Consider pallet strapping. It has width W. When the strap is flat, it has some maximum breaking strength B.
Now, let's put one twist in it over X feet. Mentally we have a VERY skinny isoceles triangle with width W, height X. Cut it in half to make a right triangle.
The length of the centerline of the strap is X. But the edge is the hypotenuse, H of the triangle and has length $$H = \sqrt{X^2+(W\pi)^2}$$
Suppose we use 1/2" strapping and there is a half twist over a distance of 4 feet. This gives a difference between the center line and the edge of
$$H = \sqrt{48^2+(\pi/2)^2} -48$$
This gives a number of about 0.025" or about 1/2000 of the length.
Now if this material had an insanely high modulus of elasticity, even a modest force would cause it to tear starting at some point on the edge of the twist.
Alternately, it would reach the material's elastic limit (not return to it's original dimension on being untensioned) on the edge, leaving it with a permanent inherent twist.
If you want to demonstrate this effect, use paper adding machine tape, and a pair of wide jaw welding vice grips. The paper is quite strong if the load is applied evenly, but with an added twist it is much more spectacular in it's failure.
Given a stress/strain graph, how do I calculate the change in breaking strength or elastic limit due to a a partial twist in a flat ribbon.
Application: I'm designing a porous trampoline mat, and am considering polyester pallet strapping for the web matererial. This comes in various widths ranging form 1/4" to over 1" and in various forms including linear and woven. The linear form has a higher tensile strength/weight ratio, but tends to split if flexed.
When a jumper depresses the surface of a the trampoline he forms a cone. If he depresses a 2 m wide mat by a meter, then the sides of the code around his feet are 20-45 degrees twisted, corresponding to a twist per 8-16 meters. Most of the load however is carried by the webs that run underneath his feet. It gets messy in a hurry.
