Solid Mechanics | 28. Timoshenko Beam Theory by Abraham | Learn Smarter
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Knowledge
28. Timoshenko Beam Theory

The chapter discusses the Timoshenko Beam Theory (TBT) in detail, comparing it with the Euler-Bernoulli Beam Theory (EBT) and exploring important concepts such as governing equations, shear strain, and buckling. The chapter presents mathematical formulations, focuses on practical applications, and examines conditions under which each theory should be applied. Furthermore, the chapter explains the phenomenon of beam buckling and provides methods for calculating critical buckling loads.

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Sections

  • 1

    Timoshenko Beam Theory

    The Timoshenko Beam Theory (TBT) enhances the Euler-Bernoulli beam theory by introducing cross-section rotation and shear deformation, allowing for a more accurate analysis of beam behavior under loading.

    Learning Practice

  • 1.1

    Introduction

    The introduction to Timoshenko Beam Theory (TBT) highlights the differences from Euler-Bernoulli Beam Theory (EBT) by emphasizing the independence of deflection and cross-section rotation.

    Learning Practice

  • 1.2

    Governing Equations

    This section explains the governing equations of Timoshenko Beam Theory, highlighting the relationship between deflection, cross-section rotation, shear stress, and bending curvature.

    Learning Practice

  • 1.3

    Example

    This section demonstrates how to apply Timoshenko Beam Theory (TBT) to solve a cantilever problem involving a transverse load.

    Learning Practice

  • 1.4

    When To Use Ebt/tbt?

    The section discusses when to apply Euler-Bernoulli Beam Theory (EBT) versus Timoshenko Beam Theory (TBT) based on structural conditions and resultant errors.

    Learning Practice

  • 2

    Buckling Of Beams

    This section discusses the critical phenomenon of buckling in beams, defining the buckling load and its significance in engineering design.

    Learning Practice

  • 2.1

    Introduction

    This section introduces the Timoshenko beam theory, contrasting it with the Euler-Bernoulli theory by emphasizing the independence of deflection and cross-section rotation.

    Learning Practice

  • 2.2

    Finding Buckling Load

    This section discusses how to determine the buckling load of a beam using Euler-Bernoulli theory, emphasizing the importance of this critical load in preventing structural failure.

    Learning Practice

References

ch28.pdf

Class Notes

Memorization

What we have learnt

  • Timoshenko Beam Theory intr...
  • The shear strain is connect...
  • Buckling load calculations ...

Final Test

Revision Tests