Solid slab deflection calculations 2

[Gus14]

I analyzed a 15 cm solid slab ( 8.8 m By 4.8 m ) with ( 200 mm x 1000 mm ) beams along the perimeter of the slab on SAFE software as in figure 1. The superimposed dead loads are 2 Kn/m2 and live loads 2 Kn/m2. The maximum deflection was 33 mm. Then I edited the model by adding two columns at the middle of the long span but the deflection was significantly reduced to 11 mm as in figure 2.

Figure 1 results made more sense than figure 2 because the slab length to width ratio is close to 2 and therefore it will act more like a one-way solid slab and require more thickness. So why is there a large difference in results?

Fig 1,

https://files.engineering.com/getfile.aspx?folder=dde34c29-ec21-44d7-a3ca-331c7d64d40f&file=Fig1.PNG

Fig 2

https://files.engineering.com/getfi...c8-3f8b-4a17-bcf2-2640f9c9b57b&file=Fig_2.PNG

 

[phamENG]

Makes sense to me. Both of them are predominantly one way slabs, but the FEM is accounting for the perimeter beams and you're getting two way action in both. The addition of the columns isn't changing the way the slab is behaving, it's changing the way the beams are behaving. If you want the one with extra columns to be a 2 way slab with even less deflection, add a beam between the two middle columns.

 

[Gus14]

Thank you phamENG for replying, Would you please elaborate on how the added columns changed the behavior of the beam?. Do you agree with the 11 mm deflection result in figure 2?

 

[phamENG]

I didn't run the numbers but it sounds like a plausible result relative to the first one. My brain is calibrated in imperial, for what that's worth.

It changes the behavior of the beams because it takes it from a a single span beam of span L to a continuous 2-span beam with each span equal to L/2. That's a pretty significant change in stiffness.

The slab is still spanning left to right between the beams in the long direction, it's just in the second one those beams don't deflect as much.

 

[Jamie112]

The max deflection at the middle of the slab you are getting is the cumulative result of beam deflection plus slab deflection. Adding a column on both side at the mid span of the beams reduces the deflection of the beam and thus the cumulative result of the slab, which is the main reason that you are having different absolute deflections.
If the compare the relative deflection (the difference between the central point one to the mid span of the beam one) of fig one and fig two, they should be quite close, thought not exactly the same.

 

[Gus14]

The slab is still spanning left to right between the beams in the long direction, it's just in the second one those beams don't deflect as much.

I understood.

 

[Gus14]

Thank you for replying Jamie112,

The max deflection at the middle of the slab you are getting is the cumulative result of beam deflection plus slab deflection.

You are right, I forgot to take that into account.