The situation when the static equilibrium of a structure depends on the torsional resistance of elements of the structure is illustrated in Fig.1 where a L-shaped cantilever carries a load at the tip. The longitudinal beam is subjected to a twisting moment equal to Wa and it is necessary that the beam can resist this twisting action otherwise the beam will collapse. The twisting moment Wa is equilibrium torsion and requires a torsional design covering both ultimate and serviceability states.

Fig.1 Equilibrium torsion

Compatibility torsion arises when members are subjected to twisting moments in order to preserve continuity of displacements, but torsional resistance is not required to maintain equilibrium. Fig.2 shows an intersection of two beams. Only the longitudinal beam carries an external load W normal to the plan of the grid formed by the two beams.

Fig.2 Compatibility torsion

a

W

W

If the two beams are rigidly connected, when the longitudinal beam sags under the action of force W, the transverse beam must rotate for compatibility reasons. This rotation is called compatibility torsion. This torsion is not needed to maintain equilibrium. The EC2 suggests in section 6.3.1(2) that the minimum longitudinal and shear reinforcement normally provided can produce sufficient resistance against excessive cracking caused by compatibility torsion.