Geometric Nonlinearity

Large displacements/rotations and large independent deformations relative to the frame element's chord (also known as P-Delta effects) are taken into account in SeismoStruct, through the employment of a total co-rotational formulation developed and implemented by Correia and Virtuoso [2006].

The implemented total co-rotational formulation is based on an exact description of the kinematic transformations associated with large displacements and three-dimensional rotations of the beam-column member. This leads to the correct definition of the element's independent deformations and forces, as well as to the natural definition of the effects of geometrical non-linearities on the stiffness matrix.

The implementation of this formulation considers, without loosing its generality, small deformations relative to the element's chord, notwithstanding the presence of large nodal displacements and rotations. In the local chord system of the beam-column element, six basic displacement degrees-of-freedom and corresponding element internal forces are defined, as shown in the figure below.

Notes

1. If a given beam or column is anticipated to experience large deformations relative to the chord connecting its end nodes (i.e. p-delta effects), this effect can be taken into account by using 2-3 elements per member, which is enough for most cases.
2. It is noted that when assessing single piers, geometric nonlinearity coupled with a non-baricentrical neutral axis may lead to spurious axial load levels.