vertical_from_q

compas_tna.equilibrium.vertical_from_q(form, scale=1.0, density=1.0, kmax=100, tol=0.001, display=False)

Compute vertical equilibrium from the force densities of the independent edges.

Parameters:

formFormDiagram

The form diagram

scalefloat

The scale of the horizontal forces. Default is 1.0.

densityfloat, optional

The density for computation of the self-weight of the thrust network. Set this to 0.0 to ignore self-weight and only consider specified point loads. Default is 1.0.

kmaxint, optional

The maximum number of iterations for computing vertical equilibrium. Default is 100.

tolfloat

The stopping criterion. Default is 0.001.

displaybool

Display information about the current iteration. Default is False.

Notes

The force densities stored in the Form Diagram are the ratios of lengths of corresponding edges in the Form and Force Diagram. This means they are not yet scaled with the scale of the horizontal forces. The horizontal forces stored in the diagram are scaled.

\[\begin{split}q_i &= scale * \frac{l_{i, force}}{l_{i, form}} \\ &= \frac{h_{i, form}}{l_{i, form}} \\ &= \frac{f_{i, thrust}}{l_{i, thrust}}\end{split}\]