Reinforced concrete bridges - Computational Analysis and Design of Bridge Structures - page 115

The use of shear modulus, β G (with 0 < β ≤ 1), known as shear
retention, improved most of numerical difficulties and improved the real-
ism of cracking phenomena generated during the FEAs. A variable value
of reduction factor has been selected to represent changes in shear stiffness
(Darwin 1993).
As a general rule, moderately sophisticated elements such as four-node,
two-dimensional isoparametric elements and eight-node, three-dimensional
brick elements worked well. These elements usually provide the best results
when used in conjunction with four- and eight-point Gauss integration,
respectively. Higher-order elements provide locally more realistic defor-
mation and strain fields. For macroscopic representation, element size
and consideration of strain softening (fracture considerations) may not be
important.
For better understanding the behavior of structures including general
crack locations as well as concrete and steel stresses, it is advised to have
a more refined mesh and a model that includes fracture considerations for
concrete. Also, to capture the nonlinear behavior, the load step size must
be kept small.
4.4.3 FRc/FRp modeling
Researchers have studied the behavior and modeling of RC members
strengthened with FRP composites using FEM. The finite element model
uses a smeared cracking approach for the concrete and 3D-layered elements
to model FRP composites.
For research or forensic study purposes, 3D RC elements and layered
solid elements can be used to simulate the behavior of FRP-strengthened
RC structural elements (e.g., beams) using nonlinear FEM packages, such
as ANSYS (2005). For RC, the 3D solid element (SOLID65 in ANSYS) with
eight nodes and three degrees of freedom at each node, translations in the
nodal x , y , and z directions, can be used. This element is capable of plastic
deformation, creep, crushing in concrete, and cracking in three orthogonal
directions at each integration point. Solid elements simulate the nonlinear
material behavior with a smeared crack approach. When cracking occurs at
an integration point, material properties are adjusted to effectively model a
smeared band of cracks, rather than discrete cracks.
When a principal stress at an integration point in a concrete element
exceeds the tensile strength, stiffness is reduced to zero in that principal
direction perpendicular to the cracked plane. Cracking can be simulated
at each integration point in three directions. FRP composites are modeled
with 3D-layered structural solid elements (SOLID46 in ANSYS) having the
same number of nodes and degrees of freedom as the concrete elements.
The solid element allows for different material layers with different orienta-
tions and orthotropic material properties in each layer. Steel reinforcement