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A cantilever beam of length, L, and flexural rigidity, EI, is subjected to an end moment ,M, as shown in the figure. The deflection of the beam at $x=\frac{L}{2}$ is

The state of stress on an element is as shown in the figure. If $E=2\times {10}^{5}N/m{m}^2$ and Poisson's ratio $=0.3$, the magnitude of the stress $\sigma$ for no strain in $BC$ is

For the beam - system as shown, If the slope at M is zero, then the ratio $\frac{T}{S}$ is

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A thin cylindrical vessel of mean diameter D and of length 'L' closed at both ends is subjected to a water pressure 'p'. The value of hoop stress and longitudinal stress in the shell shall be respectively

Match List-I (Elastic constant) with List-II (Definition) and select the correct answer using the codes given below the lists:

A beam (El = constant) of span L is subjected to clockwise moments M at both the ends A and B. The rotation of end A works out to be

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For an elastic material, Poisson's ratio is $\mu$, Modulus of Elasticity is $E$, Modulus of Rigidity is $C$ and Bulk Modulus is $K$. $\mu$ is expressible in terms of $K$ and $C$ as

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In terms of bulk modulus (K) and modulus of rigidity (G), Poisson's ratio can be expressed as

In a cantilever of span L subjected to a concentrated load of W acting at a distance of $\frac{L}{3}$ from the free end, the deflection under load will be

Two shafts AB and BC, of equal length and diameters d and 2d, are made of the same material. They are joined at B through a shaft coupling, while the ends A and C are built-in(cantilevered). A twisting moment T is applied to the coupling. If $T_A$ and $T_C$ represent the twisting moments at the ends A and C, respectively, then

A thin cylinder of thickness ${}^{\prime }{t}^{\prime }$, width ${}^{\prime }{b}^{\prime }$ and internal radius ${}^{\prime }{r}^{\prime }$ is subjected to a pressure ${}^{\prime }{p}^{\prime }$ on the entire internal surface. What is the change in radius of the cylinder? ($\mu$ is the Poisson's ratio and $E$ is the modulus of elasticity) ?

A cantilever beam of length $L$ is subjected to a moment $M$ at the free end. The moment of inertia of the beam cross section about the neutral axis is $I$ and the young's modulus is $E$. The magnitude of the maximum deflection is

In the cantilever beam PQR shown in figure below, the segment PQ has flexural rigidity EI and the segment QR has infinite flexural rigidity.



The deflection of the beam at ${}^{\prime }{R}^{\prime }$ is

A cantilever carries a load P at C as shown in the given figure







The deflection at B is

Match List-I with List-II and select the correct answer using the codes given below the lists:

If the hinged end of a propped cantilever of span L settles by an amount $\delta ,$ then the rotation of the hinged end will be

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A steel bar 300 mm long and having 24 mm diameter, is turned down to 18 mm diameter for one third of its length. It is heated 30°C above room temperature, clamped at both ends and then allowed to cool to room temperature. If the distance between the clamps is unchanged, the maximum stress in the bar $(\alpha =12.5\times {10}^{-6}per°C$ and $E=200GN/m^2)$ is

The Mohr's circle give below corresponds to which one of the following stress conditions.

A simply supported beam AB of span 4m is subjected to terminal couples as shown in the figure below .







If EL is in $kN-m^2$, what is the magnitude of the central deflection iof the beam in metres ?

A simply supported beam is subjected to a uniformly distributed load of intensity w per unit length, on half of the span from one end. The length of the span and the flexural stiffness are denoted as l and EI respectively. The deflection at mid-span of the beam is

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If $E=2.06\times {10}^{5}N/m{m}^2$, an axial pull of $60kN$ suddenly applied to a steel rod $50mm$ in diameter and $4m$ long. It causes an instantaneous elongation of the order of

When a column is fixed at both ends corresponding Euler's criterion load is

A member having length L, cross-sectional area A and modulus of elasticity E is subjected to an axial load W. The strain energy stored in this member is

Given that $m=\frac{E_s}{E_t},I_t=$ Moment of inertia of timber portion and $I_s$ = Moment of inertial of a flitched beam made of steel and timber is given by

Two circular mild steel bars $A$ and $B$ of equal lengths $l$ have diameters $d_A=2cm$ and $d_B=3cm$. Each is subjected to a tensile load of magnitude $P$. The ratio of the elongations of the bars $l_A/l_B$ is

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