Recent questions in Mechanics of deformable bodies

At the peak (also denoted as UTS) of an engineering stress vs. engineering strain curve for ductile metal, the engineering strain is $0.2$. The corresponding true stress ...

Which among the following options is/are CORRECT unit(s) of stress?$\mathrm{Nm}^{2}$$\text{Pa}$$\text{Nm}$$\mathrm{N} / \mathrm{m}^{2}$

A $\text{2D}$ state of stress at a point in a body is given by $\sigma_{x x}=-40 \mathrm{~MPa}$, $\sigma_{y y}=100 \mathrm{~MPa}$ and $\tau_{x y}=50 \mathrm{~MPa}$.The ra...

Sum of the principal stresses of a $\text{2D}$ stress state $\left[\begin{array}{cc}11 & 4 \\ 4 & 5\end{array}\right]$ is $\_\_\_\_$ (in integer).

One column with square cross section of side $r$ and another column with rectangular cross section of breadth $p$ and width $q(<p)$ are made from the same material. Both ...

Two prismatic rods of identical lengths are designed for the same strain energy density when subjected to the same axial load. One of the rods is made of steel (Young's m...

A $\text{2D}$ stress state of pure shear is shown in the figure.Which one of the following options is equivalent to the given stress state?Figures are not to scale.

The bending moment diagram for a simply supported beam is piecewise linear as shown in the figure. The bending moment $M(\mathrm{x})$ at $\mathrm{x}=0.5 \mathrm{~m}$ is $...

A thin walled cylindrical container of diameter $2$ $\mathrm{m}$ and wall thickness of $2.5$ $\mathrm{cm}$ is made of steel whose Young's modulus is $200$ $\mathrm{GPa}$ ...

A solid axial bar made of steel with Young's modulus, $200$ $\mathrm{GPa}$ and Poisson's ratio, $0.3$, is subjected to uniaxial stress of $50$ $\mathrm{MPa}$.The absolute...

$\text{EFGH}$ (solid lines) is the initial configuration and $\mathrm{E}^{\prime} \mathrm{F}^{\prime} \mathrm{G}^{\prime} \mathrm{H}^{\prime}$ (dashed lines) is the defor...

A simply supported beam of length $l=2 \mathrm{~m}$ is subjected to a concentrated moment $M=150 \mathrm{~kNm}$ at a distance $l / 2$ from the left end as shown in the fi...

A rectangular plastic specimen with a cross-sectional area of $240 \mathrm{~mm}^{2}$ is subjected to tension with a force of $15000$ $\mathrm{N}$ resulting in elastic def...

Consider a spring-mass system with mass $m$ and spring stiffness $k$ as shown in the illustration. At time $t=0$, the mass is displaced by $P$ units and the velocity of t...

​​​​The Mohr's circle corresponding to an infinitesimal element is shown in the figure. The plane $\text{PQ}$ in the infinitesimal element, at an angle of $\theta$ from t...

The two-dimensional state of stress, in an infinitesimal element, is given by$\sigma_{x x}=800 \mathrm{MPa}, \sigma_{x y}=300 \mathrm{MPa}$ and $\sigma_{y y}=0 \mathrm{MP...

Consider a beam with a square box cross-section as shown in the figure. The outer square has a length of $10 \: \mathrm{mm}$. The thickness of the section is $1 \: \mathr...

For a certain linear elastic isotropic material, the Young's modulus is $140 \: \mathrm{GPa}$ and the shear modulus is $50 \: \mathrm{GPa}$.The Poisson's ratio for the ma...

​​​​Which one of the following vertical columns, of circular cross-section, sustains the highest load without buckling?Cantilever column with a length $\text{L}$ and cros...

A closed thin cylindrical tank with a mean diameter $\mathrm{d}=300 \mathrm{~mm}$ and thickness $\mathrm{t}=2 \mathrm{~mm}$, is subjected to a uniform internal gas pressu...

​​​An infinitesimal square element $\text{PQRS}$ is shown in the figure. The $x$ and $y$ axes are also marked in the figure. The strains on the element are given by$\vare...

The figure shows the stress distribution across an internal surface of a rectangular beam of height $30 \: \mathrm{mm}$ and depth $10 \: \mathrm{mm}$. The normal stress d...

A vertical column fixed at one end is subjected to a compressive axial load at the free end. The column's section modulus, $\text{EI}$, is $9.82 \times 10^{5} \: \mathrm{...

A simply-supported beam, with a point load $\text{P}=150 \: \mathrm{kN}$ at a distance of $\text{L} / 3$ from the left end, is shown in the figure. The elastic-strain ene...

A simply-supported beam has a circular cross-section with a diameter of $20 \: \mathrm{mm}$ , area of $314.2 \mathrm{~mm}^{2}$, area moment of inertia of $7854 \mathrm{~m...

A bar of length $\text{L}=1 \mathrm{~m}$ is fixed at one end. Before heating its free end has a gap of $\delta=0.1 \mathrm{~mm}$ from a rigid wall as shown in the figure....

​​​During material testing, stress is applied from time $t_{i}$ to $t_{f}$ as shown below:The corresponding strain responses for three different materials are shown in pl...

Mechanical behaviour of a crystalline ceramic material is best described asductilebrittleviscoelasticViscoplastic

The engineering stress $(\sigma)$ vs. engineering strain $(\varepsilon)$ curve obtained by conducting uniaxial tension test on a steel specimen is shown in the figure $\t...

A mass $M$ is hung from a frictionless, massless pulley. The pulley is suspended by using an inextensible, massless rope of which one end is directly fixed to a support, ...

A simply-supported beam of rectangular cross-section $\text{(width $w$ and height $h$)}$ is subjected to the loads as shown in the figure $\text{(i)}$. The enlarged view ...

A solid circular shaft of diameter $100$ mm is subjected to a torque $3 \pi \mathrm{kNm}$. Which of the following statements about the state of stress in the shaft is/are...

A spring is connected to an elastic bar as shown in the figure. The spring has a stiffness constant of $10^{7} \mathrm{~N} / \mathrm{m}$. The bar is 70 mm long, and has a...

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 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 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 cylindrical pressure vessel is constructed by bolting two symmetric halves of flanged semi-cylindrical shells. A cross-sectional view of the vessel is shown in the figu...

\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}{|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...