Advisory Boards of quite a few national bodies dealing with engineering education. Advanced Mechanics of. SOLIDS Third Edition. L S Srinath Former Director. Read Advanced Mechanics of Solids: 3e book reviews & author details and more at Free delivery on by Prof L S Srinath (Author). out of 5 stars. Buy Advanced Mechanics of Solids: 3e on ✓ FREE SHIPPING on qualified orders.

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He is a distinguished alumnus of IIT, Chicago. Professor Srinath has authored several books and papers and has been on Advisory Boards of quite a few national bodies soliids with engineering education. No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise or stored in srinaath database or retrieval system without the prior written permission of the publishers. Sdinath program listings if any may be entered, stored and executed in a computer system, but they may not be reproduced for publication.

Ajay Shukla General Manager: Vibha Mahajan Sponsoring Editor: Surabhi Shukla Executive—Editorial Services: Sohini Mukherjee Senior Production Manager: P L Pandita General Manager: Michael J Cruz Product Manager: Rajender P Ghansela Asst. However, neither Tata McGraw-Hill nor its authors guarantee the accuracy or completeness of any information published herein, and neither Tata McGraw-Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information.

This work is published with the understanding that Tata McGraw-Hill and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought.

Typeset at Astral Pre Media Pvt. Analysis of Stress 1. Analysis of Strain 2. Bending of Beams 6. Thermal Stresses 9. Temperature Symmetrical about Wrinath 9. Beam Columns Introduction to Composite Mecuanics The second edition provided an opportunity to correct several typographical errors and wrong answers to some problems.

Also, in addition, based on many suggestions received, a chapter on wrinath materials was also added and this addition was well received.

## Advanced Mechanics of Solids

Since this is a second-level course addressed to senior level students, many suggestions were being received solidd add several specialized topics. While it was difficult to accommodate all suggestions in a book of this type, still, a few topics due to their splids needed to be included and a new edition became necessary. As in the earlier editions, the first five chapters deal with the general analysis of mechanics of deformable solids.

The contents of these chapters provide a firm foundation to the mechanics of deformable solids which will enable the student to analyse and solve a variety of strength-related design problems encountered in practice. The second reason is to bring into focus the assumptions made in obtaining several basic equations. Instances are many where equations presented in handbooks are used to solve practical problems without examining whether the conditions under which those equations were obtained are satisfied or not.

The treatment starts with Analysis of stress, Analysis of strain, and Stress— Strain relations for isotropic solids. These chapters afvanced quite exhaustive and include materials not usually found in standard books.

Chapter 4 dealing with Theories of Failure or Yield Criteria is a general departure from older texts. This treatment is brought earlier because, in applying any design equation in strength related problems, an understanding of the possible factors for failure, depending on the material properties, is acvanced desirable. Chapter 5 deals with energy methods, which is one of advacned important topics and hence, is discussed in great detail.

The discussions in this chapter are important because of their applicability to a wide variety of problems.

Several worked examples illustrate the applications of these theorems. This chapter also discusses the validity of Euler—Bernoulli hypothesis in the derivations of beam equations. Torsion is covered in great detail in Chapter 7. Torsion of circular, elliptical, equilateral triangular bars, thin-walled multiple cell sections, etc.

Another notable inclusion in this chapter is the torsion of bars with multiply connected sections which, lz spite of its importance, is not found in standard texts. Analysis of axisymmetric problems like composite tubes under internal and external pressures, rotating disks, shafts and cylinders can be found in Chapter 8.

Stresses and deformations caused in bodies due to thermal gradients need special attention because of their frequent occurrences. Usually, these problems are treated in books on Thermoelasticity.

The analysis of thermal stress problems are not any more complicated than the traditional problems discussed in books on Advanced Mechanics of Solids. Chapter 9 in this book covers thermal stress problems. Elastic instability problems are covered in Chapter In addition to topics on Beam Columns, this chapter exposes the student to the instability problem as an eigenvalue problem.

