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MECHANICS OF MATERIALS ® With Applications in Excel MECHANICS OF MATERIALS ® With Applications in Excel Bichara B. Muvdi Souhail Elhouar CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper Version Date: 20150603 International Standard Book Number-13: 978-1-4665-7071-9 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Muvdi, B. B. Mechanics of materials : with applications in Excel / authors, Bichara B. Muvdi and Souhail Elhouar. pages cm Includes bibliographical references and index. ISBN 978-1-4665-7071-9 1. Materials--Mechanical properties. 2. Materials--Data processing. 3. Microsoft Excel (Computer file) I. Elhouar, Souhail. II. Title. TA404.8.M88 2016 620.1’10285554--dc23 2015016936 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To our families for their patience and encouragement. Contents Preface Authors Chapter 1 Axial Loads 1.1 Introduction 1.2 Internal Axial Force 1.2.1 Concentrated Force 1.2.2 Sign Convention 1.2.3 Distributed Forces 1.3 Normal and Shearing Stresses 1.3.1 Normal Stress 1.3.2 Stress Element 1.3.3 Shearing Stress 1.3.4 Stresses on Inclined Planes 1.3.5 Units 1.3.6 Sign Convention 1.4 Normal Strain and Stress–Strain Diagrams 1.4.1 Normal Strain 1.4.2 Units 1.4.3 Sign Convention 1.4.4 Mechanical Properties 1.4.5 Design Considerations 1.5 Load-Deformation Relations 1.6 Statically Indeterminate Members 1.6.1 Temperature Effects *1.7 Stress Concentration *1.8 Impact Loading Review Problems Chapter 2 Torsional Loads 2.1 Introduction 2.2 Internal Torque 2.2.1 Concentrated Torque 2.2.2 Sign Convention 2.2.3 Distributed Torques 2.3 Stresses and Deformations in Circular Shafts 2.3.1 Shearing Strain 2.3.2 Sign Convention 2.3.3 Shearing Stress and Shearing Deformation 2.3.4 Material Properties in Shear 2.3.5 Stress Element 2.3.6 Stresses on Inclined Planes 2.4 Statically Indeterminate Shafts 2.5 Design of Power-Transmission Shafts 2.6 Stresses under Combined Loads 2.6.1 Hooke’s Law in Two Dimensions *2.7 Stress Concentration *2.8 Impact Loading *2.9 Shafts of Noncircular Cross Sections 2.9.1 Analytical Solutions 2.9.2 Experimental Solutions 2.9.3 Application to Torsion of a Long, Thin Rectangle 2.9.4 Special Cases 2.9.4.1 Narrow Circular Section with Thin Slit 2.9.4.2 Sections Composed of Narrow Rectangles 2.9.5 Application to Torsion of Thin-Walled Tubes *2.10 Elastoplastic Behavior Review Problems Chapter 3 Bending Loads: Stresses 3.1 Introduction 3.2 Internal Shear and Moment 3.2.1 Shear and Moment at Specified Positions 3.2.2 Sign Convention 3.2.3 Shear and Moment Functions: Shear and Moment Diagrams 3.3 Load, Shear, and Moment Relationships 3.4 Bending Stresses under Symmetric Loading 3.5 Shearing Stresses under Symmetric Loading 3.5.1 Longitudinal Surfaces Normal to Loads 3.5.2 Shear Flow 3.6 Stresses under Combined Loads 3.7 Allowable-Stress Design *3.8 Stress Concentration Review Problems *Chapter 4 Bending Loads: Additional Stress Topics 4.1 Introduction 4.2 Beams of Two or Three Materials Loaded Symmetrically 4.2.1 General Principles 4.2.2 Application to Reinforced Concrete 4.3 Bending Stresses under Unsymmetric Loading 4.3.1 Arbitrary Centroidal Axes 4.3.2 Principal Centroidal Axes 4.4 Thin-Walled Open Sections: Shear Center 4.4.1 Symmetric Bending 4.4.2 Unsymmetric Bending 4.5 Curved Beams 4.6 Elastoplastic Behavior: Plastic Hinge 4.6.1 Shape Factor 4.6.2 Plastic Hinge 4.7 Fatigue Review Problems Chapter 5 Bending Loads: Deflections under Symmetric Loading 5.1 Introduction 5.2 Moment–Curvature Relationship 5.3 Deflection: Two Successive