Название: Engineering Mechanics 2: Strength of Materials: An introduction with many examplesАвтор: Christian Mittelstedt
Издательство: Springer
Год: 2023
Страниц: 328
Язык: английский
Формат: pdf (true), epub
Размер: 23.5 MB
This book follows the classical division of engineering mechanics as taught at universities in Germany and is devoted to strength of materials, i.e. the determination of stresses and of deformations in elastic bodies. The aim of this book is to provide students with a clear introduction and to enable them to formulate and solve engineering problems in this field. For this purpose, the book provides a number of examples.
In a solid (a so-called continuum) under load, a stress state will develop. Due to the load, deformations occur in the solid, thus displacements of the individual body points occur. Displacements are accompanied by strains, the so-called strain state is formed. For a three″ =dimensional body, the above quantities – displacements, strains, stresses – are described by the following set of equations under a given load and prescribed boundary conditions:
- Kinematic equations: The so-called kinematic equations establish a relationship between the displacements and the resulting strains.
- Constitutive equations: The so-called constitutive equations establish a relationship between the stresses and the strains. In the case of linear elasticity, the constitutive equations are described by Hooke’s law.
- Equilibrium conditions: Equilibrium must be ensured at every point of the solid under consideration.
The plane stress state is a very important and practically relevant simplification in the case of thin-walled plane structures loaded in their plane, the so-called disks. First, all the necessary basic equations describing the plane stress state are summarized. After that, the topic of stress transformation is discussed. It turns out that extremal normal stresses, the so-called principal stresses, occur under certain orientations of the coordinate system. Similarly, maximum shear stresses occur under certain directions. A very useful tool for the graphical interpretation of a plane stress state is the so-called Mohr’s stress circle. Students are enabled to formulate and solve simple problems in the plane stress state and to determine stress states under different orientations of the employed Cartesian coordinate system. In addition, students will learn how to analyze plane stress states using Mohr’s stress circle.
This book is intended for university students of mechanical engineering, civil engineering, mechanics, but also all other courses in which the contents of this book play a role.
Contents:
Introduction to linear elasticity – Plane stress state – Bars – Beams – Beam deflections – Shear stresses in beams – Torsion – Energy methods – Buckling of bars
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