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.