JNTU
JNTU B.Tech II STRENGTH OF MATERIALS - I Previous Question Paper (April/May - 2018 - R13)
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
Derive an expression for Young’s modulus in terms of Bulk modulus and Poisson’s ratio.
Answer
The relationship is given by E = 3K(1 - 2μ), where E is Young's modulus, K is Bulk modulus, and μ is Poisson's ratio. This is derived from the volumetric strain εv = εx + εy + εz = (σ/E)(1 - 2μ) and the definition of Bulk modulus K = σ/εv.
Derive an expression for strain energy stored in a body when the load is applied gradually.
Answer
For a gradually applied load P, the load increases linearly from 0 to P. The average load is P/2. The work done (strain energy U) is the area under the load-extension diagram: U = (1/2) × P × δ, where δ is the final extension. Substituting δ = PL/AE, we get U = P2L / 2AE.
What do you mean by Thrust diagram?
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Draw the SFD and BMD for a cantilever of length L carrying a gradually varying load from zero at the free end to ‘w’ per unit length at the fixed end.
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What is the difference between bending stress and direct stress?
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Define shear centre and the principle involved in locating the shear centre.
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Write about Principal stress theory.
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What are the different Theories of Failures?
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State Mohr’s theorems.
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Mention any two advantages of Conjugate beam method over moment area method.
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Part B
A weight of 30kN is supported by two brass rods and a steel rod each 10mm in diameter and symmetrically placed. When unloaded, each rod is 1m long. Assuming E for steel and brass as 205 kN/mm2 and 102 kN/mm2 respectively, find the load carried by each rod. Also determine elongation of each rod.
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The allowable tensile stress in M.S bar is 80N/mm2. A M.S rod is 4m long and 50mm in diameter. What maximum tensile load can be suddenly applied to the rod? Take E for M.S as 200kN/mm2. Also determine the energy stored by the rod.
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Explain different types of stresses and strains.
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The intensity of loading on a simply supported beam of 5m span increases uniformly from 8kN/m at one end to 16kN/m at the other end. Find the position and magnitude of the maximum bending moment. Also draw SFD and BMD.
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Find the reactions and also draw the SFD and BMD for a simply supported beam carrying a uniformly varying load from zero at each end to ‘w’ per unit length at the centre.
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Prove that relation:
Where, M= Bending moment, σ = Bending stress, E= Young’s modulus, I= Moment of inertia, y= Distance from N.A, R= Radius of curvature.
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The shear force acting on a beam at a section is F. The section of the beam is triangular base ‘b’ and of an altitude ‘h’. The beam is placed with its base horizontal find the maximum shear stress and shear stress at the neutral axis.
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A point in a strained material is subjected to stresses, using Mohr’s circle method, determine the normal and tangential stresses across the oblique plane. Check the answer analytically.
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Determine the diameter of a bolt which is subjected to an axial pull of 12KN together with a transverse shear force of 6KN, when the elastic in tension is 300N/mm2, factor of safety= 3.0 and poisson’s ration is 0.3 using maximum principal stress theory and maximum principal strain theory.
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Calculate the slope and the deflection at principal locations for the beam. Use moment area method. Take EI = 1.0 × 105 kN-m2.
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Find the deflection at the free end of a cantilever of length ‘L’ subjected to udl of intensity ‘w’ per unit length over its entire span. Use Double Integration method.
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Determine slope at A and Deflection under load point C, using Conjugate beam method.
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