CHAPTER 7 FINITE ELEMENT ANALYSIS -...
Transcript of CHAPTER 7 FINITE ELEMENT ANALYSIS -...
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CHAPTER 7
FINITE ELEMENT ANALYSIS
7.1 SCOPE
For reinforced concrete, improvement of calculation methods and
analysis of behaviour by either creating a model on computer or counting with
analytical calculation methods were used extensively in recent years. Finite
element method is a numeric method used by different engineering branches
in order to solve the problems of engineering requiring special analyses such
as stress analysis. To investigate the behaviour of the new AFA and FA
beams are expensive, time consuming, and elaborate experimental analyses
are required. If a suitable and reliable numerical model is developed, a wider
parametric investigation can be performed and a reduction in time and cost
can be achieved.
Typically, the behaviour of beams was studied by full-scale
experimental investigations. The results are compared to theoretical
calculations that estimate ultimate strength and deflections in the beams.
Finite element analysis can be used to model the behaviour numerically to
confirm these calculations, as well as to provide a valuable supplement to the
laboratory investigations, particularly in parametric studies. Finite element
analysis, as used in structural engineering, determines the overall behaviour of
a structure by dividing it into a number of simple elements, each of which has
well-defined mechanical and physical properties.
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This chapter contains a report on the investigation made using
Finite Element Method (FEM). Models were developed to simulate the
behaviour of AFA and FA beams from linear through nonlinear response and
up to failure. To create the models ANSYS package version 11(ANSYS 11.0,
Manuals) was used. Comparisons were made for load-strain plots at selected
locations on the beams, load-deflection plots at mid span and loads at failure.
Modelling simplifications and assumptions developed during this research are
presented. The study compared the ultimate load carrying capacity of the
beams from the FEM analysis with measured failure load from load tests.
7.2 MODELLING OF STRUCTURES USING ANSYS
Modelling is one of the most important aspects for the FE analysis.
Accuracy in the modelling of element type and size, geometry, material
properties, boundary conditions and loads are absolutely necessary for close
numerical idealization of the actual member. Modelling the complex
behaviour of reinforced concrete, which is anisotropic and non homogeneous,
is a difficult challenge in the finite element analysis of Civil Engineering
structures.
7.2.1 Element Types Used for Modelling
The following were the element types used in the simulation.
SOLID 65 for concrete
LINK 8 for Reinforcement
SOLID65 elements were used to model the concrete material. This
element is defined by eight nodes and has the isotropic material properties.
This element is capable of cracking (in three orthogonal directions), crushing,
plastic deformation, and creep. The geometry, node locations, and the
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coordinate system for this element are shown in Figure.7.1. Solid65 element
is capable of incorporating one material property for concrete and up to three
rebar materials for rebars, which are assumed to be uniformly distributed
throughout the concrete element in a defined region of the finite element
mesh. This type of reinforcement model is mainly used in analyzing structures
which are large in volume of concrete, namely foundations.
Figure 7.1 Solid 65 element type
LINK 8 is a 3D spar element. It is a uniaxial tension-compression
element with three degrees of freedom at each node. Plasticity, creep,
swelling and stress stiffening capabilities were included. A Link8 element
was used to model the links. Two nodes were required for this element. Each
node had three degrees of freedom, – translations in the nodal x, y, and z
directions. The element was also capable of plastic deformation. The
geometry and node locations for this element type are shown in Figure.7.2
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Figure 7.2 Link 8 element type
7.2.2 Material Properties
Development of a model for the behaviour of concrete is a
challenging task. Concrete is a quasi-brittle material and has different
behaviour in compression and tension. Material nonlinearity was used in the
analysis. For concrete the following nonlinear material properties given in
Table 7.1 are considered. A summary of ANSYS model of specimen is given
in table 7.2
Table 7.1 Material properties
Material Particulars
Concrete Poisson’s ratio=0.2
Grade of concrete=25 MPa Modulus of ElasticityE(according to replacements of additives added)
Steel Young’s Modulus E=2*105 MPa
Poisson’s ratio=0.3, Yield strength=415 MPa
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Table 7.2 Summary of ANSYS model of the specimen
Categories ANSYS Model Details
Types of elements
Concrete
Steel
Solid 3D, concrete 65
Solid 3D, link 8
Model descriptions
Length of beams
Size of beams
Loading pattern of beam
Full scale model
2000mm
100x200x2000
Two point loading
The elastic modulus and flexural strength of concrete were found
using the following equations:
For FA concrete
Ec = 4200 fck
fcr = 0.785 fck
where, Ec, fck and fcr are in MPa
For AFA concrete ,
Ec = 5300 fck
fcr = 0.85 fck
where, Ec, fck and fcr are in MPa.
