Sample Solutions Manual for Mechanics of Materials 1st Edition Clarence Silva pdf PDF

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Authors: Clarence W. de Silva
Published: CRC 2013
Edition: 1st
Pages: 256
Type: pdf
Size: 22MB
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FOLFNKHUHWRGRZQORDG

SOLUTIONS MANUAL FOR

MECHANICS OF MATERIALS

by

Clarence W. de Silva

Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

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FOLFNKHUHWRGRZQORDG

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2014 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: 20130709 International Standard Book Number-13: 978-1-4398-7738-8 (Ancillary) 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. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

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FOLFNKHUHWRGRZQORDG CONTENTS Preface

v

Chapter 1

MECHANICS OF MATERIALS

1

Chapter 2

STATICS—A REVIEW

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Chapter 3

STRESS

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Chapter 4

STRAIN

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Chapter 5

MECHANICAL PROPERTIES OF MATERIALS

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Chapter 6

AXIAL LOADING

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Chapter 7

TORSION IN SHAFTS

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Chapter 8

BENDING IN BEAMS

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Chapter 9

STRESS AND STRAIN TRANSFORMATIONS

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FOLFNKHUHWRGRZQORDG PREFACE This manual is prepared primarily to assist the instructors who use the textbook Mechanics of Materials. It provides complete solutions to the end of chapter problems of the book. Mechanics of Materials is an introductory book on the subject. It serves as both a textbook and a reference book for engineering students and practicing professionals. As a textbook it is suitable for the first course on the subject. Mechanics of Materials deals with the internal effects (primarily stresses and strains) in a deformable solid body due to external loads acting on it. The subject is also known as “Strength of Materials” or “Mechanics of Deformable Solids.” More advanced material on the subject is found under such headings as “Theory of Elasticity” and “Continuum Mechanics.” The subject is useful in a variety of engineering areas including mechanical, civil, mining, materials, electrical, aerospace, and biomechanical engineering. It provides theory, formulas, methods, and techniques that are directly applicable in the modeling, analysis, design, testing, and regulating of engineering devices and structures such as automobiles, airplanes, robots, machine tools, engines, bridges, elevated guideways, and buildings. The textbook consists of 9 chapters and 5 appendices. It is an outgrowth of the author’s experience in teaching an undergraduate course in Mechanics of Materials for large classes of students in Mechanical, Civil, Manufacturing, Materials and Mineral Engineering and Engineering Physics, and in teaching other courses in Statics, Dynamics, Modeling, Vibration, Instrumentation, Testing, and Design. Practical considerations, design issues, and engineering techniques are presented throughout the book. A simplified and snap-shot style is used in presenting more advanced theory and concepts. The book is concise, avoiding unnecessarily lengthy and uninteresting discussions, for easy reference and comprehension. To maintain clarity and the focus and to maximize the usefulness of the book, the author presents the material in a manner that is convenient and useful to anyone with a basic engineering background.

Clarence W. de Silva Vancouver, Canada

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Chapter 1:FOLFNKHUHWRGRZQORDG MECHANICS OF MATERIALS Solution 1.1 Mechanics of materials mainly concerns developing relationships between the “internal” effects, such as stresses and strains caused by external loads acting on a deformable body/structure. It is important in engineering because it is fundamental in the design and development of engineering systems. In particular, a mechanical design may concern such capabilities as strength and flexibility (deformation) of the system. Strength is governed by the maximum stress the critical components in the system can withstand. This depends on the allowable stress (yield stress or ultimate stress). Yield stress is the stress beyond which the component suffers irreversible (permanent) deformation. Ultimate stress is the stress at which the component fails (fractures). Normally, a factor of safety is used with respect to these limiting stresses, in the design, because it is not desirable for a mechanical structure to operate very close to its ultimate stress or even yield stress and due various factors of uncertainty it is not possible to exactly know the most critical component and its locations of possible failure. In some mechanical designs, level of deformation is included as a design specification. Examples include allowable movements of a vehicle suspension systems, bridges, and overhead guideways; movements of electrical components such as circuit-breakers, relays, and switches. The subject Mechanics of materials has wide application practically all fields of engineering, such as in mechanical engineering, mining engineering, civil engineering, biomedical, and electrical and electronic engineering.

