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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.
190
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
191
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:
192
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
193
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.
194
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.
195
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
196
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.
197
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)
198
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.
199
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
200
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.
201
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
202
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
203
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
204
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
205
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
206
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
207
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
208
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
209
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.
210
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
211
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
212
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
214
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.