## Strength of Materials - Dec 2014

### Mechanical 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.

### Answer any four:

**1 (a)** A circular log of timber has diameter D. Find the dimensions of strongest rectangular section to resist moment, one can cut from this log.(5 marks)
**1 (b)** Explain beams of Uniform strength.(5 marks)
**1 (c)** Derive expression for deformation of uniformly Tapering Rectangular section bar.(5 marks)
**1 (d)** State at least three difference between Torque and Bending Moment.(5 marks)
**1 (e)** State the assumption made in theory of torsion.(5 marks)
**2 (a)** Find the value of P, stress in steel and copper wires if the rigid beam AD rotates clockwise causing a deflection of 3 mm at the D. E_{s}×10^{5} MPa, E_{c}=1×10^{5} MPa,
(10 marks)
**2 (b)** A short hollow cylindrical column carries a compressive load of 450kN. Determine the maximum permissible eccentricity of load, if the allowable compressive stress is 75/mm^{2} & allowable tensile stress is 20N/mm^{2}. The external and internal diameters are 200mm and 125mm respectively. Draw the variation of actual resultant stress across the section of the column.(10 marks)
**3 (a)** Draw S.F.D and B.M.D. for the beam shown. E is an internal hinge.
(10 marks)
**3 (b)** The end of thin cylinder, 180 mm internal diameter and wall thickness 4 mm are closed by rigid plates and it is then filled with liquid. The cylinder is now subjected to an axial compressive force of 40 kN. Due to this the liquid pressure rises by 0.1 N/ mm^{2}. Assume E=2.1 × 10^{5} N/mm^{2} and 1/m=0.3, calculate the bulk module of liquid.(10 marks)
**4 (a)** Find maximum bending stress at point C on the beam AE shown in figure. Note that the cross section of the beam is in form of inverted T.
(10 marks)
**4 (b)** At 20°C, a gap of 0.5 mm exists between the ends of rods as shown. Taking for aluminium E_{AL}=70GPa, a_{AL}=23×10^{-6}/°C, A_{AL}=2000 mm^{2} and for steel E_{s}=190 GP_{a}, a_{s}=18×10^{-6}/°C, A_{a}=800 mm^{2}. When the temperature reaches 140°C determine:

b) Exact length of aluminium rod.

(10 marks)

**5 (a)**Determine the diameter of the shaft to transmit 1 MW rotating at 220 RPM and the working conditions to be satisfied are:

a) that the shaft not twist more than 1° on length of 12 diameters and

b) the shear stress must not exceed 60N/mm

^{2}. Take C=84KN/mm

^{2}.(10 marks)

**5 (b)**Find Euler's cripping load for hollow cylindrical column of 200 mm external diameter and 25 mm thick, Both ends of the column, are hinged and length of the column is 6 m. Take E=8×10

^{4}N/mm

^{2}. Compare Euler's cripping load with Rankine's cripping load for the same column. Take f

_{c}=550 MPa & α=1/1600. For what length of the column the critical loads by Euler's and Rankine's formula will be equal to each other.(10 marks)

**6 (a)**Determine the deflection at B and the slop at D for simply supported beam as shown. Also find the maximum deflection and its location. Take E=2×10

^{5}N/mm

^{2}and I=300×10

^{8}mm

^{4}. (10 marks)

**6 (b)**The compound bar shown in figure consists of a 30mm diameter steel rod encased in a copper tube of internal diameter 30mm and external diameter 40mm. Find the stresses produced in steel and copper rod when a load of 100N falls from a height of 40 mm. Take E

_{s}=2×10

^{5}N/mm

^{2}. E

_{c}=1×10

^{5}N/mm

^{2}. (10 marks)