Question

A state of plane stress consists of a tensile stress of ox=3 MPa, 0,=5 MPa, and txy=-7 MPa a. Draw the original unrotated element and the corresponding 2-D Mohr's circle construction showing the x-face and y-face coordinates. b. Calculate the principal stresses, o, and O2 and their corresponding principal angles, 0p1,0p2 and show all of these on your Mohr's circle construction and a properly oriented stress element c. Calculate the maximum shear stresses, ITmax and their corresponding angles of maximum shear stress, 0,1,0, and show all of these on your Mohr's circle construction and a properly oriented stress element.

Answer 1

Aus Given that, u = 3 MPa vy: 5 MPa = -7MPa 2-D moho's circle eny. Anya) : Umrotuke element and the corresponding 775 5MPa Lxfox = 3MPa exy Impa of fixi) - Enrolate element 4 Ink (of ery Top Oy A Gmin pery T ko 2 Crede figli) - Mohor's Circle

Anx). Calculation of principal stressed and their comesponding principal angles o - on-of) + cry !! 3+5+ 3-5 2 2 N = 4 + /1+49 11.07 MPa outy a+ try Eng 2 3+5 2 13-5 2 2 = 4 - 1449 = -3.071 MPa Angle of Principal stresses: tan 20p, 2 Tuy 2x6-72 Le (ourg) (3-5) tan 2 Op = tan (32=40930 2 40.93+ go' = 130.930 our

Ans() : Maximum shear stress (Times) and their corresponding angle of maximum shear stress. :- Tmax = 07-03 11.07-(-3.071) 2 Tmax = 7.07 MPa Angle of Maximum shear_sbess :- tan 20s, = -(0x-og 2 cry = (3-5) - tan20s, = .1 287 205, = tan (4) = -8.33" = -4.06. 7 Os, Oss Os, + 90º = -4.06 +90° - 85.93° OSY