This is an important concept that a student has to appreciate. Energy methods as those of Rayleigh—Ritz, Timoshenko, use of trigonometric series, etc. Introduction to the mechanics sinath composites is found in Chapter Modern— day engineering practices and manufacturing industries make use of a variety of composites. This chapter provides a good foundation to this topic. Xdvanced subject material is a natural extension from isotropic solids to anisotropic solids.

Stress concentration and fracture are fo considerations in engineering design.

Using the theory-of-elasticity approach, problems in these aspects are discussed in books solely devoted to these. However, a good introduction to these important topics can be provided in a book of the present type.

Chapter 12 provides a fairly good coverage with a sufficient number of worked examples. Several practical problems can mchanics solved with confidence based on the treatment provided. While SI units are used in most of numerical mechanucs and problems, a few can advanxed found with kgf, meter and second units. This is done deliberately to make the student conversant with the use of both sets of units since in daily life, kgf is used for force and weight measurements.

In those problems where kgf units are used, their equivalents in SI units are also given.

The web supplements can be accessed at http: Their names are given below. Lastly, I wish to thank my family members for their patience, support and love given to me during the preparation of this manuscript. The starting point for discussion can be either the analysis of stress or the analysis of strain. In books on the theory of elasticity, one usually starts with the analysis of strain, which deals with the geometry of deformation without considering the forces that cause the deformation.

However, one is more familiar with forces, though the measurement of force is usually done through the measurement of deformations caused by the force.

Books on the strength of materials, begin with the analysis of stress. The concept of stress has already been introduced in the elementry strength of materials. In general, a structural member or a machine element will not possess uniform geometry of shape or size, and the loads acting on it will also be complex.

For example, an automobile crankshaft or a piston inside an engine cylinder or an aircraft wing are subject to loadings that are both complex as well as dynamic in nature. In such cases, one will have to introduce the concept of the state of stress at a point and its analysis, which will be the subject of discussion in this chapter. However, we shall not deal with forces that vary with time. It will be assumed that the matter of the body that is being considered is continuously distributed over its volume, so that if we consider a small volume element of the matter surrounding a point and shrink this volume, in the limit we shall not come across a void.

In reality, however, all materials are composed of many discrete particles, which are often microscopic, and when an arbitrarily selected volume element is shrunk, in the limit one may end up in a void. But in our analysis, we assume that the matter is continuously distributed. Such a body 2 Advanced Mechanics of Solids is called a continuous medium and the mechanics of such a body or bodies is called continuum mechanics.

In general, the body will be subjected to two types of forces— p body forces and surface forces. The F1 y F2 body forces act on each volume element of the body. Examples of this kind of force are the gravitational R3 force, the inertia force and the mag1 netic force.

The surface forces act P on the surface or area elements of 1 the body. When the area considered R1 lies on the actual boundary of the R2 F3 body, the surface force distribution o x is often termed surface traction. F r, are concentrated forces, z while p is a distributed force.

### Advanced Mechanics Of Solids – L. S. Srinath – Google Books

It is explicitly assumed that under the action of both body forces and surface forces, the body is in equilibrium. Let P be a point inside the afvanced with coordinates x, y, z.

Let the body be cut into two parts C and D by a plane passing through point P, as shown in Fig. If we consider the F1 free-body diagrams of C and D, then p F2 each part is in equilibrium under the action of the externally applied forces and the internally distributed forces C across the interface.

Hence the stress at srinaty point depends not only on the location of the point identified by adganced x, y, z but also on the plane passing through the point identified by direction cosines nx, ny, nz of the outward drawn normal.

Advanced Mechanics of Solids 4 1. The totality of all stress vectors acting on every possible plane passing through the point is defined to be the state of stress at the point. It is the knowledge of this state of stress that is of importance to a designer in determining the critical planes and the respective critical stresses. It will be shown in Sec. This can be resolved into two components, one along the normal n and the other perpendicular to n. We n have, therefore, the relation: