Models for Simulating the Seismic Response of Concrete Structures - Dynamic Behavior of Concrete and Seismic Engineering - page 238

where G is the elastic shear modulus: G = E/2(1+ Q ) , and parameters D y and D z are
correction factors that take non-uniform shear stress distribution into account.
We observe that all kinematic hypotheses presuppose the absence of any
warping. Torsion behavior does not respect Saint-Venant's theory, and the shear
strain distribution is only valid for circular sections.
Figure 7.3. Principle of multi-fiber models
When beam elements without any shear strain are used (Bernouilli's
assumption), the shear forces are generally chosen to be equal to the bending
moment derivative.
Figure 7.4. Example of a curvature-moment relationship