JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II STRENGTH OF MATERIALS – II Previous Question Paper (August/September - 2022 - R15)
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Main
Obtain the expressions for stiffness, shear stress induced and deflection of a closed coiled helical spring.
Answer
For a closed coiled helical spring with wire diameter d, mean coil radius R, number of turns n, and shear modulus G, subjected to an axial load W, the spring acts primarily in torsion. The torque T on the wire is W × R.
1. Shear Stress: The maximum shear stress τ is given by the torsion formula τ = (T × r) / J, where r = d/2 and J = (π × d4) / 32. Substituting T = W × R, we get:
2. Deflection: The total length of the wire is L = 2 × π × R × n. Using the strain energy method or the relation δ = θ × R where θ is the angle of twist (θ = (T × L) / (G × J)), the axial deflection δ is:
3. Stiffness: Stiffness (k) is defined as the load per unit deflection (W / δ):
What must be the length of a 5mm diameter Aluminium wire so that it can be twisted through one complete revolution without exceeding a shear stress of 42 MN/m2. Take (shear modulus) G = 27 GN/m2.
Answer
Given: diameter d = 0.005 m, shear stress τ = 42 × 106 N/m2, shear modulus G = 27 × 109 N/m2, and angle of twist θ = 2π radians (one revolution).
The relationship between shear stress, shear modulus, radius, and angle of twist is given by:
Rearranging to solve for length L:
Substituting the values where r = d/2 = 0.0025 m:
Calculating the result:
A solid aluminum shaft 1m long and 100 mm diameter is to be replaced by hollow steel shaft of the same length and same external diameter. The angle of twist per unit torsional moment over total length is same for both the shafts. If the modulus of rigidity of steel is thrice that of aluminum, find the inner diameter of the steel shaft.
Answer
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An open coiled helical spring of wire diameter 12 mm, mean coil radius 84mm, helix angle 20 degrees carries an axial load of 480 N. Determine the shear stress and direct stress developed at inner radius of the coil.
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Derive the expression for crippling load when column with one end fixed and other end hinged.
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A steel column is of length 8 m and diameter 600 mm with both ends hinged. Determine the crippling load by Euler’s formula. Take E = 2.1 × 105 N/mm2.
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Find Euler’s crippling load for a hollow cylindrical steel column of 38mm external diameter and 2.5mm thickness. The length of column is 2.3m hinged at both ends. Take E=205GPa. Also find crippling load by Rankine’s formula. Take fc = 335kN/mm2, Rankine’s constant, ɑ = 1/7500.
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What are the assumptions made in the derivation of stresses in a curved bar which is subjected to a bending moment?
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A square chimney, 30 m high, has a flue opening of size 1.5 m × 1.5 m. Find the minimum width required at the base for no tension if the masonry weighs 20kN/m3 and the wind pressure is 1.5kN/m2. The permissible stress in the masonry is 1kN/m2.
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A short column of external diameter 30 cm and internal diameter 20 cm carries an eccentric load of 60 kN. Find the greatest eccentricity which the load can have without producing tension on the cross-section.
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Find the maximum bending moment in a beam –column with simply supported ends and is subjected to axial load ‘P’ N at two end supports and also carrying a uniformly distributed load ‘q N/m’ at its mid-span.
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How will you find out the resultant stress in unsymmetrical bending?
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A beam of rectangular section 80mm wide and 120mm deep is subjected to a bending moment of 150kN-m. The plane of loading is inclined at 45° to the y-y axis of the section. Locate the neutral axis of the section and calculate the maximum bending stress induced in the section.
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Sketch the shear flow distribution when a thin walled L-section is subjected to a vertical load.
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A compound cylinder is made by shrinking a cylinder of external diameter 200 mm and an internal diameter 160 mm over another cylinder of external diameter 160 mm and internal diameter 120 mm. The radial pressure at the junction after shrinking is 9 N/mm2. Find the final stress set up across the section, when the compound cylinder is subjected to an internal fluid pressure of 50 N/mm2.
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