Recent questions tagged solid-mechanics

A plane strain problem (in $\text{X - Y}$ plane) must satisfy the condition:$\sigma_{z z}=0$$\epsilon_{z z}=\epsilon_{x z}=\epsilon_{y z}=0$$\sigma_{x x} \neq \sigma_{x y...

Which one of the following stress conditions represents the state of pure shear stress?

Linearly elastic, homogeneous, uniform bars $\text{BCD}$ and $\text{FG}$ shown in the figure have fixed supports at $\text{B}$ and $\text{G}$, respectively. For both the ...

A thin-walled spherical gas balloon of radius $R$ and wall thickness $t(t \ll R)$ is subjected to an internal (gauge) pressure $p$. The maximum tensile and shear stresses...

Black dot shown in the figure qualitatively represents the shear centre of the angle section. The option which represents the position of the shear centre is:

A plane truss consists of two linearly elastic, homogeneous, identical members, namely PQ and QR. Both members have length ( $L$ ), cross-sectional area ( $A$ ), and modu...

The plane frame has a hinge and a roller support, and is loaded as shown in the figure. Both the columns have same height.What is the absolute value of the maximum bendin...

Two identical blocks $\text{A}$ and $\text{B}$ are connected by a rigid rod. The blocks rest against vertical and horizontal planes, as shown in the figure. The coefficie...

A homogenous, linearly elastic rod $\text{AB}$ is connected to a linearly elastic spring $\text{BC}$ in between the fixed supports at $\text{A}$ and $\text{C}$, as shown ...

Let the state of stress at a point in a body be the difference of two plane states of stress shown in the figure. Consider all the possible planes perpendicular to the $x...

A steel beam supported by three parallel pin-jointed steel rods is shown in the figure. The moment of inertia of the beam is $8 \times 10^{7} \mathrm{~mm}^{4}$. Take modu...

​​​​​Consider the frame shown in the figure under the loading of $100 \mathrm{kN} . \mathrm{m}$ couples at the joints $B$ and $G$. Considering only the effects of flexura...

​​​​​Consider the beam $\text{ACDEB}$ given in the figure. Which of the following statements is/are correct:Bending moment is zero between the points $A$ and $C$There is ...

For the beam and loading shown in the figure, the second derivative of the deflection curve of the beam at the mid-point of AC is given by $\alpha M_{0} / 8 E I$. The val...

Consider the rigid bar $ABC$ supported by the pin-jointed links $BD$ and $CE$ and subjected to a load $P$ at the end $A$, as shown in the figure. The axial rigidities of ...

Consider a reinforced concrete beam section of $300 \: \mathrm{mm}$ width and $700 \: \mathrm{mm}$ depth. The beam is reinforced with the tension steel of $2000 \: \mathr...

Consider the beam section shown in the figure, with $\bar{y}$ indicating the depth of neutral axis $(NA)$. The section is only subjected to an increasing bending moment. ...

A $3 \mathrm{~m}$ long, horizontal, rigid, uniform beam $\mathrm{PQ}$ has negligible mass. The beam is subjected to a $3 \mathrm{kN}$ concentrated vertically downward for...

​​​​​For a thin-walled section shown in the figure, points $\text{P, Q}$, and $\text{R}$ are located on the major bending axis $\mathrm{X}-\mathrm{X}$ of the section. Poi...

​​​​​A linearly elastic beam of length $2 l$ with flexural rigidity $E I$ has negligible mass. A massless spring with a spring constant $k$ and a rigid block of mass $m$ ...

A homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio $(l / r)$ of $105$, where $l$ is the bar length and $r$ is the radius ...

For the $6 \mathrm{~m}$ long horizontal cantilever beam $\mathrm{PQR}$ shown in the figure, $\mathrm{Q}$ is the midpoint. Segment $\mathrm{PQ}$ of the beam has flexural r...

The horizontal beam $\mathrm{PQRS}$ shown in the figure has a fixed support at point $\mathrm{P}$, an internal hinge at point $Q$, and a pin support at point $R$. A conce...

​​​​​The beam shown in the figure is subjected to a uniformly distributed downward load of intensity $q$ between supports $\text{A}$ and $\text{B}$.Considering the upward...

​​​​​A homogeneous shaft $\text{PQR}$ with fixed supports at both ends is subjected to a torsional moment $\mathrm{T}$ at point $\mathrm{Q}$, as shown in the figure. The ...

A circular solid shaft of span $L=5 \mathrm{~m}$ is fixed at one end and free at the other end. A torque $T=100 \mathrm{~kN}$.m is applied at the free end. The shear modu...

When a simply-supported elastic beam of span $L$ and flexural rigidity $E I$ ( $E$ is the modulus of elasticity and $I$ is the moment of inertia of the section) is loaded...

In a two-dimensional stress analysis, the state of stress at a point is shown in the figure. The values of length of $\text{PQ, QR,}$ and $\text{RP}$ are $4, 3,$ and $5$ ...

A beam is subjected to a system of coplanar forces as shown in the figure. The magnitude of vertical reaction at Support $\text{P}$ is ______________________ $\text{N}$ (...

A $2\text{D}$ thin plate with modulus of elasticity, $E=1.0 \mathrm{~N} / \mathrm{m}^{2}$, and Poisson's ratio, $\mu=0.5$, is in plane stress condition. The displacement ...

A hanger is made of two bars of different sizes. Each bar has a square cross-section. The hanger is loaded by three-point loads in the mid vertical plane as shown in the ...

Consider a doubly reinforced RCC beam with the option of using either $\text{Fe250}$ plain bars or $\text{Fe500}$ deformed bars in the compression zone. The modulus of el...

Consider the beam shown in the figure (not to scale), on a hinge support at end $\mathrm{A}$ and a roller support at end $\mathrm{B}$. The beam has a constant flexural ri...

The infinitesimal element shown in the figure (not to scale) represents the state of stress at a point in a body. What is the magnitude of the maximum principal stress (i...

The cross-section of a girder is shown in the figure (not to scale). The section is symmetric about a vertical axis $(Y-Y).$ The moment of inertia of the section about th...

For a linear elastic and isotropic material, the correct relationship among Young’s modulus of elasticity $(E)$, Poisson’s ratio $(\nu),$ and shear modulus $(G)$ is$G= \f...

Which of the following statements(s) is/are correct?If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with...

Consider two linear elastic rods $HI$ and $IJ$, each of length $b$, as shown in the figure. The rods are co-linear, and confined between two fixed supports at $H$ and $J....

A uniform rod $KJ$ of weight $w$ shown in the figure rests against a frictionless vertical wall at the point $K$ and a rough horizontal surface at point $J.$ It is given ...