Attempt any four

1 (a)
Derive the relationship between shear force, bending moment and intensity of loading .

5 M

1 (b)
If two pieces of material A and B have the same bulk modulus, but the value of modulus of elasticity for B is 1% greater than that for A, find the value of rigidity for the material B in terms of modulus of elasticity and modulus of rigidity for materials A.

5 M

1 (c)
Derive an expression for longitudinal stress and circumferential stress for the thin cylinder.

5 M

1 (d)
Explain the concept of beam of uniform strength.

5 M

1 (e)
State the assumption made in the theory of pure torsion.

5 M

2 (a)
A tensile load of 50 kN is acting on the rod of 50mm diameter and length of 5m. Determine the length of a bore of 25mm that can be made central in the rod, if the total extension is not to exceed by 25 percent under the same tensile load. Take E=2.05×10

^{5}N/mm^{2}
10 M

2 (b)
A beam ABCD of span 8m is supported at A,B,and D , has an internal hinge at C. Span AB is of 4m carries a U.D.L. of 20kN/m. Span CD is of 2m carries a U.D.L of 20kN/m find the support reactions and draw the S.F.D and B.M.D

10 M

3 (a)
A solid rof of bronze 20 mm in a diameter is surrounded by fitting steel cylinder of external diameter 28mm. If the permissible bending stress in bronze and steel are 100N/mm

^{2}and 150N/mm^{2}, find the moment of resistance of composite section. The Young's modulus for steel may be taken as 1.75 times that of bronze.
10 M

3 (b)
What are the principle planes and principle stresses? Explain the Mohr's circle method for two perpendicular direct stresses with state of simple shear.

6 M

3 (c)
A beam of triangular cross-section with base b and height h is used with the base horizontal calculate intensity of shear stress at neutral axix and at height h/2. Plot the variation of shear stress intensity over the section.

4 M

4 (a)
A circular shaft has to transmit 550kW power at 115RPM . Allowable shear stress=78MPa. Find i) the required diameter of the solid shaft. ii) The dimaeter of the hollow section, such that internal diameter=0.75 external diameter.

10 M

4 (b)
A column of 6 m effective length is to be made from 3 plates(fig 8) Using E=210GPa, find the factor of safety with respect to buckling for an axial load of 17kN. Use Euler's theory.

6 M

4 (c)
Write a note on temperature stresses.

4 M

5 (a)
A bar is subjected to a tensile load of 50kN. Bar diameter =32 mm Gauge length=300 mm, extension=0.114mm, change in diameter =0.00366 mm, find poissons ratio, Young's modulus, bulk modulus and modulus of rigidity

6 M

5 (b)
Write a short note on fitched beams

4 M

5 (c)
An element in a stressed body is subjected to normal stresses on mutually perpendicular directions (fig.9) determine the normal, tangenitial & resultant stresses on a plane P-P inclined as shown. Either use analytical method or graphical method.

10 M

6 (a)
The steel pipe, 500 mm long is filled with concrete & subjected to an axial compressive load of 90kN. Determine the stress in the concrete and the steel due to this loading. The pipe has on outer diameter=80mm & an inner diameter=70mm E

_{ steel }=200 Gpa, E_{ concrete}=24 Gpa.
6 M

6 (b)
Determine the maximum torque that can be applied safely to a solid shaft of diameter 260mm. The permissible angle of twist=1.3 degrees in a length of 6m & the shear stress is not exceed 61 Mpa. Take modulus of rigidity G=90Mpa.

6 M

6 (c)
Locate the core or kernel of i-section with the properties top & bottom flange (150mm×10mm), web 280mm × 10mm. Overall depth =300mm.

8 M

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