Winter 2016 Strength of Materials Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY
DIPLOMA ENGINEERING – SEMESTER – 3 • EXAMINATION – WINTER- 2016
Subject Code: 3331904 Date: 28-11-2016
Subject Name: Strength of Materials
Time: 10:30 AM TO 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. Use of programmable & Communication aids are strictly prohibited.
5. Use of only simple calculator is permitted in Mathematics.
6. English version is authentic.

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Q.1 Answer any seven out of ten. 14

1. Define Stress and Stain.

2. Define Bulk Modulus and Modulus of Rigidity.

3. Explain Section Modulus and Radius of Gyration.

4. Explain Hogging Moment and Sagging Moment.

5. Define Slope and Deflection in Beam.

6. Define Principal Plane and Principal Stress.

7. Write Values of Effective Length of column for various column end conditions.

8. Draw figure with dimensions of Core or Kernal of a Rectangular and Circular section.

9. Define Torque and Angle of Twist.

10. Draw the figure with dimensions of Specimens of Izod impact test and Charpy impact test.

Q.2 (a) A mild steel bar having Dia. 20 mm. and Length 1000 mm. is subjected to Axial Tensile force of 150 KN, find the final Length and Dia. of a bar.
Take Modulus of Elasticity = 2 X 105 MPa and Poisson’s Ratio = 0.25. 03

OR

(a) A mild steel bar having cross sectional area = 750 sq. mm. is subjected to Axial Forces as shown in Fig.-1. Find the deformation in the length of bar. Take Modulus of Elasticity = 2 X 105 MPa. 03

(b) Concrete Column having dimensions 300 mm. X 300 mm. is reinforced with 4 Steel bars of 20 mm Dia. Column is subjected to Axial Comp. force of 1000 KN. Find the stresses in Steel and Concrete. Take Modular Ratio = 25 03

OR

(b) A steel bar having Dia. 25 mm. and Length 4 m. is fixed at temperature of 20o C if temperature rise to 45o C find Temperature Stresses developed in bar for (1) No Yield condition and (2)Support yield by 1 mm.  Take Modulus of Elasticity = 2 X 105 MPa and Co-efficient of thermal expansion
= 12 X 10-6 /oC 03

(c) Explain in details Stress Strain Diagram for Mild Steel Specimen 04

OR

(c) Define (1) Strain Energy (2) Resilience (3) Proof Resilience and (4) Modulus of Resilience. 04

(d) Find Moment of Inertia Ixx and Iyy of a T- Section given in Fig.-2 04

OR

(d) A hollow rectangular section having size 250 mm. X 500 mm. and thickness is 25 mm. used as a cantilever beam having span 3 m. and loaded with UDL of 50 KN/m over entire span and Point Load 75 KN at free end. Find Slope and Deflection at free end. Take Modulus of Elasticity
 = 2 X 105 MPa. 04

Q.3 (a) Simply Supported beam having rectangular cross section of size 150 mm. X 300 mm. and span 6 m. is loaded with UDL of 30 KN/m over entire span. Find Slope at supports and deflection at mid span. Take Modulus of Elasticity = 2 X 10 5 MPa 03

OR

(a) Draw Bending Moment Diagram and Shear Force Diagram for a Cantilever Beam Shown in Fig.-3 03

(b) Write down Equation of Bending and explain each term 03

OR

(b) Write down Equation of Torsion and explain each term 03

(c) Draw Bending Moment Diagram and Shear Force Diagram for a Simply Supported Beam Shown in Fig.-4 04

OR

(c) Simply Supported Beam having span 4m. loaded with U.D.L. of 20 KN/m over entire span and central Point Load of 10 KN. If maximum permissible bending stress must not exceed 25 N/mm2 find cross sectional dimensions of Beam. Take Depth of Beam is twice the Breadth (d =2b). 04

(d) At a point in a strained material is subjected to mutually perpendicular tensile stresses of 200 Mpa and 100 Mpa. Determine the intensities of Normal, Tangential and Resultant Stresses on a plane inclined to 30o to the axis of the minor stress. 04

OR

(d) A cast Iron hollow section having 100 mm. external dia. And 75 mm. internal dia. Used as 3 m. long column. Using Rankine’s formula determine crippling load when both ends are fixed.
Take fc = 500 N/mm2 and α = 1/1600. 04

Q.4 (a) Rectangular column section 150 mm. X 250 mm. of Mild Steel is fixed at both ends having 6 m. length. Find the Euler’s crippling load. Take Modulus of Elasticity = 2 X 105 MPa 03

OR

(a) A 2 m. long shaft having dia. 300 mm. subjected to Torque of 200 KN-m. Find the Shear Stress and Angle of Twist in the Shaft Take Modulus of Rigidity = 8 X 104 MPa. 03

(b) At a point on a strained material is subjected to tensile stress of 200 Mpa and shear stress of 75 Mpa. Using Mohr Circle Diagram determine intensities of Normal, Tangential and Resultant stresses on a plane inclined to 60o to the axis of tensile stress. 04

OR

(b) A circular column of 300 mm. dia. is subjected an eccentric load of 100 KN with an eccentricity of 50 mm. Find the maximum and minimum stresses produced in column.
 Draw the stress diagram 04

(c) A rectangular column of 250 mm X 500 mm. is subjected to a point load 250KN acting at one of its outer edge. Calculate stresses at all corner of column. Also draw stress diagram. 07

Q.5 (a) Write note with sketches on (1) Types of Supports (2) Types of Loads and (3) Types of             Beams 04

(b) Explain Perpendicular Axes theorem and Parallel Axes Theorem 04

(c) Write factors affecting slope and deflection in a Beam 03

(d) Write classification of Engineering Materials 03

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