Footfall Response Factor 1

[l______40mm______l]

Hi all, I'm looking for some guidance on the difference between the resonant/steady state and transient vibration.

I'm designing a steel staircase in a public building and I'm currently checking it for footfall vibrations. I'm doing the analysis in Autodesk Robot Structural Analysis package and am using the SCI P354 guide (Design of Floors for Vibration 2009) for the design criteria. I want to limit my response factor/multiplying factor to 24 as per Table 5.3 from the SCI guide (public stairs).

At the moment I've got a very stiff staircase with a high natural frequency. I'm getting a Resonant response factor of 11 and a Transient response factor of 83.

I've heard mixed information as to whether you can simply just take Resonant response factor or whether you need to consider both.

Any advice would be appreciated.

Cheers,
40mm

 

[Agent666]

Which one (or both) that needs to be checked really depends on the frequency. For high frequency systems only the transient response needs to be checked. Refer to section 6.3 in P354 for the cut-off frequency between the two behaviours.

When you say stiff, what is the frequency? Is it a high or low frequency system. For low you check both, for high you only check the transient response.

 

[l______40mm______l]

Thanks Agent666, the fundamental frequency is 18 Hz so it's well in the high frequency range.

Any suggestions apart from increasing the stiffness to reduce the transient response factor? Even though it helps I can't really add mass to the system without changing the design intent.

 

[Agent666]

Got a picture/sketch of your stair, without knowing what you are dealing with it is hard to say.

I think as well you'll get far less complaints from users about a transient response than for a resonant response issue. So you could just see what it's like but have a plan B up your sleeve.

The hard thing regarding vibrations is it's all very subjective, one person might not find a certain vibration response concerning, while the next person may be concerned there is something wrong with the stair and have a perception that it's going to fall down or something.

 

[l______40mm______l]

It's basically a spiral staircase supported by a central circular hollow section, UC (I-section) cantilevered beams and PFC (C section) stringers. The treads and external balustrades are comprised of steel plates so I modelled them in to try to replicate the actual stiffness as opposed to the stick model of the stair I'm using to check strength/deflection. Note that I have fixed all supports and releases in the footfall model.

I really appreciate your help on this. I often read these threads and it's MVPs like yourself that make these forums so helpful.

 

[Agent666]

I'd imagine going to a larger PFC doesn't help.

But I'm perhaps a little dubious on how the PFC and treads and handrails are all connected together analytically seeing the results. Seeing how you get the worst response out on the edge where you effectively have this handrail acting like a deep stiff member.

Is it all meshed up to a fine enough mesh to capture the response? I'm not overly familiar with robot, we have a copy in my office but I've never used it much.

But not withstanding that, you're obviously getting the largest response where no one is logically going to walk up the stair (right on the outer edge of the treads), so keep that in mind. If you were to eliminate the footfall load you consider from the outermost and innermost regions of the treads how would it look? The peak response usually corresponds to the observer being at the same location of the applied transient vibration force. So as someone else being on the stair some way distant from this (say standing still a few treads higher), is the response satisfactory at that location.

 

[Agent666]

I kind of think as well if you're into the modelling of all the treads using plates, then you potentially should also be modelling the CHS and PFC using plate elements in a similar way. Otherwise you're not modelling the stiffness of the tread to CHS wall connections adequately. As treads connect to a frame member, so at the point of connection you're not accounting for wall of CHS deforming or anything like that. No idea if of significance to your problem though.

 

[l______40mm______l]

The balustrade does help quite a bit, the Rf increasing to 150 when I remove it. It is a deep stiff element but it's only supported by the stringer on the outside edge.
I've used a relatively fine mesh (0.05m).

I agree that it's not realistic that people will be walking on the external edges of the stair. This does help a bit, I could probably justify ~60 at the moment.

I'll play around with the modelling and see if it helps.

The response factor criteria I'm using does seem to be aimed at the resonant response factor. Does anyone know if a different criteria can be used for transient vibrations?
Otherwise I'll bump up the member sizes.

Thanks!

 

[Agent666]

Even just a single vertical strut as follows might offer a substantial improvement, adding further supports effectively around the curve, but alters the aesthetic.

Are you sure the PFC's and UC's are connected to the plates along there full length and not just at the ends of the frame elements, are they meshing also with the plate elements?

I believe the same limits apply for checking the transient response, as the limits are derived from the comparison to baseline curve acceleration. Ultimately any response is compared to a multiplier on the baseline 0.005m/s^2 acceleration as noted in section 6.5.3 of P354.

 

[blihpandgeorge]

this doesnt initially strike me a risky stair, if the outer balustrade is structural there is quite a bit of structure in this. i assume the balustrade is continously welded? notwithstanding, have you looked at thicker wall CHS? this would stiffen the rotation at the root of the cantilever

as already said, dynamics is very subjective to the person and there is a difference as well between perceiving movement and objecting to movement. there is ultimately an element of engineering judgement particularly when it comes to more transient and geometric elements such as stairs. floors and bridges more readily have people doing different functions happening at the same time (someone concentrating whilst someone else is moving), however i expect this is also partially built into the acceptance criteria.

the person walking is less likely to feel any dynamics as they are moving themselves and the nature of the stair is that it is unlikely to have another person waiting on the stair when another person is walking up. Further it is only the ends of the treads that have very high values, at best there is only 1 foot here, with the other foot appearing to be closer to the 22 - 30 range.