full steps answer please. The state of plane stress at a point in a member is sh
ID: 1862476 • Letter: F
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full steps answer please.
The state of plane stress at a point in a member is shown on the element. By representing the state of stress on the Mohr's circle, determine: [15 Marks] the principal stresses. the maximum in plane shear stress and the associated normal stress. the corresponding orientation of the element for each case (a) and (b). with respect to the element shown. Plot the maximum in plane shear stress, the associated normal stress, and the principal stress on the same element including their orientation. [5 Marks]Explanation / Answer
P be normal stresses
T be shear stresses.
Px = 90 MPa
Py = 20 MPa
Txy = 60 MPa
The equation of Mohr's Circle is:
(P - (1/2)(Px + Py))^2 + T^2 = (1/4)(Px - Py)^2 + Txy^2
(P - 55)^2 + T^2 = 4825
a)Principle stresses are: P1 = 55 -sqrt(4825) = -14.46 MPa
P2 = 55 +sqrt(4825)= 124.46 MPa
b) Maximum Shear Stress = sqrt(4825) = 69.46 MPa
P1 = P2 = 55 MPa
c)Tan 2x = 2T/(Px - Py) => 2x = 59.74 deg.
x = orientation = 29.87 deg.
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