MECHANICS OF MATERIALS
11th Edition
ISBN: 9780137605521
Author: HIBBELER
Publisher: RENT PEARS
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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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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.
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.
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:
(α) σχ
= 180 MPa, σy = 100 MPa
(b) σx = 180 MPa, Txy =
(c) σx = -160 MPa, Txy
= 150 MPa
(d) Txy
100 MPa
= 100 MPa
Chapter 10 Solutions
MECHANICS OF MATERIALS
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