Classical Beam Theories of Structural Mechanics

1. Front Matter

   Pages i-xiii

   PDF

2. Introduction to Continuum Mechanical Modeling

   • Andreas Öchsner

   Pages 1-5

3. Euler–Bernoulli Beam Theory

   • Andreas Öchsner

   Pages 7-66

4. Timoshenko Beam Theory

   • Andreas Öchsner

   Pages 67-104

5. Higher-Order Beam Theories

   • Andreas Öchsner

   Pages 105-131

6. Comparison of the Approaches

   • Andreas Öchsner

   Pages 133-140

7. Outlook: Finite Element Approach

   • Andreas Öchsner

   Pages 141-144

8. Answers to Supplementary Problems

   • Andreas Öchsner

   Pages 145-173

9. Back Matter

   Pages 175-186

   PDF

This book provides a systematic and thorough overview of the classical bending members based on the theory for thin beams (shear-rigid) according to Euler-Bernoulli, and the theories for thick beams (shear-flexible) according to Timoshenko and Levinson. The understanding of basic, i.e., one-dimensional structural members, is essential in applied mechanics. A systematic and thorough introduction to the theoretical concepts for one-dimensional members keeps the requirements on engineering mathematics quite low, and allows for a simpler transfer to higher-order structural members. The new approach in this textbook is that it treats single-plane bending in the x-y plane as well in the x-z plane equivalently and applies them to the case of unsymmetrical bending. The fundamental understanding of these one-dimensional members allows a simpler understanding of thin and thick plate bending members.

Partial differential equations lay the foundation to mathematically describe the mechanical behavior of all classical structural members known in engineering mechanics. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, these partial differential equations that describe the physical problem can be derived. Nevertheless, the fundamental knowledge from the first years of engineering education, i.e., higher mathematics, physics, materials science, applied mechanics, design, and programming skills, might be required to master this topic.

• Bending Members
• Frame Members
• Euler-Bernoulli Beam
• Timoshenko Beam
• Levinson Beam
• Shear-rigid beams
• Shear-flexible
• Single-plane bending

• Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen am Neckar, Germany

  Andreas Öchsner

Andreas Öchsner is Full Professor for Lightweight Design and Structural Simulation at Esslingen University of Applied Sciences, Germany. Having obtained a Dipl.-Ing. degree in Aeronautical Engineering at the University of Stuttgart (1997), Germany, he served as a research and teaching assistant at the University of Erlangen-Nuremberg from 1997 to 2003, while working to complete his Doctor of Engineering Sciences (Dr.-Ing.) degree. From 2003 to 2006, he was an Assistant Professor at the Department of Mechanical Engineering and Head of the Cellular Metals Group affiliated with the University of Aveiro, Portugal. He spent seven years (2007–2013) as a Full Professor at the Department of Applied Mechanics, Technical University of Malaysia, where he was also Head of the Advanced Materials and Structure Lab. From 2014 to 2017, he was a Full Professor at the School of Engineering, Griffith University, Australia, and Leader of the Mechanical Engineering Program (Head of Discipline and Program Director).

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