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Finite Element Application to Slab-column Connections Reinforced with Glass
Fibre-Reinforced Polymers
Qi Zhang
Faculty of Engineering
Memorial University of Newfoundland
April, 2004
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
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Contents
Introduction__________________________________________________________3
Modeling Slab-Column Connection _______________________________________5
1. Concrete constitutive model _________________________________________7
1.1 Solid 65 element description ______________________________________7
1.2 Concrete properties _____________________________________________8
1.3 The Consideration of Solid65 Element Input Data_____________________13
2. GFRP reinforcement constitutive model _______________________________18
2.1 Link8 Element Description _______________________________________18
2.2 GFRP Reinforcement Properties __________________________________19
2.3 Smear and Discrete Reinforcement Consideration ____________________20
3. Boundary Condition and Spring constitutive model ______________________23
3.1 Link10 Element Description ______________________________________23
3.2 Boundary Condition ____________________________________________24
4. Finite Element Discretization________________________________________25
5. Numerical Implementation _________________________________________27
6. Verification in the Elastic Stage______________________________________32
Comparison of Finite Element Analysis to Test Results _______________________35
Finite Element Analysis Results Versus Modified Code Predictions _____________40
Summary and Conclusion _____________________________________________41
Reference__________________________________________________________43
Appendix: ANSYS CODE (GSHD1) ______________________________________45
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Introduction
In recent years there has been increased interest in the use of fiber-reinforced polymers (FRP)
for concrete structures. As one of the new promising technologies in construction, FRP material
solves the durability problem due to corrosion of steel reinforcement. Glass fiber reinforced
polymer (GFRP) composites have been used for reinforcing structural members of reinforced
concrete bridges. Many researchers have found that GFRP composite reinforcement instead of
steel is an efficient, reliable, and cost-effective means of reinforcement in the long run.
In the structural elements, the flat slab has the large surface exposed to the outside corrosive
environment, such as bridge decks, ocean oil flat slabs and parks. The flat slab system offers
advantages for efficient design, the overall construction process, notably in simplifying the
installation of services and the savings in construction time. However, a slab-column connection
in the flat slab system is frequently subjected to the significant transverse shear forces, which
can produce a punching shear failure. Punching in the vicinity of a column is a possible failure
mode for reinforced concrete flat slabs. Many researchers have exerted their efforts to
investigate the punching strength of slabs, due to the undesirable suddenness and catastrophic
results of punching failure. However, there is no generally accepted treatment for the punching
resistance of flat slabs because of the complicated dependence of shear strength on their
flexural behavior as well as the fact that it is difficult to observe their internal inclined cracks.
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Furthermore, most FRP elements exhibit a relatively low modulus of elasticity and lack the
yield-line characteristic of traditional steel reinforcement. It is unsafe to predict the punching
strength of column-slab connections in terms of directly extending or simply introducing to a
material coefficient to the models and equations based on steel reinforcement. Thus, it is
motivated to improve the understanding of the punching failure mechanisms and to establish a
reliable method for predicting the punching strength of column-slab connections reinforced with
GFRPs.
This paper, therefore, will present the application of the finite element method for the numerical
modeling of punching shear failure mode using a widely accepted code, ANSYS [ANSYS, 1998].
Based on properly modeling and simulating the experiments [Rashid, 2004] carried out in the
Faculty of Engineering at Memorial University of Newfoundland, the behavior of slab-column
connections reinforced with GFRPs will be investigated.
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
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Modeling Slab-Column Connection
A n extensive description of previous studies on the application of the finite element method to
the analysis of reinforced concrete structures and the underlying theory and the application of the
finite element method to the analysis of linear and nonlinear reinforced concrete structures is
presented in excellent state of-the-art reports by the American Society of Civil Engineers in 1982
[ASCE 1982]. The results from the FEA are significantly relied on the stress-strain relationship of
the materials, failure criteria chosen, simulation of the crack of concrete and the interaction of the
reinforcement and concrete.
Because of these complexity in short- and long-term behavior of the constituent materials, the
ANSYS finite element program (ANSYS 1998), operating on a Windows 2000 system, introduces
a three-dimension element Solid65 which is capable of cracking and crushing and is then
combined along with models of the interaction between the two constituents to describe the
behavior of the composite reinforced concrete material. Although the Solid65 can describe the
reinforcing bars, this study uses an additional element, Link8, to investigate the stress along the
reinforcement because it is inconvenient to collect the smear rebar data from Solid65. Due to the
general experiment process in the structural lab, the edge of slab is free to lift, which is different
with the simple support along all four edges according to the lines of contra flexure. Then, a
spring element, Link10, along the edge, is included in this study to reflect the actual setup of
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
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slab-column connection. The constructed model using ANSYS is shown in Fig.1. The detail of
specimens is listed in the Table 1.