The FEA calibration study included modeling of a AFA concrete
beam with dimensions and properties corresponding to beams tested
experimentally. To create the finite element model in ANSYS there are
multiple tasks that have to be completed for the model to run properly.
Models can be created using command prompt line input or the Graphical
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User Interface (GUI). For this model, the GUI was utilized to create the
model. This section describes the different tasks and entries used into created
the FE calibration model.
7.2.3 Finite Element Discretization
As an initial step, a finite element analysis requires meshing of the
model. In other words, the model is divided into a number of small elements,
and after loading, stress and strain are calculated at integration points of these
small elements. An important step in finite element modeling is the selection
of the mesh density. The convergence of results is obtained when an adequate
number of elements are used in a model. This is practically achieved when an
increase in the mesh density has a negligible effect on the results. Therefore,
in this finite element modeling a convergence study was carried out to
determine an appropriate mesh density.
The finite element models dimensionally replicated the full-scale
transverse beams. That is, an AFA or FA beam with a cross section of 100 x
200 x 2000mm with the same material properties were modeled in ANSYS
with an increasing number of elements. A number of response parameters
were compared, including tensile stress, deflection at the center bottom fiber
of the beam, and compressive stress at the center top fiber of the beam. The
three parameters were determined at the mid span of the beam and compared.
If the mesh density is increased higher, then, convergence
problems arise. Based on trial solutions only, the required mesh density was
selected. All the nodes were merged with one another to provide a stiff model.
The following figures show how the various parts of beams were modelled.
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7.2.4 Meshing
To obtain good results from the solid 3D, concrete 65 elements, and
the use of hexagonal mapped mesh is recommended. Therefore, mesh was set
up such that hexahedral elements were created. The meshing is done with
mesh tool menu which has global set containing the size of the element
divisions which defines the size of the element which is formed. As the size
of the elements decreases the elements are increased in number by means of
which results are obtained are too accurate. As the elemental number
increases, the time consuming for solving a problem for the particular load
increases thereby requiring more memory space in the computer. The
meshing of reinforcing bar was done in the procedure mentioned above from
which the size of the element for bars should be reduced very low because the
bar diameter is very less.
7.2.5 Numbering Controls
The command merges items of separate entities that have the same
locations. These items will be merged into single entities. Caution must be
taken when merging entities in a model that has already been meshed because
the order in which merging occurs is significant. Merging key points before
nodes can result in some of the nodes becoming “orphaned”; that is nodes
lose their association with the solid modes. The orphaned nodes can cause certain
operations such as boundary condition transfer, surface condition transfers and so
on to fail, care must be taken to always merge in the order that the entities appear.
All precautions were taken to ensure that everything was merged in the proper
order. Also the lowest number was retained during merging.
7.2.6 Loads and Boundary Conditions
Displacement boundaries are needed to constraint the model to get
a unique solution. To ensure that the model acts the same way as the
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experimental beam, boundary conditions need to be applied at the points of
symmetry, the supports and loading exist. The support was modeled as a
hinged support on left side of the beam and the right side as the roller,
maintaining the support specification is fixed with effecting length as 2000 mm
and 500 mm being left as overhanging equally on both side of beam.
7.2.7 Analysis Process for the Finite Element Model
The finite element analysis of the model was set up to examine
different behaviors. Here the analysis was done linearly to find deflection,
stress, strain plots and to validate with experimental values.
7.2.8 Flexure Beams
Totally 39 beams were modeled for flexure comprising with
Activated Fly Ash (AFA) and Fly Ash(FA) as additives. Control mix beams
were also been modelled and compared with other mix. The size and cover
provided to the beams were maintained constant as 100 x 200 x 2000 mm and
20 mm respectively. For beams 2 numbers of 10 mm dia bars at tension face
was provided and 2 nos of 8 mm diameter was provided as HYSD bars at
compression face. 6 mm diameter 2 legged stirrups at 125mm c/c were
provided for shear reinforcement.
7.2.9 Post Processing
There are two types of post processing in ANSYS 10.0 program;
general and time history. The later provides a step by step variation of any
desired variable such as stress strain at various nodes or within any element in
the model. The former provides and listing capabilities for the ultimate results
(last time step) such as deformations, contour plots of stress and strains allow
an automatic output of time history. Figure 7.3 shows FEM model of a beam
and Figure 7.4 represents meshing of the beam. The loads and boundary
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conditions were applied to the beam and is shown in Figure 7.5.The material
properties assigned for the analysis is shown in Table 7.3.
