3. Given the following stress functions, = 3x² + 3y² − σ₁ = 3y² o₂ = 3x+y-z+ 6x = -Z Tay=z-6xy-² T₁₂ = x+y= ²/ Tyz=0 (a) show that the above stress state is in equilibrium (b) for the stress state at point x = 1/2, y = 1, and z = 3/4, determine the principal stresses.

3. Given the following stress functions, = 3x² + 3y² − σ₁ = 3y² o₂ = 3x+y-z+ 6x = -Z Tay=z-6xy-² T₁₂ = x+y= ²/ Tyz=0 (a) show that the above stress state is in equilibrium (b) for the stress state at point x = 1/2, y = 1, and z = 3/4, determine the principal stresses.

Materials Science And Engineering Properties

1st Edition

ISBN:9781111988609

Author:Charles Gilmore

Publisher:Charles Gilmore

Chapter9: Time, Temperature, And Mechanical Properties

Section: Chapter Questions

Problem 9.3P

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3. Given the following stress functions,
σ¸ = 3x² +3y² − z
σ₁ = 3y²
o₂ = 3x + y −z + ¾
Ty=z-6xy-³
Txz = x+y= ²³/
Tyz = 0
(a) show that the above stress state is in equilibrium
(b) for the stress state at point x = 1/2, y = 1, and z =
stresses.
3/4, determine the principal

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