Trying to determine tensioned fabric reactions
Trying to determine tensioned fabric reactions
(OP)
Hi there,
I am trying to determine the support reactions for a large fabric membrane (30' x 65') subjected to gravity (acting normal to the large surface) as well as static differential air pressure of .01" water column (also acting vertically downward). The fabric is clamped continuously along its circumference to a rigid structure. The weight of the fabric is 100 lbs. and is pre-tensioned so as to limit sag to approximately 10" at its maximum deflection point. For all intents and purposes, the fabric will not experience any significant strain at these loads.
Thanks for helping.
Paul
I am trying to determine the support reactions for a large fabric membrane (30' x 65') subjected to gravity (acting normal to the large surface) as well as static differential air pressure of .01" water column (also acting vertically downward). The fabric is clamped continuously along its circumference to a rigid structure. The weight of the fabric is 100 lbs. and is pre-tensioned so as to limit sag to approximately 10" at its maximum deflection point. For all intents and purposes, the fabric will not experience any significant strain at these loads.
Thanks for helping.
Paul






RE: Trying to determine tensioned fabric reactions
0.01" H2O is a very small wind speed (only 0.025mb) ... is that real ? (or is this inside ?)
Quando Omni Flunkus Moritati
RE: Trying to determine tensioned fabric reactions
RE: Trying to determine tensioned fabric reactions
If the sheet is initially flat, you can't get any sag without having either wrinkling or strain.
RE: Trying to determine tensioned fabric reactions
I agree about the strain. I was trying to say that under these loads the fabric doesn't change its dimensions by any appreciable amount (it behaves more like thin metal than say spandex, for example).
RE: Trying to determine tensioned fabric reactions
with fabric tension being the dominant load, the supports will see an over-turning moment, or do you have a compression strut and a tension cable?
Quando Omni Flunkus Moritati
RE: Trying to determine tensioned fabric reactions
Not sure I know what an over-turning moment is.
No tension struts or cables. The fabric edges are clamped between two pieces of steel. If I can figure out the tension in the fabric, I can figure the reactions. It's the fabric tension that's got me.
RE: Trying to determine tensioned fabric reactions
Weight of fabric = 100 lbs
Weight of equivalent water = approx. 100 lbs
Assume the fabric is only supported on the 65' sides.
Total vertical reaction at each edge = 100 lbs
The deflection mid-span is 10", half the span is 180" so with similar triangles the vertical reaction is 1800 lbs.
Net tension is about 1800 lbs. Spread that over 65' and you get 28 lbs/ft.
I don't know anything about the fabric or how you plan on clamping it, but I think 28 lbs/ft is achievable. It would be more accurate to get the tension considering the additional support of the 30' side and the steeper angle at the supports....but both of these conditions would reduce the required clamping force. I would take a look at how much clamping force I can count on and if it gives me a reasonable factor of safety I would call it a day.
RE: Trying to determine tensioned fabric reactions
If you consider a one foot wide strip of fabric spanning 30' and disregard the 65' span, the fabric is nearly parabolic in its deflected shape.
w = 100/65*30 + 0.01*62.5/12 = 0.1034 psf
M = wL2/8 = 0.1034(30)2/8 = 11.6'#/' or 140"#/'.
T = M/sag = 140/10 = 14#/'.
T is the tension per foot of width at midspan which is also the horizontal component of tension throughout the span. The tension at each end is only slightly more than that, approximately 14.1 #/'.
BA
RE: Trying to determine tensioned fabric reactions
RE: Trying to determine tensioned fabric reactions
I am assuming the tension in the "membrane" is uniform throughout (assuming the fabric is isotropic), and that the 30' clamps contribute to the work being done by the 65' clamps. So they should reduce the average horizontal reaction for the system? And that's the rub. How does the reaction change as you approach the corners and show the contribution of those short ends? It's actually the 30' ends that are the biggest problem (space/weight restrictions). I can't over-engineer those ends. Am I over-thinking this?
RE: Trying to determine tensioned fabric reactions
BA's solution is obviously more accurate than mine. It would have been just about the same amount of work for me to take it that extra step, but I admit I was feeling lazy last night. My point in that post was that using very rough approximations (on the conservative side) you still get a reasonable reaction. And with BA's solution, the reaction is even more reasonable. Again, I don't how you intend on clamping the fabric (maybe you could share that with us), but 14 lbs/ft seems like it shouldn't be a problem.
RE: Trying to determine tensioned fabric reactions
i think another difference in the two calc's is the span considered ...
adjust BA's calc for the 65' span ... M is approx 4x (double span squared), so T is about 60 lbs/ft.
BUT this says all the moment is reacted along one side or the other. using both sides might work like ...
