JNTU
JNTU B.Tech II STRENGTH OF MATERIALS II Previous Question Paper (May - 2019 - R15)
Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks and may have a, b, c as sub questions.
PART - A
State the assumptions made in the theory of pure torsion.
Answer
The assumptions made in the theory of pure torsion are:
- The material of the shaft is homogeneous and isotropic.
- The shaft is subjected to pure torsion, meaning the twisting moment is applied at the ends and no shear force is present.
- The cross-sections of the shaft, which are plane and circular before twisting, remain plane and circular after twisting.
- The cross-sections of the shaft, which are plane and circular before twisting, do not warp or distort axially.
- The shear stress is proportional to the radius, varying linearly from zero at the center to a maximum at the outer surface.
- The shaft is of uniform circular cross-section.
Determine the energy stored in a close coiled helical spring of mean diameter 120 mm, the diameter of the spring wire is 8 mm and the number of coils in the spring is 12 subjected to an axial load of 10 kN. Take the modulus of rigidity is 0.8 × 105 N/mm2.
Answer
Given:
Mean diameter of the spring, D = 120 mm
Diameter of the spring wire, d = 8 mm
Number of coils, n = 12
Axial load, W = 10 kN = 10 × 103 N
Modulus of rigidity, G = 0.8 × 105 N/mm2
The energy stored in a close-coiled helical spring subjected to an axial load is given by the formula:
where L is the total length of the spring wire and k is the spring stiffness.
The spring stiffness k is given by:
First, calculate the spring stiffness:
The total length of the spring wire, L, is the circumference of the mean diameter multiplied by the number of coils:
Now, calculate the energy stored:
Converting to Joules (1 J = 1 N-m = 1000 N-mm):
What is the significance of Rankine’s empirical formula?
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What are the limitations of Euler’s column theory?
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Define core of a section and draw the core of a rectangular section ‘B×D’.
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What are the conditions to be checked for the stability of a dam?
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Indicate the location of shear center of a symmetrical channel section.
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Define the principal axes of a cross-section.
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What is the necessity of shrinkage allowance in the process of fabrication of compound cylinders?
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A thin cylindrical shell of internal diameter 1250 mm and 10 mm thick is subjected to an internal fluid pressure of 5 N/mm2. Determine the maximum shear stress.
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PART - B
Design a hollow steel shaft of length 3 m to transmit 120 kW at 300 rpm. The shear stress is to be limited to 75 N/mm2 and the angle of twist in not to exceed 0.5° per meter length of shaft. Assume the internal diameter of the shaft is half the external diameter. Use the modulus of rigidity is 0.85 × 105 N/mm2.
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A solid circular shaft is subjected to a bending moment of 300 kNm in addition to a twisting moment of 125 kNm. If the yield stress of the shaft material is 325 N/mm2, design the shaft according to the (a) maximum shearing stress and (b) maximum principal stress theories of failures.
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A cast iron column of hollow circular section has outside diameter 300 mm, thickness 22 mm and length 6.6 m is fixed at both ends. Determine the safe load carrying capacity of the column with a factor of safety of 3. The Rankine’s constants are fc = 550 MPa and α = 1/1600. Also find the Euler’s buckling load. Adopt E = 1 × 105 N/mm2.
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A curved beam semi-circular in plan has 5 m radius and supported on three equally spaced supports. The beam carries a uniformly distributed load of 50 kN/m of the circular length. Analyse the beam and draw the twisting moment diagram.
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A steel hinged-hinged I- strut, 50 mm × 100 mm × 6 mm, of length 3 m is subjected to an axial load of 60 kN in addition to a transverse uniformly distributed load 20 kN/m length over its entire span. Determine the bending moment.
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A 50 m high RC chimney is subjected to the horizontal wind pressure of 3 kN/m2. The external diameter of the chimney tapers from 4.5 m at the base to 2.5 m at the top. The internal diameter at the base is 3 m. Draw the stress distribution across the base-section.
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A simply supported steel beam of span 3.6 m has I-section 125 mm × 200 mm × 10 mm is subjected to equal and opposite moments of 10 kNm acting at the ends of the beam in a plane making an angle 30° with respect to vertical and passing through the centroid of the section. Determine the maximum stresses induced at any cross-section of the beam.
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A simply supported steel beam of span 3 m has an unequal angle section 90 mm × 60 mm × 12 mm with the longer leg vertically downward. The beam is subjected to uniformly distributed load of 5 kN/m over its entire span in a vertical plane passing through the centroid of the cross-section. Determine the maximum deflection.
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Derive the expressions for the longitudinal and circumferential stresses for a thin cylinder of length ‘L’, internal diameter ‘d’ and thickness ‘t’ subjected to an internal fluid pressure of ‘p’.
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A thin steel spherical shell has 750 mm internal diameter and 12 mm thickness. Find the change in the diameter and volume of the spherical shell if it is subjected to an internal fluid pressure of 5 N/mm2.
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A steel compound cylinder is composed of a tube of 300 mm external diameter and 250 mm internal diameter shrunk on to a tube of 250 mm external diameter and 200 mm internal diameter. The radial pressure at the junction of the two tubes is 20 N/mm2. Draw the variation of hoop stress across the wall thickness of the compound cylinder if it is subjected to an internal fluid pressure of 100 N/mm2.
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