Load sharing floor and beams problem

[cve60069]

Hello

I am having to design a thin (60mm) reinforced-concrete slab that will be supported on a grillage of one-way spanning beams (Picture) and I need to check the whole for a concentrated 100kN load in the centre of the slab. The concrete and steel are free of each other.

I am assuming that the slab will be able to spread the load across the joists and the maximum deflection will be beneath the point-load.

I need to check the stress and deflection in the concrete and steel and am not sure how to proceed. Any help in analysing a load sharing structure would be appreciated.

Regards

 

[hokie66]

The slab is too thin to support a 100 kN point load. When your design of the slab is thick enough, and you have checked bending and punching shear, then you can design the steel beams. Only the beams on each side of the load should be considered to share the load.

 

[csd72]

'I am assuming that the slab will be able to spread the load ...'

We are not paid to assume, we are paid to justify these things to the best engineering knowledge at the time.

Sounds like you need a mentor on this one as this is too broad a question to be adequately covered in a forum.

 

[MiketheEngineer]

And what if the load is accidentally put right over one of the steel beams??

 

[msquared48]

And why would you use tee sections rather than wide flanges? Seems like there would be a high likelihood of lateral instability in the lower portion of the web.

Mike McCann
MMC Engineering

 

[paddingtongreen]

If the slab is continuous, the most likely situation, there will be more load on the beams due to the continuity of the slab. It will reduce the load on the adjacent beams.

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

 

[cve60069]

Thanks for the advice.

I am not checking the slab. The slab will be as thick as required; I am checking the behavior of the joists. I am not convinced that the load will be shared between two joists but over all the joists, not equally. Tests on similar structures show the loads exceed 100kN but the math do not confirm this. I am trying to understand the influence the two structures have on each other.

Regards

 

[hokie66]

Then all we can say is that the deflections have to be consistent. The way the joists and slab interact depends on their respective stiffnesses. Assuming that all the load is transferred to the adjacent joists is a typical design assumption, not an attempt to model the exact structural behaviour. If this is a research project, happy hunting.

 

[ishvaaag]

I am with Mike, the load can be over one of the supporting members and then a joint in the slab as well. In the absence of topping (and to some extent even with some toppings) one can't assume any part of the point load going elsewhere than directly to your supporting members at your 100 kN or 10 tonnes value. Itis not the case of a bad statement of the load, 1 kN? This is one usual value for 1 person for maintenance of roofs (other live or snow loads apart). 10 tonne is more for a middle to light size truck crane leg or so, something unlikely to be set willingly on 60 mm thickness.

Respect how to analyze it well, you will need previously the max range of the loading slabs themselves, the dead weight may be significant enough to influence the design of your steel part.

 

[cve60069]

Hi. Thanks for the advice. The slab is being designed to spread the point-load over the ribs. It takes four ribs to support 100kN in my model without the slab.

If I treat the top slab as a plate with all sides simply supported (see pdf). The slab being supported of a series of simply supported beams. The plate and beams are free to rotate. The beams are restrained horizontally and are close together.

Would I be safe to assume that the ribs would act as a plate with an EI equal to the EI of a rib multiplied by the number of ribs.

I would allow the plates to deflect 1mm (say) and calculate the P from plate deflection formula where

Plate deflection = rib deflection = 1

Once I know P, I can then calculate the deflection and stresses.

Am I right or very wrong?

 

[hokie66]

Plate deflection formulae do not apply to a concrete slab such as this. Sagging plates act in tension, and concrete is weak in tension. The ribs cannot be expected to deflect equally if the slab is supported on all sides.

Is this a real structural issue or a research problem? If you can provide the actual design parameters, perhaps we can suggest a solution.

 

[ishvaaag]

In a FLOOR able to impart load through transversal continuity and stiffness to the ribs one verifies that when one applies the point load over 1 of the (central) ribs the moment solicitation there do not reach the value as if applied only in just one rib module, but lower value. I have somewhere a worksheet for the situation based in what stated in some books (I think it shared over 3 to 5 ribs the point load) but I am unable to find it now, even if it should be in this computer. A FEM analysis that shows such transversal continuity and stiffness can show you the same.

However, when continuity is a problem, or the slab stiffness relative to the support below is weak, one can't assume much of the load goes to any other part than to what below, such for reactions and shears when the wheels reach the supporting parts in bridges, or like when in your case you have the load over one rib where there is a joint in the slab and the slab is as weak as to not be able to significantly affect the forcibly conjoint deflection there, what most would suspect is the case when the load is 10 ton and the (concrete) slab thickness 60 mm.

In any case, the proper set of FEM analyses with the proper interfacing parts' restraints and constraints should reveal any aspect you are interested in.

 

[cve60069]

Thanks for the interest.

The design is a real problem. It is a smoke-outlet from a basement. Normally designed spanning one-way but are cast supported on four sides. Its the way the outlets are built. See newageglass.co.uk - Merchants Square or Cafe Royal for example.

The fire-brigade have to smash through the slab in 7-blows. The outlet ranges from from 80mm to 130mm thick and 1200mm wide. The slabs have to support 100kN (75kN in London) - not direct but over an area of 300mm square. Rib centres are 150mm or 165mm. We are going to build some and have them tested (hopefully) at Kingston University. I am trying to predict the behaviour of the slab and design an optimum rib. The ribs are normally concrete but I am also designing an outlet in steel and concrete but I need the slab to spread the load for the ribs to be "up to it". The lights deflect very little, 2 - 3mm.

For now, I am wishing to write down the formula to allow me to calculate the stresses in the structure, regardless of the materials - or - create an FEM of the structure. I would prefer the hand-method as I do not own any FEM.

Oh! and the slab is waffle.

 

[hokie66]

Huh? A waffle slab has ribs in both directions. Maybe that is what you need.

 

[cve60069]

I have been directed to the section on the forum discussing the "effective width" of slabs under concentrated load (do not how to place a link). I think this may be the way to calculate the load redistribution from the slab to the ribs.

This is a very good forum. Thank you all.