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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 _________.
[2018 : 2 Marks, SetI]
(a) 120 x 10^{6}
(b) 60 x 10^{6 }
(c) 0.0
(d) 120 x 106
Solution:
So the answer is (d).
Q.2. A 2 m long, axially loaded mild steel rod of 8 mm diameter exhibits the loaddisplacement (Pδ) behaviour as shown in the figure.
Assume the yield stress of steel as 250 MPa. The complementary strain energy (in Nmm) stored in the bar up to its linear elastic behaviour will be ________.
[2017 : 2 Marks, SetII]
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 γ_{xy} at this point is expressed as 0.001 k (in rad), the value of k is _________.
[2017 : 1 Mark, SetII]
(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 crosssectional area of 100 mm^{2} and 60 mm^{2}. Young’s modulus of 2 x 10^{5} MPa and 3 x 10^{5} MPa, and length of 400 mm and 900 mm, respectively. The strain energy (in Nmm up to one decimal place) in the bar due to the axial load is _________.
[2017 : 2 Marks, SetI]
Solution:
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.
[2015 : 2 Marks, SetI]
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, SetII]
Solution:
= 5.0 MPa
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