eciv 320 structural analysis i internal loadings in structural members sections 4.1 – 4.5 study...
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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