Handbook of Engineering Mathematics, American Society of Metals (ASM) (Page 65) catenary

[rowingengineer]

Wondering if anyone has this book and if they would be willing to share page 65 or the page with catenary . I only want to confirm an equation so am not keen to purchase the whole book, but if people think it is worth it I will try to track down a copy.

Also would anyone have the DASMA Rolling Sheet Door Calculations for wind locks paper?

http://www.nceng.com.au/

"Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning."

 

[CANPRO]

Its on google books. It lets you search for keywords and returns a portion of the page. You might have some luck with that. The link is below

http://books.google.ca/books?ei=QP1...thematics&focus=searchwithinvolume&q=catenary

 

[rowingengineer]

Thanks Caneit, but I did try this resource, the page I want shows up as a very small exert, for some reason I can get the whole page. The formula I want is there, but I really wanted the whole page, so i could see why they adopt the equation when L is large compared to D.

http://www.nceng.com.au/

"Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning."

 

[Denial]

That looks very like the standard simplified formula for the curved length of a "horizontal" cable whose midspan sag (d) is small relative to its overall horizontal length (l).[ ] What more do you need to know about it?

 

[Denial]

They adopt this equation when the cable is adequately taut (ie when the sag D is small relative to L) because under this condition the "true" catenary shape of the hanging cable can be adequately represented by a parabolic shape, resulting in easier mathematics.

 

[rowingengineer]

Denial,
I was hoping that they hadn't adopted a "sag" centenary shape as the deflected shape of the roller door will not match a "sag" condition. I was hoping that had adopted somehow an equation that better represented the situation.

http://www.nceng.com.au/

"Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning."

 

[Denial]

Better representation of WHAT situation?[ ] A catenary is a catenary is a catenary.

 

[dhengr]

RE:
I think you start out with a fairly light stiffness door panel spanning as a simple beam, btwn. the two tracks. Either from a uniform wind loading or from a single projectile, I would treat this as we would a regular simple beam (panel section); bending, deflection, finally some panel buckling, yielding, maybe some plastic hinge starting. At this point you have a deflected shape with Δ several times the thickness of the panel, and we know that regular beam theory no longer really works with these large Δ’s, so switch to a sagging cable analysis with this deflected shape. Using wire rope, catenary shape theory really doesn’t work when the cable is assumed to be a straight line (very taught), the tension forces to hold it there go to infinity. I would treat this as the two step problem above, and I gotta think some more about where to switch or what exactly happens btwn. the two.

 

[dhengr]

RE:
Look in SlideRuleEra’s collection of std. ref. books, etc. I think he has a book or two on wire rope and tension structures, the various formulas, etc.

 

[rowingengineer]

Thanks Dhengr, I will take a look

Denial,
I disagree a gravity catenary is different to a pressure catenary.

In the gravity catenary case the load is always acting with the vertical axis, hence it is what I would refer to as a sag situation.

In the pressure case the load changes direction as the roller door deflects, here the load will always be perpendicular to the surface.

These should result in different profiles of deflection I would suggest.

http://www.nceng.com.au/

"Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning."

 

[paddingtongreen]

If the door was locked down at the bottom and weightless, or of insignificant weight, the profile would would be a catenary; however, if the weight is significant, it adds that weight to the tension in a linear way from top to bottom. What confuses me here is that the door is running in tracks that will prevent this horizontal deflection and that converts it into a number of panels spanning from track to track.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[Denial]

Catenary. Some definitions from generally reputable sources.

Wikipedia:[ ] in physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends.

Wolfram's MathWorld:[ ] the curve a hanging flexible wire or chain assumes when supported at its ends and acted upon by a uniform gravitational force.

Merriam-Webster on line:[ ] the curve assumed by a cord of uniform density and cross section that is perfectly flexible but not capable of being stretched and that hangs freely from two fixed points.

My printed version of the Oxford English dictionary:[ ] curve formed by uniform chain hanging freely from two points not in same vertical line.

None of the above includes anything about "pressure".

 

[chicopee]

DASMA has a ton of data sheets on their web site, have you checked them out?
Here are some of their articles:
DASMA Door and Access Systems Manufacturers Association
Rolling Door Wind Load Determination - Effective Wind Area
Wind Load Calculations For Rolling Doors .pdf eBooks for Free.

 

[BAretired]

The door deflection curve is neither a catenary nor a parabola. It is an arc of a circular curve. Pressure is radial. Tension is constant throughout.

BA

 

[paddingtongreen]

BA, in the absence of its own weight, I completely agree, but when its own weight is considered, it must change. In the pure pressure configuration, the tension is uniform, but the inclusion of its own weight increases the tension with distance from the bottom.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[dhengr]

It’s a tension field or tension panel assuming a curved shape due to the wind pressure. Much like a catenary wire rope acting against a uniform gravity load, although not exactly. As long as the panels are joined together by a lapped joint btwn. them, I would expect the DL to be carried by the panels below. Otherwise, I don’t know how else to deal with the DL, at the moment. This probably is a good problem for a FEA program, where you can model both the gravity load (DL) and the wind pressure on a door panel, or on the whole door of panels. You’ve never shown us any of the details of the door, or the tracks and wheels, or the structural hooks which must go over the track to actually provide the support at the ends of the tension panels. And, we’ve never talked about what constitutes door failure. Does the door have to operate well after a storm or does it just have to keep the flying debris out and the building fairly well enclosed.

 

[BAretired]

paddingtongreen,

I agree that the dead weight of the door changes the statics. I think the solution considering door weight and wind combined would be iterative because the shape of the deflection curve governs the direction of the applied pressure.

BA

 

[chicopee]

The construction of their rolling doors lead me to believe that each panel act as beam rigidly supported at the ends. Loads on each panel can be either uniform from wave (water) action, concentrated from direct hits, triangular from air pressure developed from sideway air movement. That's my two cents.