Biaxial Bending in Concrete Beams

[neffers]

Can anybody give me some insight on how to handle biaxial bending in concrete beams. The Beam doesn't have any axial load...just bending in 2 directions. How do you account for the combined bending. I can't find anything in the ACI except for columns with Biaxial bending and axial load. Any help would be appreciated. Thanks

 

[dlew]

neffers,

I would size the top and bottom reinforcing bars of the beam for the vertical moment, and the side rebars for the horizontal moment. I would count the corner bars only as 1/2 bar because one corner rebar may be stressed by both moments.

Similarly, I would design the shear ties in such way that they provide the shear reinforcement required by each loading direction. I would use only 70% of the concrete shear strength (Vc) to account for the skew direction of the shear force.

This method may not be theoretically exact, but it is simple and, I believe, is conservative.

Regards

AEF

 

[RiBeneke]

You must also check concrete stresses in bending.
Here you would probably have substantial overlap of the 2 compression zones, so you should add the compressive stresses.

 

[ehasa59]

Adding to what RiBeneke said, wouldn't it be useful if you analize the section considering a rotation in the neutral axis since the bending plane is different to the one we normally use? Remember that you have a resultant bending moment which components are the vertical and lateral.

 

[southard]

While I may be very very late on this topic. The florida department of transportation has a MathCAD program available (free) to download. It computes Biaxial moment interaction diagrams for column design. It's good for beams too. Just use P =0, and check the moment capacity at the right resultant bending orientation. Part of my thesis was on the procedure that this program uses.

And as the previous reader eluded too rotating the n.a. is how the program generates the 3D interaction diagram. From the 3D diagram 2D interaction diagrams are extracted.

Also in some older version of ACI codes there are short cut methods using combined stress ratios (interaction equations). They are very conservative. Using the above program is easier and more economical.

later,
John

PS: If there are any questions I can be emailed a southardengineering@yahoo.com

 

[desertfox]

Hi neffers

I am no structural engineer but I wondered, assuming that the loads on the beam were through the neutral axis and at right angles to each other could you not use the principle of superposition ie:- calculate stresses and deflection for
the beam taking each load seperately.


regards

desertfox

 

[dik]

If the one moment is considerably smaller than the other, then the approach suggested by delew will give you a workable solution. If the Florida DOT has a mathcad program, it is likely worth the effort to review it and see how it works. The problem with a more rigorous solution of biaxial bending is that neutral axis and the bending axis are generally different and there is a lot of iteration in obtaining a 'correct' solution.