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CHAPTER 7
ANALYTICAL PROGRAMME USING ABAQUS
7.1 GENERAL
With the advances in modern computing techniques, finite element
analysis has become a practical and powerful tool for engineering analysis
and design. In Structural Engineering, development of structural design code
equations or redeveloping them is a continuous process and requires a wide
range of experimental studies. Performing many number of experiments is
costly, time consuming and hence uneconomical. On the other hand
conducting experiments is a compulsion for the research to progress. The
problem gets enormously simplified with the use of ABAQUS 6.9 (2009).
ABAQUS is a highly sophisticated, general purpose finite element program,
designed primarily to model the behaviour of solids and structures under
externally applied loading.
7.2 FEATURES OF ABAQUS SOFTWARE
ABAQUS includes the following features:
Capabilities for analysing both static and dynamic problems
The ability to model very large changes in shape of solids, in
both two and three dimensions
A very extensive element library, including a full set of
continuum elements, beam elements, shell and plate elements.
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A sophisticated capability to model contact between solids
An advanced material library, including the usual elastic and
elastic – plastic solids; models for foams, concrete, soils,
piezoelectric materials and many others
Capabilities to model a number of phenomena of interest,
including vibrations, coupled fluid/structure interactions,
acoustics, buckling problems and so on.
7.3 ABAQUS MODELLING
Figures 7.1 and 7.2 show the modelling of ordinary and seismic
joint and fibre reinforced joint. By using partition command the ordinary
model is separated in the joint region.
Figure 7.1 Modelling of Concrete
in Ordinary Joint
Figure 7.2 Modelling of Concrete
in Fibrous Joint
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Figures 7.3 and 7.4 show the modelling of longitudinal and lateral
reinforcement in ordinary and fibre reinforced joint and seismic joint. In
ordinary joint the spacing of shear reinforcement is 40 mm. In the seismic
joint the spacing of shear reinforcement is 20 mm up to a distance of 180 mm
(2db ) in the beam from the face of the column and 90 mm (db ) from the top
and bottom face of the beam in column and for the remaining the spacing was
40 mm, where db is the effective depth of beam.
Figure 7.3 Modelling of Reinforcement
in Ordinary and Fibrous
Joint
Figure 7.4 Modelling of
Reinforcement
in Seismic Joint
7.4 ELEMENTS USED
Solid 3D elements 8-node brick (C3D8) were used to model ordinary
concrete and 4-node linear tetrahedron (C3D4) were used to model fibre
reinforced concrete in the joint. Two node linear 3D truss element (T3D2)
were used to model the reinforcement steel.
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7.4.1 Solid Element C3D8 and C3D4)
The Figure 7.5 shows C3D8 element which is an 8-noded brick
element having eight nodes at their corners. These elements use linear
interpolation in each direction and are often called linear elements or first-
order elements. These elements have only three displacement degrees of
freedom and are Stress/displacement elements. C3D4 is a 4-node linear
tetrahedron element and three degrees of freedom at each node.
Figure 7.5 Linear Element Figure 7.6 Truss Element
(8- Node Brick Element) (T3D2)
7.4.1.1. Reason for Choosing the Element
These are the standard volume elements of ABAQUS. These
elements can be composed of a single homogeneous material or can include
several layers of different materials for the analysis of laminated composite
solids. These are Stress/displacement elements and used in the modelling of
linear or complex nonlinear mechanical analyses. Stress/displacement
elements can be used for static and quasi-static analysis. However, good
meshes of hexahedral elements usually provide a solution of equivalent
accuracy at less cost. Quadrilaterals and hexahedra (C3D8) have a better
convergence rate than triangles and tetrahedra, and sensitivity to mesh
orientation in regular meshes. However, triangles and tetrahedra are less
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sensitive to initial element shape, whereas first-order quadrilaterals and
hexahedra perform better if their shape is approximately rectangular.
For stress/displacement analyses the first-order tetrahedral element
C3D4 is a constant stress tetrahedron, which should be avoided as much as
possible; the element exhibits slow convergence with mesh refinement. This
element provides accurate results only in general cases with very fine
meshing. Therefore, C3D4 is recommended only for filling in regions of low
stress gradient in meshes of C3D8.
7.4.2 3-D Truss Element (T3D2)
Figure 7.6 shows the 3-D truss element (T3D2). These are three
dimensional truss element having two degrees of freedom. Truss elements are
used in two and three dimensions to model slender, line-like structures that
support loading only along the axis or the centerline of the element. No
moments or forces perpendicular to the centerline are supported. A 2-node
straight truss element, which uses linear interpolation for position and
displacement, has a constant stress. It is defined that the cross-sectional area
associated with the truss element as part of the section definition. When truss
elements are used in large-displacement analysis, the updated cross-sectional
area is calculated by assuming that the truss is made of an incompressible
material, regardless of the actual material definition. Truss elements have no
initial stiffness to resist loading perpendicular to their axis.
