net 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⭈m Force newton N kg⭈m/s2 Force per unit length newton per meter N/m (Intensity of force) Frequency hertz Hz s⫺1 Length meter m (base unit) Mass kilogram kg (base unit) Moment of a force; torque newton meter N⭈m Moment of inertia (area) meter to fourth power m4 Moment of inertia (mass) kilogram meter squared kg⭈m2 Power watt W J/s (N⭈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⫺3 m3 Volume (solids) cubic meter m3 www.net 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 ⫽ 1 000 000 000 000.000 000 000 001 Note: The use of the prefixes hecto, deka, deci, and centi is not recommended in SI.net This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience.
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For your course and learning solutions, visit www. Purchase any of our products at your local college store or at our preferred online store www. Printed in Canada 1 2 3 4 5 6 7 13 12 11 www.net 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 2.2 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 3.2 Torsional Deformations of a Circular Bar 171 3.3 Circular Bars of Linearly Elastic Materials 174 v www.net vi CONTENTS 3.5 Stresses and Strains in Pure Shear 193 3.6 Relationship Between Moduli of Elasticity E and 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 4.2 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 5.2 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 6.3 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 www.net CONTENTS vii 7 Applications of Plane Stress (Pressure Vessels and Combined Loadings) 439 7.2 Spherical Pressure Vessels 440 7.3 Cylindrical Pressure Vessels 446 7.4 Combined Loadings 454 Chapter Summary & Review 470 Problems 471 8 Deflections of Beams 485 8.2 Differential Equations of the Deflection Curve 486 8.3 Deflections by Integration of the Bending-Moment Equation 492 8.4 Deflections by Integration of the Shear-Force and Load Equations 503 8.5 Method of Superposition 509 Chapter Summary & Review 518 Problems 519 9 Columns 531 9.2 Buckling and Stability 532 9.3 Columns with Pinned Ends 536 9.4 Columns with Other Support Conditions 547 Chapter Summary & Review 558 Problems 559 10 Review of Centroids and Moments of Inertia (Available on book website) 10.2 Centroids of Plane Areas 10.3 Centroids of Composite Areas 10.4 Moments of Inertia of Plane Areas 10.5 Parallel-Axis Theorem for Moments of Inertia 10.6 Polar Moments of Inertia 10.7 Products of Inertia 10.8 Rotation of Axes 10.9 Principal Axes and Principal Moments of Inertia Problems www.net viii CONTENTS References and Historical Notes R1 Appendix A Systems of Units and Conversion Factors A1 Appendix B Problem Solving B1 Appendix C Mathematical Formulas C1 Appendix D Properties of Plane Areas D1 Appendix E Properties of Structural-Steel Shapes E1 Appendix F Properties of Solid Timber F1 Appendix G Deflections and Slopes of Beams G1 Appendix H Properties of Materials H1 Answers to Problems 571 Index 585 www.net James Monroe Gere 1925–2008 James Monroe Gere, Professor Emeritus of Civil Engineering at Stanford University, died in Portola Valley, CA, on January 30, 2008. Jim Gere was born on June 14, 1925, in Syracuse, NY.
He joined the U. Army Air Corps at age 17 in 1942, serving in England, France and Germany. After the war, he earned undergraduate and master’s degrees in Civil Engineering from the Rensselaer Polytechnic Institute in 1949 and 1951, respectively. He worked as an instructor and later as a Research Associate for Rensselaer between 1949 and 1952.
He was awarded one of the first NSF Fellowships, and chose to study at Stanford. He received his Ph. in 1954 and was offered a faculty position in Civil Engineering, beginning a 34-year career of engaging his students in challenging topics in mechanics, and structural and earth- quake engineering. He served as Department Chair and Associate Dean of Engineering and in 1974 co-founded the John A.
Blume Earthquake Engineering Center at Stanford. In 1980, Jim Gere also became the founding head of the Stanford Committee on Earthquake Preparedness, which urged campus members to brace and strengthen office equipment, furniture, and other contents items that could pose a life safety hazard in the event of an earthquake. That same year, he was invited as one of the first foreigners to study the earthquake-devastated city of Tangshan, China. Jim retired from Stanford in 1988 but con- tinued to be a most valuable member of the Stanford community as he gave freely of his time to advise students and to guide them on various field trips to the California earthquake country.
Jim Gere was known for his outgoing manner, his cheerful personality and wonderful smile, his athleticism, and his skill as an educator in Civil Engineering. He authored nine text- books on various engineering subjects starting in 1972 with Mechanics of Materials, a text that was inspired by his teacher and mentor Stephan P. His other well-known text- books, used in engineering courses around the world, include: Theory of Elastic Stability, co-authored with S. Timoshenko; Matrix Analysis of Framed Structures and Matrix Algebra for Engineers, both co-authored with W.
Weaver; Moment Distribution; Earthquake Tables: Structural and Construction Design Manual, co-authored with H. Krawinkler; and Terra Non Firma: Understanding and Preparing for Earthquakes, co-authored with H. Respected and admired by students, faculty, and staff at Stanford University, Professor Gere always felt that the opportunity to work with and be of service to young people both inside and outside the classroom was one of his great joys. He hiked frequently and regu- larly visited Yosemite and the Grand Canyon national parks.
He made over 20 ascents of Half Dome in Yosemite as well as “John Muir hikes” of up to 50 miles in a day. In 1986 he Jim Gere in the Timoshenko hiked to the base camp of Mount Everest, saving the life of a companion on the trip. James Library at Stanford holding a was an active runner and completed the Boston Marathon at age 48, in a time of 3:13. copy of the 2nd edition of this James Gere will be long remembered by all who knew him as a considerate and loving text (photo courtesy of Richard man whose upbeat good humor made aspects of daily life or work easier to bear.
His last proj- Weingardt Consultants, Inc.) ect (in progress and now being continued by his daughter Susan of Palo Alto) was a book based on the written memoirs of his great-grandfather, a Colonel (122d NY) in the Civil War.net Preface—Brief Edition, SI Mechanics of materials is a basic engineering subject that, along with statics, must be understood by anyone concerned with the strength and physical performance of structures, whether those structures are man- made or natural. At the college level, mechanics of materials is usually taught during the sophomore and junior years.