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Q.1. A plate in equilibrium is subjected to uniform stresses along its edges with magnitude σxx = 30 MPa and σyy = 50 MPa as shown in the figure.The Young’s modulus of the material is 2 x 1011 N/m2 and the Poisson’s ratio is 0.3. If σzz is negligibly small and assumed to be zero, then the strain εzz is _________.
[2018 : 2 Marks, Set-I]
(a) -120 x 10-6
(b) -60 x 10-6
(c) 0.0
(d) 120 x 10-6
Solution: So the answer is (d).
Q.2. A 2 m long, axially loaded mild steel rod of 8 mm diameter exhibits the load-displacement (P-δ) behaviour as shown in the figure.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]
Solution:Elastic strain:
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:Complementary stain energy:
It means there seems some error in the given data.
Q.3. In a material under a state of plane strain, a 10 x 10 mm square centred at a point gets deformed as shown in the figure.If the shear strain γxy at this point is expressed as 0.001 k (in rad), the value of k is _________.
[2017 : 1 Mark, Set-II]
(a) 0.50
(b) 0.25
(c) -0.25
(d) -0.50
Ans. (d)
Solution:
According to the sign convention:
In question, since angle has been increased, therefore, shear strain should be negative.
Q.4. Consider the stepped bar made with a linear elastic material and subjected to an axial load of 1 kN, as shown in the figure.Segments 1 and 2 have a cross-sectional area of 100 mm2 and 60 mm2. Young’s modulus of 2 x 105 MPa and 3 x 105 MPa, and length of 400 mm and 900 mm, respectively. The strain energy (in N-mm up to one decimal place) in the bar due to the axial load is _________.
[2017 : 2 Marks, Set-I]
Solution:
[2016 : 2 Marks, Set-II]
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 105 MPa. When subjected to a load P = 30πkN, the deflection at point A is ___ mm.
[2015 : 2 Marks, Set-I]
Solution:
Total elongation,
AB is uniform
BC is tapered
= (9 + 6) mm = 15 mm
Q.8. For the state of stresses (in MPa) shown in the figure below, the maximum shear stress (in MPa) is _______.
[2014 : 2 Marks, Set-II]
Solution:
= 5.0 MPa
[2014 : 2 Marks, Set-II]
If the load Pequals 100 kN, which of the following options represents forces P1 and P2 in the springs at points ‘1’ and ‘27'?
[2011 : 2 Marks]
Which of the following options represents the deflections δ1 and δ2 at points ‘Y and ‘2’? [2011 : 2 Marks]
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