Mechanics of materials

622 Pages·2012·44.801 MB·English

by  James M Gere, Barry J Goodno

PRINCIPAL UNITS USED IN MECHANICS
International System (SI)
Quantity
Unit Symbol Formula
Acceleration (angular) radian per second squared rad/s2
Acceleration (linear) meter per second squared m/s2
Area square meter m2
Density (mass) kilogram per cubic meter kg/m3
(Specific mass)
Density (weight) newton per cubic meter N/m3
(Specific weight)
Energy; work joule J N(cid:2)m
Force newton N kg(cid:2)m/s2
Force per unit length newton per meter N/m
(Intensity of force)
Frequency hertz Hz s(cid:3)1
Length meter m (base unit)
Mass kilogram kg (base unit)
Moment of a force; torque newton meter N(cid:2)m
Moment of inertia (area) meter to fourth power m4
Moment of inertia (mass) kilogram meter squared kg(cid:2)m2
Power watt W J/s
(N(cid:2)m/s)
Pressure pascal Pa N/m2
Section modulus meter to third power m3
Stress pascal Pa N/m2
Time second s (base unit)
Velocity (angular) radian per second rad/s
Velocity (linear) meter per second m/s
Volume (liquids) liter L 10(cid:3)3m3
Volume (solids) cubic meter m3
SELECTED PHYSICAL PROPERTIES
Property SI
Water (fresh)
weight density 9.81 kN/m3
mass density 1000 kg/m3
Sea water
weight density 10.0 kN/m3
mass density 1020 kg/m3
Aluminum (structural alloys)
weight density 28 kN/m3
mass density 2800 kg/m3
Steel
weight density 77.0 kN/m3
mass density 7850 kg/m3
Reinforced concrete
weight density 24 kN/m3
mass density 2400 kg/m3
Atmospheric pressure (sea level)
Recommended value 101 kPa
Standard international value 101.325 kPa
Acceleration of gravity
(sea level, approx. 45°latitude)
Recommended value 9.81 m/s2
Standard international value 9.80665 m/s2
SI PREFIXES
Prefix Symbol Multiplication factor
tera T 1012 (cid:4) 1 000 000 000 000.
giga G 109 (cid:4) 1 000 000 000.
mega M 106 (cid:4) 1 000 000.
kilo k 103 (cid:4) 1 000.
hecto h 102 (cid:4) 100.
deka da 101 (cid:4) 10.
deci d 10(cid:3)1 (cid:4) 0.1
centi c 10(cid:3)2 (cid:4) 0.01
milli m 10(cid:3)3 (cid:4) 0.001
micro (cid:5) 10(cid:3)6 (cid:4) 0.000 001
nano n 10(cid:3)9 (cid:4) 0.000 000 001
pico p 10(cid:3)12 (cid:4) 0.000 000 000 001
Note:The use of the prefixes hecto, deka, deci, and centi is not recommended in SI.
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Mechanics of
Materials
BRIEF EDITION,SI
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Mechanics of Materials
BRIEF EDITION,SI
James M. Gere
Late Professor Emeritus,Stanford University
Barry J. Goodno
Georgia Institute of Technology
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Mechanics of Materials, Brief Edition, SI © 2012Cengage Learning
James M. Gere and Barry J. Goodno
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1 2 3 4 5 6 7 13 12 11
Contents
James Monroe Gere ix
Preface—Brief Edition, SI x
Symbols xvi
Greek Alphabet xix
1 Tension,Compression,and Shear 3
1.1 Introduction to Mechanics of Materials 5
1.2 Normal Stress and Strain 6
1.3 Mechanical Properties of Materials 15
1.4 Elasticity, Plasticity, and Creep 24
1.5 Linear Elasticity, Hooke’s Law, and Poisson’s Ratio 27
1.6 Shear Stress and Strain 32
1.7 Allowable Stresses and Allowable Loads 43
1.8 Design for Axial Loads and Direct Shear 49
Chapter Summary & Review 55
Problems 57
2 Axially Loaded Members 89
2.1 Introduction 90
2.2 Changes in Lengths of Axially Loaded Members 90
2.3 Changes in Lengths Under Nonuniform Conditions 99
2.4 Statically Indeterminate Structures 106
2.5 Thermal Effects, Misfits, and Prestrains 115
2.6 Stresses on Inclined Sections 127
Chapter Summary & Review 139
Problems 141
3 Torsion 169
3.1 Introduction 170
3.2 Torsional Deformations of a Circular Bar 171
3.3 Circular Bars of Linearly Elastic Materials 174
v
vi CONTENTS
3.4 Nonuniform Torsion 186
3.5 Stresses and Strains in Pure Shear 193
3.6 Relationship Between Moduli of Elasticity Eand G 200
3.7 Transmission of Power by Circular Shafts 202
3.8 Statically Indeterminate Torsional Members 207
Chapter Summary & Review 211
Problems 213
4 Shear Forces and Bending Moments 233
4.1 Introduction 234
4.2 Types of Beams, Loads, and Reactions 234
4.3 Shear Forces and Bending Moments 239
4.4 Relationships Between Loads, Shear Forces,
and Bending Moments 248
4.5 Shear-Force and Bending-Moment Diagrams 253
Chapter Summary & Review 264
Problems 266
5 Stresses in Beams 279
5.1 Introduction 281
5.2 Pure Bending and Nonuniform Bending 281
5.3 Curvature of a Beam 282
5.4 Longitudinal Strains in Beams 284
5.5 Normal Stresses in Beams (Linearly Elastic Materials) 289
5.6 Design of Beams for Bending Stresses 302
5.7 Shear Stresses in Beams of Rectangular Cross Section 311
5.8 Shear Stresses in Beams of Circular Cross Section 321
5.9 Shear Stresses in the Webs of Beams with Flanges 324
5.10 Composite Beams 332
Chapter Summary & Review 347
Problems 350
6 Analysis of Stress and Strain 377
6.1 Introduction 379
6.2 Plane Stress 380
6.3 Principal Stresses and Maximum Shear Stresses 388
6.4 Mohr’s Circle for Plane Stress 398
6.5 Hooke’s Law for Plane Stress 415
6.6 Triaxial Stress 418
Chapter Summary & Review 422
Problems 425