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
- A 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 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 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_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_forwardTo 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 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_forwardYou 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_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_forward
- Indicate the points on the stress-strain diagram which represent the proportional limit and the ultimate stress.arrow_forwardThe graphical representation of fatigue strength on the Y axis to the number of stress cycles on the X axis is called as Gerber Line O S-N Curve O Soderberg Line O Goodman Linearrow_forwardBar 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
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Understanding Failure Theories (Tresca, von Mises etc...); Author: The Efficient Engineer;https://www.youtube.com/watch?v=xkbQnBAOFEg;License: Standard youtube license