B.E./B.Tech. degree examination, november/december 2007

ANNA UNIVERSITY

B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2007 

Fourth Semester - Automobile Engineering (Regulation 2004)

STRENGTH OF MATERIALS

(Common to Mechanical Engineering / Mechatronics Engineering/ Metallurgical Engineering/Production Engineering)

Time: Three hours

Answer ALL Questions.

Maximum: 100 Marks

Part A (10 x 2 = 20 marks)

1. Define the terms Poisson's ratio and Bulk modulus.

Ans. Refer Page no. 1.127 & 1.126, Question no. 11 & 12.

2. Explain the effect of change of temperature in a composite bar.

Ans. A composite member is composed of two or more different material, joined together in such a way that the system is elongated or compressed as a single unit.

Load carried by two materials is same.

i.e., σ1 Α1 = σ2 Α2

Total strain e1 + e2 = −t (α1 + α2)

3. Sketch the bending moment diagram of a cantilever beam subjected to udl over the entire span.

4. The section modulus with respect to xx-axis of a rectangle of width ‘b' and depth 'd' is ――― and in case of circle, the section modulus is ―――.

Ans.

5. Express the strength of a solid shaft.

Ans. Strength of a solid shaft is given by

6. Give the expression for finding deflection of a closely coiled helical spring.

Ans. Refer Page no. 3.143, Question no. 15.

7. Write the equation giving maximum deflection in case of a simply supported beam subjected to udl over the entire span.

Ans. 

8. Give the equivalent length of a column for any two end conditions. 

NOT IN SYLLABUS

9. A boiler of 800 mm diameter is made up of 10 mm thick plates. If the boiler is subjected to an internal pressure of 2.5 MPa, determine circumferential and longitudinal stress.

Ans.

Given:

d = 800 mm

t  = 10 mm

p = 2.5 MPa = 2.5 × 106 Pa = 2.5 × 106 N/m2

= 2.5 N/mm2

Solution:

10. Define principal planes and principal stresses.

Ans. Refer Page no. 1.124, Question no. 1.

Part B (5 × 16 = 80 marks)

11. (a) In an experiment, a bar of 25 mm diameter is subjected to a pull of 70 kN. The measured extension on gauge length of 200 mm is 0.09 mm and the change in diameter is 0.0040 mm. Calculate the Poisson's ratio and the values of three moduli.

Ans. Refer Page no. 1.92, Example 1.45.

[OR]

(b) A reinforced concrete column 500 mm x 500 mm in section is reinforced with 4 steel bars of 20 mm diameter, one in each corner. The column is carrying a load of 750 kN. Determine the stresses in concrete and steel bars. Take Es = 210 GPa and Ec = 14 GPA. Also, calculate load carried by steel and concrete.

Ans. Refer Page no. 1.41, Example 1.25.

12. (a) Draw shear force and bending moment diagram for the simply supported beam shown in Fig.1. Also find the maximum bending moment and its position.

Ans. Refer Page no. 2.40, Example 2.15.

[OR]

(b) Two beams are simply supported over the same span and have the same flexural strength. Compare the weights of these two beams, if one of them is solid and the other is hollow circular with internal diameter half of the external diameter.

Ans. 

For solid beam

13. (a) A solid shaft is subjected to a torque of 1.6 kN-m. Find the necessary diameter of the shaft, if the allowable shear stress is 50 MPa. The allowable twist is 1°for every 20 diameters length of the shaft. Take C = 80 GPa. 

Ans. Refer Page no. 3.20, Example 3.15.

[OR]

(b) A closely coiled helical spring of round steel wire 5 mm in diameter having 12 complete coils of 50 mm mean diameter is subjected to an axial load of 150 N. Find the deflection of the spring and the maximum shearing stress in the material. Modulus of rigidity (C) = 80 GPa. Also, find stiffness of the spring.

Ans. Refer Page no. 3.124, Example 3.65.

14. (a) A beam is loaded as shown in Fig.2. Determine the deflection under the load points. Take E = 200 GPa and 1= 160 × 106 mm4.

Ans. Refer Anna University Solved Question Papers, May/June 2006, Question 14 (a).

[OR]

(b) An I section joist 400 mm × 200 mm × 20 mm and 6 m long is used as a strut with both ends fixed. What is Euler's crippling load for the column? Take E = 200 GPa.

NOT IN SYLLABUS

15. (a) A cylindrical vessel 2 m long and 500 mm in diameter with 10 mm thick plates is subjected to an internal pressure of 2 MPa. Calculate the change in volume of the vessel. Take E = 200 GPa and Poisson's ratio = 0.3 for the vessel material.

Ans. Refer Page no. 5.11, Example 5.6.

[OR]

(b) A plane element in a boiler is subjected to tensile stresses of 400 MPa on one plane and 200 MPa on the other at right angles to the former. Each of the above stresses is accompanied by a shear stress of 100 MPa. Determine the principal stresses and their directions. Also, find maximum shear stress. 

Ans. Refer Page no. 5.18, Example 5.11.