7.4.2.1 Assigning a Material Definition to a Set of Truss Elements
A set is a named region or collection of entities on which we can
perform various operations such as assign section properties in the Property
module, create contact pairs with contact node sets and surfaces in the
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Interaction module, define loads and boundary conditions in the Load module
and request output from specific regions of the model in the Step module. A
geometry set contains geometric objects (cells, faces, edges and vertices) that
are selected from one of the following types of parts or from instances of
these parts. Geometry set is created for a set of reinforcement bars in each
part. A material definition is associated with each solid section definition for
each set. No material orientation is permitted with truss elements.
7.4.2.2 Embedded Element
The embedded element technique is used to specify that an element
or groups of elements are embedded in host elements. The embedded element
technique can be used to model rebar reinforcement. ABAQUS searches for
the geometric relationships between nodes of the embedded elements and the
host elements. If a node of an embedded element lies within a host element,
the translational degrees of freedom at the node are eliminated and the node
becomes an “embedded node.” The translational degrees of freedom of the
embedded node are constrained to the interpolated values of the
corresponding degrees of freedom of the host element. Embedded elements
are allowed to have rotational degrees of freedom, but these rotations are not
constrained by the embedding.
7.5 MATERIAL PROPERTY
Property module is used to perform the following tasks:
Define materials
Define beam section profiles
Define sections
Assign sections, orientations, normals, and tangents to parts
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A material definition specifies all the property data relevant to a
material. A material definition is specified by including a set of material
behaviours and the property data is supplied with each material behaviour.
The material editor is used to specify all the information that defines each
material. ABAQUS/CAE assigns the properties of a material to a region of a
part when a section referring to that material is assigned to the region.
7.6 MATERIAL BEHAVIOUR
7.6.1 Concrete
Concrete damaged plasticity model (CDP) was used for defining
concrete in plastic range. The concrete damaged plasticity model provides a
general capability for modelling concrete and other quasi-brittle materials in
all types of structures. This model uses concepts of isotropic damaged
elasticity in combination with isotropic tensile and compressive plasticity to
represent the inelastic behaviour of concrete. The concrete damaged plasticity
model is based on the assumption of scalar (isotropic) damage and is designed
for applications in which the concrete is subjected to arbitrary loading
conditions, including cyclic loading. The model takes into consideration the
degradation of the elastic stiffness induced by plastic straining both in tension
and compression. It also accounts for stiffness recovery effects under cyclic
loading. Concrete stress- strain behaviour under uniaxial compression after
elastic range (0.7fc) should be defined in terms of stress versus inelastic strain
(crushing strain) (Danesh et al. 2008).
7.6.2 Reinforcement
Longitudinal and transverse steel reinforcement behaviour was
defined as an elastic-plastic material using a bilinear curve. Slope of the
plastic range (Danesh et al. 2008) was assumed to be about one percent of
steel modulus of elasticity. To introduce plasticity, kinematic hardening
option was used.
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7.7 MESHING
ABAQUS/CAE provides with a variety of tools for controlling
mesh characteristics. The density of a mesh is specified by creating seeds
along the edges of the model to indicate where the corner nodes of the
elements should be located and the shape of the mesh elements are also
selected.
Figure 7.7 Meshing Model of Ordinary
and Seismic Joint
Figure 7.8 Meshing Model
of Fibrous Joint
The meshing technique is chosen-free, structured or swept where
applicable. The element type is selected and assigned to the mesh by choosing
the element family, geometric order and shape along with specific element
controls. In the present study the fibre portion in the joint is meshed using free
meshing and remaining concrete portion is meshed with structured meshing.
Figures 7.7 and 7.8 show the meshing model of ordinary and seismic joint and
fibre reinforced joint. Tie constraint is used to tie the interface between
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ordinary concrete and fibre concrete. A tie constraint ties two separate
surfaces together so that there is no relative motion between them. This type
of constraint allows us to fuse together two regions even though the meshes
created on the surfaces of the regions may be dissimilar.
7.8 LOADING AND BOUNDARY CONDITIONS
The numerical model is used to simulate the same conditions of the
test specimens. The cyclic load is applied on a node which is at a distance of
50 mm from the free end of the top and bottom of the beam in eight to ten
steps. Displacement at the point of load is obtained after the Finite Element
Analysis. Displacement/rotation boundary condition is used to constrain the
movement of the selected degrees of freedom to zero or to prescribe the
displacement or rotation for each selected degree of freedom. In the present
study on the both the ends of the column the displacement in the two
directions were set to zero (both ends of the columns were hinged).
7.9 FINITE ELEMENT ANALYSIS RESULTS
7.9.1 General
A numerical simulation makes sense only if it corresponds to the
real model. Therefore, a numerical model specimen with the same properties
of the experimental specimen was analyzed to verify its accuracy.
