Winter 2014 Strength of Materials Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY
Diploma Engineering - SEMESTER–III • EXAMINATION – WINTER • 2014
Subject Code: 3331904 Date: 03-12-2014
Subject Name: Strength of Materials
Time: 10:30 am - 01:00 pm Total Marks: 70

Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. English version is considered to be Authentic.

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Q.1 Answer any seven out of ten. 14

1. Differentiate between shear stress and bending stress.

2. Define linear strain and lateral strain.

3. Define Modulus of Elasticity and Bulk Modulus.

4. Define radius of gyration and slenderness ratio.

5. Write the Euler’s equation defining the notations.

6. What do you understand by Malleability and Ductility?

7. Define shear force and bending moment.

8. Mention four tests conducted to determine the hardness and impact strength of
materials

9. Write the units of (i) Bending Moment (ii) Shear Stress (iii) Modulus of
Rigidity ( iv) Angle of Twist

10. Define Principal Plane and Principal Stress.

Q.2 (a) A steel bar 20 mm in diameter and 3.5 m long is subjected to an axial tensile
load of 50 KN. The increase in length is 1.75 mm. Calculate the stress and
strain and Young’s Modulus. 03

OR

(a) A brass bar 20 mm diameter and 8 m length is rigidly fixed. Calculate the
temperature stress induced when it is heated from 20° C to 50° C. E = 2 x 105
N/mm2 and α = 10 x 10 -6
/ 0C 03

(b) A rectangular beam having 150 mm x 120 mm cross section carries UDL of
8 KN/m. Find out the span of the simply supported beam if allowable bending
stress is 120 N/mm2. 03

OR

(b) A UDL of 20 KN/m is acting on a cantilever beam of length 3 m. Calculate the
slope and deflection of the beam at the free end. E = 2 x 105 N/mm2 and
I = 2 x 106 mm4 03

(c) A beam is loaded as shown in the Figure 1. Calculate the shear force and
bending moment at various points and draw the shear force and bending
moment diagram. 04

OR

(c) A beam is loaded as shown in the Figure 2. Calculate the shear force and
bending moment at various points and draw the shear force and bending
moment diagram. 04

(d) Draw the shear stress distribution diagram for (i) Rectangular section (ii) T
Section (iii) I section (iv) Circular section. 04

OR

(d) State and explain the parallel axes theorem and perpendicular axes theorem. 04

Q.3 (a) Write down the assumptions made in the simple bending theory. 03

OR

(a) A cantilever beam is of 2 m span having its cross section 200 mm x 300 mm. If maximum bending stress is not to exceed 10 N/mm2, find the value of point load that can be placed at its free end. 03

(b) Define slope and deflection of beam. 03

OR

(b) A rectangular column of Mild Steel of size 200 mm x 300 mm is fixed at both ends. The length of the column is 4 m. Calculate Euler’s load.
Take E = 2 x 105 N/mm2 03

(c) Calculate the M.I. of L section of size 90 mm x 90 mm x 8 mm. 04

OR

(c) Define Section Modulus, Polar Moment of Inertia, Neutral axis and Point of contraflexure. 04

(d) Draw the core of rectangular, hollow rectangular, circular and hollow circular sections. 04

OR

(d) A square column of 300 mm side is carrying a vertical load of 60 KN at eccentricity of 100 mm on x-x axis. Determine the minimum and maximum stress intensities in the section. Also, draw the stress distribution diagram. 04

Q.4 (a) Determine the diameter of shaft which will transmit 100 KW at 150 RPM. The maximum shear stress is limited to 50 N /mm2. 03

OR

(a) Find the power a solid shaft of 40 mm diameter can transmit at 150 RPM, if the maximum shear stress is not to exceed 60 N/mm2 03

(b) A rectangular column 200 mm x 400 mm in size carrying 10 KN load on axis bisecting the thickness with eccentricity of 50 mm. Calculate maximum and minimum stresses in the material. 04

OR

(b) Draw the different end conditions of column with effective length. 04

(c) Define strain energy and modulus of resilience. An axial pull of 50 KN is suddenly applied to a steel bar 2 m long and 1000 mm2 in cross sectional area. If modulus of elasticity of steel is 200 KN/mm2, find the strain energy stored in the bar. Also find the modulus of resilience. 07

Q.5 (a) At a point in a strained material two mutually perpendicular principal tensile stresses of 80 N /mm2 and 40 N/mm2 are acting. Find the normal, tangential and resultant stresses on a plane making 20° with the major principal plane. 04

(b) Write a note on different types of loads, supports and beams with neat sketches 04

(c) Write a short note on the applications of Aluminum and its alloys. 03

(d) What is the limitation of Euler’s formula for calculating safe load in columns and struts? Name any other formula for calculation of safe load in columns. 03

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