1)Figure 1 shows an element with stresses.Angle 1TyxTxyTyxFigure 1Point A(-x-direction stress 60MPA(compression), y-direction stress40MPA(tension), negative shear stress 30MPAa)From basic priciples determine the stresses on the plane of the indicated angle 1. (30°)Show al calculations. Draw the orientation of the stress block for this scenario.

Answered: Angle 1 Oy Tyx Figure 1 Point…

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

1)
Figure 1 shows an element with stresses.
Angle 1
Tyx
Txy
Tyx
Figure 1
Point A(-x-direction stress 60MPA(compression), y-direction stress
40MPA(tension), negative shear stress 30MPA
a)
From basic priciples determine the stresses on the plane of the indicated angle 1. (30°)
Show al calculations. Draw the orientation of the stress block for this scenario.

Expert Solution

Step 1

The given values are -

$σ_{x} = - 60 M P a, σ_{y} = 40 M P a, τ_{x y} = - 30 M P a θ = 30 °$

The stresses on inclined plane are - $σ_{x}', σ_{y}' a n d τ_{x y}'$

$σ_{x}' = \frac{σ_{x} + σ_{y}}{2} + \frac{σ_{x} - σ_{y}}{2} c o s 2 θ + τ_{xy} s i n 2 θ σ_{x}' = \frac{- 60 + 40}{2} + \frac{(- 60 - 40)}{2} c o s 60 ° - 40 s i n 60 ° σ_{x}' = - 69.64 MPa σ_{y}' = \frac{σ_{x} + σ_{y}}{2} - \frac{σ_{x} - σ_{y}}{2} \cos 2 θ - τ_{xy} \sin 2 θ σ_{x}' = \frac{- 60 + 40}{2} - \frac{(- 60 - 40)}{2} \cos 60 ° + 40 \sin 60 ° σ_{x}' = - 49.64 MPa$