Figure 7.3 Model of beam
Figure 7.4 Meshing of beam Figure 7.5 Loads and boundarycondition
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Table 7.3 The material properties assigned for the beam model with theMix M1
Materialnumber Material Element
typeReal
constant Material properties
1 Concrete SOLID65Set1
VR1 = 0 LinearIsotropic
EX(MPa) = 24824PRXY = 0.2
Multilinearelastic
Strain Stress (MPa)1. Point 0.00035 7.542. Point 0.00067 13.223. Point 0.00090 16.604. Point 0.0017 23.765. Point 0.0021 24.65
Concrete ShrCf-Op. = 0.4ShrCf-Cl. = 1UnTensSt. (MPa) = 2.98UnCompSt.(MPa) = -1BiCompSt. = 0HydroPrs. = 0BiCompSt. = 0UnTensSt. = 0TenCrFac = 0
2 Steel rod
LINK8 Set2(10mm) Area = 79
LinearIsotropic
EX(MPa) = 2,0E+5PRXY= 0.3
BilinearIsotropic
fy (MPa) 430Tan.Mod. 0
LINK8 Set3(8mm) Area = 50
LinearIsotropic
EX(MPa) = 2,0E+5PRXY= 0.3
BilinearIsotropic
fy (MPa) 430Tan.Mod. 0
LINK8 Set4(6mm) Area = 28
LinearIsotropic
EX(MPa) = 2,0E+5PRXY= 0.3
BilinearIsotropic
fy (MPa) 430Tan.Mod. 0
In Figures 7.6- 7.10 the sequence of the modeling is given .The
soild model of the beam with boundary condition is given in Figure 7.6 Solid
model of the beam with boundary conditions. Rebars given in the beam are
modeled and shown in Figure 7.7. The meshing is shown in Figure7.8.
Meshed model with loads and boundary conditions is shown in Figure 7.9 and
the analysed beam showing the crack pattern and crushing of concrete is
given in Figure 7.10.
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Figure 7.6 Solid model of the beam with boundary conditions
Figure 7.7 Rebar in the beam Figure 7.8 Meshed model of beam
Figure 7.9 Meshed model of thebeam with loads andboundary conditions
Figure 7.10 Cracks and crushing of AFA beam
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7.3 ANALYSIS
Initially linear analysis was carried out. Having confirmed the
results in the linear range, nonlinear analysis was performed.
7.3.1 Linear Analysis
Results of the proposed finite element model are verified against
results experimentally obtained from beam tests. The behaviour of the model
were investigated throughout the loading history from the first application of
the load to service load.
7.3.2 Nonlinear Analysis
In nonlinear analysis, the total load applied to a finite element
model was divided into a series of load increments called load steps. At the
completion of each incremental solution, the stiffness matrix of the model was
adjusted to reflect nonlinear changes in structural stiffness before proceeding
to the next load increment. The ANSYS programm uses Newton-Raphson
equilibrium iterations for updating the model stiffness. Newton-Raphson
equilibrium iterations provide convergence at the end of each load increment
within tolerance limits. A force convergence criterion with a tolerance limit
of 5% was adopted for avoiding the divergence problem. Equilibrium
iterations to be performed were relaxed up to 100.
7.4 RESULTS AND DISCUSSION
This section compares the results from the ANSYS finite element
analysis with the experimental data for the beams. The following comparisons
were made: ultimate deflection plots at mid span, stress contour and loads at
failure. Also discussed are the summaries of the maximum stresses occurring
in the composite beams for the finite element models. The data from the finite
element analyses were collected at the same locations as the load tests for the
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full-size beams. The following results were obtained from ANSYS for all the
tested specimens.
Deflection contours at failure load
Bending stress distribution
Failure load
Deflections were found out for various load values. The
development of cracks was captured at various load intervals. Tables 7.4 to
7.6 compares the results obtained using the proposed finite element model
with those obtained from the experimental tests. It is evident from Tables 7.4
to 7.6 shows that the numerical analysis can predict both the failure load and
the displacement up to service load of the new system with acceptable
accuracy
Table 7.4 Result comparison of experimental and FEM analysis B1 Series
Sl.No. ID
Strength at28 days
