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

The Youngâ€™s modulus of the material is 2 x 10^{11} N/m^{2} and the Poissonâ€™s ratio is 0.3. If Ïƒ_{zz} is negligibly small and assumed to be zero, then the strain Îµ_{zz} is [2018 : 2 Marks, Set-I]

Solution:

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_____.[2017 : 2 Marks, Set-II]

Elastic strain

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

Complementary stain energy.

It means there seems some error in the given data.

If the shear strain Î³

(a) 0.50

Ans.

According to the sign convention,

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

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

âˆ´ Length have no effect on thermal stress.

âˆ´ Axial stress is only â€˜Ïƒâ€™.

(a) 0.00

(b) 0.25

(c) 0.50

(d) 1.00

Volumetric strain

â‡’

As Î”V = 0

Total elongation,

AB is uniform

BC is tapere

= (9 + 6) mm = 15 mm

= 5.0 MPa

(a) 1000, 75 and 25

(b) 1250, 150 and 50

(c) 1500, 225 and 75

(d) 1750, 300 and 100

Ans.

Loading after removing the cable,

Bending moment = 50 x 3 = 150 kNm

Shear force = 50kN

(a) F= 56.389 kN and Î¸ = 28.28

(b) F = - 56.389 kN and Î¸ = - 28.28

(c) F = 9.055 kN and Î¸ = 1.414

(d) F = - 9.055 kN and Î¸ = - 1.414

Ans.

For no swinging force should be balanced i.e.,

or

Dividina ea. (ii) by eq. (i) we get

Substituting

or

(a) caused due to dead load only

(b) caused due to live load only

(c) caused due to cyclic load only

(d) independent of load

Ans.

Creep strains occur with time at a constant level of stress. So they occur due to permanent load i.e., Dead Load.

(a)

(b)

(c)

(d)

Ans.

(a) R

(b) R

(c) R

(d) R

Ans.

(a)

(b)

(c)

(d)

Ans.

The free diagram of the beam is shown below,

From similar triangles, we get,

â‡’ ...(i)

Taking moments about hinge, we get,

(a) 4

(b) 3

(c) 2

(d) 1

Ans.

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