MECHANICS OF MATERIALS
11th Edition
ISBN: 9780137605521
Author: HIBBELER
Publisher: RENT PEARS
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Textbook Question
Chapter 10.7, Problem 59P
A material is subjected to plane stress. Express the distortion energy theory of failure in terms of σx, σy, and τxy.
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1. We can visualize the factor of safety for an arbitrary stress using a surface in principal stress space. For
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Three cases of plane stress at yield or fracture are shown in the figures. Examine each case and determine what type of failure is likely to occur. Limit the choice of criteria to the maximum normal-stress, distortion-energy, and maximum shear-stress theories. Explain your reasoning.
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...
Ch. 10.5 - Determine (a) the principal strains at A, (b) the...Ch. 10.6 - For the case of plane stress, show that Hookes law...Ch. 10.6 - to develop the strain tranformation equations....Ch. 10.6 - Determine the associated principal stresses at the...Ch. 10.6 - Determine the applied load P. What is the shear...Ch. 10.6 - If a load of P = 3 kip is applied to the A-36...Ch. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - Solve Prob. 1061 using the maximum distortion...Ch. 10.7 - Solve Prob.1063 using the maximum distortion...Ch. 10.7 - Prob. 70PCh. 10.7 - The plate is made of Tobin bronze, which yields at...Ch. 10.7 - If a machine part is made of titanium (TI-6A1-4V)...Ch. 10.7 - The components of plane stress at a critical point...Ch. 10.7 - If Y = 50 ksi, determine the factor of safety for...Ch. 10.7 - Prob. 82PCh. 10.7 - If the yield stress for steel is Y = 36 ksi,...Ch. 10.7 - Prob. 84PCh. 10.7 - The state of stress acting at a critical point on...Ch. 10.7 - The shaft consists of a solid segment AB and a...Ch. 10 - In the case of plane stress, where the in-plane...Ch. 10 - The plate is made of material having a modulus of...Ch. 10 - If the material is machine steel having a yield...Ch. 10 - Determine if yielding has occurred on the basis of...Ch. 10 - The 60 strain rosette is mounted on a beam. The...Ch. 10 - Use the strain transformation equations to...Ch. 10 - If the strain gages a and b at points give...Ch. 10 - Use the strain-transformation equations and...Ch. 10 - Use the strain transformation equations to...Ch. 10 - Specify the orientation of the corresponding...
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- The principal stresses at a critical point in plane stress are o and 0.250. The yield stress for the material is oy = 250 MPa. The magnitude of MPa. (Correct up to two decimal places) o that will cause yielding according to the maximum distortion energy theory isarrow_forwardA material is subjected to plane stress. Express the maximum shear stress theory of failure in terms of sx, sy, and txy. Assume that the principal stresses are of different algebraic signs.arrow_forwardThe state of stress acting at a critical point on a wrench is shown. Determine the smallest yield stress for steel that might be selected for the part, based on the maximum distortion energy theory.arrow_forward
- Q1: A ductile bar of aluminum 1010 alloy. Using the distortion-energy and maximum- shear-stress theories determine the factors of safety for the following plane stress states: (α) σχ = 180 MPa, σy = 100 MPa (b) σx = 180 MPa, Txy = (c) σx = -160 MPa, Txy = 150 MPa (d) Txy 100 MPa = 100 MPaarrow_forwardUsing 2 of the 3 given equations: σ = F/A ε = δ/L σ = E * ε calculate the original length, in mm, of a circular tube that experience a compression stress of 80 MPa . The deformation of the tube is 0.684 mm and E = 70 000 MPa. Make sure to write which equations of the three above you used.arrow_forwardA brittle material has the properties Sut = 30 kpsi and Suc = 90 kpsi. Using the brittle Coulomb- Mohr and modified- Mohr theories, determine the factors of safety for the following states of plane stress: a. x = 20 kpsi, Txy = −10 kpsi b. σx = - 15 kpsi, σy = 10 kpsi, Txy = -15 kpsiarrow_forward
- To determine the nominal or engineering stress and strain experienced by a specimen of a material while it is subjected to a tension test, and to be able to read important values from a conventional stress-strain diagram obtained from the test. A tension test is being conducted on a steel-rod specimen with a gauge length of L0=50 mm and initial diameter of d0=13 mm. Data were collected to form the conventional stress-strain diagram as shown. From the diagram, f = 506 MPa , e = 689 MPa , g = 585 MPa , and h = 0.146 mm/mm . A) Assuming that the strain remains constant throughout the region between the gauge points, determine the nominal strain ε experienced by the rod if it is elongated to L = 53.0 mm . B) Assuming that the stress is constant over the cross-sectional area and if the tension force used is P = 16.0 kN , find the nominal stress experienced by the rod. C)Determine the force P needed to reach the ultimate stress in the steel-rod specimen.arrow_forwardThe specimen shown has been cut from a 5-mm-thick sheet of vinyl (E= 3.10 GPa) and is subjected to a 1.5-kN tensile load. It is given that /= 58 mm. Dimensions in mm A в 10 D P'= 1.5 kN P = 1.5 kN 25 25 - 40- Determine the total deformation of the specimen. The total deformation of the specimen is mm.arrow_forwardThe block is subjected to a force V = 48 kN . What is the resulting deflection Δ?arrow_forward
- Q1: A ductile bar of aluminum 1010 alloy. Using the distortion-energy and maximum- shear-stress theories determine the factors of safety for the following plane stress states: (a) σx = 180 MPa, σy = 100 MPa (b) σx = 180 MPa, Txy = 100 MPa (c) σx = -160 MPa, Txy = 100 MPa = 150 MPa (d) Txyarrow_forwardThe yield stress for a zirconium-magnesium alloy is sY = 15.3 ksi. If a machine part is made of this material and a critical point in the material is subjected to in-plane principal stresses s1 and s2 = -0.5s1, determine the magnitude of s1 that will cause yielding according to the maximum shear stress theory.arrow_forwardProblem 1·16 At a point in a structural member subjected to plane stress, the state of stress is : 0x =70 MPa, ơ, MPa. Determine which of the theories of failure will predict failure by yielding for this state of stress if the yield strength of the material in tension and compression is 250 MPa. 56 MPa, txy -28arrow_forward
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Understanding Failure Theories (Tresca, von Mises etc...); Author: The Efficient Engineer;https://www.youtube.com/watch?v=xkbQnBAOFEg;License: Standard youtube license