Failure Load (kN) Deflection (mm)
Experimental ANSYS A/E Experimental ANSYS A/E
1 CM 27.3 30 23.2 0.78 15.6 14.0 0.92 F1 19.0 18 18.7 1.04 13.0 13.7 1.063 F2 19.6 20 14.0 0.7 12.6 12.6 1.04 F3 19.8 24 14.2 0.6 13.7 13.0 0.955 F4 18.5 17 11.6 0.69 11.9 11.9 1.06 F5 18.0 16 14.5 0.91 11.0 11.0 1.07 F6 17.7 16 12.3 0.77 10.6 10.6 1.08 AF1 28.0 27 22.5 0.84 16.2 16.2 1.09 AF2 28.5 28 21.2 0.76 17.4 17.0 0.9810 AF3 29.4 32 26.0 0.82 18.2 18.2 1.011 AF4 29.6 35 25.3 0.73 29.3 29.3 1.012 AF5 29.8 47 36.0 0.77 33.7 33.7 1.013 AF6 28.25 29 19.9 0.69 26.2 26.2 1.0
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Table 7.5 Result comparison of experimental and FEM analysis B2Series
Sl.No. ID Strength
at 28 daysFailure Load (kN) Deflection (mm)
Experimental ANSYS A/E Experimental ANSYS A/E1 CM 26.5 28.0 25.20 0.90 12.0 10.20 0.852 F1 19.5 18.0 18.72 1.04 13.0 13.26 1.023 F2 19.3 20.0 16.0 0.80 13.5 12.83 0.954 F3 18.8 17.0 12.75 0.75 12.5 11.25 0.905 F4 18.3 16.0 12.0 0.75 11.5 9.77 0.856 F5 17.8 14.0 12.88 0.92 11.0 9.90 0.907 F6 17.4 13.7 11.68 0.85 9.0 7.65 0.858 AF1 26.6 25.0 21.0 0.84 15.0 14.25 0.959 AF2 27.0 26.0 20.8 0.80 17.0 16.66 0.98
10 AF3 27.5 30.0 24.6 0.82 18.5 18.13 0.9811 AF4 28.8 36.0 30.6 0.85 30.0 28.50 0.9512 AF5 27.0 33.0 26.4 0.80 29.5 28.32 0.9613 AF6 26.5 27.0 24.3 0.90 23.5 21.15 0.90
Table 7.6 Result comparison of experimental and FEM analysis B3 Series
Sl.No. ID Strength at
28 daysFailure Load (kN) Deflection(mm)
Experimental ANSYS A/E Experimental ANSYS A/E1 CM 25.2 24.0 21.6 0.90. 12.0 10.2 0.85
2 F1 18.8 20.0 18.0 0.90 13.7 13.26 1.02
3 F2 18.3 19.5 18.52 0.95 13.0 12.82 0.95
4 F3 17.9 17.0 15.3 0.90 12.0 11.25 0.90
5 F4 17.25 16.0 13.6 0.85 11.0 9.77 0.85
6 F5 16.15 14.0 13.3 0.95 11.0 9.9 0.90
7 F6 16.0 11.0 10.8 0.98 9.0 7.65 0.85
8 AF1 26.0 24.0 23.5 0.98 14.5 14.25 0.95
9 AF2 26.5 25.0 23.8 0.95 16.5 16.66 0.98
10 AF3 26.8 34.0 32.6 0.96 27.0 18.13 0.98
11 AF4 26.6 32.0 28.8 0.90 25.0 28.5 0.95
12 AF5 26.35 28.0 25.2 0.90 24.5 28.32 0.96
13 AF6 26.0 26.0 22.1 0.85 22.0 26.2 1.0
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7.5 STRESS CONTOURS OF BEAMS
The stress contours of the beams B1C1 and B1F2 are given in
Figure 7.11 and 7.12. For AFA concrete beams the stress contours of the
analysed beams are given in Figures 7.13 and 7.14 .
Figure 7.11 Stress contour for B1C1 Figure 7.12 Stress contour for B1F2
Figure 7.13Stress contour for B1AF5 Figure 7.14 Stress contour for B1AF6
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7.6 DISPLACEMENT OF BEAMS
The displacement profile of the beams AF5 and F3 are given in
Figures 7.15 and 7.16.
Figure 7.15 Displacement of AF5 beam
Figure 7.16 Displacement of F3 beam
7.7 DEFLECTION PLOTS FOR BEAMS
The deflection plots of sample beams of the beams F3 and AF5 are
given in Figures 7.17 and 7.18 .
Figure 7.17 Deflection of F3beam
Figure 7.18 Deflection of AF5 beam
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7.8 STRAIN PLOTS FOR BEAMS
The strain plots of sample beams of the beams AF5 and F3 are given
in Figures 7.19 and 7.20.
Figure 7.19 Strain of AF5 beam Figure 7.20 Strain of F3 beam
7.9 KEY FINDINGS
In this work to validate the experimental results obtained from the
investigation of behavior of Activated Fly ash concrete beams, was performed
with ANSYS. In general the specimens modeled with ANSYS showed higher
values of ultimate load and deflections when compared to the results of
experimental work. The following important conclusions are drawn from this
study,
The ultimate loads obtained from the ANSYS modeling for
the test specimens were higher than the corresponding
specimens tested in laboratory in the range of 13% to 20%.
The behavior of beams in load deflection characteristics of FE
modeling shows good agreement with experimental value.
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The deflection of the beam is 33.7 mm, the higher value
obtained for the AFA with 50% replacement. The results
predicted by the ANSYS beam model for water binder ratio
0.45, the stress and strain values were in good agreement with
experimental data.
The results from FE modelling using ANSYS have a good
agreement with experiments.