## Strength of Materials - Dec 2014

### Mechanical Engg (Semester 4)

TOTAL MARKS: 100

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

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

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.

### Solve any one question from Q1 and Q2

**1 (a)** A homogeneous 800 kg bar AB is supported at either end by a cable as shown in figure 1. Calculate the smallest area of each cable if the stress is not to exceed 90 MPa in bronze and 120 MPa in steel.
(6 marks)
**1 (b)** Draw SFD and BMD for the beam loaded as shown in the figure 2 below.
(6 marks)
**2 (a)** An aluminium rod is rigidly attached between a steel rod and a bronze rod as shown in the figure 3. Axial loads are applied at the positions indicated. Find the maximum value of P that will not exceed a stress in steel of 140 MPa, in aluminium of 90 MPa, or in bronze of 100 Mpa.
(6 marks)
**2 (b)** Draw SFD and BMD for the beam loaded as shown in the Figure 4.
(6 marks)

### Solve any one question from Q3 and Q4

**3 (a)** A cantilever beam, 30 mm wide by 100 mm high and 3 m
long, carries a load that varies uniformly from zero at the
free end to 2000 N/m at the wall. Compute the magnitude
and location of the maximum flexural stress.(6 marks)
**3 (b)** The cantilever beam has rectangular cross-section of 50 mm (W) × 150 mm (H) is 3 m long and loaded by an end force of 10 kN. The material is steel with E = 210 GPa. Find the maximum deflection of the beam and maximum stress. Take E = 200 GPa.(6 marks)
**4 (a)** For the problem described in question 3(b) determine the
type and magnitude of the stress in a fiber 20 mm from
the top of the beam at a section 2 m from the free
End.(6 marks)
**4 (b)** For the problem described in question 3(b) determine the slope
of the free end of the cantilever beam.(6 marks)

### Solve any one question from Q5 and Q6

**5 (a)** A hollow steel shaft 2 m long is required to transmit a torque
of 15 kN-m. The total angle of twist in this length is not
to exceed 3° and the allowable shearing stress is 110 MPa.
Determine the inside and outside diameter of the shaft if
G = 90 GPa.(6 marks)
**5 (b)** A steel bar of rectangular cross-section 60 mm - 80 mm and
pinned at each end is subject to axial compression. If the
proportional limit of the material is 210 MPa and E = 210
GPa, determine the minimum length for which Euler's equation
may be used to determine the buckling load.(7 marks)
**6 (a)** A solid circular shaft is required to transmit 114 kW while
turning at 24 rev/s. The allowable shearing stress is 90 MPa.
Find the required shaft diameter.(6 marks)
**6 (b)** A rectangular steel bar 45 mm × 55 mm in cross-section,
pinned at each end and subjected to axial compression. The
bar is 2.3 m long and E = 210 GPa. Determine the buckling
load using Euler's formula and corresponding stress.(7 marks)

### Solve any one question from Q7 and Q8

**7** A cylindrical steel shell is subjected to an internal pressure of 5.6 MPa. The mean radius of the cylinder is 325 mm and thickness is 12 mm. If the material has a yield point of 300 MPa, determine the factor of safety using:

(a) the maximum normal stress theory, and

(b) the von Mises theory.(13 marks)
**8** A material is subjected to two mutually perpendicular direct stresses
of 93.5 MPa tensile (in y direction) and 42.5 MPa compressive
(in x direction), together with a shear stress of 44 MPa. The shear
couple acting on planes carrying the 93.5 MPa stress is clockwise
in effect. Calculate:

(a) magnitude and nature of the principal stresses;

(b) magnitude of the maximum shear stresses in the plane of the given stress system;

(c) direction of the planes on which these stresses act.(13 marks)