*Frame beam supported on bearing beam of another frame*

In project <b_334-1> of *Holo*BIM, the supporting beam b1 has cross-section 300/500 and span* l _{1}=4.0 m*, whereas the supported beam b2 on b1 has identical cross-section 300/500 and span

*Bending moment diagrams of the structure*

If the effective torsional stiffness of the supporting beam is taken equal to 100% of its corresponding full torsional elastic stiffness, then the bending moment of the left (indirect) support of the supported beam b2 is equal to *M=-40.4 kNm.*

(Effective torsional stiffness taken equal to the 100% of the full elastic stiffness)

*M=-40.4 kNm* should be placed at the top fibers and anchored inside the supported beam b1. In the span, the reinforcing bars, designed for bending moment *M=87.9 kNm* should be placed at the bottom fibers. The bending moment of the supported beam b2 transfers a torsional moment *M _{T}=M/2=40.4/2=20.2 kNm* onto the supporting beam b1, as shown on the corresponding diagram of torsional moments. In conclusion, the supporting beam b1 should be designed for torsion.

*φ _{z,0}: the elastic angular deformation at time t=0
φ_{z,∞}.: the elastic angular deformation at time t=∞*

The rotation angle *φ** _{z,t}* of the supporting beam b1 will be increasing over time t, due to creep. As

This is why the European Standards [*EC2, **§**5.3.2.2(2)*] allow us to consider pinned supports for both beams and slabs. Otherwise, either the creep should be taken into account or the effective stiffness should be limited to a small percentage (e.g. 10%) of the full elastic stiffness.

The assumption of zero torsional stiffness provides a solution in the case of a simply supported beam. However, in the case of a cantilever beam, this turns out to be invalid, because the isostatic structure becomes a mechanism by diminishing its rotational restraint and thus transforming the support from fixed to pinned.

The assumption of effective torsional stiffness limited to 1% of the elastic stiffness gives the correct results for both frames and thus for all types of frames.

*Bending moment diagrams of the structure*

In the case of the simply supported beam b2, with an effective torsional stiffness 1% of the respective full elastic one, the indirect support of b2 on b1 practically behaves as pinned without transferring any torsional moment to the supported beam b1. The beam b2 should be designed only for bending moment *M=110.9 kNm* along its span, which is significantly greater than the moment *87.9 kNm* of the previous case with an effective torsional stiffness equal to the full elastic one.

*Effective torsional stiffness equal to 1% of the elastic stiffness, project
bending moment, (2) torsional moment <b_334-2>*

The support of the cantilever beam, on the bearing beam of the frame, behaves as fully restrained and transfers the moment of the support (*-64.1 kNm*) as a torsional moment to the bearing beam.In an isostatic structure with respect to torsion, such as structure II, no matter how small the torsional stiffness of the bearing beam is, the torsional moments remain intact.

- In general, the torsional stiffness of beams should be considered insignificant at least on site-casting.
- Similar functionality is also provided for the slab-beam support as shown in the next paragraph.