Mechanics of Materials
9th Edition
ISBN: 9780133254426
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Textbook Question
Chapter 10.3, Problem 10.21P
using Mohr’s circle.
10−6. The state of strain at a point on the bracket has components of εx = 150(10−6), εy = 200(10−6), γxy = −700(10−6). Use the strain transformation equations and determine the equivalent in-plane strains on an element oriented at an angle of θ = 60° counterclockwise from the original position. Sketch the deformed element within the x–y plane due to these strains.
10−7. Solve Prob.10-6 for an element oriented θ = 30° clockwise.
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The state of plane strain on an element is represented by the following components:
Ex
=D340 x 10-6, ɛ, = , yxy
Ey
=D110 x 10-6,
3D180 x10-6
ху
Draw Mohr's circle to represent this state of strain.
Use Mohrs circle to obtain the principal strains and principal plane.
For the state of a plane strain with εx, εy and γxy components: (a) construct Mohr’s circle and (b) determine the equivalent in-plane strains for an element oriented at an angle of 30° clockwise. εx = 255 × 10-6 εy = -320 × 10-6 γxy = -165 × 10-6
For the given plane strain state, use Mohr's circle to determine the strain state associated with the x' and y' axes rotated to θ indicated in the table:
\epsilon_x
\epsilon_y
\gamma_{xy}
θ
-500\mu
250\mu
120\mu
-15°
Chapter 10 Solutions
Mechanics of Materials
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