Bi-axial Shear in a Concrete Beam with Torsion

[TexCE2009]

I have a concrete beam that is taking on a load that is creating torsion in the beam as well as bending and shear about two axis. I have the bi-axial bending worked out for the beam design, but I am having issues with the shear and torsion design. Can the design be looked at independently by using Vux and Tu, and then considering Vuy and Tu? My understanding of the truss model is that the shear carried in a plane is carried by the legs of the stirrup parallel to the shear and therefore the shears could be designed for separately.

Is this a correct interpretation?

 

[BAretired]

Stirrups must carry shear and torsional shear. The effect on the stirrup is not independent...it is additive.

BA

 

[TexCE2009]

I understand that the stirrups carry shear and torsional shear. My question is can you look at Vux + Torsion as one case and then Vuy + torsion as a second case and then design with the controlling case.

 

[csd72]

I dont think it really works that way.

I would think you would need to analyse the resultant diagonal shear on the section rather than the two separately.

 

[hokie66]

I think Tex is on the right track. A stirrup has 4 legs, and the combined force would be different in each one with his described condition. The Vux and Vuy forces are divided equally in their respective directions, but the torsion forces are equal and opposite in those directions. So you would just find the maximum of the four forces and design for that.

 

[csd72]

hokie,

But as it is a continuous loop then tension along the two sides will also cause tension in the top and bottom.

 

[ishvaaag]

Perhaps a useful trick would be to make explicit the 3 D morsch analogy in some 3D strut and tie -line frame- model; the bigger difficulty would be that we would have to lump some stirrups together to keep some reasonable angle for the notional concrete struts. Distributed steel in the faces also would need to be lumped at corners and then back-redistributed for useful result. The model would be just as a segment of the vertical column truss in a construction crane.

 

[ishvaaag]

In my previously proposed model the concrete strut part must have the section (and stiffness) consistent with the wanted stirrup separation, otherwise concrete would show excess of stress far soon than in reality required, demanding a far too bigger section.

 

[ishvaaag]

What means that for cases with significant torsion and close stirrups you can take for the struts the whole section concentrical to the plane of the stirrups (from face); if strut stress reamins this way tolerable, the steel design can proceed along the determined forces, and if not, bigger section is required.

 

[csd72]

good points ishvaag.

 

[abusementpark]

I usually just added the two shear components directly and treated it as uni-axial shear and torsion, hoping that it is conservative.

 

[hokie66]

csd72,
The modern code provisions for reinforcing for torsion are supposed to allow for the concrete internal "strut" action. Design provisions for torsion represent what is probably the most significant change between ACI318-63 and the later versions. Similar for Australian standard.

The tension in a stirrup varies as you go around the loop.

 

[csd72]

hokie,

Yes but that does not stop you modelling it as strut and tie to make sure you understand its behaviour.

Agree with the varying stirrup tension, about half of it gets taken out at each corner so the top and bottom tensions are only about half as much as the side ones but nevertheless it needs to be taken into account.

The complexity comes in when you are considering the effect of tension stiffening on the shear capacity.Biaxial shear for this would be different to uniaxial shear though I have never gone into this one in depth.

 

[ishvaaag]

I really have not looked yet that, hokie, but makes me think that if what ACI now says is that now in some way we can account on the concrete inside the outer notional shell core to resist torsion, then if we want to extoll the full capacity of the section in torsion, a more complicates strut and tie model than proposed above is needed. I imagine that it can be devised, anyway.

 

[ishvaaag]

erratum

well, shell "core", shell zone.

and then "complicated" or "complex".

 

[BAretired]

I misunderstood the original question. I agree with Tex and hokie that you can determine which leg of the stirrup is critical and design for that.

BA

 

[Lubna88]

hi
i could not understand the ideas of designing beam due to biaxial shear and torsion
if anyone pleaaaaaaaaase have example or simple idea plz tell me