac{- 40 + 70}{2}) + \sqrt{{(\frac{- 40 - 70}{2})}^{2} + {(- 50)}^{2}} \\ = & 15 + \sqrt{3025 + 2500} \\ = & 15 + 74.33 \\ = & 89.33 M P a \end{array}$

Hence, maximum principal stress = 89.33 MPa

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