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CHAPTER 7

FINITE ELEMENT ANALYSIS

7.1 SCOPE

In Engineering applications, the physical response of the

structure to the system of external forces is very much important.

Understanding the response of these components during loading is

crucial to the development of an overall efficiency and safe structure.

Different methods have been utilized to study the response of structural

components. Experimental programs are usually carried out to predict

the physical responses of the structure. While this is a method that

produces real life response, it is always necessary to validate the

experimental results for better understanding of the structure. The finite

element analysis can be effectively utilized to study these components.

In recent years, the use of finite element analysis has increased

due to the progressing knowledge and the capabilities of computer

software and hardware. It has now become the choice method to analyze

concrete structural components. The use of computer software to model

these elements is much faster, and extremely cost-effective. 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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Taking into account the fact that the numerical models should be based

on reliable test results and also experimental and numerical analyses

should complement each other in the investigation of a particular

structural phenomenon, Commercial finite element software ANSYS

version 11.0 was chosen for this study.

The present investigation focuses on the modelling of beams

reinforced with Prefabricated Cage using the ANSYS. A three-

dimensional model is proposed in which all the main structural

parameters and associated nonlinearities are included and the beams are

analysed both in the linear and non-linear stage. In the linear stage, the

deflections are found out and the deflection contour and deformed shape

are plotted. In the non linear analysis, the failure loads and failure crack

pattern are found out and are validated with that of the experimental and

theoretical results.

7.2 ANSYS

Advances in computational features and software have brought

the finite element method within the reach of both academic research

and engineers in practice by means of general-purpose nonlinear finite

element analysis packages, with one of the most used package nowadays

being ANSYS. The program offers a wide range of options regarding

element types, material behaviour and numerical solution controls as

well as graphic user interfaces, auto-meshers and sophisticated

postprocessors and graphics to speed the analyses. ANSYS includes

dedicated numerical models for the nonlinear response of concrete under

loading. These models usually include a smeared crack analogy to

account for the relatively poor tensile strength of concrete, a plasticity

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algorithm to facilitate concrete crushing in compression regions and a

method of specifying the amount, distribution and the orientation of any

internal reinforcement.

The internal reinforcement may be modelled as an additional

smeared stiffness distributed through an element in a specified

orientation or alternatively by using discrete strut or beam elements

connected to the solid elements. The beam elements would allow the

internal reinforcement to develop shear stresses but as these elements in

ANSYS are linear, no plastic deformation of the reinforcement is

possible. The smeared stiffness and link modelling options allow the

elastic-plastic response of the reinforcement to be included in the

simulation at the expense of the shear stiffness of the reinforcing bars.

7.3 ANSYS MODELLING OF PCRC BEAMS

Modelling is one of the most important aspects in ANSYS

Finite Element analysis. Accuracy in the modelling of element type and

size, geometry, material properties, boundary conditions and loads are of

absolute necessary for close numerical idealization of the actual

member. A good idealization of the geometry reduces the running time

of the solution considerably. A three dimensional structure can be easily

analyzed by considering it as a two dimensional structure without any

variation in results. Creative thinking in idealizing and meshing the

structure helps not only in considerable reduction of time but also in less

memory usage of the system.

Finite element modeling of specimen in ANSYS consists of

the following three phases:

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Selection of element type

Assigning material properties

Modelling and meshing the geometry

7.3.1 Element Types

Selection of proper element types is another important

criterion in finite element analysis. The following are the element types

used in the ANSYS modelling of PCRC beams.

Ansys element Type Material

SOLID 65 Concrete

SOLID 45 Steel plates and supports

SHELL 63 Cold-formed steel sheet

7.3.1.1 Solid 65

ANSYS provides a dedicated three-dimensional eight noded

solid isoparametric element, Solid65, to model the nonlinear response of

brittle materials based on a constitutive model for the triaxial behaviour

of concrete after Williams and Warnke (Fanning 2001). This element is

capable of cracking (in three orthogonal directions), crushing, plastic

deformation, and creep. The geometry, node locations, and the

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

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region of the FE mesh. This type of smeared reinforcement model is

mainly used in analyzing structures which are large in volume of

concrete, e.g., foundations.

