MECHANICS OF MATERIALS
11th Edition
ISBN: 9780137605521
Author: HIBBELER
Publisher: RENT PEARS
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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.
The state of plane stress at a critical point in a steel machine bracket is shown. If the yield stress for steel is sY = 36 ksi, determine if yielding occurs using the maximum distortion energy theory.
Q1: A ductile bar of aluminum 1010 alloy.
Using the distortion-energy and maximum-
shear-stress theories determine the factors
of safety for the following plane stress
states:
(a) σx = 180 MPa, σy = 100 MPa
(b) σx = 180 MPa, Txy = 100 MPa
(c) σx = -160 MPa, Txy = 100 MPa
= 150 MPa
(d) Txy
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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- 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 MPaarrow_forwardQ1: A ductile bar of aluminum 1010 alloy. Using the distortion-energy and maximum- shear-stress theories determine the factors of safety for the following plane stress states: (α) σχ = 180 MPa, σy = 100 MPa (b) σx = 180 MPa, Txy = (c) σx = -160 MPa, Txy = 150 MPa (d) Txy 100 MPa = 100 MPaarrow_forwardA 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 isarrow_forward
- The 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_forwardSolve Q1: A ductile bar of aluminum 1010 alloy. Using the distortion-energy and maximum- shear-stress theories determine the factors of safety for the following plane stress states: (a) a, 180 MPa, a, 180 MPa, T., (b), (e) a, (d) T., 150 MPa 100 MPa 100 MPa -160 MPa, Ty=100 MPa Q3: The bar below is made of carbon steel (1035-hot rolled) and is loaded by the forces F = 0.55 kN, P = 8.0 kN, and T = 30 N m. Compute the factors of safety, based upon the distortion-energy theory. Q2: for the shaft shown below answer the following: 1. Find the factor of safety in point H if the shaft is made from carbon steels 1030 hot rolled and the shaft diameter is 32 mm. 2. Find the diameter of the shaft if it made from wrought-aluminum alloy 2024 heat treated and the factor of safety is 2. 3. Select suitable carbon steel alloy for that shaft if its diameter is 25 mm and factor of safety required is 1.5. 0.2 Q4: The figure shows a shaft mounted in bearings at A and D and having pulleys at B and C. The…arrow_forwardThe bxd xhrubber blocks shown are used in a double U shear mount to isolate the vibration of a machine from its supports. An applied load of P- 750 N causes the upper frame to be deflected downward by 4.9 mm. Determine the average shear strain and the shear stress in the rubber blocks. Assume b 16 mm, d 28 mm, and h= 28. Double U anti-vibration shear mount Rubber block dimensions Shear deformation of blocks Answers: Average shear strain- rad. Average shear stress- kPa. 478316arrow_forward
- If 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_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_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_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