Answer:
The principal stresses are σp1 = 27 ksi, σp2 = -37 ksi and the shear stress is zero
Explanation:
The expression for the maximum shear stress is given:
![\tau _{M} =\sqrt{(\frac{\sigma _{x}^{2}-\sigma _{y}^{2} }{2})^{2}+\tau _{xy}^{2} }](https://tex.z-dn.net/?f=%5Ctau%20_%7BM%7D%20%3D%5Csqrt%7B%28%5Cfrac%7B%5Csigma%20_%7Bx%7D%5E%7B2%7D-%5Csigma%20_%7By%7D%5E%7B2%7D%20%20%7D%7B2%7D%29%5E%7B2%7D%2B%5Ctau%20_%7Bxy%7D%5E%7B2%7D%20%20%20%20%7D)
Where
σx = stress in vertical plane = 20 ksi
σy = stress in horizontal plane = -30 ksi
τM = 32 ksi
Replacing:
![32=\sqrt{(\frac{20-(-30)}{2} )^{2} +\tau _{xy}^{2} }](https://tex.z-dn.net/?f=32%3D%5Csqrt%7B%28%5Cfrac%7B20-%28-30%29%7D%7B2%7D%20%29%5E%7B2%7D%20%2B%5Ctau%20_%7Bxy%7D%5E%7B2%7D%20%20%7D)
Solving for τxy:
τxy = ±19.98 ksi
The principal stress is:
![\sigma _{x}+\sigma _{y} =\sigma _{p1}+\sigma _{p2}](https://tex.z-dn.net/?f=%5Csigma%20_%7Bx%7D%2B%5Csigma%20_%7By%7D%20%3D%5Csigma%20_%7Bp1%7D%2B%5Csigma%20_%7Bp2%7D)
Where
σp1 = 20 ksi
σp2 = -30 ksi
(equation 1)
equation 2
Solving both equations:
σp1 = 27 ksi
σp2 = -37 ksi
The shear stress on the vertical plane is zero
Answer and Explanation:
The answer is attached below
Boats float because the gravity is acting down on it and the buoyant force is acting up on the ship.
Answer:
This doesn't represent an equilibrium state of stress
Explanation:
∝ = 1 , β = 1 , y = 1
x = 0 , y = 0 , z = 0 ( body forces given as 0 )
Attached is the detailed solution is and also the conditions for equilibrium
for a stress state to be equilibrium all three conditions has to meet the equilibrum condition as explained in the attached solution
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