JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II MECHANICS OF SOLIDS Previous Question Paper (July/August - 2021 - R15)
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Main
Derive the relationship between modulus of elasticity, modulus of rigidity and bulk modulus.
Answer
The relationships between the elastic constants are derived by considering the deformation of a cubic element subjected to various stress states. Let E be the Young's modulus, G be the modulus of rigidity, K be the bulk modulus, and μ be Poisson's ratio.
1. Relationship between E, G, and μ:
2. Relationship between E, K, and μ:
To derive the relationship between E, G, and K, we eliminate μ from the two equations above.
From the first equation:
Substitute this into the second equation:
Rearranging to group terms with E:
Solving for E, we obtain the final relationship:
A bar of brass 20 mm is enclosed in a steel tube of 40 mm external diameter and 20 mm internal diameter. The bar and the tubes are initially 1.2 m long and are rigidly fastened at both ends using 20 mm diameter pins. If the temperature is raised by 60°C, find the stresses induced in the bar, tube and pins. The modulus of elasticity, E = 200 GPa for steel and 100 GPa for brass. The coefficient of thermal expansion for steel and brass are 11.6 × 10-6/°C and 18.7 × 10-6/°C.
Answer
To find the stresses, we first calculate the cross-sectional areas:
Let P be the compressive force induced in both members due to the temperature rise ΔT = 60°C. The compatibility condition states that the total length change of the brass bar and the steel tube must be equal:
Substituting the given values (Eb = 100 GPa, Es = 200 GPa):
Solving for P:
The stresses induced are:
The pins experience a shear force equal to P. Since the pins are in double shear:
A simply supported beam of 10 m span carries a load, uniformly varying from zero at the left end to 100 kN/m at the right end. Draw the Shear Force and Bending Moment diagrams. Determine the position and magnitude of the maximum BM in the beam.
Answer
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Explain about different types of beams and draw the S.F.D and B.M.D when the beams are subjected to U.D.L of W kN/m.
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Derive the bending equation:
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An isosceles triangular section of base 200 mm and depth 300 mm has to carry a shear force of 200 kN. Find the maximum shear stress, the shear stress at 1/3 points of the depth, and draw a shear stress distribution diagram. Also find the shear stress at the centroidal axis.
Answer
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Explain about Mohr's circle of stresses.
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A solid shaft is required to transmit 300 kW at 120 rpm. The shear stress of the material must not exceed 80 MPa.
Find the diameter required.
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If the shaft is replaced by a hollow one with a diameter ratio of 3:5 and the maximum shear stress remaining unchanged, calculate the percentage saving in weight that could be obtained.
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