Single Span Railing Analysis

[ahypek]

We currently have an interior stair railing that was specified by the EoR for us to fabricate that does not pass NYCBC calculations now that some dimensional changes have occurred. We're trying to avoid a major change order here as we have ordered all of the pipe.

The rail has two end posts 1-1/4SCH80 and a top rail 1-1/4SCH40.

Typical calculations as per AMP521 + AISC LRFD involve using overly conservative assumptions like simply supported guardrails and cantilevered posts free to translate/rotate at one end.

At the moment these railing are 1.14 required/available under those assumptions and most certainly less than 1 with more thorough analysis.

Typically I'd reduce the 1.6 load factor to make it work for the EoR but unlike ASCE/AISC, NYCBC lists the rail loads under "LIVE LOADS." Since this is a single span endpost there's no reduction factor either.

Being that I am not currently using any structural analysis software, everything works if I idealize this post as fixed at one end, free to deflect but not rotate at other. (which is how I expect it to behave as opposed to it being free to rotate at one end)

Does anyone have a problem with my assumption of the guardrail providing significant rotational restraint and insignificant lateral restraint?

EDIT: Just wanted to reiterate that I have absolutely zero concern about the strength and stability of the system.

 

[JStephen]

I don't really see what would prevent it from rotating at the end.
You might also check if actual yield is higher than assumed.

 

[ahypek]

Realistically, you'd have a rotation and translation spring.

 

[JAE]

everything works if I idealize this post as fixed at one end, free to deflect but not rotate at other. (which is how I expect it to behave as opposed to it being free to rotate at one end)

I don't think a vertical guard rail post is inhibited in any significant way from rotating at the top. The adjoining horizontal pipe would only restrict rotation if at the opposite end it was fixed to an immovable boundary condition, which it is not. It is fixed to another pipe that does have some rotational resistance but you'd have to model all that to see what level of restraint there is.

The only other thing is how much load-sharing is there between posts. If you apply a 200 lb. load at the top of one post, does the opposite end help a bit in limiting the bending in the loaded post.

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[BridgeSmith]

I'll second JStephen's suggestion to check the mill certs, and share the concern about assuming it is fixed for rotation. The only resistance to rotation perpendicular to the railing (which I assume is the loading direction of interest) is the torsional stiffness of the pipe, which won't be much, considering the small angle of rotation and the length of the top rail.

 

[ahypek]

I'm awaiting the mill certs.

While I do agree that realistically the guardrail does not inhibit rotation completely, we can all agree that the reaction would be much lower than 200*(height of the post) right?

 

[canwesteng]

Is the post or the rail failing? If you're going to go this route and the post is anchored to concrete (brittle failure) make sure the anchorage is designed for the most conservative loading. As long as you don't have any other potential brittle failure modes on the rail (weld perhaps), you can model it this way, but I'd check deflection as if it were simply supported.

 

[ahypek]

Rail is good to go with the uniform and concentrated load under conservative boundary conditions.

Post is the only thing that is just under the required yield strength with a concentrated load applied at the top.

Anchors have a 4x FOS of them, so no issue there.

 

[JAE]

I'd agree that the moment is somewhat lower than 200 x height. But not "much" lower as you describe.



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[structuralsteelhead]

I would assume that the ends of the rail 'may' see some partial fixity due to the torsional resistance of the fully welded connection to the guardrail posts (if this is such the case). However, if you are using 1 1/4" pipe, schedule 80 on the posts and exceeding anything much further than 4 feet with regards to the post spacing, and a 42" top rail height, you may already have some issue on the posts as well. But I understand this is not your question.

If you truly feel you have some fixity at the rail connections to the posts which I agree to be the case due to some torsional restraint of the guardrail posts, and feel the time spent behind the desk will prove your case, (1/10/100 rule) and will save you/your client a large material change order, you should approach the client with your beliefs that if you spend some 'compensated' time and effort to run the calcs, you may be able to support your design methodology to a degree to convince yourself and the plan checker you have done your due diligence and provided an acceptable level/standard of care to the design. Estimate the torsional restraint/rotation of the posts, and reapply the estimated partial fixity to end connections. This may take a couple of iterations before you reach your results if not using a structural design program. Since you are using 1 1/4" diameter for your posts and rails,...I would also check total deflection at midspan of the rail, combining deflections of the posts plus the rail deflections. I believe service loads should be used for this check. Your design should include proof of weld strength and base material are capable of providing the restraint you claim to occur at the connections.

A Cadillac post and rail design, but the numbers will not lie and they may get you out of that change order mess.

 

[JAE]

Just did a quick model - two posts fixed at the base - 4 ft. apart - with a 3.5 ft. height to a horizontal pipe - sizes per your original post above.
With a 0.2 kip lateral load x 1.6 applied to one post top - we get a moment of 0.834 ft-kips vs. .2 x 1.6 x 3.5 = 1.12 ft-kips.

That is 75% of the independent post-load moment. So perhaps your "much lower" is somewhat correct.

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[BridgeSmith]

"...free to deflect vertically..."

Huh?

"...we can all agree that the reaction would be much lower than 200*(height of the post) right?"

Unless there's some restraint in the system that I'm not aware of, no I can't say I'd agree with that. As I said, the torsional stiffness of the top rail is not significant enough through the small deformation it would see before yielding of the post, to reduce the reaction any significant amount.

 

[ahypek]

While I'm waiting on the mill certs, I just had a friend e-mail me results from a model in SAP.

Here's what I've got:

1. Cantilever with 0 restraint at one end: 1.17 k-ft
2. Cantilever free to translate but not rotate: 0.59 k-ft
3. SAP: 0.72 k-ft

 

[ahypek]

structuralsteelhead; The post is side mounted now so I've got just over 42" of cantilever (this is where the problem began). Welds and base metal are good to go.

Thanks for the confirmation JAE.

HotRod10; the "free to deflect vertically" is just a direct quote. In this case, it would be lateral.

 

[JAE]

What is your post spacing?
Your numbers are in the range of my 0.834 k-ft. listed above but perhaps my 4 ft. post spacing was closer than yours and thus the help from the adjacent post was more.

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[structuralsteelhead]

OP, now seeing you are more concerned with the post. I'm typically using 1 1/2" diameter sch80 to make the 200# pt load work, but its been while since I've made the calc. On another note, Post installed Anchors should include omega factor (2.5) unless you jump through a lot of other hoops. Check ACI, appendix D. Sounds like you have enough safety factor to cover it.

 

[BridgeSmith]

JAE, with the posts that close, I can definitely see how the moment could decrease that much, but I suspect the reduction would dissipate rapidly as the post spacing increases.

 

[ahypek]

Great news gentlemen, my supplier sent A500 GR. C pipe and the yield on the cert are 62000 psi.

 

[structuralsteelhead]

Sorry, slow to read responses. You've got some FEM'ers on it. You're in good hands, Ahypek,....I'm out!

 

[JAE]

Our work here is done...

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