MECHANICS OF MATERIALS
11th Edition
ISBN: 9780137605521
Author: HIBBELER
Publisher: RENT PEARS
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Chapter 10.7, Problem 62P
Solve Prob. 10−61 using the maximum distortion energy theory.
10−61. The yield stress for a zirconium-magnesium alloy is σY = 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 σ1 and σ2 = −0.5σ1, determine the magnitude of σ1 that will cause yielding according to the maximum shear stress theory.
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If a machine part is made of Ti-6A1-4V titanium and a critical point in the material is subjected to plane stress,
such that the principal stresses are σ1 and σ2 = 0.501, 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.
Hint: Refer to the inside cover the textbook for material section properties.
123.41 MPa 173.41 MPa 156.16 MPa
173.41 MPa -123.41 MPa -256.16 MPa
2.22 1.68 1.94
1.94 1.68 2.22
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
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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
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- 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) Txyarrow_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_forwardDetermine the factor of safety as per tresca's max shear stress theoryarrow_forward
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