Figure 7.1 SOLID65 – 3D Reinforced Concrete Solid

7.3.1.2 Solid 45

SOLID 45 is a three dimensional brick element used to model

isotropic solid problems. It has eight nodes, with each node having three

translational degrees of freedom in the nodal X, Y, Z directions. This

element may be used to analyze large deflection, large creep strain,

plasticity and creep problems. The element is used to model the steel

plates provided at support and loading plates. It has no real constants.

This element is illustrated in Figure 7.2.

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Figure 7.2 SOLID 45-3D Plain Concrete Solid

7.3.1.3 Shell 63

SHELL 63 is used to model the thin walled structures

effectively. This has both bending and membrane capabilities. Both

inplane and normal loads were permitted. The element had six degrees of

freedom at each node. The element is defined by four nodes, four

thicknesses, elastic foundation stiffness and the orthotropic material

properties. Stress stiffening and large deflection capabilities were included.

For PCRC Beams, steel sheet was modeled by using SHELL 63. The

geometry and node locations for this element type are shown in Figure 7.3.

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Figure 7.3 SHELL 63 – Elastic Shell

7.3.2 MATERIAL PROPERTIES

7.3.2.1 Concrete

Development of a model for the behaviour of concrete is achallenging task. Concrete is a quasi-brittle material and has differentbehaviour in compression and tension. Figure 7.4 shows a typical stress-strain curve for normal weight concrete. Material nonlinearity was usedin the analysis. For concrete the following nonlinear material propertieswere considered.

Figure 7.4 Typical Stress-strain Curve for Normal Weight Concrete

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As per the ANSYS concrete model, two shear transfer

coefficients, one for open cracks and the other for closed ones are used

to consider the amount of shear transferred from one end of the crack to

the other.

Following are the input data required to create the material

model for concrete in ANSYS.

Elastic Modulus, (Ec)

Poisson’s Ratio, ( )

Ultimate Uniaxial compressive strength, (fck)

Ultimate Uniaxial tensile strength, (ft)

Shear transfer coefficient for opened crack, ( 0)

Shear transfer coefficient for closed crack, ( c)

Poisson’s ratio for concrete was assumed to be 0.2 for all the

beams. Damien Kachlakev et. al. (2000) conducted numerous

investigations on full-scale beams and they found out the shear transfer

coefficient for opened crack was 0.2 and for closed crack was 1. The

two shear transfer coefficients are used to consider the retension of shear

stiffness in cracked concrete.

Even though the above parameters are enough for the ANSYS

non-linear concrete model, it is better to keep a stress-strain curve of

concrete as a backbone for achieving accuracy in results. Hence it was

attempted to input stress – strain curve.

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The stress-strain curve for concrete can be constructed by

using the Desayi and Krishnan (1964) equations. Multi-linear kinematic

behaviour is assumed for the stress-strain relationship of concrete which

is shown in Figure 7.5. It is assumed that the curve is linear up to

0.3 fc’. Therefore, the elastic stress-strain relation is enough for finding

out the strain value.

= = 0.3 (7.1)

Figure 7.5 Simplified Compressive Uniaxial Stress-Strain Curvefor Concrete

The Ultimate strain can be found out from the following

formula.

= (7.2)

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The total strain in the non-linear region is calculated and

corresponding stresses for the strains are found out by using the

following formula.

& ) = (7.3)

The above input values are given as material properties for

concrete to define the non-linearity.

In compression, the stress-strain curve of concrete is linearly

elastic up to about 30% of the maximum compressive strength. Above

this point, the stress increases gradually up to the maximum

compressive strength, and then descends into a softening region and

eventually crushing failure occurs at an ultimate strain cu. In tension,

the stress-strain curve for concrete is approximately linearly elastic up to

the maximum tensile strength. After this point, the concrete cracks and

the strength decreases gradually to zero.

ANSYS has its own non-linear material model for concrete. Its

reinforced concrete model consists of a material model to predict the

failure of brittle materials, applied to a three-dimensional solid element

in which reinforcing bars may be included. The material is capable of

cracking in tension and crushing in compression. It can also undergo

plastic deformation and creep. Three different uniaxial materials,

capable of tension and compression only may be used as a smeared

reinforcement, each one in any direction. Plastic behaviour and creep

can be considered in the reinforcing bars too. For plain cement concrete

model, the reinforcing bars can be removed.