Fig.1 ANSYS numerical model representation of experimental specimens
Table 1: Details of tested slabs
Slab No.
Compressive
strength
(MPa)
Tensile
strength
(MPa)
Steel yield
strength
(MPa)
Ec
(MPa) Efrp (MPa)
Column
size (mm)
Average
depth
(mm)
Spacing
(mm)
GFRP
ratio p%
GS1 40 3.78 630 28400 42000 250 150 240 1.18
GS3 29 3.23 630 24200 42000 250 150 170 1.67
GSHD1 33 3.43 630 25700 42000 250 200 170 1.11
GSHD2 34 3.51 630 26300 42000 250 200 240 0.79
GSHS1 92 5.76 630 38600 42000 250 150 170 1.67
GSHS2 86 5.57 630 37500 42000 250 150 240 1.18
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The assumptions made in the description of material behavior are summarized below:
• The concrete material is assumed to be initially isotropic elastic.
• The stiffness of concrete and reinforcement is formulated separately. The results are then
superimposed to obtain the element stiffness.
• The smeared crack model is adopted in the description of the behavior of cracked concrete.
Cracking in more than one direction is represented by a system of orthogonal cracks, and the
crack direction changes with load history (rotating crack model).
• The reinforcing GFRP is assumed to carry stress along its axis only and the perfect bond
relationship between concrete and GFRP rebar.
1. Concrete constitutive model
1.1 Solid 65 element description
Solid65, an eight-node solid element, is used to model the concrete with or without reinforcing
bars. The solid element has eight nodes with three degrees of freedom at each node �
translations in the nodal x, y, and z directions. The element is capable of plastic deformation,
cracking in three orthogonal directions, and crushing. The geometry and node locations for this
element type are shown in Fig.2.
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Fig.2: Solid65 ���� 3-D reinforced concrete solid (ANSYS 1998)����
The eight nodal points is also along with a 2X2X2 Gaussian integration scheme. This is used for
the computation of the element stiffness matrix. The element’s displacement field in terms of the
nodal displacements and the shape functions can be written as:
(1)
(2)
(3)
1.2 Concrete properties
Concrete is a heterogeneous material made up of cement, mortar and aggregates. Its
mechanical properties scatter widely and cannot be defined easily. For the convenience of
analysis and design, however, concrete is often considered a homogeneous material in the
macroscopic sense. Because of the cracking of concrete in tension, crushing of concrete in
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
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compression, the time-dependent effects of creep, shrinkage and temperature variation, the
nonlinear response of concrete members can be observed (Fig.2). This highly nonlinear
response can be roughly divided into three ranges of behavior: the uncracked elastic stage, the
crack propagation and the plastic (yielding or crushing) stage.
Fig.2: Typical uniaxial compressive and tensile stress-strain curve for concrete (Bangash 1989)
Before concrete cracking takes place, the behavior of concrete could be regarded as a linear
isotropic material. The stress-strain matrix [Dc] of solid65 element is defined as
(4)
The nonlinear response of concrete is mainly controlled by progressive cracking that results in
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
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localized failure. After concrete cracking takes place, the critical section of the structural member
is weakened, and then the stress of concrete and reinforcement will be redistributed. Different
with the discrete cracks model [Ngo and Scordelis, 1967], in which crack occurs during a load
cycle but the need to change the topology and the redefinition of nodal points of concrete model
greatly reduce the speed of the process, Solid65 element automatically generates cracking
without redefining the element mesh. These models depict the effect of many small cracks that
are “smeared” across the element in a direction perpendicular to the principal tensile stress
direction [Darwin, 1993].
Observing the Fig.2, the stress-strain curve for concrete is linearly elastic up to about 30 percent
of the maximum compressive strength. Above this point, the crack is developed in the concrete
and the stress increases gradually up to the maximum compressive strength. The stress-strain
relations are modified in this stage to represent the presence of a crack in the concrete. A plane
of weakness in a direction normal to the crack face and a shear transfer coefficient �t are
introduced in the solid65 element. The shear strength reduction for those subsequent loads
which induce shear across the crack surface is considered by defining the value of�t. This is very
important to accurately predict the loading after cracking, especially when calculating the
strength of concrete member dominated by shear, such as slab-column connection and shear
wall. The detailed analysis of the shear transfer coefficient will be presented later.
