2.27. The stress components at a given point in an engineering component are es-timated to be oxy=4.1 ksi, ơyy=0 ksi, ơz =0.9 ksi, ory =-3.1ksi, ơyz = 1.2 ksi,Ozx =0 ksi. Estimate the factor of safety against yielding using von Mises' theory ifthe uniaxial yield stress of the material is Sy =17.2 ksi.

Answered: 2.27. The stress components at a given…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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2.27. The stress components at a given point in an engineering component are es-
timated to be oxy=4.1 ksi, ơyy=0 ksi, ơz =0.9 ksi, ory =-3.1ksi, ơyz = 1.2 ksi,
Ozx =0 ksi. Estimate the factor of safety against yielding using von Mises' theory if
the uniaxial yield stress of the material is Sy =17.2 ksi.

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Von Mises theory OR Maximum shear strain energy theory: It states that inelastic action at any point in a body,under any combination of stress begins, when the strain energy of distortion per unit volume absorbed at the point is equal to the strain energy of distortion absorbed per unit volume at any point in a bar stressed to the elastic limit under the state of uniaxial stress as occurs in a simple tension/compression test.

$\frac{1}{2} [{(σ_{1} - σ_{2})}^{2} + {(σ_{2} - σ_{3})}^{2} + {(σ_{3} - σ_{1})}^{2}] \leq {(\frac{σ_{y}}{F O S})}^{2} G i v e n σ_{1} = σ_{x x} = 4.1 k s i, σ_{2} = σ_{y y} = 0 k s i, σ_{3} = σ_{z z} = 0.9 k s i a n d y i e l d s t r e s s S_{y} = σ_{y} = 17.2 k s i$

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