came1pt8 - \ Fx = 0 And, ∂σ y + ∂τ xy + ∂τ yz + Fy...

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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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Unformatted text preview: \ Fx = 0 And, ∂σ y + ∂τ xy + ∂τ yz + Fy = 0 ∂ y ∂ x ∂ z ∂ (-2.y 2 ) + ∂ (z +4.x.y -7 )+ ∂ ( 0 )+ Fy = 0 ∂ y ∂ x ∂ z -4.y + 4.y +0 +Fy = 0 \ Fy = 0 ∂σ z + ∂τ zx + ∂τ zy + Fz = 0 ∂ z ∂ x ∂ y ∂ ( 3.x +y+ 3.z-5 ) + ∂ ( -3.x +y+1 ) + ∂ ( 0) + Fz = 0 ∂ z ∂ x ∂ y 3-3+0+Fz = 0 \ Fz = 0 Final Answer: = = = F F F Z Y X...
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This note was uploaded on 11/22/2011 for the course EML 6653 taught by Professor Law during the Fall '09 term at University of South Florida - Tampa.

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came1pt8 - \ Fx = 0 And, ∂σ y + ∂τ xy + ∂τ yz + Fy...

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