Finite Element Analysis of Steel and Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 498

concrete slab deck, then we keep an aspect ratio of approximately 1:1:1
(width height length) and we start through the depth of the concrete slab
and extend towards the length. The maximum aspect ratio is 1:1:5 in regions
with high stress gradient. Structural steel members and concrete slab decks
having cross sections that are symmetric about one or two axes can be mod-
eled by cutting half or quarter of the member, respectively, owing to sym-
metry. Use of symmetry reduces the size of the finite element mesh
considerably and consequently reduces the computational time significantly.
Detailed discussions on how symmetry can be efficiently used in finite ele-
ment modeling are presented in [ 5.1 , 5.3 ] . However, researchers and mod-
elers have to be very careful when using symmetry to reduce the mesh size of
the individual components of bridges and the whole bridges. This is attrib-
uted to the fact that most structural steel members that have slender cross
sections can fail owing to local buckling or local yielding. Failure due to local
buckling or local yielding can occur in any region of the structural steel
member due to initial local and overall geometric imperfections. Therefore,
the whole structural steel members have to be modeled even if the cross sec-
tion is symmetric about the two axes. In addition, symmetries have to be in
loading, boundary conditions, geometry, and material properties. If the cross
section is symmetric but the bridge component or the whole bridge is sub-
jected to different loading along the length or width of the bridge or the
boundary conditions are not the same at both ends, the whole bridge com-
ponent or the whole bridge has to be modeled. Therefore, it is better to
define symmetry in this topic as correspondence in size, shape, and position
of loads; material properties; boundary conditions; residual stresses due to
processing; and initial local and overall geometric imperfections that are
on opposite sides of a dividing line or plane. The posttensioned concrete
slabs tested and modeled by Ellobody and Bailey [ 5.4 ] are examples of
how using symmetry can considerably limit the size of the mesh and result
in a significant saving in the solution time (see Figures 5.17 and 5.18 ). A
combination of C3D8 and C3D6 elements available within the ABAQUS
[1.29] element library was used to model the concrete slab, tendon, and
anchorage elements. The slab had dimensions of 4300 1600 160 mm
(length width depth). Due to symmetry, only one quarter of the slab
was modeled ( Figure 5.17 ) and the total number of elements used in the
model was 6414, including the interface elements. A sensitivity study was
carried out and it was found that a mesh size of 24 mm (width),
23.25 mm (depth), and 100 mm (length), for most of the elements, achieved
accurate results. All nodes at symmetry surfaces (1) and (2) were prevented to