Solution 1.2  Archimedes Biography: Archimedes of Syracuse (c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors. Contribution: This treatise was thought lost until the discovery of the Archimedes Palimpsest in 1906. In this work Archimedes uses infinitesimals, and shows how breaking up a figure into an infinite number of infinitely small parts can be used to determine its area or volume. Archimedes may have considered this method lacking in formal rigor, so he also used the method of exhaustion to derive the results. As with The Cattle Problem, The Method of Mechanical Theorems was written in the form of a letter to Eratosthenes in Alexandria.  Da Vinci Biography: Leonardo da Vinci (1452-1519) was born in Florence, Italy, and was a prestigious artist, inventor, engineer and scientist. Throughout his lifetime, he also lived in Milan, Bologna,

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Rome and Venice. Despite being Italian, he spent the last years of his life in a house that he was FOLFNKHUHWRGRZQORDG given in France. Contribution: Leonardo da Vinci used the concept of gears and torque in his inventions. In doing so, he created the concept of moments, which are very important in modern day statics and in the mechanics of materials.  Galileo Biography: Galileo Galilei 15 February 1564– 8 January 1642) was an Italian physicist, mathematician, astronomer and philosopher who played a major role in the Scientific Revolution. Galileo was born in Pisa (then part of the Duchy of Florence), Italy, and the first of six children of Vincenzo Galilei, a famous lutenist, composer, and music theorist, and Giulia Ammannati. Four of their six children survived infancy, and the youngest Michelangelo (or Michelagnolo) also became a noted lutenist and composer. Galileo's full name was Galileo di Vincenzo Bonaiuti de' Galilei. At the age of 8, his family moved to Florence, but he was left with Jacopo Borghini for two years. He then was educated in the Camaldolese Monastery at Vallombrosa, 35 km southeast of Florence. Contribution: Galileo's theoretical and experimental work on the motions of bodies, along with the largely independent work of Kepler and René Descartes, was a precursor of the classical mechanics developed by Sir Isaac Newton.  Newton Biography: Sir Isaac Newton (4 January 1643 – 31 March 1727 [OS: 25 December 1642 – 20 March 1726]) was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is considered by many scholars and members of the general public to be one of the most influential people in human history. Contribution: His 1687 publication of the Philosophiæ Naturalis Principia Mathematica (usually called the Principia) is considered to be among the most influential books in the history of science, laying the groundwork for most of classical mechanics. In this work, Newton described universal gravitation and the three laws of motion which dominated the scientific view of the physical universe for the next three centuries. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws by demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the Scientific Revolution. Newton built the first practical reflecting telescope and developed a theory of colour based on the observation that a prism decomposes white light into the many colours that form the visible spectrum. He also formulated an empirical law of cooling and studied the speed of sound. In mathematics, Newton shares the credit with Gottfried Leibniz for the development of the differential and integral calculus. He also demonstrated the generalized binomial theorem, developed Newton's method for approximating the roots of a function, and contributed to the study of power series. Newton remains uniquely influential to scientists, as demonstrated by a 2005 survey of members of Britain's Royal Society asking who had the greater effect on the history of science and made the greater contribution to humankind, Newton or Albert Einstein. Royal Society scientists deemed Newton to have made the greater overall contribution on both.  Bernoulli

