Recent questions and answers in 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 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...

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 ...

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...

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 ...

​​​​​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...

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 $2\text{D}$ 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 ...

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...

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....

The hoop stress at a point on the surface of a thin cylindrical pressure vessel is computed to be $30.0\text{ MPa}$. The value of maximum shear stress at this point is$7...

A semi-circular bar of radius $\text{R m}$, in a vertical plane, is fixed at the end $G$, as shown in the figure. A horizontal load of magnitude $\text{P kN}$ is applied ...

Strain hardening of structural steel meansexperiencing higher stress than yield stress with increased deformationstrengthening steel member externally for reducing strain...

A solid circular torsional member $\text{OPQ}$ is subjected to torsional moments as shown in the figure (not to scale). The yield shear strength of the constituent materi...

A frame $\text{EFG}$ is shown in the figure. All members are prismatic and have equal flexural rigidity. The member $\text{FG}$ carries a uniformly distributed load $\tex...

An elevated cylindrical water storage tank is shown in the figure. The tank has inner diameter of $\text{1.5 m}$. It is supported on a solid steel circular column of diam...

A propped cantilever beam $\text{EF}$ is subjected to a unit moving load as shown in the figure (not to scale). The sign convention for positive shear force at the left a...

The state of stress in a deformable body is shown in the figure. Consider transformation of the stress from the $\text{x-y}$ coordinate system to the $\text{X-Y}$ coordin...

Refer the truss as shown in the figure (not to scale).If load, $F=10\sqrt{3}\text{ kN}$, moment of inertia, $I=8.33\times 10^{6}\text{ mm}^4$, area of cross-section, $A=1...

A planar elastic structure is subjected to uniformly distributed load, as shown in the figure (not drawn to the scale)Neglecting self-weight, the maximum bending moment g...

A cantilever beam $\textbf{PQ}$ of uniform flexural rigidity (EI) is subjected to a concentrated moment M at $\textbf{R}$ as shown in the figure The deflection at the fre...

The flange and web plates of the doubly symmetric built-up section are connected by continuous $10\:mm$ thick fillet welds as shown in figure (not drawn to the scale). Th...

A prismatic linearly elastic bar of length $L$, cross-sectional area $A$, and made up of a material with Young’s modulus $E$, is subjected to axial tensile force as shown...

The planar structure $RST$ shown in the figure is roller-supported at $S$ and pin-supported at $R.$ Members $RS$ and $ST$ have uniform flexural rigidity $(EI)$ and $S$ is...

In a material under a state of plane strain, a $10 \times 10$ mm square centered at a point gets deformed as shown in the figure.If the shear strain $\gamma_{xy}$ at this...

A hallow circular shaft has an outer diameter of $100 $ mm and inner diameter of $50 $ mm. If the allowable shear stress is $125$ MPa, the maximum torque (in kN-m) that t...

An element is subjected to biaxial normal tensile strains of $0.0030$ and $0.0020$. The normal strain in the plane of maximum shear strain isZero$0.0010$$0.0025$$0.0050$

Assuming that there is no possibility of shear buckling in the web, the maximum reduction permitted by $\text{IS 800-2007}$ in the (low-shear) design bending strength of ...

The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is subjected to a vertical shear force of $8 \: kN$. The beam is symmetrical about...

A closed thin-walled tube has thickness, $t$, mean enclosed area within the boundary of the centerline of tube’s thickness, $A_m$, and shear stress, $\tau$. Torsional mom...

For a channel section subjected to a downward vertical shear force at its centroid, which one of the following represents the correct distribution of shear stress in flan...