SHAPE FINDING FOR THE "RADIAL TENT"
Introduction. This computer program determines shape for the so-called "radial tent". (See Figure 1.) The radial tent is a cable net with both radial and circumferential cables. The user is allowed to specify the number of radial cables, the number of circumferential cables, the vertical force component in the radial cables, reference forces in the circumferential cables, and the base. The program returns the shape which is the position of the interior points.
FIGURE 1: Schematic of Radial Tent
Figure 2: Vertical Section Through Tent
There are two free-body diagrams of importance here: Figure 2 shows a vertical section of a node and Figure 3 shows a horizontal section. In the calculations below, vertical and circumferential equilibrium are forced while radial equilibrium is used to determine the radial coordinates. The equilibrium equations are solved iteratively by freeing one radial coordinate at a time.
Figure 3: Horizontal Section Through Node
There are four terms (see Figure 4) in the radial equilibrium equation:
These terms must sum to zero as H1 + H2 + H3 - H4 = 0. The program uses this equation to obtain a new value for Rnew . This requires the solution of a quadratic.
Figure 4: Schematic Showing Horizontal Forces
Computer Program in Fortran