The stress-strain relations for a material that has cracked in one direction only become:
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
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(5)
where the superscript ck signifies that the stress strain relations refer to a coordinate system
parallel to principal stress directions with the xck axis perpendicular to the crack face. Rt, the
slope as defined in Fig.3, works with adaptive descent and diminishes to 0.0 as the solution
converges.
Fig.3 Strength of Cracked Condition
ft = uniaxial tensile cracking stress
Tc = multiplier for amount of tensile stress relaxation
If the crack closes, then all compressive stresses normal to the crack plane are transmitted
across the crack and only a shear transfer coefficient c for a closed crack is introduced. Then
[Dck] can be expressed as:
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(6)
The transformation of [Dck] to element coordinates has the form
(7)
where [Tck] is the transformation matrix.
The matrices and equations of the stress-strain relations for concrete that has cracked in more
than one direction are detailed in the theory reference of ANSYS, 1998.
In addition to cracking, the concrete will be failed in uniaxial, biaxial, or triaxial compression. The
concrete is assumed to crush in that condition. A three-dimensional failure surface for concrete is
shown in Fig. 4. The most significant nonzero principal stresses are in the x and y directions,
represented by �xp and �yp, respectively. Three failure surfaces are shown as projections on
the �xp-�yp plane. The mode of failure is a function of the sign of �zp (principal stress in the z
direction). For example, if �xp and �yp are both 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 [ANSYS 1998].
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Fig.4 Failure Surface in Principal Stress Space with Nearly Biaxial Stress
1.3 The Consideration of Solid65 Element Input Data
ANSYS requires input data for material properties of Solid65 element as elastic modulus (Ec),
ultimate uniaxial compressive strength ( 'cf ), ultimate uniaxial tensile strength (modulus of
rupture, ( rf ), poisson’s ratio (�), density (γ ), shear transfer coefficient for an open crack ( t),
shear transfer coefficient for an close crack ( c), compressive uniaxial stress-strain relationship
for concrete. If the Solid65 element includes the representation of reinforcement, up to three
rebar could be defined in Solid65 element through the real constants: reinforcement material
number (Matn), volume ratio (VRn) and orientation angles (THETAn and PHIn), where n
represents the up to 3 rears.
MacGrewgor (2000) defined the elastic modulus and the ultimate uniaxial tensile strength ( rf )
as follows:
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5.1'
230067003600Ec �
�
���
�����
�� += γ
cf (7)
'6.0 cr ff = (8)
The density (γ ) and the poisson’s ratio (�) of concrete are considered as 2300 kg/mm3 and 0.2.
The ultimate uniaxial compressive strength ( 'cf ) was measured through cylinder concrete test
(Rashid, 2004).
The shear transfer coefficient for a closed crack c is widely accepted within 0.9 to 1.0. The shear
transfer coefficient, t represents conditions of the crack face. The value of t ranges from 0.0 to
1.0, with 0.0 representing a smooth crack (complete loss of shear transfer) and 1.0 representing
a rough crack (no loss of shear transfer) [ANSYS 1998]. The value of t used in many studies of
reinforced concrete structures, however, varied between 0.05 and 0.25 [Bangash 1989; Huyse,
et al. 1994; Hemmaty 1998]. A number of preliminary analyses were attempted in this study with
various values for the shear transfer coefficient within 0.125-1.0, the results are shown in the
Fig.5. Although there is no significant difference of the ultimate loading with the different t,
accompanying with the increase of t, the ultimate loading is slightly increased after the
displacement is beyond 3mm.
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Fig.5.Investigation of shear transfer coefficient during the small deflection
0
50000
100000
150000
200000
250000
0.0 2.0 4.0 6.0 8.0 10.0 12.0
displacement (mm)
ult
imat
e lo
adin
g (
N) Bt0.8_Bc1.0
Bt0.5_Bc1.0
Bt1.0_Bc1.0
Bt0.3_Bc0.9
Bt0.125_Bc0.9
It is possible that the ultimate loading will have larger divergence if the larger displacement takes
place. GFRPs with the lower modulus of elasticity will lead to the larger deflection than the
normal structure member reinforced with steel. The experiment conducted by Rashid [Rashid,
2004] proves this assumption. Thus, the ultimate loading should be sensitive to t. Fig. 6
simulated the load-deflection curve according to the specimen GSHS2, which proves the larger
difference of ultimate loading and deflection due to different t in the condition of displacement
more than 15mm. Since convergence problems were encountered at low loads with t less than
0.1. Therefore, the shear transfer coefficient t used in this study was equal to 0.2, which gives a
good agreement with the change of stiffness of the specimen as well as the ultimate loading.�
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In describing the uniaxial compression stress-strain behavior of concrete many empirical
formulas have been proposed. These are summarized in ASCE (1982). Fig.7 shows the simplest
of the nonlinear models, the linearly elastic-perfectly plastic model, which was used by Lin and
Scordelis (1975) in a study of reinforced concrete slabs and walls. Fig.7 also shows a piecewise
linear model in which the nonlinear stress-strain relation is approximated by a series of
straight-line segments. Although this is the most versatile model capable of representing a wide
range of stress-strain curves, the softening branch of the concrete stress-strain relation is found
to be related to the numerical difficulties in solution convergence during nonlinear iterations.
