stiffnesses. Chapter 4 treats a higher beam bending theory according to
Timoshenko. This theory considers the contribution of the shear force on the
deformation. Chapter 5 introduces a simple treatment of elasto-plastic bending
problems under the consideration of the thin beam formulation. The so-called
layered approach is applied to linear-elastic/ideal-plastic material behavior and is
restricted to monotonic loading.
All derivations in chapters two to four follow a common approach: based on the
three basic equations of continuum mechanics, i.e. the kinematics relationship, the
constitutive law, and the equilibrium equation, the partial differential equations,
which describe the physical problem, are presented. The finite difference method is
then used to derive approximate equations for the corresponding structural member.
In order to deepen the understanding of the derived equations and theories, each
technical chapter collects at its end supplementary calculation problems. A short
solution for each problem is included at the end of this book. It should be noted that
these short solutions contain major steps for the solution of the problem and not
only, for example, a numerical value for the final result. This should ensure that
students are able to successfully master these problems. I hope that students find
this book a useful complement to many classical textbooks. I look forward to
receiving their comments and suggestions.
Esslingen, Germany
Andreas Öchsner
October 2020
viii
Preface
Timoshenko. This theory considers the contribution of the shear force on the
deformation. Chapter 5 introduces a simple treatment of elasto-plastic bending
problems under the consideration of the thin beam formulation. The so-called
layered approach is applied to linear-elastic/ideal-plastic material behavior and is
restricted to monotonic loading.
All derivations in chapters two to four follow a common approach: based on the
three basic equations of continuum mechanics, i.e. the kinematics relationship, the
constitutive law, and the equilibrium equation, the partial differential equations,
which describe the physical problem, are presented. The finite difference method is
then used to derive approximate equations for the corresponding structural member.
In order to deepen the understanding of the derived equations and theories, each
technical chapter collects at its end supplementary calculation problems. A short
solution for each problem is included at the end of this book. It should be noted that
these short solutions contain major steps for the solution of the problem and not
only, for example, a numerical value for the final result. This should ensure that
students are able to successfully master these problems. I hope that students find
this book a useful complement to many classical textbooks. I look forward to
receiving their comments and suggestions.
Esslingen, Germany
Andreas Öchsner
October 2020
viii
Preface