Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Chapter 10.7, Problem 82P
To determine
The yielding occurs using the maximum distortion energy theory.
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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.
Problem 1: The stress state at a critical point on a steel part (Sy = 250 MPa) is shown below.
Determine whether yielding occurs according to the Maximum Distortional Energy (Von
Mises) failure theory.
60 MPa
40 MPa
70 MPa
A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 350 MPa. Using the distortion-
energy and maximum-shear-stress theories, determine the factors of safety with the following principal stresses.
σA = 90 MPa, and oß = -98 MPa
The factor of safety from the maximum-shear-stress theory is
"
and the factor of safety from the distortion-energy theory is
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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- A 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_forwardThe state of stress at a point in member is given by: 50 60 100 60 40 80 MPa 100 80 20 A torsion test performed on a specimen made of the same material shows that yielding occurs at a shearing stress of 140 MPa. Examine using maximum distortion energy theory if yielding will be occur under the state fo stress.arrow_forward(i) Determine the state of stress at point B on the cross-section of the post at section a-a. (ii) Find the design factor based on distortion energy theory and the maximum shear stress theory if the yield strength is 40000 psi. (Note: Point B is located inside the tube with a distance of 2 inches from the center of the cross-section.)arrow_forward
- If a shaft is made of a material for which sY = 75 ksi, determine the maximum torsional shear stress required to cause yielding using the maximum distortion energy theory.arrow_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_forwardYou are designing a driveshaft for a motor from a material with G = 15,000 ksi. The specifications for the project require a solid shaft to be used. Based on the location of the motor, the driveshaft has a length L = 9.55 ft. The motor provides 67 hp at a rotation rate of 2475 rpm.Your design requires φ ≤ 0.905° over the length of the shaft. Additionally, the maximum shear stress in the material τmax ≤ 4.0 ksi.Determine rmin, the minimum radiusarrow_forward
- 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.arrow_forwardA 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_forwardIf sY = 50 ksi, determine the factor of safety for this loading against yielding based on (a) the maximum shear stress theory and (b) the maximum distortion energy theory.arrow_forward
- The 38 mm diameter shaft is made of a steel for which the yield strength is = 250 MPa. Using maximum distortions energy criterion (Von-Mises), determine the magnitude of the torque T for which yield occurs when P = 240 kN.arrow_forwardQuestion 3: The 60 mm diameter solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the absolute maximum and minimun shear stresses on the outer surface of the shaft and specify their locations, measured from the fixed end A. Take : AA= 1.6 BB = 0.9 CC = 1200 AN/ m 2 kN-m/m AA m CC Nm B вB m Solution : = CC N-m TAB CC N-m 2o0ox N.m CC N.marrow_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_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