Covers All 9 Chapters
SOLUTIONS + LECTURE SLIDES
, CONTENTS
Preface v
Chapter 1 MECHANICS OF MATERIALS 1
Chapter 2 STATICS—A REVIEW ?
Chapter 3 STRESS ?
Chapter 4 STRAIN ?
Chapter 5 MECHANICAL PROPERTIES OF MATERIALS ?
Chapter 6 AXIAL LOADING ?
Chapter 7 TORSION IN SHAFTS ?
Chapter 8 BENDING IN BEAMS ?
Chapter 9 STRESS AND STRAIN TRANSFORMATIONS ?
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, 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
@Seismicisolation
@Seismicisolation
, Chapter 1: 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,
@Seismicisolation
@Seismicisolation
SOLUTIONS + LECTURE SLIDES
, CONTENTS
Preface v
Chapter 1 MECHANICS OF MATERIALS 1
Chapter 2 STATICS—A REVIEW ?
Chapter 3 STRESS ?
Chapter 4 STRAIN ?
Chapter 5 MECHANICAL PROPERTIES OF MATERIALS ?
Chapter 6 AXIAL LOADING ?
Chapter 7 TORSION IN SHAFTS ?
Chapter 8 BENDING IN BEAMS ?
Chapter 9 STRESS AND STRAIN TRANSFORMATIONS ?
@Seismicisolation
@Seismicisolation
, 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
@Seismicisolation
@Seismicisolation
, Chapter 1: 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,
@Seismicisolation
@Seismicisolation
