Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Chapter 10.3, Problem 14P
Use the strain transformation equations to determine (a) the in-plane principal strains and (b) the maximum In-plane shear strain and average normal strain. In each case, specify the orientation of the element and show how the strains deform the element within the x–y plane.
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A differential element is subjected to plane strain that has the following components; Px = 950(10-6), Py = 420(10-6), gxy = -325(10-6). Use the strain transformation equations and determine (a) the principal strains and (b) the maximum in-plane shear strain and the associated average strain. In each case specify the orientation of the element and show how the strains deform the element.
The strain components, ex= 940 micro strain, ey= -360 micro strain and yxy=830micro strain are given for a point in body subjected to plane strain. Determine;
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Confirm your answer by means of Mohr's circle of strain and determine the linear strain on an axis inclined at 20 degrees clockwise to the direction of ey
The state of strain at the point on the spanner wrench has components of Px = 260(10-6), P y = 320(10-6), and gxy = 180(10-6). Use the strain transformation equations to determine (a) the in-plane principal strains and (b) the maximum in-plane shear strain and average normal strain. In each case specify the orientation of the element and show how the strains deform the element within the x–y plane.
Chapter 10 Solutions
Mechanics of Materials
Ch. 10.3 - Prove that the sum of the normal strains in...Ch. 10.3 - The state of strain at the point on the arm has...Ch. 10.3 - The state of strain at the point on the leaf of...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Determine the equivalent state of strain on an...Ch. 10.3 - Determine the equivalent state of strain which...Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Determine the equivalent state of strain, which...Ch. 10.3 - Solve Prob.103 using Mohrs circle. 103. The state...Ch. 10.5 - The strain at point A on the bracket has...
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- An element of material in plain strain is subjected to shear strain xy = 0.0003. (a) Determine the strains for an element oriented at an angle = 30°. (b) Determine the principal strains of the clement. Confirm the solution using Mohr’s circle for plane strain.arrow_forwardAn element of material in plain strain has the following strains: x = 0.001 and y = 0.0015. (a) Determine the strains for an element oriented at an angle = 250. (b) Find the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.arrow_forwardAn element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy = 0.0003. (a) Determine the strains for an element oriented at an angle = 20°. (b) Determine the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.arrow_forward
- - 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction?arrow_forwardThe state of strain at the point on the support has components of ex = 350( 10-9), ey = 400( 10-6), Use the strain-transformation equations to determine (a) the in-plane principal strains and (b) the maximum in-plane shear strain and average normal strain. In each case specify the orientation of the element and show how the strains deform the element within the x-y plane. yxy = -675( 10-), Also draw the Mohr Circlearrow_forwardThree readings are obtained from an equiangular strain gage rosette mounted on a free and unloaded surface of a part. Determine the magnitude of the principal strains and their orientation with respect to the 0° gage. Check the results with a Mohr circle.Assume The three known strains are all linear strainsarrow_forward
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