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On the element shown in the given figure, the stresses are:

${\sigma }_x=110MPa$

${\sigma }_y=30MPa$

${\tau }_{xy}={\tau }_{yx}=30MPa$

${\sigma }_1,{\sigma }_2$



The radius of Mohr's circle and the principal stresses ${\tau }_1,{\tau }_2$ are (in MPa)

Three wires of steel 1, 2 and 3, each having area A support a load W as shown in the figure below. What is the ratio between collapse load and the load corresponding to yielding of one of the wires?

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1. 8

The stress - strain curve for an ideally plastic material is

A thin-walled long cylindrical tank of inside radius r is subjected simultaneously to internal gas pressure p and axial compressive force F at its ends. In order to produce 'pure shear' state of stress in the wall of the cylinder, F should be equal to

A column of height H and area at top $A$ has the same strength throughout its length, under its own weight and applied stress $p_0$ at the top. Density of column material is $p$. To satisfy the above condition, the area of the column at the bottom should be

The ratio of the flexural strength of two beams of square cross-section, the first beam being placed with its top and bottom sides horizontally and the second beam being placed with one diagonal horizontally, is

For the case of a slender column of length $l$, and flexural rigidity $EI$ built in at its base and free at the top, the Euler's critical buckling load is

Which one of the following diagrams indicates the shear stress distribution for the beam as shown in the figure below?

A circular shaft shown in the figure is subjected to torsion T at two points A & B. The torsional rigidity of portions CA & BD is $G{J}_1$ and that of portion AB is $G{J}_2$. The rotations of shaft at points A and B are ${\theta }_1$&${\theta }_2$. The rotation ${\theta }_1$ is

The value of modulus of elasticity for a material is $200GN/m^2$ and Poisson's ratio is $0.25$. What is its modulus of rigidity?

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Two shafts A and B are made of the same material. The diameter of shaft B is twice that of shaft A. The ratio of power which can be transmitted by shaft A to that of shaft B is (If maximum shear stress remains the same)

What is the vertical displacement at the point C of the structure shown in the figure given below ?

In a system two weightless rigid bars AB and BC of length 'a' each having hinge supports at the' ends A and C, respectively, are connected to each other at B by a frictionless hinge (internal hinge). The rotation at the hinge is restrained by a rotational spring of stiffness k and system assumes a straight line configuration ABC. The rotation at the supports due to vertical load P acting at joint B is

For a block with Young's Modulus of its material being 210 GPa and its Poisson's Ratio being 0.25, when subjected to a stress system as shown in the figure, what is the magnitude of the stress $\sigma$ for no strain along AB?

A mild steel bar, $1.5m$ long, has a square section $40mm\times 40mm$. The bar is subjected to a two-dimensional stress, ${\sigma }_x=310N/mm\left(tensile\right)$ and ${\sigma }_y=300N/mm$ (compressive). $E=2\times {10}^{5}N/m{m}^2$, Poisson's ratio $\mu =0.3$. The elongation of the bar in the direction of ${\sigma }_x$ will be

1. 12.56

1. 15707.96

1. 0

A beam has triangular cross-section, having base 'b' and altitude 'h'.If a section of the beam is subjected to a shear force F, the shear stress at the level of neutral axis in the cross-section is given by

A square steel bar ol 50 mm side and 5 m long is subjected to a load where upon it absorbs a strain energy of 100 J. What is its modulus of resilience?

