**MODEL PAPER**

**B.E. DEGREE EXAMINATION.**

**Fourth Semester**

**Mechanical Engineering**

**CE 251 — STRENGTH OF MATERIALS**

(Common to Second Semester Mechatronics Engineering)

Time : Three hours Maximum : 100 marks

Answer ALL questions.

Assume any additional data required and indicate it clearly.

PART A — (10 ´ 2 = 20 marks)

- A bar of varying cross–section consists of two sections of lengths and with cross–sections and . It is subjected to an axial pull
*F*. Find the total elongation. - The Young’s modulus of a material is 200 kN/mm
^{2}and its rigidity modulus is 80 kN/mm^{2}. Determine its bulk modulus. - What is point of contraflexure? In which beam will it occur?
- Derive the relation between the intensity of load and shear force, in bending theory.
- Draw the shear stress distribution diagram for a
*I*–section. - Derive an expression for the power transmitted by a circular shaft in S.I. units, which is subjected to a torque
*T*in Nm. - Distinguish between close coil and open coil helical springs.
- Derive an expression for the longitudinal stress in a thin cylinder subjected to an uniform internal fluid pressure.
- What is the normal stress on an inclined plane in a block when it is subjected to two mutually perpendicular normal stresses and shear stress?
- State the condition for the use of Macaulay’s method.

PART B — (5 ´ 16 = 80 marks)

- Draw the SF and BM diagram for the beam shown in Fig. Q. 11. Find the values at important points and indicate in the diagram.

Fig. Q. 11

- (a) A bar 20 mm in diameter and 10 m long was subjected to an axial pull of 50 kN. The extension of the bar was found to be 0.1 mm, while decrease in the diameter was found to be 0.15 mm. Find the Young’s modulus, Poisson’s ratio, rigidity modulus and bulk modulus of the material of the bar.

Or

** **(b) An aluminium rod 22 mm diameter passes through a steel tube of 25 mm internal diameter and 3 mm thick. The rod and tube are fixed together at the ends at a temperature of 30°C. Find the stresses in the rod and tube when the temperature is raised to 150°C.

** ** ,

** ** , .

- (a) A timber beam 240 mm wide and 360 mm deep is simply supported. It carries a udl of 20 kN/m over the entire span. Find the span length if the allowable bending stress is not to exceed 8 N/mm
^{2}.

Or

** **(b) A hollow shaft is to transmit 300 kW at 80 rpm. The internal diameter is 0.6 of the external diameter. The maximum torque is 40% more than the mean torque. If the shear stress is not to exceed 60 N/mm^{2}, find the external and internal diameters of the shaft.

- (a) A thin cylinder 1.5 m internal diameter and 5 m long is subjected to an internal pressure of 2 N/mm
^{2}. If the maximum stress is limited to

160 N/mm^{2}, find the thickness of the cylinder.*E*= 200 kN/mm^{2}and Poisson’s ratio = 0.3. Also find the changes in diameter, length and volume of the cylinder.

Or

** **(b) At a point in a strained material the horizontal tensile stress is

80 N/mm^{2} and the vertical compressive stress is 140 N/mm^{2}. The shear stress is 40 N/mm^{2}. Find the principal stresses and the principal planes. Find also the maximum shear stress and its planes.

- (a) A simply supported beam of uniform flexural rigidity EI and span
*l*, carries two symmetrically placed loads*P*at one–third of the span from each end. Find the slope at the supports and the deflection at mid–span. Use moment area theorems.

Or

** **(b) A simply supported beam of span *l*, carries a udl of w/unit length from the left hand support upto the centre of the beam. Find the mid–span deflection by strain energy method.

good