Eccentric loading of beam at support

In design approach (A), defined in Section 9.7.2, the beam support must be able to resist the torsional moment at the beam end. This means simple calculations of equilibrium torsion, which is statically determinate.

In design approach (B) the free rotation is often not fully developed. When using hidden steel corbels placed in the rotation centre of the beam and/or week columns the conditions can be regarded as ‘free to rotate’. In these cases the calculation model is simple.

If the rotation is partially restrained at the beam supports, a more complex situation appears and a more advanced analysis is needed. This problem is statically indeterminate and the actual torsional moment and its distribution along the structural member depend on the rigidities of the interacting elements and their connections within the system as described in Section 9.7.1.

When torsion appears in beams, the beam itself should have sufficient torsional capacity and the resulting torsional moments at the ends of the beam must be resisted at the supports. However, in compatibility torsion the torsional moment depends on the rigidities and decreases when the beam cracks in torsion.

There are various alternatives to resist a torsional moment at beam end supports. In case of wide beams it might be possible to balance the torsional moment by an eccentricity of the reaction force in the support, see Fig. 9-63. In case of one-sided ledge beams this means that the support reaction might act mainly on the ledge itself, see Fig. 9-64. The connection zones of the supporting as well as of the supported elements must be designed and detailed accordingly to withstand the reaction in this eccentric location. The strut and tie method is appropriate for this purpose. The reaction is of course associated with small deformations in the support connection, which means that the tilting is not fully prevented.

Fig. 9-63: A moderate torsional moment can be balanced at the beam support by an eccentric support reaction, a) support fully in compression, b) support partially in compression

Fig. 9-64: At ledge beams the reaction might be concentrated towards the ledge, which must be considered in the design and detailing of the beam end

If the support joint is provided with a soft bearing, an eccentricity of the reaction force might result in an unacceptable or undesirable tilting of the beam at the support due to the flexibility of the bearing. To obtain a stiffer torsional restraint the connection can for instance be provided with eccentrically arranged bolts, see Fig. 9-65.

Fig. 9-65: Eccentric bolt increases the torsional restraint at the support and reduces the tilting of the beam even if the bolt is not needed with regard to the torsional resistance, a) tilting of beam without bolt, b) tilting prevented by bolt

e

N

a) b)

a) b)

In case of greater torsional moments and/or more narrow beams, it might be impossible to resist the torque just by an eccentric reaction. Instead the connection must be designed so that a force couple can be established to balance the torque. Force couples can be established by compressive, tensile or shear forces established by the basic force transfer mechanisms described in Chapters 6, 7, and 8.

Some examples will be presented in the following.

On column heads the only possibility is to establish a force couple by vertical forces. A simple and common solution is to use a support bolt in an eccentric position or twin bolts as shown in Fig. 9-66 a. With this solution the beam can still move rather freely in relation to the support in the longitudinal direction. Alternatively the beam can be connected by welds between weld plates, see Fig. 9-66 b. In this case longitudinal movements are restrained and the corresponding restraint forces must be considered in the design.

a) b)

Fig. 9-66: Examples of torsion resistant connections at beam supports where a vertical force couple balances the torsional moment, a) eccentric bolts (Courtesy ‘PCI Design Manual on Connections’), b) weld plate and eccentric welded joints

In case of beam supports on corbels, the column, which passes behind the beam end, gives a possibility to establish torsional transfer by horizontal forces in a force couple. Fig. 9-67 shows examples where a steel plate or a hollow steel section protrudes from the column face into a recess in top of the beam.

The steel plate, which is welded to the column, can slide in the ‘tray’ in order to prevent negative moments from developing. The horizontal force caused by the torsional moment is resisted by edge pressure between the plate welded to the column and the ‘tray’ in the top of the beam, and further on through the weld to the column. The balancing force couple consists of the contact force between the beam and the protruding steel detail and an opposite horizontal force developing at the support joint.

This solution is only possible in case of smaller forces. Instead of a steel plate and a ‘tray’, the connection can be made by using hollow steel sections, where the one welded to the columns fits tightly into the one embedded in the beam.

Beam-column supports with a hidden support knife require special considerations with regard to transfer of torsional moments. Even if the support knife itself has a large capacity for torsion, the beam end might tilt slightly due to the clearance for the support knife in the recess. To prevent this tilting a permanent torsion resistant connection could be provided using the solution above, see Fig. 9-67 b.

Depending upon the magnitude of the torsional moment, the hidden support knife can resist the opposite horizontal force in the force couple, or a similar solution must also be provided in the bottom of the beam. When the beam and column are large enough, double knifes could be used to balance torsion.

weld plates

Fig. 9-67: Examples of torsion resistant connections at beam support where a horizontal force couple balances the torsional moment, a) beam support on corbel, b) beam support with hidden ‘support knife’. In case of greater forces hollow steel sections should be used instead of steel plates