Mechanics and Strength of Materials

Vitor Dias da Silva

Mechanics and Strength

of Materials

ABC

Vitor Dias da Silva

Department of Civil Engineering

Faculty of Science & Technology

University of Coimbra

Polo II da Universidade - Pinhal de Marrocos

3030-290 Coimbra

Portugal

E-mail: vdsilva@dec.uc.pt

Library of Congress Control Number: 2005932746

ISBN-10 3-540-25131-6 Springer Berlin Heidelberg New York

ISBN-13 978-3-540-25131-6 Springer Berlin Heidelberg New York

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Preface To The English Edition

The ﬁrst English edition of this book corresponds to the third Portuguese

edition. Since the translation has been done by the author, a complete review

of the text has been carried out simultaneously. As a result, small improve-

ments have been made, especially by explaining the introductory parts of some

Chapters and sections in more detail.

The Portuguese academic environment has distinguished this book, since

its ﬁrst edition, with an excellent level of acceptance. In fact, only a small

fraction of the copies published has been absorbed by the school for which it

was originally designed – the Department of Civil Engineering of the Univer-

sity of Coimbra. This fact justiﬁes the continuous eﬀort made by the author to

improve and complement its contents, and, indeed, requires it of him. Thus,

the 423 pages of the ﬁrst Portuguese edition have now grown to 478 in the

present version. This increment is due to the inclusion of more solved and pro-

posed exercises and also of additional subjects, such as an introduction to the

fatigue failure of materials, an analysis of torsion of circular cross-sections in

the elasto-plastic regime, an introduction to the study of the eﬀect of the plas-

tiﬁcation of deformable elements of a structure on its post-critical behaviour,

and a demonstration of the theorem of virtual forces.

The author would like to thank all the colleagues and students of Engi-

neering who have used the ﬁrst two Portuguese editions for their comments

about the text and for their help in the detection of misprints. This has greatly

contributed to improving the quality and the precision of the explanations.

The author also thanks Springer-Verlag for agreeing to publish this book

and also for their kind cooperation in the whole publishing process.

Coimbra

V. Dias da Silva

March 2005

Preface to the First Portuguese Edition

The motivation for writing this book came from an awareness of the lack of

a treatise, written in European Portuguese, which contains the theoretical

material taught in the disciplines of the Mechanics of Solid Materials and

the Strength of Materials, and explained with a degree of depth appropriate

to Engineering courses in Portuguese universities, with special reference to

the University of Coimbra. In fact, this book is the result of the theoretical

texts and exercises prepared and improved on by the author between 1989-94,

for the disciplines of Applied Mechanics II (Introduction to the Mechanics of

Materials) and Strength of Materials, taught by the author in the Civil Engi-

neering course and also in the Geological Engineering, Materials Engineering

and Architecture courses at the University of Coimbra.

A physical approach has been favoured when explaining topics, sometimes

rejecting the more elaborate mathematical formulations, since the physical

understanding of the phenomena is of crucial importance for the student of

Engineering. In fact, in this way, we are able to develop in future Engineers

the intuition which will allow them, in their professional activity, to recognize

the diﬀerence between a bad and a good structural solution more readily and

rapidly.

The book is divided into two parts. In the ﬁrst one the Mechanics of

Materials is introduced on the basis of Continuum Mechanics, while the second

one deals with basic concepts about the behaviour of materials and structures,

as well as the Theory of Slender Members, in the form which is usually called

Strength of Materials.

The introduction to the Mechanics of Materials is described in the ﬁrst

four chapters. The ﬁrst chapter has an introductory character and explains

fundamental physical notions, such as continuity and rheological behaviour.

It also explains why the topics that compose Solid Continuum Mechanics

are divided into three chapters: the stress theory, the strain theory and the

constitutive law. The second chapter contains the stress theory. This theory is

expounded almost exclusively by exploring the balance conditions inside the

body, gradually introducing the mathematical notion of tensor. As this notion

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