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7.3.2.2 Failure Criteria for Concrete

ANSYS non-linear concrete model is based on William-

Warnke failure criteria. As per the William-Warnke failure criteria, at

least two strength parameters are needed to define the failure surface of

concrete. Once the failure is surpassed, concrete cracks if any principal

stresses are tensile while crushing occurs if all the principal stresses are

compressive. Tensile failure consists of a maximum tensile stress

criterion. Unless plastic deformation is taken into account, the material

behaviour is linearly elastic until failure. When the failure surface is

reached, stresses in that direction have a sudden drop to zero, provided

there is no strain softening neither in compression nor in tension. This

indicates that the descending portion in strain-strain curve of concrete is

not considered in ANSYS non-linear concrete model.

Figure 7.6 3-D Failure Surface for Concrete

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A three-dimensional failure surface for concrete is shown in

Figure 7.6. The most significant non-zero principal stresses are in the x

and y directions respectively. Three failure surfaces are shown as the

projections on the xp- yp plane. The modes of failure are the function of

the sign of ZP (principal stress in Z direction). For example, if xp and

yp, both are negative (compressive) and ZP is slightly positive (tensile),

cracking would be predicted in a direction perpendicular to ZP.

However, if ZP is zero or slightly negative, the material is assumed to

crush. In a concrete element, cracking occurs when the principal tensile

stress in any direction lies outside the failure surface. After cracking, the

elastic modulus of concrete element is set to zero in the direction

parallel to the principal tensile stress direction. Crushing occurs when all

principal stresses are compressive and lie outside the failure surface.

Subsequently, the elastic modulus is set to zero in all directions and the

element effectively disappears.

7.3.2.3 Non-Linear Material Model for Steel

The steel for the finite element models was assumed to be an

elastic-perfectly plastic material (Deric John Oehlers 1993) and identical

in tension and compression. Properties like young’s modulus and yield

stress, for the steel reinforcement used in this FEM study were found out

by conducting the required tests on the sample specimens. Poisson’s

ratio of 0.3 was used for the steel reinforcement. Bilinear kinematic

material model was adopted in this study. Figure 7.7 shows the stress-

strain relationship used in this study.

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Figure 7.7 Stress-Strain Curve for Steel

A summary of material properties used for modeling all the

beams are shown in Table 7.1. These values were used for calculating

the important properties required for specifying material non-linearity.

Table 7.1 Material Properties

Series Material Properties (In N/ mm2)fck Ec ft fy E

A

Concrete

22.75 0.238 x105 2.74 - -B 27.86 0.264 x105 3.11 - -C 32.23 0.284x105 3.32 - -D 23.05 0.240 x105 2.81 - -E 27.21 0.261 x105 3.07 - -F 33.78 0.291x105 3.43 - -G 33.10 0.288 x105 3.38 - -H 38.80 0.311x105 3.97 - -I 45.20 0.336x105 4.60 - -J 32.80 0.286x105 3.33 - -K 38.30 0.309x105 3.92 - -L 44.20 0.332x105 4.60 - -

A, B,C,D,E,F,G,H,I

CR sheet (1.6mm) - - - 245.0 1.84 x 105

CR sheet (2.0mm) - - - 262.0 1.81 x 105

CR sheet (2.5mm) - - - 279.0 1.83 x 105

J,K,LCR sheet (1.6mm) - - - 397.0 2.01 x 105

CR sheet (2.0mm) - - - 402.0 1.99x 105

CR sheet (2.5mm) - - - 404.0 2.01x 105

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7.3.3 Modelling the Geometric Shape

A quarter of the full beam was used for modeling by taking

advantage of the symmetry of the beam and loadings. Planes of

symmetry were required at the internal faces. At a plane of symmetry,

the displacement in the direction perpendicular to that plane was held at

zero. The geometrical details of the beams modelled are given in

Table 7.2. By taking advantage of the symmetry of the beams, a quarter

of the full beam was modeled as in Figure 7.8. Ideally, the bond strength

between the concrete and steel reinforcement should be considered.

