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 81P
If σY = 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.
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A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 350 MPa. Using the distortion-
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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
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.
Determine 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.
Chapter 10 Solutions
Mechanics of Materials
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- A loading condition is shown below. The wires at point A and D both made from a steel with the yield strength (Sy) of 190 MPa with 2 mm diameter. Using either maximum shear stress theory or distortion energy theory, determine the maximum load P that can be applied before yielding happens in the wires.arrow_forwardIf the material is machine steel having a yield stress of sY = 700 MPa, determine the factor of safety with respect to yielding if the maximum shear stress theory is considered.arrow_forwardA thin-walled cylinder of diameter 40 mm is subjected to an internal pressure of 5 N/mm² and a torque of 100 Nm. If the material of the cylinder has a yield stress in simple tension of 150 N/mm determine the required wall thickness using the Tresca and von Mises theories of elastic failure. Ans. 0.81 mm (Tresca), 0.74 mm (von Mises).arrow_forward
- A rectangular steel block is subjected to a triaxial loading of three uniformly distributed forces. If ν = 0.30 and E = 200 GPa, determine the single uniformly distributed load in the x direction that would produce the same deformation in the z direction as the original loading. Fx = 10kN, Fy = 15 kN, Fz = 20 kN, L = 600 mm, W = 400 mm, & D = 800 mm.arrow_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_forwardThe 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.arrow_forward
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- A machine component made of a ductile material is subjected to a variable loading with Omin=-50 MPa and o = 50 MPa. If the corrected endurance max limit and the yield strength for the material are o=100 MPa and o, = 300 MPa, respectively, the factor of safety isarrow_forwardA tension test was performed on a steel specimen having an original diameter of 12.5 mm and gauge length of 50 mm. The data is listed in the table. Plot the stress–strain diagram and determine approximately the modulus of elasticity, the yield stress, the ultimate stress, and the rupture stress. Use a scale of 25 mm = 140 MPa and 25 mm = 0.05 mm/mm. Redraw the elastic region, using the same stress scale but a strain scale of 25 mm = 0.001 mm/mm.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
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