The state of stress at a point in a structural member may be represented by a two-dimensional stress system in which o, = 100 N/mm², 6, = -80 N/mm² and r,y = 45 N/mm?. Determine the direct stress on a plane inclined at 60° to the positive direction of a, and also the principal stresses. Calculate also the inclination of the principal planes to the plane on which o, acts. Verify your answers by a graphical method. Ans. 6, = 16 N/mm², o1 = 110.6 N/mm², on=-90.6 N/mm², 0 = – 13.3° and –103.3°.

Q.b.

1. The stress condition on a two-dimensional infinitesimal material element is shown in Fig. 1 Fig. 1 60 MPа A 50 MPа В 30 MPа A. Describe the state of stress on: (i) Face A (ii) Face B B. State the sign convention for stress components on faces A and B in the: (i) Physical-space (ii) Mohr-Circle-space C. Draw the Mohr circle for the stress element in Fig. 1

The given stresses are 0x = 48 MPa, 0x =- 32 MPa, and Txy = 20 MPa. The rotation angle 0 = 30°.Use the stress transformation equations to determine the stresses on an element that is rotated bythe given angle 0 and show the calculated stresses on the rotated element.