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 74P
If a machine part is made of titanium (TI-6A1-4V) and a critical point in the material is subjected to plane stress, such that the principal stresses are σ1 and σ2 = 0.5σ1, 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.
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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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- 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.arrow_forwardIn the attached 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 500 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_forwardA bracket is under a loading condition is shown below. It's made from a steel with the yield strength (Sy) of 420 MPa. Using either maximum shear stress theory or distortion energy theory, determine the maximum load P that can be applied before yielding happens.arrow_forward
- A steel with a yield stress of 300 MPa is tested under a state of stress whereσ2 = σ1/2 and σ3 = 0. What is the stress at which yielding occurs if it isassumed that:(a) The maximum-normal-stress criterion holds?(b) The maximum-shear-stress criterion holds?(c) The distortion-energy criterion holds?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_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_forward
- 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_forward1. A ductile hot-rolled steel bar has a yield strength in tension and compression of 350 MPa. Using the distortion-energy and maximum-shear-stress theories, determine the factors of safety for the following plane stress state: 75 MPa 50 MPa 50 MPaarrow_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
- In 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_forward(Suppose you need to design a tension test machine capable of testing specimens that have nominal ultimate stresses as high as σu = 100 ksi . How much force must the machine be capable of generating? Assume the testing specimen has the ASTM shape shown. Answer for this is 19.6 kip) (If the maximum nominal strain is ϵf = 0.7 just before the test specimen fractures and the test machine operates by moving only one grip, how far must that grip be designed to travel? The total length of the deforming part of the specimen is 3 in. Answer for this is 2.10 in) Do not know if this info is needed but this was the other 2 partsarrow_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=2 in and initial diameter of d0=0.5 in. Data were collected to form the conventional stress-strain diagram as shown. From the diagram, f = 73.0 ksi , e = 101.0 ksi g=83.0ksi, and h=0.15in/in Part A - Nominal or engineering strain in the rod 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 = 2.5 in . Express the nominal strain in inches per inch to three significant figures. Part B - Nominal or engineering stress in the specimen Assuming that the stress is constant over the cross-sectional area and if the tension force used is P = 8.0 kips ,…arrow_forward
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