## Sunday, January 5, 2014

### DESIGN FUNICULAR STRUCTURES

Graphic vector are powerful means to design funicular structures, like arches and  suspension roofs; providing both form and forces under uniform and random loads.

Arch
Assume:

1 Arch structure

2  Parabolic arch by graphic method

Process:
Draw AB and AC (tangents of arch at supports)
Divide tangents AB and AC into equal segments
Lines connecting AB to AC define parabolic arch envelope

3 Arch profile

Process:
Define desired arch rise D (usually D = L/5)
Define point A at 2D above supports
AB and AC are tangents of parabolic arch at supports
Compute vertical reactions R = w L /2

4  Equilibrium vector polygon at supports (force scale: 1” = 50 k)  Process:

Draw vertical vector (reaction R)
Complete vector polygon (diagonal vector parallel to tangent)
Measure vectors (H = horizontal reaction, F = max. arch force)

Note:

The arch force varies from minimum at crown (equal to horizontal reaction), gradually increasing with arch slope, to maximum at the supports.