At a point on the free surface of a steel automotive component , a strain rosette was used to obtain normal strains of εa = 439 με, εb = –200 με, and εc = 418 με. Determine normal strain εx at the point.

At a point subjected to plane stress on the surface of a socket extension, the stresses are σx = –80 MPa, σy = 0 MPa, and τxy = 45 MPa. Determine the magnitude of the maximum in-plane shear stress at the point.

At a point in a body subjected to plane strain, the strains are εx = –430 με, εy = 130 με, and γxy = –680 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 backhoe, the stresses are σx = –80 MPa, σy = 10 MPa, and τxy = 40 MPa. Determine the angle θp corresponding to the orientation of the principal planes at the point.

At a point in a body subjected to plane strain, the strains are εx = 100 με, εy = 390 με, and γxy = –220 μrad. Determine normal strain εt at the point for a counterclockwise coordinate rotation of 59°.

At a point subjected to plane stress on the surface of a gusset plate, the stresses are σx = –8 ksi, σy = 9 ksi, and τxy = 9 ksi. Determine principal stress σp1 at the point.

At a point subjected to plane stress on the surface of a compressed air cylinder, the stresses are σx = 30 MPa, σy = 90 MPa, and τxy = 10 MPa. Determine normal stress σt at the point for a counterclockwise coordinate rotation of 74°.

At a point subjected to plane stress on the surface of a compressed air cylinder, the stresses are σx = 90 MPa, σy = –90 MPa, and τxy = –30 MPa. Determine normal stress σt at the point for a clockwise coordinate rotation of 85°.

At a point subjected to plane stress on the surface of a structural-steel member, the stresses are σx = 9 ksi, σy = 19 ksi, and τxy = –4 ksi. Determine the center σcenter of the corresponding in-plane Mohr’s circle.

A silicone rubber wristband has an initial length of 105 mm and a width of 12 mm. If the wearer imparts a normal stress of 470 kPa in the length direction while putting it on, what is the corresponding change in width?