However, in this study, perfect bond between materials was assumed.

Nodes of the CR sheet shell elements were connected to those of

adjacent concrete solid elements in order to satisfy the perfect bond

assumption.

Figure 7.8 Quarter Beam Model

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Table 7.2 Summary of the Beam Details

Sl.No

BeamId

tsmm

Bmm D mm Span

m

YieldStrength of

Steel(N/mm2)

Ast(mm2)

Compressiveof concrete

(N/mm2)1 A1 1.6 150 200 2.50 245.0 208 22.752 A2 2.0 150 200 2.50 262.0 260 22.753 A3 2.5 150 200 2.50 279.0 325 22.754 B1 1.6 150 200 2.50 245.0 208 27.865 B2 2.0 150 200 2.50 262.0 260 27.866 B3 2.5 150 200 2.50 279.0 325 27.867 C1 1.6 150 200 2.50 245.0 208 32.238 C2 2.0 150 200 2.50 262.0 260 32.239 C3 2.5 150 200 2.50 279.0 325 32.23

10 D1 1.6 150 200 2.50 245.0 208 23.0511 D2 2.0 150 200 2.50 262.0 260 23.0512 D3 2.5 150 200 2.50 279.0 325 23.0513 E1 1.6 150 200 2.50 245.0 208 27.2114 E2 2.0 150 200 2.50 262.0 260 27.2115 E3 2.5 150 200 2.50 279.0 325 27.2116 F1 1.6 150 200 2.50 245.0 208 33.7817 F2 2.0 150 200 2.50 262.0 260 33.7818 F3 2.5 150 200 2.50 279.0 325 33.7819 G1 1.6 150 200 2.50 245.0 432 33.1020 G2 2.0 150 200 2.50 262.0 432 33.1021 G3 2.5 150 200 2.50 279.0 432 33.1022 H1 1.6 150 200 2.50 245.0 432 38.8023 H2 2.0 150 200 2.50 262.0 432 38.8024 H3 2.5 150 200 2.50 279.0 432 38.8025 I1 1.6 150 200 2.50 245.0 432 45.2026 I2 2.0 150 200 2.50 262.0 432 45.2027 I3 2.5 150 200 2.50 279.0 432 45.2028 J1 1.6 150 200 2.50 397.0 262 32.8029 J2 2.0 150 200 2.50 402.0 262 32.8030 J3 2.5 150 200 2.50 404.0 262 32.8031 K1 1.6 150 200 2.50 397.0 262 38.3032 K2 2.0 150 200 2.50 402.0 262 38.3033 K3 2.5 150 200 2.50 404.0 262 38.3034 L1 1.6 150 200 2.50 397.0 262 44.2035 L2 2.0 150 200 2.50 402.0 262 44.2036 L3 2.5 150 200 2.50 404.0 262 44.20

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7.3.4 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. A 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

modelling, 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, a PCRC beam with a cross section of

150 x 200 x 2500mm with the same material properties were modeled in

ANSYS with an increasing number of elements. A convergence of

results is obtained when an adequate number of elements is used in a

model. If the mesh density is increased higher, then convergence

problems arise. Based on trial solutions only, the required mesh density

is selected. For the PCRC beams, totally 1464 elements were provided.

All the nodes were merged with one another to provide a stiff

model. The merge operation is useful for tying separate, but coincident

parts of a model together. By default, the merge operation retains the

lowest numbered coincident item. Higher numbered coincident items are

deleted. When merging entities in a model that has already been

meshed, the order in which multiple NUMMRG commands are issued is

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significant. If you want to merge two adjacent meshed regions that have

coincident nodes and keypoints, always merge nodes (NUMMRG,

NODE) before merging keypoints (NUMMRG,KP). Merging keypoints

before nodes can result in some of the nodes becoming orphaned, i.e.,

the nodes lose their association with the solid model. Orphaned nodes

can cause certain operations (such as boundary condition transfers,

surface load transfers etc.) to fail.

After a NUMMRG, NODE is issued and some nodes may be

attached to more than one solid entity. As a result, subsequent attempts

to transfer solid model loads to the elements may not be successful.

