Mechanics of materials: with applications in Excel

941 Pages·2016·35 MB·English

by  Bichara B. Muvdi

MECHANICS OF MATERIALS
®
With Applications in Excel
MECHANICS OF MATERIALS
®
With Applications in Excel
Bichara B. Muvdi
Souhail Elhouar
CRC Press
Taylor & Francis Group
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Version Date: 20150603
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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
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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