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

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

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  1. 1
    Non-Uniform Bending

    This section discusses non-uniform bending of beams, where the bending...

  2. 1.1
    Introduction

    This section introduces the concept of non-uniform bending of beams,...

  3. 1.2
    Variation Of Σ In The Cross-Section

    This section discusses how the stress (σ) varies in the cross-section of...

  4. 2
    Variation Of Τ In The Cross-Sectional Plane

    This section discusses the variation of shear stress (τ) in the...

  5. 2.1

    The section discusses the concept of non-uniform bending in beams,...

  6. 2.2

    This section covers the concept of non-uniform bending of beams, detailing...

  7. 3
    Variation In Τ For Some Representative Cross-Sections

    This section explores the variations in shear stress (τ) across different...

  8. 3.1
    Rectangular Cross-Section

    This section discusses the distribution of shear stress in rectangular beams...

  9. 3.2
    Circular Cross-Section

    This section discusses the characteristics and calculations for shear stress...

  10. 3.3
    I-Beam Cross-Section

    This section discusses the characteristics of I-beam cross-sections,...

What we have learnt

  • Non-uniform bending occurs when the bending moment is not constant along the length of the beam.
  • The relationship between bending moment, curvature, and shear force is critical in analyzing beam behavior.
  • Shear stress varies across the cross-sections of beams and is influenced by the shape of the section.

Key Concepts

-- Bending Moment
The moment that causes a beam to bend, dependent on applied loads and their positions.
-- Curvature
A measure of how much a beam deviates from being straight due to bending.
-- Shear Force
The force acting perpendicular to the axis of a beam, causing internal shear stress.
-- Shear Stress
The stress component parallel to the cross-section of the material in a beam due to applied shear force.
-- First Moment of Area
A measure used to calculate the distribution of shear stress across a beam's cross-section.

Additional Learning Materials

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