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Figure 7, Typical stess-strain relationship of normal concrete
0
10
20
30
40
0 0.001 0.002 0.003 0.004 0.005
strain
stre
ss (
MP
a)
piecew ise linearmodelelastic-perfectlyplastic model,
Due to this unique problem in the finite element analysis of slab-column connections, two
solution strategies have been applied in this study. The one is applying the piecewise linear
model without defining the crush of concrete, the ultimate uniaxial compressive strength ( 'cf ); the
another is involved with the crush of concrete but using the elastic-perfectly plastic model. After
comparing this two approach with the simple model (Fig. 11), the results in the Fig. 8 shows the
advantage of the latter. The elastic-perfectly plastic model gives a good prediction of ultimate
loading and displacement to the specimens.
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Fig. 8 Verification of two approaches to convengent problemusing the simple discrete model(GSHD2)
0
100
200
300
400
0 5 10 15 20 25 30 35 40
Ultimate loading (KN)
Dis
plac
emen
t (m
m) GSHD2
piecew iselinear model
elastic-perfectlyplastic model,
2. GFRP reinforcement constitutive model
2.1 Link8 Element Description
Link8 element, the three-dimensional spar element is a uniaxial tension-compression element
with three degrees of freedom at each node: translations in the nodal x, y, and z directions. As in
a pin-jointed structure, no bending of the element is considered. The element is also capable of
plastic deformation, stress stiffening, and large deflection. The geometry, node locations, and the
coordinate system for this element are shown in Fig. 9.
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Fig. 9: Link8 Element����3-D spar (ANSYS 1998)����
2.2 GFRP Reinforcement Properties
GFRP reinforcement in the experimental slab-column connections was made of typical GFRP
material. Through the tension test of GFRP reinforcement, the properties including elastic
modulus and ultimate tensile stress in this FEM study is as Fig. 10.
Elastic modulus, Es = 42,000 MPa
Yield stress, yf = 630 MPa
Poissons ratio, = 0.3
Fig. 10: the stress and strainrelationship of GFRPs rebar
0
100
200
300
400
500
600
700
0 0.004 0.008 0.012 0.016
Strain
Str
ess
(MP
a)
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2.3 Smear and Discrete Reinforcement Consideration
Beside the discrete reinforcement model adopted in this study, the reinforcement could be also
defined using the smeared reinforcement option of the Solid65 element. The amount of
reinforcement is defined by specifying a volume ratio (VRn) and the orientation angles (THETAn
and PHIn) of the rears. This approach is easy to construct the reinforced concrete model, which
has the uniform or simple reinforcement arrangement. In practice, the reinforcement in flat slabs
is normally arranged in a uniform form in different slab strips. Therefore, it is suggested to use
this smear reinforcement option when simulating the large slab model. However, the stress and
location of reinforcement is difficult to obtain in the smear model. In this study, the behavior of
slab-column connections was investigated by examining the stress distribution in the whole
specimen. The stress of the reinforcement is critical to this investigation. The discrete
reinforcement model is used in the study. On the other hand, it is motivated to construct smear
reinforcement model for comparing the discrete one, then strengthen the understanding the
difference between these two models and prepare for the future application.
For the comparison purpose, four simple models are constructed for predicting the
load-displacement relationship in an acceptable accuracy and a low consumption of computation
time. The simple model doesn’t consider the layer mesh, spring support and the column stub. In
Fig. 11 there are four models. The first three are the smear reinforcement models with different
thickness of the reinforcement layer, including the thickness of 20mm, 40mm and 100mm. The
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last one is the discrete reinforcement model with the reinforcement spacing of 240mm. The test
results of these models are plotted in the Fig.12.
It is obvious that the four models obtain the similar displacement and ultimate loading, but the
smear models got a smoother curve. In the general building codes in the world, the major
concerns of punching strength of slabs are the reinforcement ratio, the load area, the effective
depth and compressive strength of concrete. The effect of the arrangement of reinforcement on
the punching strength is ignored, which is verified in this test. Therefore, the reinforcement
spacing of the simulated models is taken as 120mm and 240mm for constructing the model
consistent with the mesh size and column size. This is different with the reinforcement spacing of
the actual tested specimens, but the reinforcement ratio is kept same.
