## Strength of Materials - May 2015

### Civil Engineering (Semester 3)

TOTAL MARKS: 80

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Assume data if required.

(4) Figures to the right indicate full marks.

### Attempt any four

**1 (a)** Derive the relationship between shear force, bending moment and intensity of loading .(5 marks)
**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 marks)
**1 (c)** Derive an expression for longitudinal stress and circumferential stress for the thin cylinder.(5 marks)
**1 (d)** Explain the concept of beam of uniform strength.(5 marks)
**1 (e)** State the assumption made in the theory of pure torsion.(5 marks)
**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 marks)
**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 marks)
**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 marks)
**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 marks)
**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 marks)
**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 marks)
**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 marks)
**4 (c)** Write a note on temperature stresses.(4 marks)
**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 marks)
**5 (b)** Write a short note on fitched beams(4 marks)
**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 marks)
**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 marks)
**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 marks)
**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 marks)