Integrations 5.4 Derivatives of the Deflection Function 5.5 Deflection: Superposition 5.6 Deflection: Area–Moment 5.6.1 Moment Diagrams by Cantilever Parts 5.7 Statically Indeterminate Beams: Two Successive Integrations 5.8 Statically Indeterminate Beams: Superposition 5.9 Statically Indeterminate Beams: Area–Moment Review Problems *Chapter 6 Bending Loads: Additional Deflection Topics 6.1 Introduction 6.2 Deflection: Singularity Functions 6.3 Deflection: Castigliano’s Second Theorem 6.4 Deflection: Unsymmetric Bending Loads 6.5 Statically Indeterminate Beams: Singularity Functions 6.6 Statically Indeterminate Beams: Castigliano’s Second Theorem 6.7 Impact Loading Review Problems Chapter 7 Analysis of Stress 7.1 Introduction 7.2 Stress at a Point 7.3 Components of Stress 7.4 Plane-Stress Transformation Equations 7.4.1 Stresses on Inclined Planes 7.4.2 Principal Stresses 7.4.3 Maximum In-Plane Shearing Stress 7.5 Mohr’s Circle for Plane Stress 7.5.1 Construction of Mohr’s Circle 7.5.2 Principal Stresses and Maximum In-Plane Shearing Stress 7.5.3 Stresses on Inclined Planes *7.6 Three-Dimensional Stress Systems 7.6.1 Mohr’s Circle for Triaxial Stress Systems: Absolute Maximum Shearing Stress 7.7 Thin-Walled Pressure Vessels 7.7.1 Cylindrical Vessels 7.7.2 Spherical Vessels *7.8 Thick-Walled Cylindrical Pressure Vessels 7.8.1 Stresses 7.8.2 Deformations 7.8.3 Special Cases 7.8.3.1 Internal Pressure Only 7.8.3.2 External Pressure Only 7.8.3.3 Shrink-Fitting Operations 7.8.3.4 Internal Pressure on Thin-Walled Cylinders *7.9 Theories of Failure 7.9.1 Brittle Material 7.9.1.1 Maximum Principal Stress Theory 7.9.1.2 Mohr’s Theory 7.9.2 Ductile Materials 7.9.2.1 Maximum Shearing Stress Theory 7.9.2.2 The Energy of Distortion Theory Review Problems Chapter 8 Analysis of Strain 8.1 Introduction 8.2 Strain at a Point: Components of Strain 8.2.1 Units and Sign Conventions 8.3 Plane-Strain Transformation Equations 8.3.1 Principal Strains 8.3.2 Maximum In-Plane Shearing Strain 8.4 Mohr’s Circle for Plane Strain 8.4.1 Principal Strains and Maximum In-Plane Shearing Strain 8.4.2 Inclined Axes 8.4.3 Development of the Relation G = E/2(1 + μ) *8.5 Three-Dimensional Hooke’s Law 8.5.1 Summary of Hooke’s Laws in One and Two Dimensions 8.5.2 Hooke’s Law in Three Dimensions 8.5.3 Volume Change: Bulk Modulus of Elasticity 8.5.4 Strain Energy: Energy of Distortion *8.6 Mohr’s Circle for Three-Dimensional Strain Systems *8.7 Strain Measurements: Strain Rosettes Review Problems Chapter 9 Columns 9.1 Introduction 9.2 Stability of Equilibrium 9.2.1 Theoretical Background 9.2.2 Column Models 9.3 Euler’s Ideal-Column Theory 9.4 Effect of End Conditions 9.4.1 Critical Load for Column Fixed at One End and Free at the Other 9.4.2 Effective Length 9.5 Secant Formula 9.5.1 Eccentrically Loaded Pin-Ended Column 9.5.2 Maximum Deflection 9.5.3 Secant Formula 9.5.4 Initially Bent Pin-Ended Columns 9.6 Design of Centrically Loaded Columns 9.6.1 Inelastic Column Buckling 9.6.2 Empirical Equations 9.6.3 Structural Steel 9.6.3.1 Short and Intermediate Columns 9.6.3.2 Long Columns 9.7 Design of Eccentrically Loaded Columns 9.7.1 Allowable-Stress Method 9.7.2 Interaction Method Review Problems

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Mechanics of Materials: With Applications in Excel® covers the fundamentals of the mechanics of materials―or strength of materials―in a clear and easily understandable way. Each chapter explains the theory of the underlying principles and the applicable mathematical relations, offering examples
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by  Bichara B. Muvdi
