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Agenda: Vector Active – Trusses Form Active – Cables, Arches Bulk Active -- Beams

Agenda: Vector Active – Trusses Form Active – Cables, Arches Bulk Active -- Beams Internal Forces + Stresses Method of Cuts --- On Chalkboard. Vector Active Structures: Utilize triangulation coupled with tension and compression to resist loads.

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Agenda: Vector Active – Trusses Form Active – Cables, Arches Bulk Active -- Beams

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  1. Agenda: Vector Active – Trusses Form Active – Cables, Arches Bulk Active -- Beams Internal Forces + Stresses Method of Cuts --- On Chalkboard

  2. Vector Active Structures: Utilize triangulation coupled with tension and compression to resist loads. The “depth” of a VAS is directly related to its ability to span a given distance. Deeper translates to lower forces and longer spans.

  3. Form Active Structures: Utilize their geometric shape / form to resist loads. The “effective depth” of a FAS is directly related to its ability to span a given distance. Deeper translates to lower forces and longer spans.

  4. Bulk Active - Beams

  5. + SM = 0 Rotational Equilibrium +

  6. Vertical Equilibrium SFy = 0 +

  7. Vertical Equilibrium SFy = 0

  8. Vertical Equilibrium SFy = 0 shear deformation + SHEAR SHEAR STRESS

  9. SM = 0 Rotational Equilibrium bending deformation + C T BENDING STRESS (tens/comp) Force Couple Bending Moment Force x lever arm

  10. fibers shorten f i b e r s e l o n g a t e neutral axis, no change in length link to beam bending animation

  11. Shear Diagram Shear Stresses Flexural Stresses Moment Diagram link to diagram animation

  12. vv shear diagram.

  13. vv shear diagram.

  14. vv shear diagram.

  15. depth Bulk Active Structures: A beam’s ability to span is based upon the amount of bulk (material) it has and exactly how this material is distributed relative to its cross-section. BEAM DEPTH IS CRITICAL

  16. Method of Cuts --- Surgery with Free Body Diagrams

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