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a).Smear Model with 20 mm thickness Rebar Layer
b).Smear Model with 100 mm thickness Rebar Layer
c).Smear Model with 40 mm thickness Rebar Layer
d).Discrete Model
Fig. 11: Smear and Discrete Model
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Fig. 12: Comparison of smear and discrete reinforce model
0
20000
40000
60000
80000
100000
120000
140000
0 5 10 15 20
displacement (mm)
Ulti
mat
e lo
adin
g (N
)
��������������� � � � � �� ������ � �
3. Boundary Condition and Spring constitutive model
3.1 Link10 Element Description
LINK10 element is a three-dimensional spar element having the unique feature of a bilinear
stiffness matrix resulting in a uniaxial tension-only (or compression-only) element. With the
tension-only option, the stiffness is removed if the element goes into compression (simulating a
slack cable or slack chain condition) [ANSYS, 1998]. The geometry, node locations, and the
coordinate system for this element are shown in Fig. 13.
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Fig. 13: Link10 Element����Tension-Only or Compression-Only Spar (ANSYS 1998)
3.2 Boundary Condition
In this study, since the effect of gravity of slab-column connection on the punching strength of
specimens is little, the simulated model is constructed in the form of one quarter of the slabs due
to the two axes of symmetry. Thus, the boundary condition of these two edges is defined as the
symmetry of displacement, which is shown in the Fig.1.
Because the specimens are simply supported on four edges that are free to lift during the tests,
the proper simulation of the boundary condition is taken into account. Link10 elements, the
special nonlinear spring elements in the transverse direction are employed along four edges of
labs in the numerical model, which is illustrated in Fig.1. The stiffness of spring elements is
numerically set to be significant high in compression and zero in tension respectively.
Furthermore, the simple support in the test is a roller support made of the steel tube and covered
with 3mm-thickness rubber. Both the steel tube and rubber will be deformed during the test, the
stiffness of spring would have been chosen carefully to represent the test simple support in the
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
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condition of relatively large deflection, so that the similar load-deflection curve to the tested
specimens could be obtained. However, the test setup tries to simulate the slab-column
connection around the conflexure line. In spite of the careful setup, the specimen could not
reflect the real deformation perfectly, while the model using ANSYS could exactly simulate this
theoretical specimen. Therefore, simply simulating the test specimen spring support could not
represent the real situation. In this study, the comparison between the specimens and models,
including the change and development of stiffness of slabs, the crack loading and the ultimate
loading are the major concern. This model can be regarded as a good reference to the real
slab-column connection in the flat slab system.
4. Finite Element Discretization
After constructed a model with volumes, areas, lines and key points, a finite element analysis
requires meshing of the model. The model is then divided into a number of small elements, and
after loading, stress and strain are calculated at integration points of these small elements (Bathe
1996). Since the FEM could approximate the real situation as close as possible depending on the
selection of the mesh density, it is a significant step in finite element modeling to choose an
appropriate mesh size to meet the requirement of accuracy and speed. 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 (Adams and
Askenazi 1998). Therefore, in this finite element modeling study the appropriate mesh size is
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
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determined by a convergence study and the behavior of slab-column connections.
Volume elements can often be either hexahedral (brick) or tetrahedral shaped, but the solid65
element comprising of 8 nodes has no center point is recommended to be meshed in the
hexahedral shape.
The ACI code (ACI, 1995) assume that the control perimeters of punching failure is located at a
distance of 0.5 times the effective depth from the edge of load (column), while the British code
(BS8110, 1985) considers a larger control perimeter, 1.5d. Furthermore, because the spring
support is used in this study, the support failure will not occur. Therefore, the mesh size in this FE
study must be small in the area around the column and the larger size can be acceptable near
the edge.
On the other hand, the column stub, slab and reinforcement are required to work together in the
discrete model used in this study. Then, the size of column and the spacing of reinforcement are
taken into consideration of determining the mesh size. The small change of the load area
(column size) gives the similar results of punching strength of slab-column connections using
either of ACI code or British code. Consistent with the reinforcement spacing 120mm and 240mm
determined in the above chapter, column stub size in the model is reduced from 250mm to
240mm, which only leads to 1% difference.
