How Do We Quantify Stress on Fabric at Support Contact Points?

[Daniel Sellers]

Suppose we have a dome of fabric supported by radial rigid beams. The pressure (air or water pressure) outside the dome is significantly higher than inside the dome (perhaps the inside is even at vacuum).

Because the material is fabric (non rigid) the compressive force from the higher pressure outside will cause a tensile stress within the fabric (please feel to correct me if there's anything wrong with the statement.

Assuming the fabric is strong enough to resist tearing, and the supports underneath are strong enough not to collapse, is the fabric under more stress at or around the contact area where the fabric meets the supports? or would the tension be evenly distributed throughout the fabric?

Intuitively it seems like the area of contact between fabric and support would be under more stress because it is being stretched over a rigid object, but if that is the case then how can we quantify the additional stress at the support?

Emphasis on the "how do we quantify" part of the question. I am willing to fallow to any links or reading recommendations that might lead me to a way to answer this question, but a simple 'yes there will be more stress there' is not what I'm looking for.

 

[Nidum]

Post a drawing showing the actual arrangement of beams and fabric covering that you have .

This is probably going to be a problem that can be analysed using membrane stress theory . There is information on the internet about this and it's specific application to tent like structures .

 

[Daniel Sellers]

This Figure should get the point across I hope.

Thanks, I will look into membrane stress theory. I've done a little reading on surface structures but haven't been able to find anything which addresses a question quite like this.

 

[Nidum]

Link

 

[JBA]

One view to take is to suppose that the radial beams are tubular in x-section such that there are not edge contacts with the fabric and without stress creating fasteners between the fabric and the beams; and then to look at the case of a strip of fabric wrapped over a beam. What that basically equates to (ignoring friction) is a strip of fabric stretched over a flat pulley; and, that would tend to indicate that the fabric tensile stress over a beam would be equal to that in the adjoining unsupported regions of the fabric. (i.e. as per a rope over a pulley).

Of course, this does not address any possible effects due to the dome shape of the structure.

 

[Daniel Sellers]

One view to take is to suppose that the radial beams are tubular in x-section such that there are not edge contacts with the fabric and without stress creating fasteners between the fabric and the beams; and then to look at the case of a strip of fabric wrapped over a beam. What that basically equates to (ignoring friction) is a strip of fabric stretched over a flat pulley; and, that would tend to indicate that the fabric tensile stress over a beam would be equal to that in the adjoining unsupported regions of the fabric. (i.e. as per a rope over a pulley).

Of course, this does not address any possible effects due to the dome shape of the structure.

So if I'm understanding you correctly you're saying that barring any sharp edges or fasteners the tensile stress in the fabric would not be significantly larger on the area of contact with the tubular beams. For some reason that intuitively doesn't seem right, but I think I've seen pretty rigorous versions of the rope and pulley you're referencing so maybe that is the case.

I'm going to keep looking into this, thanks for the replies. Any more thoughts or references would be appreciated.

 

[Nidum]

One of the big difficulties with loaded fabric over ribs type constructions is fretting . Both of the fabric and the ribs .

Fretting was a major problem for designers of the old rigid airships like the R100 and R101 .

 

[Daniel Sellers]

One of the big difficulties with loaded fabric over ribs type constructions is fretting . Both of the fabric and the ribs .

Fretting was a major problem for designers of the old rigid airships like the R100 and R101 .

I'll certainly keep that in mind, but what I'm looking for right now is a more theoretical answer about the stress in different locations if the fabric and supports where both perfect materials of some kind.