Keywords: spider web, orb web, prestressed mechanism, infinitesimal mechanism, geometric nonlinearity, order of prestress.

Among all examples of "structural engineering" in nature, spider webs are probably one of the most intriguing. From a structural engineering point of view, a spider web is a cable structure whose segments sustain only tension, and whose structural integrity is reliant on prestress for both form and load carrying capacity. Researchers have already shown examples of how the form and functions of the spider web are highly related, and a further examination from the viewpoint of i) prestressed mechanism and ii) web prestress is now provided.

There is evidence to show that a spider actually tries to build a planar web, despite the fact that it is easier to build a non-planar web, especially when the spider is near-blind. A planar web is actually a structural arrangement with degenerate geometry, i.e. it has no stiffness out of plane. While structures with inherent lack of stiffness in a particular direction are highly undesirable in ordinary structures, the spider web exploits this specific property by aligning the direction of low geometric stiffness with the most probable direction of incoming prey (i.e. perpendicular to the web). The silk threads of the web are already shown to have extraordinarily large breaking strain, so that an incoming insect (which arrives with considerable kinetic energy) can be captured, and then held, by gradual transfer of the kinetic energy to strain energy in the silk. The additional geometric flexibility greatly enhances this function of the web.

Since the spider web is a prestressed cablenet, it is intriguing to note that the spider is capable of maintaining prestress in the web both throughout construction and seemingly without fine tuning of cable lengths, when all the segments are in place. The process of ensuring a fairly uniform state of prestress is one of the more difficult tasks towards the end of construction of man-made cablenet structures. One key in discovering the spider's "secret" is in its choice of using a spiral, as opposed to concentric rings, as the structural arrangement in the web. In the ordinary linear analysis, the open-ended spiral is actually not capable of being prestressed. A geometrically nonlinear analysis however shows that prestress is possible in the spiral, but it is a second order prestress which imparts forces in the spiral that is one order magnitude lower than the prestress in the radial segments.

It is argued that such an arrangement of high prestress in the radial segments, and low prestress in the circumferential segments again aids the functions of the web in two ways. Firstly, the capture spiral (with breaking strains up to 450%) are used as the principal device to absorb the kinetic energy of the inbound prey. A low prestress in the capture threads maximise their capacity for further straining in the event of an inbound prey. Secondly, attaching a tensile spiral onto the radial threads reduces the tension in the radial threads in the hub region. Attaching a spiral with second order of prestress (i.e. with prestressing force an order of magnitude lower than the radial thread) ensures only a small reduction of radial prestress, thereby allowing an order of magnitude more spiral attachments and a web with a fine mesh. The use of second order prestress thus allows the spider to achieve full prestress in the web, both during and in the finished web, which is a vital property since the near-blind spider is highly reliant on the transmission of vibrations across the web for it to sense presence and location of captured prey.

The paper shows that the form and functions of a spider web are not simply closely related in ways already reported in the literature, but the precise arrangement of the orb web segments bring about important mechanical and structural properties that further enhance the functions of the orb web. In particular:

1)

the fact that the orb web is planar results in degenerate geometry, and allows the additional resultant flexibility to gradually slow a prey down; and

2)

the fact that a spiral, and not concentric rings, is chosen to complement radial threads induce second order prestress which,

(i)

guarantees low prestress in the capture spirals and maximise their capacity for further straining in the event of impact from an inbound prey, and

(ii)

allows the spider to maintain prestress in all of the web during, and at the end of, web construction, which is essential for vibration transmission.

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