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Fig. 14: The mesh size comparison
0
20000
40000
60000
80000
100000
120000
0 5 10 15
Displacement (mm)
Ult
imat
e lo
adin
g (
N)
�� ������ ��� � �
Therefore, the mesh size is considered as 60mm or 120mm. Using the simple model described
in the Fig.11 to check the difference of models meshed with the mesh global size of 60mm and
120mm and the mesh thickness size of 50mm, the results are illustrated in the Fig. 14. According
to this figure, it is fair to draw a conclusion that there is no significant effect on the load-deflection
relationship of the model using controlled mesh size of either the 60mm or 120mm. However, the
120mm is relatively bigger to investigate the element stress around the column because the
column size is 120mm; while the model with the mesh size of 60mm is quite time consuming: 4
hours have been spent to run this simple model. In the end, the layer mesh is selected in this
study, which is shown in the Fig. 1.
5. Numerical Implementation
The numerical implementation of the finite element model is based on the virtual work principle or
the theorem of minimum potential energy to the assemblage of discrete elements. The following
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equilibrium equations are:
(9)
The terms in Eq. 9 are derived as follows:
the stiffness matrix [K] ,
(10)
the nodal forces due to surface traction,
(11)
the nodal forces due to body forces,
(12)
the nodal forces due to initial strains,
(13)
and the nodal forces due to initial stresses
(14)
In Eqs. 9-14, the components of ][N are the shape functions, }{d is the vector of node
displacements, }{ R is the vector of applied nodal forces, }{ p is the vector of surface forces
and }{ g is the vector of body forces.
This is a system of simultaneous nonlinear equations, since the stiffness matrix ][K , in general,
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depends on the displacement vector }{d . The solution of this system of nonlinear equations is
typically accomplished with an iterative method. The load vector }{ R is subdivided into a
number of sufficiently small load increments. At the finishing point of each incremental solution,
the stiffness matrix of the model is adjusted to reflect nonlinear changes in structural stiffness
before proceeding to the next load increment. The ANSYS program (ANSYS, 1998) 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. Fig. 15 shows the use of the Newton-Raphson approach in a single degree of freedom
nonlinear analysis.
Prior to each solution, the Newton-Raphson approach assesses the out-of-balance load vector,
which is the difference between the restoring forces (the loads corresponding to the element
stresses) and the applied loads. Subsequently, the program carries out a linear solution, using
the out-of-balance loads, and checks for convergence. If convergence criteria are not satisfied,
the out-of-balance load vector is re-evaluated, the stiffness matrix is updated, and a new solution
is attained. This iterative procedure continues until the problem converges (ANSYS, 1998).
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Fig. 15, Newton-Raphson iterative solution (2 load increments) (ANSYS, 1998)����
In this study, for the reinforced concrete solid elements, convergence criteria were based on
force. In order to obtain fast and accurate convergence of this nonlinear analysis, “Line Search
Option” and “Predictor-Corrector Option “ are set on, and the convergence tolerance limits
increased to a maximum of 10 times the default tolerance limits (0.5% for force checking).
According to the test procedure in the structural lab, the displacement is applied to the specimen
by a hydraulic actuator. In the other word, the actuator imposes the constant displacement to the
slab, while the applied loading is adjusted according to the change of the stiffness of the
specimen. Therefore, the displacement is applied to the column stub in this study for simulating
the experimental process.
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For the nonlinear analysis, automatic time stepping in the ANSYS program predicts and controls
load step sizes. Based on the previous solution history and the physics of the models, if the
convergence behavior is smooth, automatic time stepping will increase the load increment up to
a selected maximum load step size. If the convergence behavior is abrupt, automatic time
stepping will split the load increment until it is equal to a selected minimum load step size.
Although the automatic time stepping could ensures that the time step variation is neither too
aggressive nor too conservative, the amount of time step still determines the initial displacement.
In this study, the reinforced concrete is cracked, which leads to dramatically reduce the specimen
stiffness, subsequent to the small deflection of the slab. It is possible to fail to detect the cracking
load if the initial amount of time step is relatively big. Therefore, the amount of time step is set
1000 to ensure to replicate the complete loading process during the test.
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 32 of 52
6. Verification in the Elastic Stage
Since the reinforced concrete slab-column connection can be regarded as the elastic plate
before the crack forms, the finite element model, simply supported, and subjected to a centrally
concentrated load, was initially investigated. These models simulated the specimen (Table 1)
had the same main parameters. Based on verification of the slabs before cracking, the slabs
were analyzed using plain concrete theory and finite element results were compared with hand
calculations.
Fig. 16a-d show relationship of the deflection and loading of the center on the top of the slabs, as
calculated by the model and by traditional hand calculations (Timoshenko, 1987). As expected,
the deflection is linear with loading, and the finite element model shows excellent correlation with
the hand calculation before the cracks form in the model. However, the models shown in the Fig.
