Bring up the Struts & Hubs window by selecting the item ‘Strut properties...’ in the ‘Struts’menu.

IMPORTANT. Because regenerating struts and hubs is CPU intensive, there are two seperate buttons ‘Apply Struts’ and ‘Apply Hubs’. Strut regeneration is not automatic because it is often desirable to ‘tweak’ the hub properties until the desired form is obtained. However, to correctly compute hub/strut intersections, you MUST regenerate struts when you have change the hubs. Conversely, you MUST regenerate the Hubs when you have changed the struts.

Struts come in various types which are suited to different construction methods. Some strut types are fixed directly to face panels, alleviating the need for hubs, whilst other strut types are only meant to be used in conjunction with hubs. To dinstinguish the difference, the strut type is appended with either “[face]” or “[edge]”. For example, “[face]” struts are built around the inside edges of a face; this means each edge corresponds to *two* struts – one on the left side of the edge and one on the right. However, “[edge]” struts are built on the edges alone, so that each edge corresponds to *one strut*.

### Edge Type Struts

Cylinder struts [edge]

1 strut per edge.

There is one single strut per quad-edge. The strut mesh is built so that the quad-edge (ORG to DEST) passes through the center of the strut. The exception to this rule is the 'Triangle' strut where the quad-edge passes through the bisected base of the triangle. (If you want a triangle strut where the quad-edge passes through the center of the triangle, use a Polygon strut and set the vertex number to 3). The Edge type struts are:

Cylinder hollow [edge] Cylinder solid [edge] Diamond square hollow [edge] Diamond square solid [edge] Ellipse solid [edge] Polygon solid [edge] Rectangle hollow [edge] Rectangle solid [edge] Square hollow [edge] Square solid [edge] Triangle solid [edge]

### Face Type Struts

Mitred struts [face]

2 struts per edge.

There are two struts per quad-edge. The strut mesh is built so that the quad-edge (ORG to DEST) passes along the top or bottom edge of the strut (this depends on which Tetragon Type is selected for the strut profile). The Face type struts are:

Tetragon [face] Tetragon mitred [face] Tetragon mitred spline [face] Tetragon mitred butt [face]

NOTE: whilst you can modify quad-edges with the modelling tools, you cannot modify struts; struts are fixed entities that may be picked for their geometrical properties only. Therefore, you cannot use the Vertex Editor with struts. However, you may use the measure tools ‘DISTANCE BETWEEN TWO POINTS’ and ‘AXIAL ANGLE’.

The full list of strut types for both [edge] and [face] are listed on the Geodesica home page.

### Slenderness ratio

Buckminster Fuller suggested a slenderness ratio of 24/1 for wood and 30/1 for steel. However, these are very general and the actual slenderenss ratio is dependent on specific material properties that can only be gleaned from the manufacturer, eg the specific alloy type, or the tensile strength of the wood in use, *e.t.c.* You must use dimensions that give a safe slenderness ratio for the material in question.

As you change the section-profile attributes, the slenderness ratio is recomputed using the maximum strut length in the manifold. The slenderness ratio is kL/R, where k is the fixity factor of the strut ends, L is the max strut length, and R is the radius of gyration for the given profile. Factor k represents the end conditions of the strut. Obviously this will depend on the hub design. Standard values for k are:

Both ends fixed: k = 0.5

One end fixed and one end pinned: k = 0.7

Both ends pinned: k = 1.0

One end fixed and one end free (cantilever compression): k = 2.0

Clearly, in a geodesic dome, k will vary somewhere between 0.5 and 1.0, depending on the hub type. It is possible, for example, that struts have a certain degree of elasticity at the hub; or they might be of a “ball and socket” type design. The default value for k is 0.5 (both ends fixed).

The first UI prototype allowed the user to select a material from a combo choice; an approximate slenderness ratio was then computed as a starting point, which the user could refine by changing profile dimensions. However, after studying the matter further, I abandoned this approach as there were are too many factors outside my control. The interface now puts everything in the hands of the engineer.

The effective slenderness ratio is now computed according to the longest strut in the manifold, based upon the section of the strut.

When examing the formulae for elementary sections that are given in the Strut profile pages that follow, the following definitions might be useful:

**The moment of intertia** of a section is the sum of the products of each elementary area of the section into the square of its distance from an assumed axis of rotation, as the neutral axis.

**The radius of gyration** of the section equals the square root of the quotient of the moment of inertia divided by the area of the section. If R = radius of gyration, I = moment of inertia, and A = area,

R = sqrt(I/A), and I/A = R^{2}

**The radius of gyration** for any section around an axis parallel to another axis passing through its center of gravity is found as follows: Let r = radius of gyration around axis through center of gravity; R = radius of gyration around another axis parallel to above; d = distance between axes: R = sqrt(d^{2} + r^{2}). Note that when r is small, R may be taken as equal to d without material error.

**The modulus of resistance** of any section to transverse bending is its moment of inertia divided by the distance from the neutral axis to the fibres farthest removed from that axis. If Z = Section modulus, I = Moment of intertia, and y = Distance of extreme fibre from axis, then Z = I/y.

Remember that in general, the forces on a strut are tensional rather than compressional. Hence Buckmister Fullers’s term “Tensegrity” – *tensional integrity*.