spiral stairs 1

[tabio]

I am in the procerss of designing a spiral stair and I do not know how to calculate the moment on the spiral column.
What are the load consideration? I am assuming all the load on one side thinking of people liningto the same side.
Do you have any ideas or suggestions?

 

[phuduhudu]

Draw a stick model of what you are analysing and it becomes quite simple. Draw a single vertical member for the column with horizontal reactions at the top and bottom and a vertical reaction at the bottom. Then draw the tread elements in elevation. As you say you need to come up with a worst load case so you could take say a point load of 1kN (one heavy person) at the end of every second tread on one side of the column. This should be conservative. Then resolve moments about one end to get your horizontal reactions. Then cut your model at various points and resolve to get the moment in the column. Bear in mind this will be the moment in that plane only and there will be another perpendicular moment. So you need to do the model twice. Carl Bauer

http://www.bauerconsultbotswana.com

 

[ishvaaag]

And well, FEM exists as of now. To draw an spiral out of line members and load it with loads equivalent to those acting won't be difficult. Normally you will provide fixity enough in one or both ends of the spiral to ensure proper transfer of forces at ends for the assumption.

If made of reinforced concrete it will be somewhat (but not completely) insensitive to eccentricity of load coming from the use of the stair. For a steel central member under the steps better model the steps as cantilevers directly.

The stairs made spiral as cantilevers from a central column are even more directly modelizable.

 

[tabio]

Thank you colleagues for your guidance.

It is a steel stair free standing for two landings. The owner does not want the stair attached on the 2nd and 3rd floors landings. In the architectural drawings the architect is proposing a 5" circular column, that based on the loads per step it will be enough as per the aisc manual.

I am treating it as single cantilivered steps. But my real question is: When the stair is in full use, that would be a full evacuation of the building, I am assuming one person per step, we are creating 28 small simultaneous moments that as Carlbauer in his post said we could consider 1KN per step. How will be the column designed?

Another consideration would be having people standing on just one side of the stair, creating a similar moment that would be aplied on the column at the steps intervals, forcing some sort of buckling stresses on the steel column.

Again, any ideas?

 

[ishvaaag]

These issue you can deal either through a K conmensurate with your in-column vertically more or less distributed load, or presently more efficiently through P-Delta analysis at the factored level of load with the column made of short segments.

After P-Delta with the if necessary reductions on axial and bending stiffness taken unto account, you can use directly the forces got for design without further amplification in one strength of materials approach if you dismiss the in-member out of alignment, which is normally safe enough given the scarce magnification resulting when the segments are short, or you use the equations in chapter H of LRFD with K=1 and non-sway since after such P-Delta Analysis the ends of the segments have been brought to a stable position and such ends can be assumed linearly fixed.

 

[ishvaaag]

On the proper K...

Pandeo de Estructuras
Felix Escrig
Publicaciones de la Universidad de Sevilla

QuUotes ELASTIC critical loads for columns

For a double pinned colum with uniform distributed load along the colum

Case II.15 at p. 56

where the forces keep orientation after buckling (gravity)
gives a critical load 1.88pi^2EI/L^2 or

K=1/1.88=0.53

Some accounted inelasticity (maybe on account of loss of stiffness cause spanish code NBE EA-95 a bigger value for K

from the formulation in Table 3.2.4.5 the same case gives K=0.729, which should be a more proper value for of K for your case since from a code, more conservative, and presumably accounting about phenomena that mere elastic buckling factor cares not.

If you provide some fixity at the base both references can guide you to lower Ks.

 

[tabio]

Again, Thank you very much for your input. It was very valuable