Recent questions tagged mechanics-of-deformable-bodies

A plane passing through a point $\text{Q}$ inside a body is shown. The unit normal of the plane is $\hat{n}=0.6 \hat{\imath}+0.8 \hat{\jmath}$, as shown in the figure. Th...

A critical point on a component is subjected to the state of stress $[\sigma]$ as given in the following. The yield strength of the material is $400$ MPa . By considering...

A beam of rectangular cross-section, as shown in the figure, is made of two perfectly bonded layers of different materials and equal thickness. The Young's moduli of the ...

A stepped beam is made of a material whose Young's modulus is $E$. The dimensions of the two stepped sections are such that the sectional moments of inertia, $I_{1}$ and ...

A unidirectional composite is prepared using $70 \%$ by volume of epoxy matrix and $30 \%$ by volume of carbon fibre. The elastic modulus of the epoxy matrix is $3.5$ GPa...

\begin{tabular}{l|l}Q. 49 & \begin{tabular}{l}A screw dislocation in a FCC crystal has Burgers vector of $\frac{a}{2}[110]$, where $a$ is the \\lattice constant. The poss...

\begin{tabular}{c|c}Q. 50 & The tensile true stress $(\sigma)-$ true strain $(\epsilon)$ curve follows the Hollomon equation: \\$\qquad \sigma=500 \epsilon^{0.15} \mathrm...

\begin{tabular}{l|l}Q. 61 & \begin{tabular}{l}The Young's modulus of a quartz piezoelectric crystal is $100 \mathrm{GPa}$. The uniaxial \\stress required to change its po...

\begin{tabular}{|c|c|}\hline Q. 68 & \begin{tabular}{l}Two equivalent descriptions of the state of stress at a point are shown in the \\figure. The normal stresses $\sigm...

\begin{tabular}{l|l}Q.69 & The state of strain at a point in a machine component is given as \\$\varepsilon_{x x}=2.5 \times 10^{-4}, \varepsilon_{y y}=2.0 \times 10^{-4}...

\begin{tabular}{|l|l|}\hline Q.70 & A thin walled, closed cylindrical vessel of inside diameter $d$ and wall thickness $t$ \\contains a fluid under pressure $p$. The figu...

\[\text { Q. } 74\]For a plane stress problem, the principal stresses are $100 \mathrm{MPa}$ and $50 \mathrm{MPa}$. The magnitude of maximum shear stress (in $\mathrm{MPa...

\begin{tabular}{|l|l|}\hline Q.76 & A cylinder made of rubber (length $=L$ and diameter $=d)$ is inserted in a rigid \\container as shown in the figure. The rubber cylind...

\begin{tabular}{|c|}\hline \begin{tabular}{l}The state of stress at the critical location in a structure is $\sigma_{x x}=420 \mathrm{MPa}$, \\$\sigma_{y y}=100 \mathrm{M...

Q. 78The figure shows a column of rectangular cross section $100 \mathrm{~mm} \times 80 \mathrm{~mm}$. Itcarries a load of $60 \mathrm{kN}$ at a point $30 \mathrm{~mm}$ f...

\begin{tabular}{|l|l}Q.79 & Consider an electric pole with dimensions as shown in the figure. Let the end $R$ be \\subjected to a vertical force $F$. The flexural rigidit...

Q.80 A uniform cantilever beam has flexural rigidity $E I$ and length $L$. It is subjected toa concentrated force $F$ and moment $M=2 F L$ at the free end as shown. Thede...

Q. 84A thin steel plate is loaded in the $x$-y plane as shown in the figure. Take thePoisson's ratio of steel to be 0.3 and the modulus of elasticity of steel to be 200$\...

Q. 86 A slender uniform elastic rod of length $1 \mathrm{~m}$ and of solid circular cross-section of diameter $50 \mathrm{~mm}$ is originally straight. It is then loaded ...

Q. 87 Consider a solid cylindrical shaft and a hollow cylindrical shaft. Both shafts are axisymmetric and elastic, and have the same cross-sectional area. The hollow shaf...