1(a)Distinguish between normal stress and shear stress. (4 Marks)

(b)Define coefficient of thermal expansion. What is the value for steel and copper? (4 Marks)

(c)Define the terms simple shear, Poisson's ratio and volumetric strain. (6 Marks)

(d) A steel flat of thickness 10 mm tapers uniformly from 60 mm at one end to 40 mm at other end in a length of 600 mm. if the bar is subjected to a load of 60 kN, find its extension. Take E = 200000 MPa. What is the percentage error if average area is used for calculating extension? (6 Marks)

2(a) Differentiate between bending moment diagram and a shear force diagram. (6 Marks)

(b) Mention some commonly encountered statically determinate beams. (4 Marks)

(c) A girder 6m long rests on two supports with equal overhangs on either side and carries a uniformly distributed load of 30 kN per metre run over the entire length. Calculate the overhangs if the maximum bending moment, positive or negative, is to be as small as possible. Draw SF and BM diagrams for the double overhang beam. (10 Marks)

3(a) Write a note on simple bending theory. (6 Marks)

(b) Derive a relation between moment and radius of curvature. (4 Marks)

(c) What are flitched beams? Mention one example. (4 Marks)

(d)A cantilever beam of span 1m has rectangular cross-section of size 200 mm x 400 mm. Determine the concentrated load which placed at the free end produce shear stress of intensity 1.5 N per square mm. Hence compute maximum bending stresses in the cross-section at the fixed end of cantilever. (6 Marks)

4(a)Derive the differential equation for deflection. What is flexural rigidity? (8 Marks)

(b)Write the steps involved in Macaulay's method. (4 Marks)

(c) A simply supported beam of span L is subjected to equal loads W/2 at each of 1/3 rd span points. Find the expressions for deflection under the load and at mid span. (8 Marks)

5(a) Write a note on the assumptions made in developing the theory of pure torsion. (4 Marks)

(b) Define polar modulus. (4 Marks)

(c) What are shear keys? Draw a figure and explain its working. (6 Marks)

(d) What percentage of strength of a solid circular steel shaft 100 mm diameter is lost by boring 50 mm axial hole in it? Compare the strength and weight ratio of the two cases. (6 Marks)

6(a) Show that when a material is subjected to shearing stresses and direct stress in one direction, the major and minor principal stresses are of opposite nature. (4 Marks)

(b)Explain the construction of Mohr's circle. (6 Marks)

(c) A shear force of 40 kN and a bending moment of 20 kN-m act at a certain cross section of rectangular beam 100 mm wide and 200 mm deep. Compute the direction of the principal stresses at a point 20 mm below the top surface. (6 Marks)

(d) Write a note on strain gauges. (4 Marks)

7(a) Differentiate between longitudinal stress and circumferential stress. (4 Marks)

(b) Prove that when fluid is admitted in a wire wound cylinder, final stresses are obtained by algebraically adding initial stresses and stresses due to fluid. (6 Marks)

(c) What is shrinkage allowance? Explain. (4 Marks)

(d) A pipe of 400 mm internal diameter and 100 mm thickness contains a fluid at a pressure 80 N per square mm. Find the maximum and minimum hoop stresses across the section. Also sketch the radial and hoop stress distribution across the section. (6 Marks)

8(a) What are the limitations of Euler's theory? (4 Marks)

(b) Write and explain Rankine's formula. (4 Marks)

(c) Write a note on Beltrami and Haigh's theory. (6 Marks)

(d) A thick steel cylinder with an internal diameter 200 mm has to withstand an internal fluid pressure of 40 N per square mm. Calculate the thickness of the metal by using maximum principal stress theory. (6 Marks)

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