1 (a)
Define i) Stress ii) Hoke's law iii)Elasticity iv) Lateral strain

4 M

1 (b)
Explain stress-strain relationship showing salient points on the diagram.

6 M

1 (c)
A stepped bar is subjected to an external loading shown in fig Q1(c). calculated the change in the length of bar. Take E= 200 Gpa for steel, E=70 Gpa for aluminium and E=100GPa for copper.

img

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10 M

2 (a)
Define i) Poisson's ratio ii) Bulk modulus.

2 M

2 (b)
Derive an expression for establishing the relationship between Young's modulus and modulus of rigidity.

6 M

2 (c)
A 25 mm diameter steel rod passes concentrically through a bronze tube 400mm long and provided with nuts and washers which are adjusted initially so that there is no end play at 20°C. Assuming that there is no bronze when one of the nuts its tight end by giving at one-tenth of a turn, the pitch of the thered being 2.5mm, take E for steel =200 kN/mm

^{2}and E for bronze=100 kN/mm^{2}
12 M

3 (a)
Define the principle planes and principal stresses.

4 M

3 (b)
Explain procedure for constructing Mohr's circle, for an element acted upon by two tensile stresses and sher stresses.

6 M

3 (c)
The state of stress in two dimensionally stressed body is as shown fig Q3(c). determine the principle planes, principle stresses, maximum shear stress and their planes.

10 M

4 (a)
Define i) Strain energy ii)Work

3 M

4 (b)
Prove that volumetric; strain in thin cylinder is given by \frac{Pd}{4tE}(5-4\mu ), with usual notations

7 M

4 (c)
A.C.I pipe has 200 mm internal diameter and 50 mm metal thickness and carries water under a pressure of 5 N/mm

^{2}. Calculate the maximum and minimum intensities of circumferential stress and sketch the distribution of circumferential stress radial pressure across the section.
10 M

5 (a)
Derive the relationship between load, shear and bending moment.

5 M

5 (b)
Briefly explain the different types of loads.

3 M

5 (c)
Draw the SFD and BMD for the loading pattern on the beam in FigQ5(c). indicate the point of contraflexure. Also locate the maximum BM with its magnitude

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12 M

6 (a)
What are the assumptions made in simple theory of bending?

4 M

6 (b)
Prove that the maximum shear stress is 1.5 times the average shear stress in beam of rectangular cross- section.

6 M

6 (c)
At a given position in a beam of uniform I-section is subjected to a bending moment of 100kN-m. Plot the variation of bending stress across the section.(Refer FigQ6(c))

img

img

10 M

7 (a)
Derive the deflection equation for the beam in the standard form

EI\frac{d^{2}y}{dx^{2}}=M(x)

EI\frac{d^{2}y}{dx^{2}}=M(x)

6 M

7 (b)
For the beam loaded as shown in fig Q7(b), find the position and magnitude of maximum, deflection. Take I=4.3×10

img

^{8}and E=200kN/mm^{2}.img

14 M

8 (a)
What are the assumptions made in simple theory of columns?

3 M

8 (b)
Derive an expression for the critical load in a column subjected to compressive load, when one end is fixed and other end is free.

7 M

8 (c)
Find the diameter of the shaft required to transmit 60kW at 150 RPM if the minimum torque is 25% more than the mean torque for a maximum shear stress of 60MPa. Find also the angle of twist in a length of 4m. Take G=80 Gpa.

10 M

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