At a point in a body subjected to plane strain, the strains are εx = 300 με, εy = 70 με, and γxy = –500 μrad. Determine the angle θp corresponding to the orientation of the principal planes at the point.

At a point subjected to plane stress on the surface of a structural-steel member, the stresses are σx = 90 MPa, σy = –60 MPa, and τxy = 90 MPa. Determine the diameter D of the corresponding in-plane Mohr’s circle.

At a point on the free surface of a steel automotive component [E = 28,100 ksi,ν = 0.15], a strain rosette was used to obtain normal strains of εa = 340 με, εb = –290 με, and εc = 10 με. Determine normal strain εx at the point.

At a point in a body subjected to plane strain, the strains are εx = –500 με, εy = –520 με, and γxy = –130 μrad. Determine principal strain εp2 at the point.

At a point subjected to plane stress on the surface of a screwdriver, the stresses are σx = 19 ksi, σy = 0 ksi, and τxy = –16 ksi. Determine the magnitude of the maximum in-plane shear stress at the point.

At a point subjected to plane stress on the surface of a compressed air cylinder, the stresses are σx = –27 ksi, σy = –19 ksi, and τxy = –26 ksi. Determine shear stress τnt at the point for a clockwise coordinate rotation of 84°.

At a point on the free surface of a steel automotive component [E = 28,600 ksi,ν = 0.22], a strain rosette was used to obtain normal strains of εa = 241 με, εb = –125 με, and εc = 197 με. Determine normal strain εx at the point.

At a point in a body subjected to plane strain, the strains are εx = –670 με, εy = –40 με, and γxy = –850 μrad. Determine normal strain εt at the point for a counterclockwise coordinate rotation of 55°.

At a point in a body subjected to plane strain, the strains are εx = 140 με, εy = –760 με, and γxy = 460 μrad. Determine normal strain εt at the point for a clockwise coordinate rotation of 66°.

At a point subjected to plane stress on the surface of a gusset plate, the stresses are σx = 20 MPa, σy = –20 MPa, and τxy = –100 MPa. Determine principal stress σp1 at the point.