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.
vv
shear diagram.
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