Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Chapter 10.7, Problem 84P
To determine
The smallest yield stress for steelbased on the maximum distortion energy theory.
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Problem #1: Re-evaluate the beam from the Module 3 homework. Recall that you determine the principal stresses
at point A and B on the beam.
Note: Assume the yield strength is 248 MPa.
Part A: Based on that information, determine if any of the failure criteria (Rankine's theory, Tresca criterion, and
Von Mises criterion) predict failure by yielding at either A or B. Present the factor of safety for all three criteria.
Part B: Based on the results of Part A and what we know about the failure surfaces of these three criteria, do these
computed factors of safety make sense? Where does this data point land on the failure surfaces?
20 kN
100 mm
10 kN
B 100 mm
100 mm
•B
|A
50 mm 50 mm
2 m
2 m
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
The 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.
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
- The state of plane stress shown occurs at a critical point of a metal machine component. As a result of several tensile tests, it has been found that the tensile yield strength is Fy for the grade of metal used. Determine the ratio of OT/ OH shown in the figure, using the maximum-shearing-stress criterion (Tresca Hexagon). (Using Mohr circle method to calculate principle and average stresses) OX TXy Mpa Mpa Mpa MPa ob σy тху 90 -60 45 310 dy OX x Sx=Sx Sy=sy txy=txy Fy=Yield Strength Answerarrow_forwardProblem 4: The state of plane stress shown occurs in a machine component made of a steel with oYilled = 45 ksi. Take ox= 35.6 ksi. In the context of the maximum-distortion-energy criterion, for which of the following cases will yielding occur? If yielding does not occur, determine the corresponding factor of safety. a) Txy = 9 ksi b) Txy = 18 ksi c) Txy = 20 ksi 21 ksiarrow_forwardA small element at the critical section of a component is in bi-axial state of stress with two principal stresses being 360 MPa and 140 MPa. The maximum working stress according to distortion energy theory (in MPa) isarrow_forward
- y A B 3 in. D C 2 in. -2 in. 1.5 in. E.arrow_forwardIn the picture there is a sketch of a socket wrench. Assume the wrench is held at a fixed point “A”. The yield stress of the material is known to be 400 MPa. Answer the questions below Describe the stresses at point “A” and their causes and calculate the stresses. Determine the factor of safety against yield assuming the Tresca yield criteria. Determine the factor of safety against yield assuming the von Mises yield criteria using both principal stresses and “Cartesian” stresses. Do your values match or not, and is this expected? Explain. Do the calculated values make sense with the respect to the Tresca value? Explain, why or why not?arrow_forward1. 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.arrow_forward
- The main stresses and directions and the maximum shear stress;The tension state for a 30° clockwise rotation.Mohr's Circle.arrow_forwardAssume suitable value for any missing data. Two cylindrical parts are to be assembled to make an interference fit. The nominal diameter of the assembly is 100 mm. Before assembly, the inner member (copper) has an outer radius that is 0.2 mm larger than the inner radius of the outer member (aluminum). If there is no other force acting on the assembly, determine the maximum and minimum principal stress in both the members. Assume Poisson's ratio of 0.3 for both the materials. Also take rj = 30 mm for copper cylinder and ro = 80 mm for aluminum cylinder.arrow_forwardThe factors of safety at point H predicted by the maximum-distortion-energy theory (von Mises criterion) can be calculated as The von Mises equivalent stresses at point H can be calculated as MPaarrow_forward
- A 6-inch diameter pulley mounted on a 2-inch shaft as shown transmits 9 kW at 1000 rpm. What is the combined stress acting on the shaft?arrow_forwarddiagram and determine approximately the modulus of elasticity, the yield stress, the ultimate stress, and the fracture 2.00 in. The data is listed in the table. Plot the stress-strain 8-1. A tension test was performed on a steel specimen n original diameter of 0.503 in. and gage length of PROBLEMS *84. origi the f having an for t and stress. Use a scale of 1 in. Dodraw the elastic region, using the same stress scale but a 20 ksi and 1 in. = 0.05 in./in. strain scale of 1 in.= 0.001 in./in. Load (kip) Elongation (in.) 0. 0. 0.0005 0.0015 1.50 4.60 8.00 11.00 0.0025 0.0035 0.0050 11.80 11.80 0.0080 0.0200 12.00 16.60 0.0400 0.1000 0.2800 20.00 21.50 19.50 18.50 0.4000 0.4600 Prob. 8-1arrow_forwardgure 1 shows a compound bar with three different diameters, d1-9mm, d2-22mm, and d3-14mm machined from solid aluminium alloy stock, subjected to a tensile load of 30kN. If Young's odulus for the alloy is 69GPA determine the stress in section 2. Answer to be provided in MPa, correct to three decimal places - do not include a unit with your answer. L1 L2 L3 d2 d3 P Figure 1arrow_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