The plateA thin plate of linear elastic materials (E = 200 GPa,0.25) is in plane stress (o, = Txz = Tyz = 0).V =heated by 100 °F and the thermalexpansion efficient of the plate is, a = 8 x 10eidsdon50 MPa1The plate is also compressed between twoperfectly smooth surfaces as shown in the figure.°F50 MPaFind the following:a. The non-zero stress in the plate.b. The change inc. The strainExathe thickness direction of the400 mmplate,and change in the thickness of thethe initial thickness is 4 mm.200 mm

Answered: A thin plate of linear elastic…

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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The plate
A thin plate of linear elastic materials (E = 200 GPa,
0.25) is in plane stress (o, = Txz = Tyz = 0).
V =
heated by 100 °F and the thermal
expansion efficient of the plate is, a = 8 x 10
eidsdon
50 MPa
1
The plate is also compressed between two
perfectly smooth surfaces as shown in the figure.
°F
50 MPa
Find the following:
a. The non-zero stress in the plate.
b. The change in
c. The strain
Exa
the thickness direction of the
400 mm
plate,
and change in the thickness of the
the initial thickness is 4 mm.
200 mm

Expert Solution

Step 1

Given that,

$M o d u l u s o f e l a s t i c i t y o f t h e m a t e r i a l, E = 200 G P a, K i n e m a t i c v i s \cos i t y o f t h e m a t e r i a l, μ = 0.25, T h e r m a l e x p a n s i o n c o e f f c i e n t, α = 8 \times 10^{- 6} \frac{1}{° F} A l s o, σ_{z} = 0, τ_{x z} = 0, τ_{y z} = 0, C h a n g e i n t e m p e r a t u r e i n p l a t e, ∆ T = 100 ° F$

(a) Calculate non-zero stress in the plate: -

For the given stress plate the dimension of the plate in the Y and Z direction is free to expand while in the X direction there is 50 MPa of pressure is applied which causes a generation of stress in the plate.

$T h e r m a l s t r e s s d u e t o t h e i n c r e a s e o f h e a t, σ = E α ∆ T σ = 200 \times 10^{9} \times 8 \times 10^{- 6} \times 100 σ = 160 M P a$

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