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**Q.1. A plate in equilibrium is subjected to uniform stresses along its edges with magnitude σ _{xx }= 30 MPa and σ_{yy} = 50 MPa as shown in the figure.**

The Young’s modulus of the material is 2 x 10^{11} N/m^{2} and the Poisson’s ratio is 0.3. If σ_{zz} is negligibly small and assumed to be zero, then the strain ε_{zz} is _________.

Solution:

So the answer is (d).

Assume the yield stress of steel as 250 MPa. The complementary strain energy (in N-mm) stored in the bar up to its linear elastic behaviour will be ________.

Note:For linear elastic material both complementary energy and strain energy is the same.

**OR**

__By considering the given graph in question, between Axial Load and Displacement, the solution will be as follows:__

It means there seems some error in the given data.

If the shear strain γ

(a) 0.50

Ans.

In question, since angle has been increased, therefore, shear strain should be negative.

Segments 1 and 2 have a cross-sectional area of 100 mm

Try yourself:An elastic bar of length L, uniform cross-sectional area A, coefficient of thermal expansion α, and Young’s modulus Eis fixed at the two ends. The temperature of the bar is increased by T, resulting in an axial stress σ. Keeping all other parameters unchanged, if the length of the bar is doubled, the axial stress would be _______. [2017 : 1 Mark, Set-I]

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Try yourself:An elastic isotropic body is in a hydrostatic state of stress as shown in the figure. For no change in the volume to occur, what should be its Poisson’s ratio?

[2016 : 2 Marks, Set-II]

[2016 : 2 Marks, Set-II]

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**Q.7. A tapered circular rod of diameter varying from 20 mm to 10 mm is connected to another uniform circular rod of diameter 10 mm as shown in the following figure. Both bars are made of the same material with the modulus of elasticity, E = 2 x 10 ^{5} MPa. When subjected to a load P = 30πkN, the deflection at point A is ___ mm. **

Total elongation,

AB is uniform

BC is tapered

= (9 + 6) mm = 15 mm

= 5.0 MPa

Try yourself:The values of axial stress (σ) in kN/m^{2}, bending moment (M) in kNm, and shear force (V) in kN acting at point P for the arrangement shown in the figure are respectively.

[2014 : 2 Marks, Set-II]

[2014 : 2 Marks, Set-II]

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Try yourself:A box of weight 100 kN shown in the figure is to be lifted without swinging. If all forces are coplanar, the magnitude and direction (θ) of the force (F) with respect to x-axis should be [2014 : 2 Marks, Set-I]

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Try yourself:Creep strains are _________. [2013 : 1 Mark]

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Try yourself:The Poisson’s ratio is defined as: [2012 : 1 Mark]

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Try yourself:A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of 'K) at points T and ‘2’, and an inclined load acts at ‘2’, as shown.

If the load Pequals 100 kN, which of the following options represents forces P_{1} and P_{2} in the springs at points ‘1’ and ‘27'?

[2011 : 2 Marks]

If the load Pequals 100 kN, which of the following options represents forces P

[2011 : 2 Marks]

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Try yourself: A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of 'K) at points T and ‘2’, and an inclined load acts at ‘2’, as shown.

Which of the following options represents the deflections δ_{1} and δ_{2} at points ‘Y and ‘2’? [2011 : 2 Marks]

Which of the following options represents the deflections δ

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Try yourself:The number of independent elastic constants for a linear elastic isotropic and homogeneous material is _________. [2010 : 1 Mark]

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