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MECHANICS OF MATERIALS ® With Applications in Excel MECHANICS OF MATERIALS ® With Applications in Excel Bichara B. Muvdi Souhail Elhouar CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper Version Date: 20150603 International Standard Book Number-13: 978-1-4665-7071-9 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Muvdi, B. B. Mechanics of materials : with applications in Excel / authors, Bichara B. Muvdi and Souhail Elhouar. pages cm Includes bibliographical references and index. ISBN 978-1-4665-7071-9 1. Materials--Mechanical properties. 2. Materials--Data processing. 3. Microsoft Excel (Computer file) I. Elhouar, Souhail. II. Title. TA404.8.M88 2016 620.1’10285554--dc23 2015016936 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To our families for their patience and encouragement. Contents Preface Authors Chapter 1 Axial Loads 1.1 Introduction 1.2 Internal Axial Force 1.2.1 Concentrated Force 1.2.2 Sign Convention 1.2.3 Distributed Forces 1.3 Normal and Shearing Stresses 1.3.1 Normal Stress 1.3.2 Stress Element 1.3.3 Shearing Stress 1.3.4 Stresses on Inclined Planes 1.3.5 Units 1.3.6 Sign Convention 1.4 Normal Strain and Stress–Strain Diagrams 1.4.1 Normal Strain 1.4.2 Units 1.4.3 Sign Convention 1.4.4 Mechanical Properties 1.4.5 Design Considerations 1.5 Load-Deformation Relations 1.6 Statically Indeterminate Members 1.6.1 Temperature Effects *1.7 Stress Concentration *1.8 Impact Loading Review Problems Chapter 2 Torsional Loads 2.1 Introduction 2.2 Internal Torque 2.2.1 Concentrated Torque 2.2.2 Sign Convention 2.2.3 Distributed Torques 2.3 Stresses and Deformations in Circular Shafts 2.3.1 Shearing Strain 2.3.2 Sign Convention 2.3.3 Shearing Stress and Shearing Deformation 2.3.4 Material Properties in Shear 2.3.5 Stress Element 2.3.6 Stresses on Inclined Planes 2.4 Statically Indeterminate Shafts 2.5 Design of Power-Transmission Shafts 2.6 Stresses under Combined Loads 2.6.1 Hooke’s Law in Two Dimensions *2.7 Stress Concentration *2.8 Impact Loading *2.9 Shafts of Noncircular Cross Sections 2.9.1 Analytical Solutions 2.9.2 Experimental Solutions 2.9.3 Application to Torsion of a Long, Thin Rectangle 2.9.4 Special Cases 2.9.4.1 Narrow Circular Section with Thin Slit 2.9.4.2 Sections Composed of Narrow Rectangles 2.9.5 Application to Torsion of Thin-Walled Tubes *2.10 Elastoplastic Behavior Review Problems Chapter 3 Bending Loads: Stresses 3.1 Introduction 3.2 Internal Shear and Moment 3.2.1 Shear and Moment at Specified Positions 3.2.2 Sign Convention 3.2.3 Shear and Moment Functions: Shear and Moment Diagrams 3.3 Load, Shear, and Moment Relationships 3.4 Bending Stresses under Symmetric Loading 3.5 Shearing Stresses under Symmetric Loading 3.5.1 Longitudinal Surfaces Normal to Loads 3.5.2 Shear Flow 3.6 Stresses under Combined Loads 3.7 Allowable-Stress Design *3.8 Stress Concentration Review Problems *Chapter 4 Bending Loads: Additional Stress Topics 4.1 Introduction 4.2 Beams of Two or Three Materials Loaded Symmetrically 4.2.1 General Principles 4.2.2 Application to Reinforced Concrete 4.3 Bending Stresses under Unsymmetric Loading 4.3.1 Arbitrary Centroidal Axes 4.3.2 Principal Centroidal Axes 4.4 Thin-Walled Open Sections: Shear Center 4.4.1 Symmetric Bending 4.4.2 Unsymmetric Bending 4.5 Curved Beams 4.6 Elastoplastic Behavior: Plastic Hinge 4.6.1 Shape Factor 4.6.2 Plastic Hinge 4.7 Fatigue Review Problems Chapter 5 Bending Loads: Deflections under Symmetric Loading 5.1 Introduction 5.2 Moment–Curvature Relationship 5.3 