1. Four Point Bending

2. Other Types of Bending Bending by Eccentric LoadingCantilever 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 AxisConstant Curvature

9. Strain Analysis for Bending  = L’ – L = (  -y)  –  = -y   x =  / L = -y  -y   x | max = c   x = (-y  c)  x | max

10. Stress Distribution in Bending  x = (-y  c)  x | max = (-y/c)  m  m = Mc/I Neutral plane should pass through the centroid.

11. Stress/Strain Distribution in Beams under Pure Bending

12. Section Modulus and Bending Stiffness  m = Mc/I  x = (-y/c)  m {  x = -My/I Define Section Modulus as S = I/c Then  m = M/S Also  x = -y  -y  My/I = Ey/   = 1/  = M/EI (EI: Bending Stiffness) Note:  /L = P/EA,  /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