16e and f are a little divergent from the hand calculations. This is because the applied uniform
load in the column area is regarded as central load on the slab. When the slab is relative thin, the
uniform load is well consistent with the simulated central load. However, the consistency is
weakened as the depth of slab increases, which shows in Fig 16e and f.
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
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Fig. 16a: Finite Element Model Verificationin the Elastic Stage
0
20
40
60
80
100
120
0 0.2 0.4 0.6 0.8
Deflection (mm)
Load
ing
(KN
)
GS1_Tested
ANSYS_GS1
Fig. 16b: Finite Element Model Verificationin the Elastic Stage
0
10
20
30
40
50
60
70
80
90
0 0.2 0.4 0.6 0.8 1
Deflection (mm)
Load
ing
(KN
)
GS3_Tested
ANSYS_GS3
Fig. 16e: Finite Element Model Verificationin the Elastic Stage
0
20
40
60
80
100
120
140
160
0 0.2 0.4 0.6 0.8 1
Deflection (mm)
Load
ing
(KN
)
GSHS1_Tested
ANSYS_GSHS1
Fig. 16f: Finite Element Model Verificationin the Elastic Stage
0
20
40
60
80
100
120
140
0 0.2 0.4 0.6 0.8
Deflection (mm)
Load
ing
(KN
)GSHS2_Tested
A_GSHS2
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 34 of 52
Fig. 16e: Finite Element Model Verificationin the Elastic Stage
0
50
100
150
200
250
0 0.1 0.2 0.3 0.4 0.5 0.6
Deflection (mm)
Load
ing
(KN
)
GSHD1_Tested
ANSYS_GSHD1
Fig. 16f: Finite Element Model Verificationin the Elastic Stage
0
50
100
150
200
250
0 0.1 0.2 0.3 0.4 0.5 0.6
Deflection (mm)
Load
ing
(KN
)
GSHD2_Tested
ANSYS_GSHD2
Further verification of the validity of finite element models using non-linear analysis may be
demonstrated by comparing the predicted response of the model with experimental results
obtained from laboratory tests. Load deflection behavior obtained from the model, was compared
to values for similar behavior obtained for the experimental specimen.
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 35 of 52
Comparison of Finite Element Analysis to Test Results
Based on the preparation and analysis for the slab-column connections constructed by ANSYS,
six finite element models were conducted for the comparison of the measured ultimate loads and
the associated deflection at the center of the tested slabs. All slabs were reinforced with GFRP
bars. The length and width of all the slabs were 1920 mm with the thickness of either 200 mm or
150 mm. Since the two-axis symmetry, the finite element models were only a quarter of the slabs.
A concrete cover of 50 mm was used for all the slabs. Due to the brittle flexural failure of the
concrete members reinforced with GFRP bars, all the slabs were initially designed to be
over-reinforced, using the reinforcement ratio more than the balanced reinforcement ratio �b.
This also achieved the punching failure because of high reinforcement ratio (Menetrey, 1998).
The slabs of GS1 and GS3 were designed for investigating the effect of reinforcement ratio on
the punching loading on the normal slab-column connection. The size effect was examined using
the slabs of GSHD1 and GSHD2 with the high depth. And the application of the high strength
concrete to slabs reinforced with GFRP was analyzed based on the slabs of GSHS1 and GSHS2.
The details of the specimens are given in Table 1.
With the application of the three-dimensional solid element, there was reasonable agreement
between the predictions by the finite element model and the measurement by the tests in
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 36 of 52
slab-column connections. The ratios of predicted-to-measured ultimate loads were in the range
form 0.82 to 1.13; the average value was 0.98 with standard deviation of 10.8. The ratios of the
associated deflections at the center of the slabs ranged from 0.68 to 0.98; and the average value
was 0.85 with standard deviation of 12.4. Table 2 presents the comparison results and Fig. 17a-d
show the comparison of the three-dimensional finite element model prediction to the test results.
Table 2: Comparison of finite element analyzes to test results in ultimate loading capacity and its associated deflection
Test result Finite Element Result Finite Element/Test Slab No.
Compressive
strength
(MPa) Pu
(KN)
Deflection
(mm)
Pu
(KN)
Deflection
(mm) Pu Deflection
GS1 40 243 41.8 246 34.6 1.01 0.83
GS3 29 236 25.1 230 22.2 0.97 0.88
GSHD1 33 431 24.2 355 16.5 0.82 0.68
GSHD2 34 383 28.6 347 21.2 0.91 0.74
GSHS1 92 405 39.0 424 38.2 1.05 0.98
GSHS2 86 329 46.3 372 45.6 1.13 0.98
It is noted from the finite element analysis that the 40% increase of reinforcement ratio only
increases around the 12% punching capacity of slab-column connections. This proves the cubic
root relationship of the reinforcement ratio and punching capacity. This relationship is defined in
the BS8110 code for the steel as reinforcement. According to the results, even although the
GFRP rears reinforcing concrete structure have the linear elastic constitutive relationship and
relatively low modulus of elasticity, different from the traditional steel reinforcement, the strength
of slab-column connections reinforced with GFRP rears could be predicted by the BS8110 code if
considering a term to represent the relationship of steel and GFRP rears.
