**Spiral Staircase Column: 20-axis bending+compression? 2

[hippo11]

Hi everyone. I am trying to determine the capacity of a 16" diameter, 3/8" thick, ~25 ft tall spiral staircase column. The worst case loading I believe would be a point loading on the end of every stair along with a loaded platform (it's a water slide staircase by the way) at the top of the staircase, creating an axial load along with bending loads around 20 axes (the stairs are at every 18 degrees.)

All I can find in the LRFD manual and steel textbooks is for biaxial bending + axial compression...

What about 20-axis bending + axial compression?

Any suggestions?

Thanks...

 

[structuresguy]

Well, that's a dilly of a pickle...

I think that you can simplify the problem by resolving each moment from each "arm" into the global X and Y directions. Then, as the moments from each arm would tend to add together, you could find the worst case bending in two directions, combined with axial compression. This would allow you to use the biaxial bending equations.

I would also check loading on one side only, to create the worst case unbalanced moments. I think the first caee (all loaded) would tend to balance each other out, if the spiral is close to 360 degrees.

I would also check localized stresses at the connection points to ensure the tube section is adequate.

I would also create a model in an analysis program like STAAD, and make sure that the results from that are similar to my hand calcs.

Sounds like a fun challenge. Good luck.

 

[hippo11]

great idea, thanks...

so that would enable me to use the biaxial bending eqn...after I resolve into X and Y axes, then I would need Mux, Muy, and Pu...I would need to do statics to find these end reactions...

but what do I use in the biaxial equation as Mux, Muy and Pu? I'll end up with an Mux,top & Mux,bot & Muy,top & Muy,bot & Pu,top (=zero, here) and Pu,bot?

Thanks!

 

[swBausch]

I think a 16" diameter would allow a welder to crawl inside and install plates to transfer force to the opposite wall.

He won't like it in there, but it's not a career.

What happens if you go larger diameter.

 

[structuresguy]

Well, you will probably have to check stress levels at several section along the height of the column: bottom, top, middle, and any other section which the geometry might result in a critical stress condition. Also, the combination is which you add the moments together may result in moving the critical section. You will have to use your judgement on that to make sure you check all pertinent load combinations.

You will then use the Mx, My, and P calculated for a stress check at each of the critical sections.

As for transfer plates, swBausch, you must be a much smaller guy than I. There is no way I would crall into a pipe that size to weld. Actually, don't really need to anyway. Stiffener rings can be welded to the outside of the pipe at the connections, if required.

Hope this helps some more.

 

[steve1]

Here's a thought.

Think of the column as a beam loaded with only applied moments all acting in the same direction (we'll get back to the origin and magnitude of these loads shortly), and consider what the shear and moment diagrams would look like.

Shear diagram would be a straight line.

Moment diagram would look like a saw tooth roof, with the zero line running through it.

If all the applied moments were equal, or if they were of symmetrical magnitude, the maximum moment would equal one half of the largest applied moment. This is what you would design for.

Now consider a spiral staircase that makes one revolution (yours may be different). Draw a plan view, locate a global coordinated system and mark your load points. Assume only one half of the circle being loaded (unbalanced case). On a global basis you can calculate Mx's and My's. Note that one set of these moments cancel. Now calculate applied moments to your column. You can either calculate individidual moments or just the maximum case. It won't matter because the maximum moment on the beam will still be one half of the maximum applied moment.

To be onservative I would assume this moment to be acting both about my column x and y axis simoutaneously.

Just a thought, hope it helps.

 

[JAE]

Good comments above by all - just another overall thought - this is a perfect example of when to be conservative in your design.

Whenever you have a higher than normal uncertainty about the loading, or about the capacity, it is up to the judgement of the engineer to design upwards to the degree that is felt prudent. In this case, there is an uncertainty about the critical loading condition as well as the capacity at that loading.

 

[CSEllc]

You really nee to input this condition into a good 3D program, STAAD...RAM ADVANSE.....Risa 3D.....SAP, etc.

regading being conservative with your design.....belts and suspenders.