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Internal Loadings in Structural Members: Analyzing Axial Loads, Shear, and Moment Functions

This section discusses the internal loadings in structural members, focusing on axial loading, flexure, and the essential concepts of shear and moment functions in beams. It covers the procedure to determine internal loadings at specified points, illustrating the significance of free body diagrams and equations of equilibrium. Various examples demonstrate how to analyze shear and moment diagrams, taking into account distributed loadings and their impacts on member design. These concepts are crucial for understanding and predicting structural behavior under loads.

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Internal Loadings in Structural Members: Analyzing Axial Loads, Shear, and Moment Functions

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  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 P P P

  3. Internal Loading in Structural Members Flexure P M V

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

  5. Sign Convention P

  6. Sign Convention

  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 inPositive 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

  12. 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) Use same approach as before but with variable location of section Pay attention to discontinuities of applied loads

  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

  18. Shear & Moment Diagrams for Beams

  19. Shear & Moment Diagrams for Beams

  20. Shear & Moment Diagrams for Beams

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