Issue NUMMRG, KP to correct this problem.

The Figures 7.9-7.11 show the modelling and meshing of

various parts of PCRC beams. Figure 7.12 shows FEM discretization of

fabricated Prefabricated Cage with reinforcement in a beam and

Figure 7.13 represents FEM discretization of concrete portion.

Figure 7.9 Modelling of Profile I Figure 7.10 Modelling of Profile II

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Figure 7.11 Modelling of Prefabricated Cage Profile III

Figure 7.12 Prefabricated Cage meshed with Quadrilateral FreeMeshing

Figure 7.13 Concrete Block Meshed with Hexahedral MappedMeshing

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7.3.5 Loading and Boundary Conditions

A steel plate of 10 mm thick and 50mm x 75mm cross section

was provided at the support to avoid the concentration of stresses.

Moreover, a single line support was placed under the centerline of the

steel plate to allow rotation of the plate. In the quarter model, as the two

sides of the beam are continuous, the displacement in the direction

perpendicular to the planes was arrested (Figure 7.14).

The full scale models were tested in two point loading. The

finite element models were loaded at the same locations as in the full-

size beams. Steel plate of 10 mm thick and 50mm x 75mm cross section

was provided at the point of loading to avoid concentration of stresses.

The load was subdivided into a number of small loads called load step.

Each load step was solved gradually and then the solution was obtained

for each load step.

Figure 7.14 PCRC Beam Model with Loading and BoundaryConditions

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7.4 ANALYSIS

Initially linear analysis was carried out. Having confirmed the

results in the linear range then nonlinear analysis was performed.

7.4.1 Linear Analysis

Results of the proposed finite element model are verified

against the results experimentally obtained from beam tests. The

behaviour of the model is investigated throughout the loading history

from the first application of the load to service load. Table 7.3 compares

the results obtained using the proposed finite element model with those

obtained from the experimental tests.

Table 7.3 Experimental and Numerical deflections at Service load

Sl.No Beam Series fckN/mm2

fyN/mm2 exp @ Ps

the @ Psmm

ANS @ Psmm

1 A1 22.75 245 2.75 2.62 1.852 A2 22.75 262 3.60 2.74 2.123 A3 22.75 279 3.18 2.56 2.634 B1 27.86 245 3.70 3.42 1.815 B2 27.86 262 3.35 2.61 2.016 B3 27.86 279 4.21 3.62 2.487 C1 32.23 245 3.06 3.85 1.728 C2 32.23 262 3.70 3.23 1.979 C3 32.23 279 3.60 3.00 2.42

10 D1 23.05 245 3.07 3.34 0.8011 D2 23.05 262 3.86 3.38 0.8912 D3 23.05 279 3.94 3.06 1.1213 E1 27.21 245 3.60 3.40 0.8414 E2 27.21 262 3.20 3.45 0.8915 E3 27.21 279 4.20 3.37 1.1016 F1 33.78 245 4.53 3.83 0.8117 F2 33.78 262 4.12 3.55 0.9018 F3 33.78 279 3.25 3.03 1.0119 G1 33.10 245 4.37 3.43 3.57

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Table 7.3 (Continued)

Sl.No Beam Series fckN/mm2

fyN/mm2 exp @ Ps

the @ Psmm

ANS @ Psmm

20 G2 33.10 262 2.93 3.16 3.7421 G3 33.10 279 3.00 2.16 3.3922 H1 38.80 245 3.90 3.53 3.5123 H2 38.80 262 3.34 2.96 3.4524 H3 38.80 279 3.17 2.35 3.5725 I1 45.20 245 3.78 3.27 3.5926 I2 45.20 262 3.60 3.29 3.7327 I3 45.20 279 2.51 2.13 3.0628 J1 32.80 397.0 3.30 3.81 3.3129 J2 32.80 402.0 4.10 3.82 3.3330 J3 32.80 404.0 2.90 3.42 3.2431 K1 38.30 397.0 4.28 3.97 2.9932 K2 38.30 402.0 5.20 4.80 3.3933 K3 38.30 404.0 4.20 3.89 2.9634 L1 44.20 397.0 2.80 3.05 2.8335 L2 44.20 402.0 3.80 3.87 2.8036 L3 44.20 404.0 4.20 3.94 2.63

7.4.2 Non-linear 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 programme

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. Failure load of each beam was obtained and

are presented in Table 7.4.

