Strength of Materials

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Strength of Materials

Vikas® Publishing House Pvt Ltd

S S BhavikattiEmeritus Professor,

BVB College of Engineering and Technology, Hubli, Karnataka

(as per revised syllabus of full time Diploma Engineering course of West Bengal State Council of Technical Education)

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Published in 2014ISBN: 978 9325 975545

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Acknowledgements are due to some of the copyright holders from whom permission is still awaited. Any omission will be corrected in future editions and copyright duly acknowledged.

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Printed in India

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Preface

‘Strenth of materials’ is a basic course for students of all branches of engineering. In this subject a student develop concept of how load acting on a structure get transferred to support and develop the skill of finding the internal forces to be resisted by the members of the structure. The students should have clear ideas about the units to be used. The book is written in SI units and standard notations used in Indian National codes.

The book is written as per West Bengal Polytechnic syllabus. It can serve as a good text book for polytechnique students of West Bengal state. Apart from them it may be a useful book for polytechnic students of other states also, since there may not be much difference between the syllabi of various state polytechniques.

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Syllabus

WEST BENGAL STATE COUNCIL OF TECHNICAL EDUCATION

FULL–TIME DIPLOMA COURSES IN ENGINEERING & TECHNOLOGY

Second semester

Unit 1 Mechanical Properties of Materials, Simple stresses & Strain

Definition of Elasticity, plasticity, ductility, malleability, hardness, fatigue, creep, brittleness. Types of loads, Types of stress – normal stress (tensile stress & compressive stress) & shear stress, Strain – longitudinal & lateral strain, Poisson ratio, Hooke’s law, Young’s modulus, Stress – strain curves for ductile material (MS) and brittle material (CI) – discussion on salient points on the stress – strain diagram, working stress, Factor of safety. (Simple problems on normal stresses and longitudinal strain, no discussion on composite section). Direct shear stress, Single shear, double shear, shear strain, modulus of rigidity. (simple Problems on direct shear in riveted joint, punching press, cotter pin, lap welded joint) Thermal stress & strain of uniform section (no discussion on composite section) simple problem. Thin cylindrical shell subjected to internal pressure – hoop stress – longitudinal stress. Simple problem.

Unit 2 Shear Force & Bending Moment

Definition of Shear force & bending moment, sign convention, Relation between shear force & bending moment, Shear force and bending moment diagrams for simply supported beam, overhanging beam and cantilever subjected to point loads & uniformly distributed load, location of point of contraflexure. (Problems to be based on simply supported beam, overhanging beam & cantilever beam).

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viii Syllabus

Unit 3 Moment of Inertia

Definition of area and mass moment of inertia, Parallel and perpendicular axes theorem (no derivation), Moment of inertia about centroidal axis of solid sections – Square, rectangular, circular, semicircular, Triangular section, Hollow sections – square, rectangular and circular cross section only. Moment of Inertia of angle section, channel, Tee, I section about centroidal axis and any other axis parallel to centroidal axis. Polar moment of inertia of circular solid and hollow section. Problems on concerned cross sections.

Unit 4 Deflection of Beam

Concepts of deflection, Maximum deflection and slope of simple supported beam subjected to point load at mid span and / or uniformly distributed load on entire span and cantilever beam subjected to point load at free end and / or uniformly distributed load on entire length. (no deduction). Simple problem on maximum deflection and slope of beam.

Unit 5 Columns & Struts

Definitions of column & strut – Buckling of column, Concept of equivalent length as per different end conditions, Critical load/ buckling load, safe load, Euler’s & Rankine’s formulae for critical/ buckling load for columns. Simple problem.

