Solid Mechanics | 24. Non-uniform Bending by Abraham | Learn Smarter
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Knowledge
24. Non-uniform Bending

The discussion centers on non-uniform bending of beams, where the bending moment varies along the length of the beam, resulting in non-constant curvature. Key formulas relating bending moments to curvature and shear forces are derived, highlighting the conditions under which shear forces affect beam cross-sections. The chapter also provides insight into how shear stress varies across different beam cross-sections, including rectangular, circular, and I-beam shapes.

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Sections

  • 1

    Non-Uniform Bending

    This section discusses non-uniform bending of beams, where the bending moment varies along the length of the beam, leading to varying shear forces and stress distributions.

    Learning Practice

  • 1.1

    Introduction

    This section introduces the concept of non-uniform bending of beams, contrasting it with pure bending.

    Learning Practice

  • 1.2

    Variation Of Σ In The Cross-Section

    This section discusses how the stress (σ) varies in the cross-section of beams under non-uniform bending, highlighting the influence of local bending moments.

    Learning Practice

  • 2

    Variation Of Τ In The Cross-Sectional Plane

    This section discusses the variation of shear stress (τ) in the cross-section of beams under non-uniform bending conditions.

    Learning Practice

  • 2.1

    Assumption

    The section discusses the concept of non-uniform bending in beams, explaining how the bending moment varies along the length of a beam under different loading conditions.

    Learning Practice

  • 2.2

    Analysis

    This section covers the concept of non-uniform bending of beams, detailing the relationship between bending moments, shear forces, and stress distributions.

    Learning Practice

  • 3

    Variation In Τ For Some Representative Cross-Sections

    This section explores the variations in shear stress (τ) across different beam cross-sections under non-uniform bending conditions.

    Learning Practice

  • 3.1

    Rectangular Cross-Section

    This section discusses the distribution of shear stress in rectangular beams subjected to shear force, emphasizing the significance of the neutral axis.

    Learning Practice

  • 3.2

    Circular Cross-Section

    This section discusses the characteristics and calculations for shear stress in circular cross-sections under non-uniform bending.

    Learning Practice

  • 3.3

    I-Beam Cross-Section

    This section discusses the characteristics of I-beam cross-sections, particularly focusing on shear stress distribution and its implications in structural engineering.

    Learning Practice

References

ch24.pdf

Class Notes

Memorization

What we have learnt

  • Non-uniform bending occurs ...
  • The relationship between be...
  • Shear stress varies across ...

Final Test

Revision Tests