A mild steel bar is in two parts having equal lengths. The area of cross-section of Part-1 is double that of Part-2. If the bar carries an axial load P, then the ratio of elongation in Part-1 to that in Part-2 will be

A tie bar $(20mm\times 10mm)$ carries a tensile load of $1kN$ as shown in the figure below. Under this load, the maximum intensity of stress over the mean value will increase by

Three coplanar forces $P_1=P_2=P_3=2t$ act at a joint $O$, as shown in figure







From the force diagram, the force R to be applied at $O$ in the same plane to keep the joint $O$ in equilibrium is given by

A simply supported beam of span L carries a point load W at midspan. The breadth 'b' of the beam along the entire span is constant. Given, f = permissible stress is bending, for a beam of uniform strength, the depth of the beam at any cross-section at a distance 'x' from the support would be

For a solid circular section of diameter ${}^{\prime }{d}^{\prime }$ the stress in a column will be compressive only if the eccentricity of the line of action of the compressive force is within

A 20 cm long rod of uniform rectangular section, 8 mm wide $\times$ 1.2 mm thick is bent into the form of a circular arc resulting in a central displacement of 0.8 cm. Neglecting second-order quantities in computations, what is the longitudinal surface strain (approximate) in the rod ?

What is the ratio of the strain energy in bar X to that in bar Y when the material of the two bars is the same? The cross-sectional areas are as indicated over the indicated lengths.

Given that for a channel section, the width of flange = b, the depth of the web between centres of flanges = h, the thickness of flange = t, the moment of intertia of the channel about the axis of bending = I, the distance of the shear centre outside the channel section from the mid- thickness of the web is

1. 3

1. 0.1587

A thin cylinder of unit length, thickness ${}^{\prime }{t}^{\prime }$ and radius ${}^{\prime }{r}^{\prime }$ is subjected to internal pressure ${}^{\prime }{p}^{\prime }$. What is the circumferential stress?

A rectangular beam of dimensions b x d is to be cut from a circular log of wood of diameter D for the beam to be strongest in bending, the dimensions will be

A thick cylindrical pressure vessel of inner diameter $D_i$ and outer diameter $D_o$ is subjected to an internal fluid pressure of intensity ${}^{\prime }{p}^{\prime }$. The variation of the circumferential tensile stress '$p_y$' in the thickness of the shell will be

Two-dimensional stress system on a block made of a material with Poisson's ratio of 0.3 is shown in the figure





The limiting magnitude of the stress so as to result in no change in length AB of the block is

A metal bar of $10mm$ diameter when subjected to a pull of $23.5kN$ gave an elongation of $0.3mm$ on a gauge length of $200mm$. The Young's modulus of elasticity of the metal will nearly be

Which one of the following Mohr's Circles represents the state of pure shear?

Two prismatic beams having the same flexural rigidity of $1000kN-m^2$ are shown in the figures.



If the mid-span deflections of these beams are denoted by ${\delta }_1$and ${\delta }_2$(as indicated in the figures) the correct option is

A simply supported beam of span L shown in the below figure is subjected to a concentrated load W at its mid - span and also to a uniformly distributed load equilvalent to W. It has a flexural rigidity of EI. What is the total deflection at its mid -point ?

In a beam AB, support A is hinged and support B is on rollers as shown below. The directions of the reactions at A and B will be as in

1. 76.923

A circular column of external diameter $D$, and internal diameter d, carries an eccentric load such that tension is developed nowhere. What shall be the diameter of the core ?

For a linear, elastic, isotropic material, the number of independent elastic constants is

If a member is subjected to tensile stress of ${}^{\prime }{p}_x^{\prime }$, compressive stress of ${}^{\prime }{p}_y^{\prime }$ and tensile stress of ${}^{\prime }{p}_z^{\prime }$, along the $X,Y$ and $Z$ directions respectively, then the resultant strain ${\epsilon }_x^{\prime }$; along the $X$ direction would be (E is Young's modulus of elasticity and 'μ' is Poisson's ratio)

A thin hollow cylinder of diameter ${}^{\prime }{d}^{\prime }$, length $L$ and thickness ${}^{\prime }{t}^{\prime }$ is subjected to an internal pressure ${}^{\prime }{p}^{\prime }$. The hoop stress in the cylinder is

1. 44.5212

Consider a circular member of diameter $D$ subjected to a compressive load $P$. For a condition of no tensile stress in the cross-section the maximum radial distance of the load from the centre of the circle is