Question

The stress state of a point is defined by σxx =−30MPa, σyy =60MPa, and σxy =−40MPa(a) Draw the corresponding Mohr’s circle. (b) Find the maximum in-plane shear stress and the corresponding normal stresses using the Mohr’s circle. (c) Illustrate your answer with a stress element showing the orientations of all stress vectors w.r.t the given state.

Answer 1

τmax = R = 60.208 MPa

σmax = 75.208 MPa

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.