explain why shear stress max = 1/2 ( stress max - stress min ) comes from

5. For the state of stress shown, determine the maximum shearing stress when $70 MPA (a) 6= = 0 MPa, (b) 6= =+45 MPa, (c) 6: = - 45 MPa. DRAW the Mohr's circles for each case. 75 MPa 150 MPa SOLUTION Of = 150 MPa. O = 70 MPa. In = 75 MPa [) (MPG) Cave =(0, +0,)=110 MPa R = 2 + xy B 6 = V403 + 752 =85 MPa (MPa ) On = Gave + R =195 MPa b = Gave - R = 25 MPa (a) 0; =0, Ca = 195 MPa, 0% =25 MPa max = 195 MPa, min = 0. max =( max - 5 min) max = 97.5 MPa (b) 0, =+45 MPa. Ga = 195 MPa. Op = 25 MPa Omx = 195 MPa, min = 25 MPa, max = (max - min) max = 85 MPa (c) O. =-45 MPa, . =195 MPa, o, = 25 MPa max = 195 MPa. min = -45 MPa. max = = (max - min ) max = 120 MPa lt