ECIV 320 Structural Analysis I

Internal Loadings in Structural Members

Sections 4.1 – 4.5Study all examples

Internal Loading in Structural Members

Axial Loading

P P P

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

Sign Convention

Internal Loadings at Specified Point - PROCEDURE

Support ReactionMay need to be calculated before Internal

Loadings

Cut the MemberPass Section parpendicular to its axis at the

specified pointAttention: 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 EquilibriumHint: Sum moments at the section about

centroidHint: Numerical Results (+) FBD OK, (-) Internal Loadings Opposite Direction

EXAMPLE

Example

Example

Shear and Moment Functions for Beams

Design ! Variations of internal Shear and Moment along AxisNormal Force is usually ignoredException: 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

Shear & Moment Diagrams for Beams

Shear & Moment Diagrams for Beams

)(xwdx

dV dxxwV )(

Shear & Moment Diagrams for Beams

Vdx

dM VdxM