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Biography: Jacob Bernoulli (also FOLFNKHUHWRGRZQORDG known as James or Jacques) (27 December 1654 – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. Jacob Bernoulli was born in Basel, Switzerland. Following his father's wish, he studied theology and entered the ministry. But contrary to the desires of his parents, he also studied mathematics and astronomy. He traveled throughout Europe from 1676 to 1682, learning about the latest discoveries in mathematics and the sciences. This included the work of Robert Boyle and Robert Hooke. Contribution: Euler–Bernoulli beam theory (also known as engineer's beam theory, classical beam theory or just beam theory) is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case for small deflections of a beam which is subjected to lateral loads only. It is thus a special case of Timoshenko beam theory which accounts for shear deformation and is applicable for thick beams. It was first enunciated circa 1750, but was not applied on a large scale until the development of the Eiffel Tower and the Ferris wheel in the late 19th century. Following these successful demonstrations, it quickly became a cornerstone of engineering and an enabler of the Second Industrial Revolution. Additional analysis tools have been developed such as plate theory and finite element analysis, but the simplicity of beam theory makes it an important tool in the sciences, especially structural and mechanical engineering.  Hooke Biography: Robert Hooke FRS (18 July 1635 – 3 March 1703) was an English natural philosopher, architect and polymath who played an important role in the scientific revolution, through both experimental and theoretical work. His adult life comprised three distinct periods: as a brilliant scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but eventually becoming ill and party to jealous intellectual disputes. These issues may have contributed to his relative historical obscurity (section: Personality and disputes). Hooke studied at Wadham College during the Protectorate where he became one of a tightly-knit group of ardent Royalists centered on John Wilkins. Here he was employed as an assistant to Thomas Willis and to Robert Boyle, for whom he built the vacuum pumps used in Boyle's gas law experiments. He built some of the earliest Gregorian telescopes, observed the rotations of Mars and Jupiter, and, based on his observations of fossils, was an early proponent of biological evolution. He investigated the phenomenon of refraction, deducing the wave theory of light, and was the first to suggest that matter expands when heated and that air is made of small particles separated by relatively large distances. He performed pioneering work in the field of surveying and map-making and was involved in the work that led to the first modern plan-form map, though his plan for London on a grid system was rejected in favor of rebuilding along the existing routes. He also came near to deducing that gravity follows an inverse square law, and that such a relation governs the motions of the planets, an idea which was subsequently developed by Newton.[4] Much of Hooke's scientific work was conducted in his capacity as curator of experiments of the Royal Society, a post he held from 1662, or as part of the household of Robert Boyle. Contribution: Hooke is known for his law of elasticity (Hooke's law), his book, Micrographia, and for first applying the word "cell" to describe the basic unit of life. Even now there is much less written about him than might be expected from the sheer industry of his life: he was at one

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time simultaneously the curator of FOLFNKHUHWRGRZQORDG experiments of the Royal Society and a member of its council, Gresham Professor of Geometry and a Surveyor to the City of London after the Great Fire of London, in which capacity he appears to have performed more than half of all the surveys after the fire. He was also an important architect of his time, though few of his buildings now survive and some of those are generally misattributed, and was instrumental in devising a set of planning controls for London whose influence remains today. Allan Chapman has characterized him as "England's Leonardo."  Euler Biography: Leonhard Euler (15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. Leonhard Euler was a Swiss mathematician and physicist. Euler studied infinitesimal calculus and graph theory and made a bunch of important discoveries. Additionally, he has done some work in mechanics, fluid dynamics, optics and astronomy. It is arguable that Euler is one of the best mathematicians of all time. Contribution: Euler worked in almost all areas of mathematics: geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory and other areas of physics. He is a seminal figure in the history of mathematics; if printed, his works, many of which are of fundamental interest, would occupy between 60 and 80 quarto volumes. Together with Daniel Bernoulli, Euler developed the Euler-Bernoulli equation, which simplifies the law of elasticity. This discovery was of utter importance in advancing engineering and mechanics. His papers on optics also helped develop the wave theory of light, which was proposed by Huygens.  D’Alembert Biography: Jean-Baptiste le Rond d'Alembert (16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist and philosopher. He was also co-editor with Denis Diderot of the Encyclopédie. Contribution: The wave equation is an important second-order linear partial differential equation of waves, such as sound waves, light waves and water waves. It arises in fields such as acoustics, electromagnetics, and fluid dynamics. Historically, the problem of a vibrating string such as that of a musical instrument was studied by Jean le Rond d'Alembert, Leonhard Euler, Daniel Bernoulli, and Joseph-Louis Lagrange.  Lagrange Biography: Joseph-Louis Lagrange (25 January 1736, Turin, Piedmont – 10 April 1813, Paris), born Giuseppe Lodovico (Luigi) Lagrangia, was an Italian-born mathematician and astronomer, who lived part of his life in Prussia and part in France, making significant contributions to all fields of analysis, to number theory, and to classical and celestial mechanics. On the recommendation of Euler and D'Alembert, in 1766 Lagrange succeeded Euler as the director of mathematics at the Prussian Academy of Sciences in Berlin, where he stayed for over twenty years, producing a large body of work and winning several prizes of the French Academy of Sciences. Lagrange's treatise on analytical mechanics (Mécanique Analytique, 4. ed., 2 vols. Paris: Gauthier-Villars et fils, 1888-89), written in Berlin and first published in 1788, offered the

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most comprehensive treatment of FOLFNKHUHWRGRZQORDG classical mechanics since Newton and formed a basis for the development of mathematical physics in the nineteenth century. Contribution: Lagrange made the papers: “Mécanique Analytique,” in which he introduced the law of virtual work. Using this law and ...