7.9.2 Number of Nodes and Elements used in the Analysis
In the above analysis we have modelled three beam column joints.
In the model the joint was modelled for ordinary concrete. The concrete was
modelled in a single part as a solid element. The reinforcements were
modelled by using 3D wires (T3D2). The reinforcements were modelled as
three sets such as beam main reinforcement, column main reinforcement and
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beam and column transverse reinforcement. For each set, different material
properties have been assigned.
The second model was used to model seismic joint. The concrete
was modelled as like the first model. The steel reinforcements were modelled
in four sets such as such as beam main reinforcement, column main
reinforcement, beam and column transverse reinforcement in the joint region
and other regions.
The third model was used to model fibre joint. In this model five
joints were modelled by changing various material properties of fibre concrete
in the joint region. The concrete was modelled in three parts as shown in
Figure 7.2.
Table 7.1 Number of Nodes and Elements used in the Finite Element
Model
Sl.No Name Model 1 (Ordinary
Joint)
Model 2 (Seismic
Joint)
Model 3 (Fibre
Joint)
1 No of
Nodes
2399 2564 2721
2 No of
Elements
a) C3D8
b) C3D4
c) T3D2
1092
-
Element No 1093
to 1813(720)
1092
-
Element No 1093
to 1978 (885)
897
Element No 898 to
4103 (3205)
Element No 4104
to 4849 (745)
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Different material properties were assigned for fibre concrete in the
joint regions and ordinary concrete in the other regions. The reinforcements
were modelled as like the first model. The fibre concrete was meshed by
using tetrahedron element. So the number of nodes and elements were
different for each model. The Table 7.1 shows the actual number of nodes and
elements used in the above three models.
7.9.3 Finite Element Analysis Results
Figures 7.9 to 7.15 show the deformed configuration of all the
specimens modelled using M25 concrete. Figure 7.16 shows the overall load
deflection curves obtained from the ABAQUS analysis. The deflection is
obtained by applying load at a distance of 50 mm from the beam tip at each
cycle up to failure. A good correlation was observed with the experimental
values in Figure 8.35. In the experimental specimen, when the loading reaches
the maximum value, a rearrangement in the load resisting mechanisms occurs.
When one of the load resisting mechanism reaches its capacity, the
rearrangement occurs again and the load decreases. The numerical model
cannot represent this phenomenon, thus near to this maximum level of
loading, numerical instabilities appear in some areas of the mesh and the
model cannot continue converging.
7.9.4 Global Structural Failure
Global structural failure is defined as a large discontinuity in the
composite structure’s overall vertical load-displacement curve.
(http://www.firehole.com/documents/ HeliusMCT-Example-Problem-
Abaqus.pdf). The overall vertical deformation of the composite structure is
quantified by using the vertical displacement at the load application point as
shown in Figure 7.9. A large discontinuity in the load-displacement curve is
indicative of very rapid growth (spreading) of localized material failures that
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occur during a particular load increment, resulting in a large degradation of
the overall stiffness of the composite structure. This definition of global
structural failure is chosen in this analysis since most experimental tests are
stopped at this point to prevent damage to expensive test equipment.
Figure 7.9 Vertical Load-Displacement Curve for the Prediction
of Failure
Figure 7.10 Displacement Pattern and Values of the Specimen II O2
Global structural
Failure
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Figure 7.11 Displacement Pattern and Values of the Specimen II S2
Figure 7.12 Displacement Pattern and Values of the Specimen II F12
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Figure 7.13 Displacement Pattern and Values of the Specimen II F22
Figure 7.14 Displacement Pattern and Values of the Specimen II F32
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Figure 7.15 Displacement Pattern and Values of the Specimen II F42
Figure 7.16 Displacement Pattern and Values of the Specimen II F52
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Figure 7.17 Overall Load-Displacement Curves for M25 Concrete
Obtained from ABAQUS
Table 7.2 Finite Element Analysis Result for Specimens Cast in M25
Concrete
Sl.
No
Specimen
Id
Ultimate load (Pu) kN Ultimate Deflection u (mm)
Upward Downward Upward Downward
1 II O2 12 12 26.57 29.48
2 II S2 16 16 29.73 32.24
3 II F12 20 20 36.25 40.08
4 II F 22 20 20 46.53 48.97
5 II F32 16 16 42.87 44.72
6 II F 42 16 16 35.65 38
7 II F 52 12 12 31.68 32.24
7.10 SUMMARY
The nonlinear finite element model was developed to simulate the
same conditions of the test specimen, using ABAQUS to compare the
experimental results. Elements used to model the steel and concrete, their
properties and behaviour, number of nodes and elements used in the model
were discussed. Reverse cyclic load was applied and its corresponding
displacement was found. The displacement pattern for each specimen and
overall load deflection curve for all the specimens were plotted.