14 lbs/ft reacts the load along the shor sides, and 14 lbs/ft along the long sides would react about 1/4 of the load, so if the short sides react 80% of the load (11 lbs/ft tension) and the long sides would react about 20% of the load (with 11 lbs/ft).
Quando Omni Flunkus Moritati
RE: Trying to determine tensioned fabric reactions
BA: Thanks for the math.
rb: I like your approximation breakdown. It satisfies my "need" to account for the differences (long v. short) and seems very reasonable and safe.
Thanks to all for helping.
RE: Trying to determine tensioned fabric reactions
Quando Omni Flunkus Moritati
RE: Trying to determine tensioned fabric reactions
If the membrane could be represented by strings evenly spaced in two orthogonal directions, strings near the edges would be shorter than those further away to allow for sag at the midpoint.
Using the string model, a long string would be 65' long at the edge, would have no curvature and would carry no load. A string at distance 'y' from the nearest edge would be curved for a distance 'y' at each end and would be straight in the central portion, i.e. without curvature. Since the shape of a cable represents, to some scale, the bending moment diagram of a simple beam, this means that this string carries uniform load for length 'y' at each end and no load in the straight central portion.
The short strings in the 'Y' direction would behave in similar fashion in the end 15', but in the central 35', the short strings would carry 100% of the load.
Using this model, the horizontal force on the 30' ends would vary uniformly from 0 at each corner to 14 #/' at midpoint and the stress in the long strings would vary accordingly.
Horizontal force on the long sides would vary from 0 at each corner to 14 #/' at 15' and would remain constant for the central length of 35'.
BA
RE: Trying to determine tensioned fabric reactions
Anyway it is structurally redundant so there is no closed form solution that can be checked for desired boundary conditions.
With a closed frame the tension in the fabric could be infinite, limited only by the strength of the fabric.
It could be loose on either the sides or the ends and still be supported in the other direction. Since you don't know how much tension preload is applied during assembly, you don't know which direction will dominate, so go safe and look at both cases as catenaries with a combined weight of fabric and pressure load.
The actual pressure load is normal to the surface, not normal to the ground, but it's close enough and is uniform.
I looked at doing similar analyses, but was frustrated by the lack of decent information about the fabric properties. Tensile rupture and tensile modulus are not easily available, nor are the effects of heat and humidity. This lack of information really hampers an FEA solution.
RE: Trying to determine tensioned fabric reactions
The string model makes sense, but admittedly is difficult to envision (the straight portion of the 65' string). Have to shift from a macro view
"A string at distance 'y' from the nearest edge would be curved for a distance 'y' at each end and would be straight in the central portion, i.e. without curvature."
Is this because of the support afforded by the short strings?
Also, I'm having trouble with how the relationship of curvature for a length of 'y' at a distance 'y' is established.
3D:
No hot air involved, just a very small differential pressure at room temps. Good point about tension preload - there's design intent, and then there's what really happens.
I too found next to nothing about fabric material properties. I tried doing some simple FEA and backing into a value for E, etc. that made the model approximate reality. Gave up in frustration.
RE: Trying to determine tensioned fabric reactions
It may be easier to envision a square plan as shown in the attached link. The gray shaded area ABCD represents the membrane in plan. The red lines are diagonals, not strings. Assume the strings in both directions are spaced at 'sp' and the overall dimension is 30' x 30'.
The strings running through the center point 'E' in each direction deflect 10" under load and are shown in green. Each green string carries a load of w*sp#/' over its full length except at point E where they share the load acting on an area of sp2. The curvature of the green strings is essentially parabolic over the entire length.
Strings in both directions at each edge of the membrane cannot deflect at all, hence they carry no load.
The remaining strings cannot deflect 10" as they are connected to strings in the orthogonal direction which restrict their movement. The two strings shown in blue occur at about the quarter point. They each carry a load of w*sp#/' between the outside edge and the diagonal but no load between the two diagonals. The straight portion of a string at the quarter point would be 7.5" below the edge in accordance with the geometry of a parabola. The ends would follow a parabolic curve.
The surface generated by the complete network of strings would be the intersection of two orthogonal paraboloids which intersect on the red diagonals. The unstressed length of each string would vary according to its distance from the edge.
When one dimension is increased from 30' to 65' as in your case, the model is simply chopped in two and each half is separated by 35' so that the central portion acts as a one way cable system.
It is important to note that the string model used above does not accurately represent a fabric membrane unless the fibers in each orthogonal direction can be elongated by the precise amount required to satisfy the assumed curvature...not an easy feat.
BA
RE: Trying to determine tensioned fabric reactions
Thanks BA. That is indeed helpful, and instructive.
I appreciate that you took the time to help.