1 / 19

Four Point Bending

Four Point Bending. Other Types of Bending. Bending by Eccentric Loading. Cantilever Bending. Various Boundary Conditions of Beams. Features of Beam Deformation. Neutral Plane and Axis of Symmetry. Assumptions for Beam Theory. Kirchhoff Hypotheses--- The cross-sections remain

reya
Download Presentation

Four Point Bending

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Four Point Bending

  2. Other Types of Bending Bending by Eccentric Loading Cantilever Bending

  3. Various Boundary Conditions of Beams

  4. Features of Beam Deformation

  5. Neutral Plane and Axis of Symmetry

  6. Assumptions for Beam Theory • Kirchhoff Hypotheses--- • The cross-sections remain • a straight plane perpendi- • cular to the mid plane. • The vertical segments • are not stretched. Bernoulli-Euler Beams

  7. Deformation of Beams under Pure Bending

  8. Curvature under Pure Bending Neutral Axis Constant Curvature

  9. Strain Analysis for Bending ex = d / L = -y/r = -yk ex |max = c/r d = L’ – L = (r-y)q – rq = -yq ex = (-y/c) ex |max

  10. Stress Distribution in Bending sx = (-y/c) sx |max = (-y/c)sm Neutral plane should pass through the centroid. sm= Mc/I

  11. Stress/Strain Distribution in Beams under Pure Bending

  12. Section Modulus and Bending Stiffness { sm= Mc/I sx = (-y/c)sm sx= -My/I Define Section Modulus as S = I/c Then sm = M/S Also ex = -y/r = -yk My/I = Ey/r k = 1/r = M/EI (EI: BendingStiffness) Note: d/L = P/EA, f/L = T/GJ

  13. Beams with Irregular Cross-sections

  14. Stress Distribution in Beams with Irregular Cross-sections

  15. Asymmetric Bending of Symmetric Beams

  16. Pure Bending of Asymmetric Beams

  17. Composite Beams

  18. Stress Distribution in Composite Beams

  19. Bending Due to Eccentric Loading

More Related