huangyhg

torsion capacity in existing rc beam
i have run into a situation on a cantilevered slab that monolithically ties into a rc beam. the proposed loading will result in an applied torsion that exceeds the torsion capacity of the rc beam. the rc beam does not have the tied (torsion resisting) stirrups, so i analyzed the capacity of the concrete section per aci 11.6.1, limiting the capacity to the cracking torque tcr. is there any additional torsion capacity that is provided by the shear stirrups (u-shaped)?? right now, it appears that my only solution is to reduce the torsion in the cantilevered slab by adding a column or some other sort of bracing near the edge of the slab. thanks in advance for any advice. p.s. this is a great site - i just stumbled on to it this morning.
samenella,
the u-shaped stirrups provide shear/torsion reinforcement for the two sides and the bottom of the rc beam. the reinforcing bars in the cantilevered slab that extend through the top of the beam and are anchored (by hook or by development length) could take torsional shear stresses on the top of the beam.
i believe you could consider the excess area of those bars, not needed to carry the moment in the slab, as contributing to the torsional reinforcement of the beam.
aef
i do not believe that the u-shaped stirrups are effective in resisting torsion. but does the slab continue past the beam? if so, the back span of the slab and the beam itself will share the negative moment based on their relative stiffnesses. since the bending stiffness of the back span is probably a lot larger than the torsional stiffness of the beam, the beam will not see much torsion.
daveatkins
dave,
the slab does in fact extend beyond the rc beam. to give you a little background - because of the relatively complex loading (circular loading pattern with 8 bearing pads) and complex slab-column-circular wall system - i have modeled using staad. to my knowledge (this is my first floor system i have modeled with staad) the stiffness of the beam and slab have been accounted for in determining the applied torsion to the beam. intuitively i would agree with you that the "back" slab would provide significant stiffness, but i'm relatively confident that this has been modeled in staad and the applied torsion that i'm seeing in the beam is reasonable. however, i'm also inclined to believe that the excess moment steel in the slab would provide at least some additional torsional capacity. any ideas on how to better quantify this mess??? thanks for your help.
i worked on a parking structure once where my supervisor told me that once a r/c beam fails in torsion, then the moment is redistributed to the slab. we justified an existing beam on that project in this manner, but i must admit i was not 100% comfortable.
aci 11.6 covers torsion design quite extensively. section 11.6.1 gives the maximum "ignorable" torsion. section 11.6.2.2(a) gives the maximum torsion that must be designed for, since in this case any additional torsion can be redistributed to the slab. section 11.6.4.1 discusses using closed stirrups for torsion.
forgive me if you have already reviewed all those sections. back to the original question--if you can get comfortable with assuming the top steel in the slab plus the u-shaped stirrups together act like closed stirrups, then i think you can justify what you are doing. conceptually, this idea has merit. but i have never justified resisting torsion in this way.
i would check, by hand, the relative stiffnesses of the beam and the slab, to make sure staad is not overestimating the torsion.
daveatkins
using staad, probably you are modelling the slab by shell elements that are connected to the beam at some nodes in the geometric center of the beam. i believe that the statical torsional moment you get by staad is correct, but the deflection is probably overestimated since if beam and shell elements are added this way staad simply adds their corresponding stiffness and does not calculate the combined stiffness that results due to the effective width of slab that is working together with the beam. i think that you should assume an angle cross sectional form comprised of beam and effective width of slab in your capacity calculations. then estimate deflections with the cracked properties of this section using staad statical torsional moment.....
i also believe that you can assume some 'closed stirrup' action due to the negative reinforcement of the slab, but probably not to full yield...
thanks to you all for your help in this matter. this is an excellent site, and i feel fortunate to have stumbled upon it. cheers
sam, an aspect that you could check is whether the formulation of the shell elements used to model the slab includes or neglects transverse shear deformations, since, depending on the span-to-thickness ratio, they would be affecting the torsion output in varying degree.
also: are you taking into account in the concrete section resisting shear the solid slab forming the flanges of the t beam?

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