Mechanics of Materials

11th Edition

ISBN: 9780137605460

Author: Russell C. Hibbeler

Publisher: Pearson Education (US)

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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 *σ _{x}*,

*σ*, and

_{y}*τ*

_{xy}.Expert Solution & Answer

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Students have asked these similar questions

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The three principal stresses at a given point are σ1 =60 MPa, σ2 =−100 MPa, σ3 =−10 MPa. If the material has a yield stress of 250 MPa, estimate the factor of safety against yielding using (i) the maximum shear stress theory and (ii) von Mises’ theory.

1. We can visualize the factor of safety for an arbitrary stress using a surface in principal stress space. For
a ductile material that yields according to a von Mises criterion with a yield stress σy, sketch the von
Mises surface in σ₁ - 02 space and sketch the stress surface that corresponds to a factor of safety FoS =
2. For a brittle material that yields according to a max normal (Rankine) criterion with a tensile strength
Gyt and a compressive strength σvc = 20yt, sketch the yield surface and the surface that corresponds
to a factor of safety FoS = 2.

# 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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions

- For a certain metal the strength coefficient K = 600 MPa and the strain hardening exponent n =0.20. During a forming operation, the final true strain that the metal experiences ε = 0.73.Determine the flow stress at this strain and the average flow stress that the metal experiencedduring the operation.
*arrow_forward*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.*arrow_forward*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 is*arrow_forward* - A material has the following properties, ultimate Sul = σul = 350mpa, the strain hardening exponent n=0.20. Determine the value for the strength coefficient K.
*arrow_forward*Determine the yield strength of a material required such that the component would not fail when subject to the following stresses sigma1 = 2 MPa and sigma 2= -15 MPa sigma 3 = 10 MPa). Use a yield criterion that assumes that yield failure will occur when the maximum shear stress in the complex system becomes equal to the limiting shear strength in a simple tensile test.*arrow_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_forward* - The block is subjected to a force V = 48 kN . What is the resulting deflection Δ?
*arrow_forward*A thin-walled cylinder of diameter 40 mm is subjected to an internal pressure of 5 N/mm² and a torque of 100 Nm. If the material of the cylinder has a yield stress in simple tension of 150 N/mm determine the required wall thickness using the Tresca and von Mises theories of elastic failure. Ans. 0.81 mm (Tresca), 0.74 mm (von Mises).*arrow_forward*At a critical point in a component, the state of stress is given as Oxx = 100 MPa, Oyy = 220 MPa, Oxy = Oyx = 80 MPa and all other stress components are zero. The yield strength of the material is 468 MPa. The factor of safety on the basis of maximum shear stress theory is (round off to one decimal*arrow_forward* - Problem 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 -28
*arrow_forward*You measure the strains ɛrx = 30E – 6 and ɛyy = 10E – 6 on the surface of a thin part (plane stress). If the part material has a elastic modulus of 100 GPa and a Poisson's ratio of - 0.35. What are the normal stresses in the x and y directions? y-direction normal stress = 2.34 MPа x-direction normal stress = 3.82 MPa O y-direction normal stress = -4.34 MPa x-direction normal stress = -8.27 MPa*arrow_forward*Bar of steel, (yield strenght Sy = 469 MPa) is subjected to the following stresses; σx = 218 MPa , σy = -158 MPa , τxy = 138 MPa Using the Distortion-Energy Theory determine the factor of safety and check is the bar will fail or not.*arrow_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