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VTU Civil Engineering (Semester 3)
Strength of Materials
May 2016
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1(a) Draw the stress versus strain curve for mild steel specimen subjected to axial tension and indicate the salient points.
5 M
1(b) Derive an expression for the deformation of the tapering cirular bar subjected to an axial force P. Use standard notations.
8 M
1(c) The bar shown in fig. Q1(c) is tested in a universal testing machine. It is observed that at a load of 40 kN the total extension is 0.285mm. Determine the Young's modulus of the material. 7 M

2(a) Derive relation between Modulus of Rigidity, Young's modulus and Poisson's ratio.
6 M
2(b) A steel rod is of 20m long at a temperature of 20°C. Find the free expansion of the bar, when the temperature is raised to 65°C. Also calculate the tempreature stress produced for the following cases: i) When the expansion of the rod is prevented. ii) When the rod is premitted to expand by 5.8mm. Take α = 12 × 10-6/°C and E = 200GPa.
6 M
2(c) A load of 2MN is applied on a column 500mm × 500mm. The column is reinforced with four steel bars of 10mm diameter, one in each corner. Find the stresses in the concrete and steel bars, Take E for steel as 2.1 × 105N/mm2 and for concrete as 1.4 ×104N/mm2.
8 M

3(a) Define : i) Principal plane ii) Principal stresses.
4 M
3(b) Determine the magnitude and direction of resultant stresses on a plane inclined at an angle of 60° to major principal stress plane, when the bar is subjected to principal stresses at a point 200MPa tensile and 100MPa compressive. Also determine the resultant stress and its obliquity.
6 M
3(c) Two wooden pieces 100mm × 100mm in cross section are glued together along line AB as shown in fig. Q3(c). What maximum axial force 'P' can be applied if the applied if the allowable shearing stress along AB is 1.2N/mm2? 10 M

4(a) Define i) Bending moment ii) Point of contraflexture.
4 M
4(b) For the cantilever beam shown in fig. Q4(b), obtain SFD and BMD. 6 M
4(c) Draw the Shear force and bending diagrams for the beam shown in Fig. Q4(c). 10 M

5(a) Derive the equation of theory of simple bending with usual notations.
6 M
5(b) A simply supported beam of span 6m has a cross section as shown in fig. Q5(b), it carries two point loads each of 30kN at a distance of 2m from each support. Calculate the bending stress and shear stress for maximum values of bending moment and shear force respectively. Draw nea diagram of bending stress and shear stress distriution across the cross section. 14 M

6(a) Explain the terms : i) Slope ii) Deflection iii) Deflection curve.
6 M
6(b) A simply supported beam 8m long, carries two concentrated loads of 80kN and 60kN at distances of 3m and 6m from left end support respectively. Calculate slope and deflection under loads. Given E = 2.0 × 105 Mpa and I = 300 ×106mm4.
14 M

7(a) State the assumptions made in the theory of Pure Torsion.
4 M
7(b) A hollow shaft to internal diameter 400mm and external diameter 460mm is required to trensmit power at 180rpm. Determine the power it can transmit, if the shear stress is not to exceed 60N/mm2 and the maximum torque exceeds the mean by 30%.
6 M
7(c) A solid circular shaft is to transmit 250kN at 100 rpm. If the shear stress is not to exceed 75N/mm2, what should be the diameter is 0.6 times external diameter, determine the size and percentage saving in weight, maximum shear stress being the same.
10 M

8(a) Derive an expression for Euler's cripping load for a column with both ends fixed.
8 M
8(b) Compare the crippling loads given by Euler's and Rankine's formula for a column of circular section 2.3 m long and of 30mm diameter. The column is hinged at both ends. Take yield stress as 335N/mm2 and $$\text Rankine's constant \alpha =\dfrac{1}{7500}$$and E = 2 × 105N/mm2.For what ratio of L/K, the Euler's formula cease to apply for this column?
12 M

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