91Ó°ÊÓ

A single strain gage is cemented to a solid 4 -in.- diameter steel shaft at an angle \(\beta=25^{\circ}\) with a line parallel to the axis of the shaft. Knowing that \(G=11.5 \times 10^{6}\) psi, determine the torque \(\mathbf{T}\) indicated by a gage reading of \(300 \times 10^{-6}\) in./in.

A single strain gage forming an angle \(\beta=18^{\circ}\) with a horizontal plane is used to determine the gage pressure in the cylindrical steel tank shown. The cylindrical wall of the tank is \(6 \mathrm{mm}\) thick, has a \(600-\mathrm{mm}\) inside diameter, and is made of a steel with \(E=200 \mathrm{GPa}\) and \(\nu=0.30 .\) Determine the pressure in the tank indicated by a strain gage reading of \(280 \mu\).

A steel pipe of 12 -in. outer diameter is fabricated from \(\frac{1}{4}\) -in.-thick plate by welding along a helix that forms an angle of \(22.5^{\circ}\) with a plane perpendicular to the axis of the pipe. Knowing that a 40 -kip axial force \(\mathbf{P}\) and an 80 -kip \(\cdot\) in. torque T, each directed as shown, are applied to the pipe, determine the normal and in- plane shearing stresses in directions, respectively, normal and tangential to the weld.

The compressed-air tank \(A B\) has an inner diameter of \(450 \mathrm{mm}\) and a uniform wall thickness of \(6 \mathrm{mm}\). Knowing that the gage pressure inside the tank is \(1.2 \mathrm{MPa}\), determine the maximum normal stress and the maximum in-plane shearing stress at point \(a\) on the top of the tank.

Determine the largest in-plane normal strain, knowing that the following strains have been obtained by the use of the rosette shown: \\[ \begin{array}{c} \epsilon_{1}=-50 \times 10^{-6} \text {in./in. } \quad \epsilon_{2}=+360 \times 10^{-6} \text {in./in. } \\ \epsilon_{3}=+315 \times 10^{-6} \text {in./in. } \end{array} \\]