Agenda Vector Active Trusses Form Active Cables Arches

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. The “depth” of a VAS is directly related to its ability to span a given distance. Deeper translates to lower forces and longer spans.

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.

Bulk Active - Beams

+ SM = 0 + Rotational Equilibrium

Vertical Equilibrium + SFy = 0

Vertical Equilibrium SFy = 0

+ shear deformation Vertical Equilibrium SFy = 0 SHEAR STRESS SHEAR

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

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

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

vv shear diagram.

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

Method of Cuts --- Surgery with Free Body Diagrams