Curved stair beam

[nickky]

Hi, i am designing a curved stair beam which is a semi-circle in plan but also raises up to the floor above. Therefore it makes an spiral. I tried to analyse the beam using computer software and I got my answers but:

1- I heard there is a method called v-load developed by AISC for analysing the cirved girders. I wanna do my own manual analysis to double check the computer results. Does anyone have any resorce or reference (like a PDF Document) explaning this method?

2- What would be your general suggestion as far as design considerations for such a member and its connections?

Thank you
Nick

 

[BAretired]

Please provide a plan view of the stair.

BA

 

[spats]

What you are describing is a helix. I too had to design such a stair using laminated wood stringers, and I was unable to find any definative design information on the subject, so I just over-did the heck out of it. Companies that design and fabricate helical stairs claim to know how to do it, but I'm not sure they'll share their information with you. Look them up, it may lead somewhere.

 

[BAretired]

This is a ling to a previous thread on a similar topic:

http://www.eng-tips.com/viewthread.cfm?qid=147144&page=1

BA

 

[BAretired]

Sorry, I meant so say link, not ling.

If the beam is a simple span, there should be no difficulty in calculating bending moments and torsional moments at any cross section as the structure is statically determinate.

BA

 

[ishvaaag]

Have found this...

http://math.uci.edu/~fwan/pdf/10_axialextensionandtorsion.pdf

http://lcvm

http://www.epfl.ch/~lcvm/articles/T06/These_2717_Chouaieb.pdf

http://math.uci.edu/~fwan/pdf/23_stretchingtwistingpurebending.pdf

I also think to remember an issueof the ietcc magazine "Informes" portrayed one RC staircase and maybe analysis but am unable to say the number.

 

[BAretired]

I think the math may be over most of our heads, ishvaaag. As I undertstand it, the planform is a semicircle. The way I would approach the problem is shown on the attached sketch.

Draw a circle representing the inner and inner line of the stair. Approximate the circular curve with a polygon. I have chosen half of an octagon, but if you want more accuracy, use more sides.

The beams are shown in green. The outer beam is supported at points 'A' and 'E'. The inner beam is supported at 'a' and 'e'.

Assume concentrated loads at each of the vertices, then from statics, calculate moments Mx, My and Mt at each vertex where Mt is the torsional moment.

BA

 

[ishvaaag]

Certainly the math is above at least my head ... it is a pity I don't ever remember the math I once learnt in surely the bigger proportion, but so demands life; and it is not the only subject matter I have forgotten. Anyway, a good moment to remember the importance of some good math apprenticeship, I'd love to have had such (that didn't), and in fact depending of the time I have I will be studying more on old good books ... I always am naive that I may one day know all these and these things, heh.

And really as long you find a statically determinate solution (the scheme permitting) one can build the stair such way, just build the solicitations from one end. Today is even as simple or more to model the spiral stair in say Autocad for a simplified model export to RISA 3D, or in its real volume in Autodesk Inventor and let say Visual Nastran 4D (or maybe Inventor itself, that now has elastic structural analysis within) mesh it in some tetrahedra, both allowing for some fixity at supports or continuity with the rest of the structure if modeled (assume not). Just seeing the kind of math and what we can do with FEM is a good remembrance of the empowerment the computerization of many of our tasks has brought, and it should be as well of the risks. There's nothing as good as to know what one has between hands.

 

[BAretired]

I believe I erred when I said the problem is statically determinate. Hmmm, need to think this one over a bit more.

BA

 

[nickky]

Thank you Gentlemen!

I appreciate your time and interest in regard to my question. Attached is the plan view of the subject stairs. As I said in my previous post, I have already analyzed the stairs by computer and just want to verify the numbers roughly. I think the method sugessted by BAritired would be the way to go. Obviously, this beam will be indeterminate but i think I can interpret the differences of numbers between the hand rough analysis and the computer results.

Based on what I found out and what I was thinking, I will be designing a beam (a box section like a HSS) which is under simultaneous effects of biaxial bending, torsion and shear. In other words all the components of a three dimensional loading pattern are present there. (even axial load is there but based on computer analysis, it is negligible).

Consequently the connection of this HSS beam to the supporting floor beam should be properly designed to handle all these effects together.

***New question***

How this beam will be constructed? I assume, it will be made of pieces of HSS tubes welded to each other. How many pieces would make sense? And if I just specify full-pen weld around the perimeter, will it be adequate to assume those pieces now act like one body?

 

[ishvaaag]

Unable to open your attachment but if you make a good pip or tube it should work, it is just find a fine fabricator and welder.

http://www.taringa.net/posts/imagenes/2571298/increibles-escaleras-en-espiral___.html

 

[RHTPE]

nickky,

There are several companies in the US that can roll a standard teel section into a helical shape. Costs to roll & transport may prove prohibitive though. But then, fabricating out of many small lengths may also be expensive.



Ralph
Structures Consulting
Northeast USA

 

[paddingtongreen]

They can't make the beam by welding short pieces together, the cut ends won't match. I don't know of anyone who can roll in two directions simultaneously, the rectangular tube would have to be run with one of its corners against the machine at a particular angle. I think they don't have the equipment for that.

I think they will have to make it from plate.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[RHTPE]

There are a few shops in the US that advertise the ability to roll helical shapes. Certainly it will depend on the member size. Check the last few issues of Modern Steel Construction (published by AISC) for their advertisements, or follow these links:

http://www.modernsteel.com/Uploads/Issues/June_2002/2002_06_bending.pdf

http://www.modernsteel.com/Uploads/Issues/May_2003/2003_05_products.pdf

http://www.modernsteel.com/products.php?cat=1

Ralph
Structures Consulting
Northeast USA

 

[nickky]

Thank you Ralph for the useful links.

Question: I was wondering if any secondary stresses will be introduced to the beam due to rolling, and if yes how would that be counted?

By the way, I also found out that, specially for wood constructions, there is the possibility of making these beams out of Glulam members. There are manufacturers who can do it like a design-build job. Apparently they have their own "secret softwares" of designing such beams.

I will provide an update as soon as I verify this second alternate for everyones information.

Anyways, Thanks everyone!

 

[JLNJ]

I would think these are indeterminate structures whose stresses are highly dependent on the degree of its support fixity (both moments and torsions).

 

[BAretired]

Consider two rings supported by four columns on the Y axis as shown in the attached sketch. Each ring is in a horizontal plane. Each ring is loaded with a uniform load.

The maximum bending moment is located at the point where each ring intersects the Y axis and can easily be calculated. Bending moment at the X axis can also be calculated and is much smaller.

Torsional moments in the ring are zero at each axis and can be calculated at any other point.

If we now perform an affine projection and separate the rings into a pair of helices at points 1 and 2 or points 3 and 4, the moments at any section are not materially changed. This should provide a good approximation to the behavior of the structure in this thread and could serve as a check on the computer output found by nickky.

BA