List of top Solid Mechanics Questions on Combined stresses asked in GATE XE

A simply-supported beam has a circular cross-section with diameter \(20 \, mm\), area \(A = 314.2 \, mm^2\), area moment of inertia \(I = 7854 \, mm^4\), and length \(L = 4 \, m\). A point load \(P = 100 \, N\) acts at the center and an axial load \(Q = 20 \, kN\) acts through the centroidal axis.

The magnitude of the offset between the neutral axis and the centroidal axis, at \(L/2\) from the left, is ............ mm (rounded off to one decimal place).

A thin steel plate is loaded in the $x$-$y$ plane as shown in the figure. Take Poisson’s ratio $\nu = 0.3$ and modulus of elasticity $E = 200 \, GPa$. The strain along $z$-direction is $\varepsilon_{zz} = -3 \times 10^{-4}$. The value of $\sigma_{yy}$ (in MPa) is .......... (rounded off to one decimal place).

A prismatic solid circular rod of diameter \( d \) is bent to introduce an offset \( s = d \) as shown. The rod is further subjected to an axial load \( P \). If the maximum longitudinal stress at a section A-B in the rod (with offset) is \( n \) times the longitudinal stress in the straight rod, the value of \( n \) (in integer) would be \(\underline{\hspace{2cm}}\). \includegraphics[width=0.5\linewidth]{image17.png}