Concrete Beam Torsional Stiffness

The torsional stiffness (constant) for concrete beams is based on the members calculated Torsional Moment Of Inertia, J. For T beam and Pan Joist sections, the flange overhang are not considered in the calculation of J, as it is assumed they will crack and be ineffective at providing significant additional torsion capacity to the beam. The torsional moment of inertia is calculated as:

J = c b^{3} (\frac{1}{3} - 0.21 \frac{b}{c})

where

b	=	Smaller dimension of beam web
c	=	Larger dimension of beam web

The calculated concrete torsional moment of inertia (constant) J can be is multiplied by the torsional constant reduction factor (1.0 - Torsional Reduction %) specified in the Analysis Criteria dialog, or by the member specific torsional cracked section factor (see Section 2.5.2).

Several of the references presented below indicate that the torsional stiffness of concrete members is significantly less than that calculated using the full gross section properties. The references also indicate that the concrete structure will behave based on the reinforcing provided, and if torsion stiffness is assumed to be small the analysis will redistribute the forces and the engineer will design for these redistributed forces. In essence the structure will behave the way it was assumed in the analysis.

For cases where torsion ensures equilibrium (i.e. no redistribution is possible) then forces cannot be redistributed and the beam section will need to be reinforced to ensure that the calculated torsion force can be resisted without excessive deformation.

The following references provide some insight into an appropriate concrete torsional stiffness reduction value.

In reference 4, the authors indicate for most situations the assumption of zero torsional stiffness can be made. They do indicate that it is still important to provide, at minimum, torsion reinforcing to prevent excessive service load cracking.
In reference 5, the author indicates that while flexural stiffness decreases maybe 50 percent from cracking, torsional stiffness drops down to 5 or 10 percent its uncracked value. The author also mentions that the consideration of the torque to be used in the design is very complex due to the cracking effect. Thus it is always better to neglect the rigidity of the members for torsion and to consider them fully cracked.
In reference 6 the authors mention that the structure will behave exactly in the same way as it was idealized in the analysis (cracked or uncracked). They suggest modeling the reinforced concrete structures with a very low torsional rigidity i.e. assume it is significantly cracked.