Examples of Finite Element Models of Steel Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 556

The study indicated that the load-carrying capacity decreases with the
increase in curvature. The authors developed a 3D finite element model
using ABAQUS [1.29]. Eight-node doubly curved thin shell element with
reduced integration points using 5 degrees of freedom per node (S8R5) was
used. Riks method in conjunction with the modified Newton-Raphson
method was employed. Residual stresses were not considered in the analysis.
The authors mentioned that although it is understood [ 6.3 , 6.4 ] that the shell
elements provided by ABAQUS at the plate midthickness could not pick up
Saint Venant torsional stresses, this effect was not of main concern in the
study since the focus was only on ultimate load-carrying capacity. The sec-
ondary girders are represented in terms of appropriate boundary conditions
at the support. In the same way, the effect of tie rods used in the experiments
to prevent the lateral buckling of the girder at the midspan was taken into
account by adopting relevant boundary conditions at the midspan. Geomet-
ric imperfections were imposed in terms of the buckled shape of the web
plates at the elastic stage. The buckled shape was obtained from ABAQUS
analyses in which the girder was loaded without any imperfection. The lat-
eral displacements and the buckling mode thus obtained at the elastic stage
were imposed in the final analyses of the girder. Convergence studies were
performed to determine the suitable finite element model for the analysis.
Three different meshes with 552, 1152, and 1506 elements were considered
in the studies. The difference between the ultimate strengths corresponding
to models with 552 elements and 1152 elements was about 9% and that
between the values corresponding to the models with 1152 and 1506 ele-
ments was around 1.8%. Therefore, finite element analysis based on 1152
elements was adopted in the finite element modeling for all the girders
curved in plan.
Floor beams of orthotropic plated bridge decks were investigated by
Corte and Bogaert [ 6.5 ] . The beams have generally elements with a low
slenderness, especially in the case of railway bridges. This is attributed to
combined flexural and shear deformations. The shear deformations can be
considerably large to be neglected. The authors discussed that in a design
according to the Pelikan-Esslinger method [ 6.6 , 6.7 ] , this deformation is
taken into account in the second stage of the calculation of the orthotropic
deck. At this stage, the additional bending moments, shear forces, and floor
beam reactions due to the floor beam flexibility are evaluated. The deflec-
tion of a directly loaded floor beam creates a distribution of the load to adja-
cent nonloaded floor beams. In addition, the deflection will affect the
longitudinal ribs, increasing the sagging moments at midspan and decreasing