JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year MECHANICS OF SOLIDS Previous Question Paper (April/May - 2023 - R13)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
Define the bulk modulus. How is it related to Young’s modulus?
Answer
Bulk modulus (K) is the ratio of direct stress to the corresponding volumetric strain within the elastic limit. It is related to Young's modulus (E) and Poisson's ratio (μ) by the formula:
In a tensile test on a mild steel specimen of original diameter 20 mm and gauge length 40 mm, the limit of proportionality load is 80 kN and the extension is 0.048 mm. Find the stress, strain and Young’s modulus.
Answer
Given: Diameter (d) = 20 mm, Gauge length (L) = 40 mm, Load (P) = 80,000 N, Extension (δL) = 0.048 mm. Area (A) = (π/4) × 202 = 314.16 mm2.
Stress (σ) = P / A = 80,000 / 314.16 = 254.65 N/mm2.
Strain (ε) = δL / L = 0.048 / 40 = 0.0012.
Young's modulus (E) = σ / ε = 254.65 / 0.0012 = 212,208 N/mm2 (or 212.21 GPa).
What is the point of contraflexure?
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Differentiate between sagging bending moment and hogging bending moment.
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What is neutral layer? Why stress and strain are zero in the neutral layer?
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Sketch the variation of shear stress across the depth T-section, showing the positions of maximum and average shear stress.
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Major Principal stress at a point is 220 MPa. The radius of Mohr’s stress circle is 70 MPa. What is the minor principal stress at the point?
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State and explain the maximum strain energy theory.
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State the assumptions of torsion theory of circular shaft.
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Distinguish between cylindrical and spherical shells.
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Part B
A bar of uniform thickness t and length L tapers uniformly from width b1 at one end to b2 at the other end (b1 > b2). If an axial tensile load P is applied at the ends and E is the Young’s modulus, derive the expression for the elongation of the bar. Also find the stresses at middle of the length.
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Prove that the stress due to sudden load is two times the stress when the same load is gradually applied.
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A copper bar of 200 mm long with sections 50 x 50 mm is subjected to a tensile stress of 20 MPa along the longitudinal axis. The increase in volume is 100 mm3. Determine the value of Poisson’s ratio, modulus of rigidity and bulk modulus, if E = 105 GPa.
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A 5-m-long beam AB carries a point load 4 kN at the end of a crank CEF and on other point load of 6 kN at D as shown in figure 1. Determine support reaction and Plot the shear force and bending moment diagrams. Identify the point of contra flexure if exists.
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Derive the relation between Shear Force, Bending Moment and rate of loading at a section of a beam.
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The shear force diagram for a cantilever beam of length 5 m is varying linearly from a value of 50 N at the fixed end to a value of zero at the free end. Determine the loading on the cantilever beam. Also draw its bending moment diagram.
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An I-section beam 350 mm x 150 mm has a web thickness of 10 mm and a flange thickness of 20 mm. The beam is simply supported over a span of 4 m. Determine the uniformly distributed load per meter length which the beam can carry, if the bending stress should not exceed 150 MPa.
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A laminated wooden beam 180 mm x 180 mm is made from three planks of the size 60 mm x 180 mm glued together all along the length of the contact surfaces. The beam is simply supported over a span of 4 m. If the allowable shear stress in the glued joint is 1 MPa, find the maximum concentrated load which the beam can carry at its mid span, neglecting self-weight of the beam.
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For the given states of stress as shown in figure 2, find out the principal stresses and maximum shear stresses using analytical approach. Also draw the Mohr’s circle of stress and indicate these values on the circle.
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The principal stresses induced at a critical point in a machine component made of steel 50C4 are as follows: σ1 = 200 MPa, σ2 = 150 MPa and σ3 = 0 MPa. The material has yield strength of 500 MPa. Calculate the factor of safety by (a) the maximum normal stress theory, (b) the maximum shear stress theory and (c) the Distortion energy theory.
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A 5-HP motor shown in figure 3 delivers 3 and 2 HP, respectively, to accessory gears B and C. Determine (a) maximum shear stress in steel shaft drive and (b) angular twist between C and A, if the angular speed of the shaft is 1000 rpm and G = 80 GPa.
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Derive the expressions for hoop and axial stresses developed in a thin cylindrical shell subjected to internal pressure.
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Diameter of a water supply pipe is 500 mm. It has to stand a water head of 50 m. If the permissible stress of the material is 25 MPa, find out the required thickness of the pipe. Consider the specific weight of water to be 9810 N/m3.
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