Deflection: Two Successive Integrations 5.4 Derivatives of the Deflection Function 5.5 Deflection: Superposition 5.6 Deflection: Area–Moment 5.6.1 Moment Diagrams by Cantilever Parts 5.7 Statically Indeterminate Beams: Two Successive Integrations 5.8 Statically Indeterminate Beams: Superposition 5.9 Statically Indeterminate Beams: Area–Moment Review Problems *Chapter 6 Bending Loads: Additional Deflection Topics 6.1 Introduction 6.2 Deflection: Singularity Functions 6.3 Deflection: Castigliano’s Second Theorem 6.4 Deflection: Unsymmetric Bending Loads 6.5 Statically Indeterminate Beams: Singularity Functions 6.6 Statically Indeterminate Beams: Castigliano’s Second Theorem 6.7 Impact Loading Review Problems Chapter 7 Analysis of Stress 7.1 Introduction 7.2 Stress at a Point 7.3 Components of Stress 7.4 Plane-Stress Transformation Equations 7.4.1 Stresses on Inclined Planes 7.4.2 Principal Stresses 7.4.3 Maximum In-Plane Shearing Stress 7.5 Mohr’s Circle for Plane Stress 7.5.1 Construction of Mohr’s Circle 7.5.2 Principal Stresses and Maximum In-Plane Shearing Stress 7.5.3 Stresses on Inclined Planes *7.6 Three-Dimensional Stress Systems 7.6.1 Mohr’s Circle for Triaxial Stress Systems: Absolute Maximum Shearing Stress 7.7 Thin-Walled Pressure Vessels 7.7.1 Cylindrical Vessels 7.7.2 Spherical Vessels *7.8 Thick-Walled Cylindrical Pressure Vessels 7.8.1 Stresses 7.8.2 Deformations 7.8.3 Special Cases 7.8.3.1 Internal Pressure Only 7.8.3.2 External Pressure Only 7.8.3.3 Shrink-Fitting Operations 7.8.3.4 Internal Pressure on Thin-Walled Cylinders *7.9 Theories of Failure 7.9.1 Brittle Material 7.9.1.1 Maximum Principal Stress Theory 7.9.1.2 Mohr’s Theory 7.9.2 Ductile Materials 7.9.2.1 Maximum Shearing Stress Theory 7.9.2.2 The Energy of Distortion Theory Review Problems Chapter 8 Analysis of Strain 8.1 Introduction 8.2 Strain at a Point: Components of Strain 8.2.1 Units and Sign Conventions 8.3 Plane-Strain Transformation Equations 8.3.1 Principal Strains 8.3.2 Maximum In-Plane Shearing Strain 8.4 Mohr’s Circle for Plane Strain 8.4.1 Principal Strains and Maximum In-Plane Shearing Strain 8.4.2 Inclined Axes 8.4.3 Development of the Relation G = E/2(1 + μ) *8.5 Three-Dimensional Hooke’s Law 8.5.1 Summary of Hooke’s Laws in One and Two Dimensions 8.5.2 Hooke’s Law in Three Dimensions 8.5.3 Volume Change: Bulk Modulus of Elasticity 8.5.4 Strain Energy: Energy of Distortion *8.6 Mohr’s Circle for Three-Dimensional Strain Systems *8.7 Strain Measurements: Strain Rosettes Review Problems Chapter 9 Columns 9.1 Introduction 9.2 Stability of Equilibrium 9.2.1 Theoretical Background 9.2.2 Column Models 9.3 Euler’s Ideal-Column Theory 9.4 Effect of End Conditions 9.4.1 Critical Load for Column Fixed at One End and Free at the Other 9.4.2 Effective Length 9.5 Secant Formula 9.5.1 Eccentrically Loaded Pin-Ended Column 9.5.2 Maximum Deflection 9.5.3 Secant Formula 9.5.4 Initially Bent Pin-Ended Columns 9.6 Design of Centrically Loaded Columns 9.6.1 Inelastic Column Buckling 9.6.2 Empirical Equations 9.6.3 Structural Steel 9.6.3.1 Short and Intermediate Columns 9.6.3.2 Long Columns 9.7 Design of Eccentrically Loaded Columns 9.7.1 Allowable-Stress Method 9.7.2 Interaction Method Review Problems

Description:
Mechanics of Materials: With Applications in Excel® covers the fundamentals of the mechanics of materials―or strength of materials―in a clear and easily understandable way. Each chapter explains the theory of the underlying principles and the applicable mathematical relations, offering examples
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