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Table 7.4 Experimental and Numerical Results

Beam Series

ExperimentalFailure Load (kN)

ANSYS FailureLoad (kN)

Pexp/PANSYS

A1 35.17 29.40 1.20A2 40.30 32.20 1.25A3 51.29 39.90 1.29B1 37.60 30.80 1.22B2 42.00 33.60 1.25B3 52.75 40.60 1.30C1 39.08 34.30 1.14C2 43.96 37.80 1.16C3 53.73 42.00 1.28D1 37.75 31.12 1.21D2 42.50 34.43 1.23D3 53.75 42.00 1.28E1 40.75 33.92 1.20E2 44.25 35.80 1.24E3 55.00 43.85 1.25F1 42.50 37.00 1.15F2 47.25 40.66 1.16F3 57.50 46.42 1.24G1 81.00 70.66 1.15G2 86.25 80.00 1.08G3 79.50 83.20 0.96H1 85.50 75.43 1.13H2 85.50 86.68 0.99H3 90.00 87.6 1.03I1 93.75 82.36 1.14I2 99.00 90.40 1.10I3 82.50 92.16 0.90J1 74.25 58.43 1.27J2 75.00 61.60 1.22J3 74.25 64.22 1.16K1 72.00 63.04 1.14K2 82.50 65.60 1.26K3 72.75 68.49 1.06L1 72.75 66.72 1.09L2 72.75 67.52 1.08L3 69.00 68.36 1.01

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7.5 RESULTS AND DISCUSSION

This section compares the results from the ANSYS finiteelement analyses with the experimental data for the full-size beams.The following comparisons are made: deflection at service stage, Crackpattern and loads at failure. The data from the finite element analyseswere collected at the same location as the load tests for the full-sizebeams. The following results were obtained from ANSYS for all thetested specimens.

Deflection contours at service load

Crack pattern

Failure load

Deflections were found out for various load values. Thecontours of deflection are shown for a selected specimen in Figure 7.15.Deformed shapes for some of the specimens are shown in Figure 7.16.The development of cracks was captured at various load intervals andfailure crack pattern is presented in Figure 7.17. The results fromANSYS were tabulated in Table 7.4.

Figure 7.15(a) DeflectionContour for D1Series

Figure 7.15(b) DeflectionContour for D2Series

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Figure 7.15(c) DeflectionContour for E2Series

Figure 7.15(d) DeflectionContour for E3Series

Figure 7.15(e) DeflectionContour for G1Series

Figure 7.15(f) DeflectionContour for G2Series

Figure 7.16(a) Deformed Shapeof A1 Series

Figure 7.16(b) Deformed Shapeof B1 Series

213

Figure 7.16(c) Deformed Shapeof C1 Series

Figure 7.16(d) Deformed Shapeof H1 Series

Figure 7.16(e) Deformed Shapeof J1 Series

Figure 7.16(f) Deformed Shapeof K1 Series

Figure 7.17 Experimental and ANSYS Crack Pattern of J3 Series

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7.6 KEY FINDINGS

A three dimensional finite element model of PCRC beams is

proposed based on the use of the commercial software ANSYS version

11.0. From the finite element analysis the following conclusions were

drawn.

Results of the numerical simulations are compared with

the experimental findings. Apparently, good agreement

is obtained from the comparison showing that the

proposed numerical simulation method is applicable for

analyzing the similar structures.

Deflections at the centre line along with progressive

cracking of the finite element model compare well to

data obtained from experimental investigations.

The failure mechanisms of PCRC beams is modelled

quite well using finite element analysis and the failure

load predicted is very close to the failure load measured

during experimental testing.

Verification and calibration of material models for cold-

formed sheet and concrete by PCRC beam test makes it

possible to predict the failure load and deflection at

service load with higher confidence.

For concrete Multi linear kinematic material model is

used whereas bilinear kinematic model gives excellent

predictions for cold-formed sheet.