Beam elements are modeled using a non-linear flexural stiffness model with linear elastic shear deformations.
In this research work, beam column elements are modeled by Euler Bernoulli beams theorem, as it is expected that the shear deformations are not considered, so the crack is simulated by a translational and rotational springs, as shown in Fig. 1.
The RC elements were modelled using beam with hinges elements, and to simulate the materials, the Mander et al. (1988) and Menegotto and Pinto (1973) proposal were adopted, respectively.
2, 3 and 4-node beam elements are used for modelling the beam major axis while linear 4-node and quadratic 9-node Lagrange elements are used as expansion functions over the cross-section.
Three types of elements were used in the full bridge model: (1) the four-nodded, shell elements were used to model the bridge deck, (2) three-nodded beam elements were used to model the I-shaped steel girders, and (3) two-nodded beam elements were used to model the reinforced concrete abutment and piles.
Furthermore two node beam elements were used to model beams.
Solid and beam elements were used to model the concrete material and reinforcing steel bars, respectively.
The 3-D degenerated shell element and 3-D degenerated curved beam element are used to model plates/shells and stiffeners, respectively.
Fibre beam elements were comprehensively used before to model the behaviour of different structural systems with great accuracy.
According to the characteristic of this kind of crack, a new spatial crack beam element is developed, and a cracked crankshaft model, which combines crack beam element and Timoshenko beam elements, is established.
