1. ECIV 320 Structural Analysis I Internal Loadings in Structural Members Sections 4.1 – 4.5 Study all examples

2. Internal Loading in Structural Members Axial Loading PPP

3. Internal Loading in Structural Members P M V Flexure

4. Internal Loading in Structural Members Internal Loadings represent the resultant of stresses distributed over the cross section

5. Sign Convention P

7. Internal Loadings at Specified Point - PROCEDURE Support Reaction May need to be calculated before Internal Loadings Cut the Member Pass Section parpendicular to its axis at the specified point Attention: Keep all distributed loadings moments and forces in their exact location.

8. Internal Loadings at Specified Point-PROCEDURE Free Body Diagram Hint: Draw FBD of segment with the least number of loads Hint: Indicate Resultants in Positive Directions

9. Internal Loadings at Specified Point-PROCEDURE Equations of Equilibrium Hint: Sum moments at the section about centroid Hint: Numerical Results (+) FBD OK, (-) Internal Loadings Opposite Direction

10. EXAMPLE

11. Example

13. Shear and Moment Functions for Beams Design ! Variations of internal Shear and Moment along Axis Normal Force is usually ignored Exception: Compressive Axial Forces (Buckling) Pay attention to discontinuities of applied loads Use same approach as before but with variable location of section

14. Shear and Moment Functions for Beams

15. Example EXAMPLE

16. Shear & Moment Diagrams for Beams Variations of V and M in a graph Form

17. Shear & Moment Diagrams for Beams