Machine component analysis with MATLAB
First edition
Dan B. Marghitu
Mihai Dupac
Table of Contents
List of tables
- Tables in Chapter Four
List of figures
- Figures in Chapter One
- Figures in Chapter Two
- Figures in Chapter Three
- Figures in Chapter Four
- Figures in Chapter Five
- Figures in Chapter Six
Landmarks
Copyright
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ISBN: 978-0-12-804229-8
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Preface
Dan B. Marghitu; Mihai Dupac
This book is intended as a supplement for courses in machine component design and as a reference for mechanical engineers. The book uses MATLAB as a tool to analyze and solve machine component problems.
The solutions of the problems are obtained analytically and numerically using MATLAB. Many figures are generated with MATLAB programs. Specific functions dealing with machine components are created. The book will assist the undergraduate and advanced undergraduate students interested in machine element analysis. The project can be used for classroom instruction and it can be used for a self-study and can also be offered as distance learning.
The chapters of the book are: stress and deflection, fatigue failure, screws, rolling bearings, lubrication and sliding bearings, and spur gears.
Chapter One
Stress and deflection
Abstract
This chapter presents some of the key elements related to the theory of stress and strain, stress analysis and deformation of mechanical parts due to the action of forces (axial, bending, or combined loads) and moments exerted on them. The presented concepts cover the definition of normal and shear stress and strain, normal and shear components, principal stress components, Mohr's circle construction for two and three-dimensional state of stress and its graphical interpretation, Hook's law and Poisson's ratio, deflection and stress energy. Several problems presenting applications of the theory are solved analytically and numerically using MATLAB.
Keywords
Stress; Strain; Stress components; Deflection; Mohr's circle; Principal stresses; Stress energy
1.1 Stress components
In the design process, the uniform distribution of stresses is usually considered, that is, the results of forces and moments applied to an element represent pure shear or pure tension. If a force F (tension) acts at the ends of a straight bar its line of action incorporates the centroid of the section. If one piece is cut and removed from the bar (made of a homogeneous material), one can replace its effect through a force F=A uniformly distributed at the cut. The normal stress can then be expressed as
= F A ,
(1.1)
where A is the bar cross-sectional area. For an element in shear the uniform shear stress distribution is
= F A .
(1.2)
Stress elements represent a convenient way to show stresses acting at some point of a body. A three-dimensional Cartesian stress element with the normal stresses x , y , and z , and the shear stresses xz , zx , xy , yx , yz , and zy , is shown in A. For the shear stresses, using the static equilibrium, results in
x z = z x , y x = x y , z y = y z .