Question

2) [10] Draw a Mohr's circle diagram and the principal and shear stress elements, all properly labeled, for the following plane stress. 0x = 20 MPa, ay = -80 MPa, Txy = -60 MPa

Answer 1

9+2 solution ; giver 6x= 20 mpa, by = -80 mpa, Exy = - Gompa. construction of mohry circle → Normal stress on x-asis and shear stress (T) on (6) Y-aris → Each radial line in the moures circle represent corresponding plane in actual structure and the halue of normal stress and shear stress in that particular plane is co-ordinate of point of intersection of radial dine (corresponding with the circumfence angle between two radial lines are two times the angle between corrosponding planes. E Conax B(-80,60) q ry o' (62,0) 116,0) Al 6 → ba BY (2,0)) (64,02 С 9 0 by -exy (207-7074 A -tman F

calculation of centre (o) and Radius (R) of the hadhr's Circle o is mid point of A'B' (Southam, o) - (20780,0) =(-30, 0) en OBB' VOB'){+(BB'j? ( COB' = 6y-Content R = OB= Gyorge 2 2 ſ y se t try (80=2014 (60)2 = 78.10 mpa calculation of Principal stresses '6, and a principal plane is the plane of zero shear so oD and oc will be principal plane 16,= .R-00 - R-Oo78.10 - 30 = 48.10m pa 025-(R +00')=-678.10 +30) - - 108.1 mpa: calculation of maximum shear stress (Emased of and of is the maximum shear stress plane and Tmane = IR 178.10 mpa