Question 1.8:
For what body forces will the following stress field describe a state of
equilibrium?
σ
x
=
-2.x
2
+3.y
2
-5.z
σ
y
= -2.y
2
σ
z
= 3.x + y + 3.z-5
τ
xy
= z + 4.x.y -7
τ
yz
= 0
τ
zx
= -3.x + y +1
Solution.
We apply differential equations of equilbrium,
∂σ
x
+
∂τ
xy
+
∂τ
xz
+ Fx = 0
∂
x
∂
y
∂
z
∂
(-2.x
2
+3.y
2
-5.z ) +
∂
(z +4.x.y -7 ) +
∂
( -3.x +y+1 ) + Fx = 0
∂
x
∂
y
∂
z
-4.x + 0 + 4.x +Fx = 0

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