modeling RC beam - hand calculation 3

[greznik91]

I have to design RC beams that are partly integrated into RC slab. I dont know how to model/calculate this since I dont trust FEM softwares for this kind of things since I almost made a huge mistake with something similar once upon a time.

RC beams are marked yellow and red line is a bearing masonry wall above beams. Design load on beams are approx. 50 kN/m.

Id model beam 1 and beam 4 as cantilever beams but Im wondering how much does beam 4 actually helps since load is transfered in direction of stiffnes (bearing wall above beams - red line)? Is it problematic that beam 1 and beam 2 are not in the same line? If I move beam 1 in the same line as beam 2 I cant design it as cantilever since it would be a simple supported beam. How would you model this?

 

[dik]

You have a support at the end of 2?

Dik

 

[greznik91]

dik, yes I do.

 

[dik]

It should extend to the outside wall, else, you have some interesting torsional issues and your beam 1 may not have a cantilever support... your simplification has merit... and many engineers might adopt a similar approach.

Dik

 

[greznik91]

about torsion... dont you think this may not be a problem since beams are partly integrated in a slab so slab can take care of torsion effects?
Im waiting for Kootk to post some interesting thoughts about this one

 

[WARose]

about torsion... dont you think this may not be a problem since beams are partly integrated in a slab so slab can take care of torsion effects?

It might.....then again it might not. Since you are not doing a FEA model you won't have those answers. You'd be stuck designing for a worst case torsion (via paper calcs)....or sizing the stirrups for the compatibility torque required by ACI 318 for a indeterminate system.

 

[KootK]

Id model beam 1 and beam 4 as cantilever beams but Im wondering how much does beam 4 actually helps since load is transfered in direction of stiffnes (bearing wall above beams - red line)?

I don't agree with this assessment. If anything, any arching in the wall system is likely to draw load disproportionately towards the cantilevered end of beam four. I see no reason to discount beam four's contribution other than, perhaps, conservative simplicity.

Is it problematic that beam 1 and beam 2 are not in the same line?

It's only a problem if you're planning to make beams one and two continuous across beam four. It all three are to be cantilevers then it's not a big deal.

If I move beam 1 in the same line as beam 2 I cant design it as cantilever since it would be a simple supported beam.

Wouldn't that be an improvement? That's exactly how I'd do it. Simpler to design, simpler to construct, and more reliable. Cantilevers have no redundancy. Although I suppose that multiple, cojoined cantilevers sort of do.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[hokie66]

Agree with KootK. Frame it with two continuous spans.

 

[greznik91]

tnx for help. I agree with what Kootk suggested in a picture above but that way I have another problem - bearing wall is no longer above beam 1 but on the edge of a slab that is 160 mm thick. Perhaps I could do it 200 mm thick from edge of beam 1 to an edge of a slab.

 

[dik]

Is the CMU wall loadbearing? if not, the 6" slab should be able to accommodate it... any issues with cold transfer?

Dik

 

[kipfoot]

Keeping the original plan, I'd consider each beam for its worst case in positive and negative bending. Perhaps it's too conservative, but if the steel can fit reasonably you could have some redundancy.

 

[dik]

kipfoot:

Your sketch at the bottom right showing the intersection of beams 1, 2, and 4 is a really bad condition to reinforce... it should be avoided if possible. You will have a mess of stirrups due to the near fixed end moment torsion condition (the support at the intersection will not behave as a simple span, but, more likely as a continuous beam) as well as the shear from the reaction of Beam 1.

Dik

 

[KootK]

but that way I have another problem - bearing wall is no longer above beam 1 but on the edge of a slab that is 160 mm thick. Perhaps I could do it 200 mm thick from edge of beam 1 to an edge of a slab.

Yeah, that's a factor. I doubt you'll be flying any forms out past that beam so the easiest is probably just to make the cantilevered slab as thick as it needs to be, bearing or no. Another option is to just fatten the beam over the B1 section. Whatever produces the most economical formwork scenario in your market. Or maybe you go back to your original proposal. It's a game of trade offs of course...

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[hokie66]

Yes, best to just make that section of the beam wider. So about 500 or 600 wide, rather than 300. Much simpler. I wouldn't want to support 50 kN/m on a slab edge.

 

[kipfoot]

dik, yes, it's not a pretty configuration, but I think it's the condition that the OP is asking about. Maybe it could have been avoided or maybe it's the result of other compromises. I don't know. In my opinion it's worth trying to solve the geometry as it is because changing it almost always creates a ripple effect of other issues.

You make a fair point about end fixity. Moments in beams 1 and 2 cannot redistribute until something cracks. I was trying to convey the idea that they should be designed so that redistribution is possible and the torsional capacity of beam 4 is not required for equilibrium of the structure.

 

[greznik91]

thank you guys for all the help.

Kootk - i was thinking about this - to fatten the beam over the B1 section. That way beam 2 in 300 mm wide and beam 1 is 550 mm wide. it looks kinda wierd to me, but i think this is still better than my original system. In this case is beam 4 needed at all? maybe the best thing is to leave beam 4 but design beam 1 and 2 as there was no beam 4. So beam 1, 2 and 3 form continuous beam that is simply supported at both ends.

 

[hokie66]

That's the way to go, and not weird at all. I would leave Beam 4 in, just so you don't have to worry about torsion in Beam 1.

 

[KootK]

In this case is beam 4 needed at all?

Designer's choice. If design the fattened beam as a continuation of the slab, then you don't have a torsion problem and you could live without B4 if you don't need it for deflection control etc. On the other hand, if you designed the fattened beam as beam in torsion, as I likely would, then B4 is pretty handle to have around for rectifying that torsion.

[/In this case is beam 4 needed at all? maybe the best thing is to leave beam 4 but design beam 1 and 2 as there was no beam 4. So beam 1, 2 and 3 form continuous beam that is simply supported at both ends.quote]

I like it.

Some questions for you:

1) without fattening the beam, how close would the interior side of your wall be from the exterior edge of the beam?

2) How thick would you have to make the slab to be able to handle 50 kN/m shear? I don't have a good feel in metric and haven't bothered to run any numbers.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[greznik91]

OK, I feel better about the whole thing now... sometimes its hard for young engineers to do something they are not that familiar with...

1) without fattening the beam, how close would the interior side of your wall be from the exterior edge of the beam? 150 mm - aprox. 6 inches

2) How thick would you have to make the slab to be able to handle 50 kN/m shear? I don't have a good feel in metric and haven't bothered to run any numbers. Well 160 mm thick slab has aprox. 60 kN/m of shear resistance which is fine, but I want to avoid that at all cost since there are openings in a bearing wall (windows) so at some parts of the wall the load on a slab edge actually exceeds shear strenght of a slab - concetration of loads between openings. To cover this slab should be 200 mm thick but i dont like that either since there will be too many levels of formwork (160 mm slab (inside), 200 mm (outside) + beams taht are partly integrated into slab. I think its easier to just fatten the beam.

 

[n3jc]

Interesting topic...

Im asking what is a proper reinforcement detail when width of the beam change in the middle of the span - like in this case from 'fattened' beam B1 to beam B2?

Is my sketch alright?