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Content

Preface vSyllabus Vii

CHAPTER 1 INTRODUCTION 3

1.1 Mechanical Properties of Materials 3 1.2 Types of Loads 6

CHAPTER 2 SIMPLE STRESSES AND STRAINS 11

2.1 Stress 11 2.2 Normal Stress 12 2.3 Shear Stress 13 2.4 Strain 13 2.5 Poisson’s Ratio 14 2.6 Stress Strain Relation 14 2.7 Percentage Elongation and Percentage Reduction in Area 16 2.8 Factor of Safety 17 2.9 Hooke’s Law 17 2.10 Extension/Shortening of a Bar 18 2.11 Bars With Cross-Sections Varying in Steps 22 2.12 Bars With Continuously Varying Cross-Sections 25 2.13 Bars Subjected to Varying Loads 29 2.13 Direct Shear Stress 35 2.14 Shear Stresses in Fillet Welds 39 2.15 Modulus of Rigidity 41 2.16 Relationship Between Modulus of Elasticit and Modulus of Rigidity 41 2.17 Thermal Stresses and Strains 43

CHAPTER 3 THIN CYLINDRICAL SHELLS 55

3.1 Assumptions 55 3.2 Circumferencial Stress f1 55 3.3 Longitudinal Stress f2 56 3.4 Changes in Dimensions of Cylinder 57

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x Content

3.5 Riveted Cylinders 61

CHAPTER 4 SHEAR FORCE AND BENDING MOMENT 69

4.1 Shear Force and Bending Moment 69 4.2 Sign Convention 71 4.3 Relationship Between Load Intensity, Shear Force and Bending Moment 71 4.4 Shear Force and Bending Moment Diagrams 72 4.5 SFD and BMD for Standared Cases 73 4.6 SFD and BMD for Beams Subjected to Various Loads 78 4.7 Short Cut Procedure 85

CHAPTER 5 MOMENT OF INERTIA 105

5.1 Area Moment of Inertia 105 5.2 Unit of Moment of Inertia 106 5.3 Polar Moment of Inertia 106 5.4 Radius of Gyration 106 5.5 Mass Moment of Inertia 107 5.6 Theorems of Moment of Inertia 107 5.7 Centroidal Moment of Inertia of Solid Sections 108 5.8 M.I of Hollow Sections 112 5.9 M.I of Built-Up Sections 115 5.10 Use of Moment of Inertia in Finding Stresses in Beams 123

CHAPTER 6 DEFLECTION OF BEAMS 149

6.1 Differential Equation for Deflection 149 Double Integration Method 151 6.2 Slope and Deflection in a Cantilever Bean Subjected to Concentrated Load at Free End 152 6.3 A Cantilever Subjected to UDL 153 6.4 Simply Supported Beam Subjected to a Central Concentrated Load 154 6.5 Simply Supported Beam Subjected to Uniformly Distributed Load 155

CHAPTER 7 COLUMNS AND STRUTS 165

7.1 Bucking Phenomenon 165 7.2 Short, Medium and Long Columns 166 7.3 Euler’s Buckling Load for Long Columns 166 7.4 Equivalent Length 172 7.5 Limitations of Euler’s Theory 173 7.6 Rankine’s Formula 174

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UNIT - I

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Introduction

Mechanical components and structural elements like bars, tubes, beams, columns, trusses, cylinders, spheres, shafts etc. are used for the benefit of mankind. The elements may be made up of timber, steel, copper, aluminium, concrete or any other material. They should be designed so as to resist safely the expected load in their service period. In transferring the loads from their point of application to the supports, they develop resisting forces and undergo deformations. To decide size and shape of these elements, one should know how to determine those internal stresses developed and the deformation the structural elements undergoes. In the subject strength of material the method of estimating internal resisting forces and deformations of the elements is covered. The first step in learning strength of materials is to understand various mechanical properties of the materials and the type of loads on the element.

LEARNING OBJECTIVES

After studying this chapter the students should• Clearly understand mechanical properties of various metals.• Know various types of loads on structural / mechanical elements.

1.1 MECHANICAL PROPERTIES OF MATERIALS

In this article, the following properties of a material are defined and briefly explained.• Rigid body

• Elasticity

• Plasticity

• Brittleness

• Hardness

• Weldability

• Machinability

• Ductility

• Malleability

• Fatigue

• Creep

• Stiffness

1C H A P T E R

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Strength Of Materials

Publisher : SChand Publications ISBN : 9789325975545 Author : S S Bhavikatti

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