B.E./B.Tech. degree examination, may/june 2009

ANNA UNIVERSITY SOLVED QUESTION PAPER

B.E./B.Tech. DEGREE EXAMINATION, MAY/JUNE 2009

Fourth Semester - Automobile Engineering

CE1262 STRENGTH OF MATERIALS

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

(Regulation 2004) Maximum: 100 Marks

Time: Three hours

Answer ALL Questions.

Part A (10 × 2 = 20 marks)

1. Define Poison's Ratio.

Ans. Refer Page no. 1.127, Question no. 12.

2. What is Thermal Stress?

Ans. Refer Page no. 1.51, Section 1.1.27.

3. Mention the different types of beams. 

Ans. Refer Page no. 2.116, Question no. 3. 

4. Write the bending moment equation. 

Ans. Refer Page no. 2.171, Question no. 1. 

5. Give torsion formula.

Ans. Refer Page no. 3.86 Question no. 3

6. Compare closed and open coiled helical springs.

Ans. Refer Page no. 3.141, Question no. 5

7. Write the equivalent length of the column for a column with

(a) One end is fixed and other end is free.

(b) Both ends are fixed

NOT IN SYLLABUS

8. What is Slenderness ratio?

NOT IN SYLLABUS

9. What is Mohr's circle method?

Ans.  Refer Page no. 1.151, Section 1.2.11.

10. What is principal stress?

Ans. Refer Page no. 1.192, Question no. 1

Part B - (5 × 16 = 80 Marks)

11. (a) A compound tube consists of a steel tube of 140 mm internal diameter and 5 mm thickness and an outer brass tube of 150 mm internal diameter and 5 mm thick. The two tubes are of same length. Compound tube carries an axial load of 600 kN. Find the stresses carried by each tube and amount of shortening. Length of the tube is 120 mm. Es = 2 × 105 N/mm2, Eb = 1 × 105 N/mm2.

Ans. Refer Page no. 1.37, Example 1.23.

[OR]

(b) A steel tube of 20 mm internal diameter and 30 mm external diameter encases a copper rod of 15 mm diameter to which it is rigidly joined at each end. If the temperature of the assembly is raised by 80°C, calculate the stresses produced in the tube. Es = 2 × 105 N/mm2, Ec = 1 × 105 N/mm2. Coefficient of linear expansion of steel and copper are 11 x 10 per °C and 18 × 10 per °C.

Ans. Refer Page no. 1.66, Example 1.37.

12. (a) A simply supported beam of span 8 m long is subjected to two concentrated loads of 24 kN and 48 kN at 2 m and 6 m from left support respectively. In addition it carries a UDL of 36 kN/m over the entire span. Draw shear force and bending moment diagrams. Mark the salient points. 

Ans. Refer Page no. 2.36, Example 2.13.

[OR]

(b) A simply supported beam of span 6 m and of I section has the top flange 40 mm × 5 mm. Bottom flange of 60 mm x 5 mm total depth of 100 mm and web thickness 5 mm. It carries an UDL of 2 kN/m over the full span. Calculate the maximum tensile stress and Maximum compressive stress produced.

Ans.  Refer Page no. 2.138, Example 2.52 and Page no. 2.142, Example 2.55. 

13. (a) A solid shaft is subjected to a torque of 45 kNm. If the angle of twist is 0.5 degree per metre length of the shaft and shear stress is not to exceed 90 MN/m2, find

 (i) Suitable diameter of the shaft

 (ii) Final maximum shear stress and the angle of twist per metre length. Modulus of rigidity = 80 GN/m2.

Ans.  Refer Page no. 3.44, Example 3.32 and Page no. 3.36, Example 3.26 

[D = 160 mm, τ = 55.95 N/mm2]

[OR]

(b) A closely coiled helical spring having 12 coils of wire diameter 16 mm and made with coil diameter 250 mm is subjected to an axial load of 300 N. Find axial deflection, strain energy stored and torsional shear stress. Modulus of rigidity = 80 GN/m2.

Ans.  Refer Page no. 3.109, Example 3.53.

14. (a) A simply supported beam of span 8 m is subjected to concentrated loads. of 24 kN, 48 kN and 72 kN at 2 m, 4 m,6 m from left support respectively. Calculate the slope and deflection at the centre and also find maximum deflection.

Ans. Refer Question no. 14(a), Anna University Solved Question Paper, May/June, 2006

[OR]

(b) Find Euler's crippling load for a hollow cylindrical cast iron column of 20 mm external diameter, 25 mm thick and 6 m long hinged at both ends.. Compare the load with crushing load calculated from Rankine's formula. fc = 550 N/mm2. Rankine's constant = 1/1600, E = 1.2 × 10 N/mm2.

NOT IN SYLLABUS

15. (a) A cylindrical shell is 1.5 m diameter and 4 m long closed at both ends is subjected to internal pressure of 3 N/mm2. Maximum circumferential stress is not to exceed 150 N/mm2. Find changes in diameter, length and volume of the cylinder. E = 2 × 105 N/mm2 Poisson's ratio = 0.25.

Ans. Refer Page no. 5.32, Example 5.22.

[OR]

 (b) At a point with in a body there are two mutually perpendicular stresses of 80 N/mm2 and 40 N/mm2 of tensile in nature. Each stress is accompanied by a shear stress of 60 N/mm2. Determine the normal, shear and resultant stress on an oblique plane at an angle of 45 degree with the axis of the major principal stress.

Solution:

Normal stress:

Tangential stress: