Simple method for analysing point loads on a two-way slab? 1

[Mohrtec]

Hi all,

I am a masters student in structural engineering & temporary works so any help, tips & pointers on how to go about the following would be very much appreciated.

I need to check the effect of compression/tension loads on a 300thk flat two way slab due to having to install a cantilever load deck (see attached images) and therefore determine if backpropping is needed. There will be two 41kN point loads acting on the edge of the slab where the deck beams sit as well as 12kN uplift forces through the props. Does anybody know of a rudimentary method to carry out this check?

The arrangement of the supporting columns/walls means the load path is more complicated than it would have been for a grid column layout (see attached for column/deck arrangement).

Thanks!

 

[jdonville]

I believe that terms of service disallow student questions.

Check limit states at each connection (bearing, punching shear, flexure, shear) and for the member(s) as a whole using the code provisions. Not rocket science.

 

[BAretired]

UoS-Stef,
I was unable to read your first attachment. The second attachment is a plan view. Some dimensions are shown but are too small to read.

If faced with that geometry, I might try to convince the architect to move the load deck a little further south. Failing that, I would consider two band beams within the slab itself, i.e. beams with a depth equal to that of the slab, in this case, 300 mm. One would be at the north edge of the slab under the pair of 41kN downward loads. The other would be under the two 12 kN upward loads and would span from the column at the left to the wall at the right.

Normal to the two band beams, the slab would be reinforced to ensure the point loads were delivered to the middle of the band beams; more like a one way than a two way slab. A third band beam running normal to the others, spanning from the elongated column at the north end to the band beam under the 12kN loads would handle the eccentricity of the northernmost band beam.




BA

 

[r13]

The arrangement of the supporting columns/walls means the load path is more complicated than it would have been for a grid column layout

Yes. Your assessment is correct.

Since you mentioned "load path", I assume you are more interested in knowing the effects on the slab, and the supports, due to the loads produced by the cantilever load deck. If this is the purpose, I suggest to perform a FEM analysis, which will give you a better feel on how the resulting stresses varying from otherwise a grid column layout. Owing to the irregularities of the layout, I don't know any simplified method can carryout the check.

After getting the results, then you shall check the local effects as point out by jdonville, or modify the deck support as suggested by BA. Hope this helps.

 

[WARose]

For MTO purposes, I developed some rules of thumb formulas (based on FEA of typical situations) for moments developed some years back. I.e. stuff like (for a 10'x10' bay, with pinned supports on all 4 sides) Mmax[lbs-in/in]=Pa/600. Where P= point load in the middle of the bay, a=width of bay on one side. For smaller "bays" that 600 number gets way smaller (i.e. 6"x6" plate, it can fall to Pa/30). The number just varies based on the dimensions involved and the stiffness of the "plates" involved.

If you don't have FEA, you may want to try Roark's handbook. (I cannot recall if he had such a solution for a point load. Certainly for full pressure.) Maybe a advanced mechanics of materials book as well.

 

[Mohrtec]

jdonville, BAretired, retired13, WARose thank you for your responses.

I believe that terms of service disallow student questions.

Check limit states at each connection (bearing, punching shear, flexure, shear) and for the member(s) as a whole using the code provisions. Not rocket science.

Although I'm a student, this is actually for work. I included that part in the post to indicate my level of experience. Checking for flexure, shear and punching shear is exactly what I've done but I'm uncertain if this is the correct way to go (or is it?) - is it as simple as just checking the slab? What about additional moments on the columns?

UoS-Stef,
I was unable to read your first attachment. The second attachment is a plan view. Some dimensions are shown but are too small to read.

If faced with that geometry, I might try to convince the architect to move the load deck a little further south. Failing that, I would consider two band beams within the slab itself, i.e. beams with a depth equal to that of the slab, in this case, 300 mm. One would be at the north edge of the slab under the pair of 41kN downward loads. The other would be under the two 12 kN upward loads and would span from the column at the left to the wall at the right.

Normal to the two band beams, the slab would be reinforced to ensure the point loads were delivered to the middle of the band beams; more like a one way than a two way slab. A third band beam running normal to the others, spanning from the elongated column at the north end to the band beam under the 12kN loads would handle the eccentricity of the northernmost band beam.

Normally I would place a beam of a specific length spanning the tops of the two props that are generating uplift onto the slab above so that the deadload of the above slab may counteract the tension. However my calculations show I would need a 13m length beam which is not feasible - there's simply not enough space for it. Furthermore for the 41kN loads I would backprop the slab on which the cantilever deck is positioned but I need to know if one level or two levels of backpropping is needed.

Yes. Your assessment is correct.

Since you mentioned "load path", I assume you are more interested in knowing the effects on the slab, and the supports, due to the loads produced by the cantilever load deck. If this is the purpose, I suggest to perform a FEM analysis, which will give you a better feel on how the resulting stresses varying from otherwise a grid column layout. Owing to the irregularities of the layout, I don't know any simplified method can carryout the check.

After getting the results, then you shall check the local effects as point out by jdonville, or modify the deck support as suggested by BA. Hope this helps.

Yes correct, I feel that one of the problems is not knowing the load path to the surrounding supports so that the structural engineer may check if columns/walls have enough capacity to acommodate them - I have no doubt that they do, but I just need to provide some calculations that show results in the right ballpark. The issue is, I work for a construction company and do not have access to the original model in order to carry out a proper FEA. All I have are drawings from the structural engineer. The only thing I can possibly do is to draw up and analyse a slab using FEA and apply point loads and boundary conditions in such a way to try to replicate the layout as per my second attachment (CAD layout), but I doubt this would be correct (or close enough to correct). This is an 8 storey concrete frame building. I've reattached the image of the crane deck that wasn't displying.

For MTO purposes, I developed some rules of thumb formulas (based on FEA of typical situations) for moments developed some years back. I.e. stuff like (for a 10'x10' bay, with pinned supports on all 4 sides) Mmax[lbs-in/in]=Pa/600. Where P= point load in the middle of the bay, a=width of bay on one side. For smaller "bays" that 600 number gets way smaller (i.e. 6"x6" plate, it can fall to Pa/30). The number just varies based on the dimensions involved and the stiffness of the "plates" involved.

If you don't have FEA, you may want to try Roark's handbook. (I cannot recall if he had such a solution for a point load. Certainly for full pressure.) Maybe a advanced mechanics of materials book as well.

Thanks. None of the books I've read 'til now covers this but i'll give it a read.

 

[r13]

Simple evaluation/verification can be done by:

1) For the loads at the north end, model a continuous edge strip in the E-W direction with far end fixed (on rigid long end wall) and/or pinned & fixed (do both on end column support). Then, carryout analysis by moment distribution method, with all expected loadings, load factors, and effects of pattern load conditions (span loaded/empty). Although it is not easy to evaluate the effects of wind load and seismic load, at least you shall consider these effects locally on the cantilever platform to produce the most unfavorable conditions. If this is an industry setting, do not forget to query if the platform will be utilized to lift heavy weights.

2) The interior loads are rather small, and are acting against the gravity loads, other then local effects (mainly punching shear), they are hardly to have significant effects on properly designed/reinforced two way slab. When you check punching shear, do not include gravity loads above. If necessary, think about modifications to spread the loads farther out. such as enlarge the footprint.

3) Lastly, you can model an interior strip in the N-S direction and imposing both or one pair of loads on it. Follow ACI recommendations on type and level of restraint/support at the ends.

The procedure above shall provide adequate, and reasonably accurate, information for you to back check the adequacy of the structure to support the added loads. But ultimately, it (adequate or not) must be confirmed by a licensed structural engineer.

 

[BAretired]

Normally I would place a beam of a specific length spanning the tops of the two props that are generating uplift onto the slab above so that the deadload of the above slab may counteract the tension. However my calculations show I would need a 13m length beam which is not feasible - there's simply not enough space for it. Furthermore for the 41kN loads I would backprop the slab on which the cantilever deck is positioned but I need to know if one level or two levels of backpropping is needed.

1. There's a slab above? Who knew?
2. There are two levels below? Who knew?
3. Your dimensions are not complete. Those that are shown are not legible.
4. The need for a 13m length of beam to resist 24kN uplift is not correct.

Back propping is a formwork issue. Back propping is not required if the props are kept in place until the concrete gains sufficient strength.

BA

 

[Mohrtec]

Simple evaluation/verification can be done by:

1) For the loads at the north end, model a continuous edge strip in the E-W direction with far end fixed (on rigid long end wall) and/or pinned & fixed (do both on end column support). Then, carryout analysis by moment distribution method, with all expected loadings, load factors, and effects of pattern load conditions (span loaded/empty). Although it is not easy to evaluate the effects of wind load and seismic load, at least you shall consider these effects locally on the cantilever platform to produce the most unfavorable conditions. If this is an industry setting, do not forget to query if the platform will be utilized to lift heavy weights.

2) The interior loads are rather small, and are acting against the gravity loads, other then local effects (mainly punching shear), they are hardly to have significant effects on properly designed/reinforced two way slab. When you check punching shear, do not include gravity loads above. If necessary, think about modifications to spread the loads farther out. such as enlarge the footprint.

3) Lastly, you can model an interior strip in the N-S direction and imposing both or one pair of loads on it. Follow ACI recommendations on type and level of restraint/support at the ends.

The procedure above shall provide adequate, and reasonably accurate, information for you to back check the adequacy of the structure to support the added loads. But ultimately, it (adequate or not) must be confirmed by a licensed structural engineer.

Thank you for this great advice.

1. There's a slab above? Who knew?
2. There are two levels below? Who knew?
3. Your dimensions are not complete. Those that are shown are not legible.
4. The need for a 13m length of beam to resist 24kN uplift is not correct.

Back propping is a formwork issue. Back propping is not required if the props are kept in place until the concrete gains sufficient strength.

Yes, I just wanted to ask the question of how one would go about analysing slabs with an irregular column layout so I didn't want to go too much into detail.
In regards to the 13m length of beam - Do you mean that the number is not correct or the approach itself? The approach is that by using a, say .305m wide beam to spread the load to the slab above I am effectively in control of how much gravity load can counter the uplift, i.e. equating the uplift and above slab deadload gives: 24kN/L = 0.305*(25*0.3) therefore L = 10.5 (not 13m)

 

[r13]

You are welcome.

A reminder, I think the platform support lack redundancy. It can be seen as over-conservative, but in practice, I would like to specify more anchorages along the edges of the platform, especially near the south end anchors. The added anchorages can also be sized and spaced to minimize the deflections of both spans.

 

[jayrod12]

When I'm checking a suspended slab I will often use a beam width of the baseplate width plus the slab thickness, many times that doubles the available width bring the rest of the requirements down significantly.