Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
expand_more
expand_more
format_list_bulleted
Videos
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.
Expert Solution & Answer
Trending nowThis is a popular solution!
Learn your wayIncludes step-by-step video
schedule04:57
Students have asked these similar questions
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.
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.
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...
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
Determine its initial angular acceleration and the horizontal and vertical reactions at the pin A.
Engineering Mechanics: Dynamics (14th Edition)
The force in each member of truss and the state of members are in tension or compression.
Engineering Mechanics: Statics & Dynamics (14th Edition)
Determine the maximum force P that can be applied without causing the two 50-kg crates to move. The coefficient...
Engineering Mechanics: Statics
1.1 What is the difference between an atom and a molecule? A molecule and a crystal?
Manufacturing Engineering & Technology
figure 4.44 shows a rectangular gate holding water behind it. If the water is 6.00 ft deep, compute the magnitu...
Applied Fluid Mechanics (7th Edition)
4.10 Calculate the horizontal force F that should be applied to the 100 lb weight shown so that the cable AB is...
Applied Statics and Strength of Materials (6th Edition)
Knowledge Booster
Learn more about
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
- 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_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_forwardA 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
- Using 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_forwardIf a machine part is made of Ti-6A1-4V titanium and a critical point in the material is subjected to plane stress, such that the principal stresses are σ1 and σ2 = 0.501, determine the magnitude of σ1 in MPa that will cause yielding according to (a) the maximum shear stress theory, and (b) the maximum distortion energy theory. Hint: Refer to the inside cover the textbook for material section properties.arrow_forwardDetermine 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
- The 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_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
- 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 MPaarrow_forwardIdentify the material that has maximum stiffness value from the following stress- strain curves. в D Strain ов ос O D O A Stressarrow_forwardConsider the two states of stress as shown in configurations I and Il in the figure below. From the standpoint of distortion energy (von-Mises) criterion, which one of the following statements is true? IIarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Understanding Failure Theories (Tresca, von Mises etc...); Author: The Efficient Engineer;https://www.youtube.com/watch?v=xkbQnBAOFEg;License: Standard youtube license