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

Internal Loading in Structural Members Axial Loading PPP

Internal Loading in Structural Members P M V Flexure

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

Sign Convention P

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.

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

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

EXAMPLE

Example

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

Shear and Moment Functions for Beams

Example EXAMPLE

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

Shear & Moment Diagrams for Beams