Civil Engineering MCQAE Level Civil Engineering
At a point in a structural member, normal stresses are sigma_x = 80 MPa, sigma_y = -40 MPa, and shear stress tau_xy = 60 MPa. The maximum principal stress is:
Engineering MechanicsMohr Circle Principal StressMEDIUM
Choose the correct answer
A
80 MPa
B
100 MPa
C
120 MPa
D
60 MPa
Correct Answer
B. 100 MPa
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Mohr circle: centre C = (sigma_x + sigma_y)/2 = (80-40)/2 = 20 MPa; radius R = sqrt(((sigma_x-sigma_y)/2)^2 + tau_xy^2) = sqrt(60^2 + 60^2) = sqrt(7200) = 84.85 MPa. Wait: (80-(-40))/2 = 60, not 60+60. R = sqrt(60^2 + 60^2) = 84.85 MPa. sigma_1 = 20 + 84.85 = 104.85 approximately 100 MPa.
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