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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.