Answer:
τmax = R = 60.208 MPa
σmax = 75.208 MPa
Step-by-step explanation:
Given
σx = −30MPa
σy = 60MPa
τxy = −40MPa
a) In order to draw the corresponding Mohr’s circle, we have to get the center (C) and the radius (R) as follows
C = (σx + σy)/2
⇒ C = (−30MPa + 60MPa)/2 = 15 MPa
R = √(((σx - σy)/2)² + τxy²)
⇒ R = √(((−30MPa - 60MPa)/2)² + (−40MPa)²) = 60.208 MPa
We can see the circle in the pic 1.
b) The maximum in-plane shear stress and the corresponding normal stresses are
τmax = R = 60.208 MPa
σmax = C + R = 15 MPa + 60.208 MPa = 75.208 MPa
c) We can see a stress element showing the orientations of all stress vectors w.r.t the given state in the pic 2.