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 37 of 52
Fig. 17a: Comparison of F.E model prediction to test result – GFRP1,3
Fig. 17b: Comparison of F.E model prediction to test result – GSHD1,2
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
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Fig. 17c: Comparison of F.E model prediction to test result – GSHS1
Fig. 17d: Comparison of F.E model prediction to test result – GSHS
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 39 of 52
Since the finite element model provides the considerable accurate prediction of the strength of
slab-column connections, some traditional confusion for investigating two-way slabs using
experimental approach could be overcome based on the finite element approach, for example,
parameter study, the crack phenomenon and the form of punching cone, the failure mechanism
of two-way slabs, the conflict of the punching shear prediction using major codes such as ACI
code and BS8110 code.
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 40 of 52
Finite Element Analysis Results Versus Modified Code Predictions
Since the two-way slab reinforced with GFRPs are a new reinforced concrete member, there
have not been an accepted approach to predict the ultimate load in the building codes.
EI-Ghandour (EI-Ghandour, 2003) has proposed an approach to modify the equation in the ACI
code using a term referring to the reinforcement stiffness to the power of 0.33; on the other hand,
he proposed to modify the equation multiplying a correction factor ��. In this study, the finite
element analysis results were compared with EI-Ghandour’s modified code predictions. This is
given in the Table 3. It is obvious that the finite element results are consistent to the equation of
the modified BS8110 code for the normal concrete strength slabs, but the equation of modified
ACI code overestimates the punching resistance in the average of 29%.
Table 3: Comparison of finite element analyzes to modified codes in ultimate loading capacity and its associated deflection
Slab
No.
Compressive
strength
(MPa)
Pu
(KN)
Pbs
(KN) Pu/Pbs
Paci
(KN) Pu/Paci
GS1 40 246 236 1.04 174 0.71
GS3 29 230 239 0.96 149 0.65
GSHD1 33 355 374 0.95 271 0.76
GSHD2 34 347 339 1.02 277 0.80
GSHS1 92 424 351 1.21 265 0.63
GSHS2 86 372 306 1.22 257 0.69
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
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Summary and Conclusion
A quarter of the full-size slab-column connections, with proper boundary conditions, were used in
ANSYS for modeling to reduce computational time and computer disk space requirements.
Concrete constitutive relationship included the elastic-perfectly plastic model, crack condition
and crush limit. GFRP reinforcement was defined linear elastic. Spring supports were the
compression only elements.
Based on the comparison of smear reinforcement model and discrete reinforcement model, the
later was used in this study because it is convenient to obtain the reinforcement information.
The layer mesh was used to obtain the enough information from critical section as well as to
reduce the computation time.
For nonlinear analysis in this study, the total displacement applied to a model was divided into a
number of load steps. Sufficiently small load step sizes are required, particularly at changes in
behavior of the reinforced concrete connections, i.e., major cracking of concrete, and
approaching failure of the reinforced concrete connections.
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 42 of 52
For closed cracks, the shear transfer coefficient is assumed to be 0.9, while for open cracks it
should be in the suggested range of 0.05 to 0.5 to prevent numerical difficulties. In this study, a
value of 0.2 was used, which resulted in accurate predictions.�
The general behavior of the finite element models represented by the load-deflection plots at
center show good agreement with the test data. However, the finite element models show slightly
more stiffness than the test data in both the linear and nonlinear ranges. �
The modified BS8110 code represents the cubic root relationship between GFRP rears and the
punching strength of slab-column connections. Thus, it shows good agreement with the
predictions based on finite element models.
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 43 of 52
Reference
Abdel Wahab EI-Ghandour1; Kypros Pilakoutas2; and Peter Waldron (2003), “Punching Shear Behavior of Fiber Reinforced Polymers Reinforced Concrete Flat Slabs: Experimental Study”, Journal of Composites for Construction, ASCE, Vol. 7, No 3, August 1, 2003, pp. 258-264 American Concrete Institute (ACI), (1995) “Building code requirements for reinforced concrete and reinforced concrete and commentary.” ACI 318-95/ACI 318R-95, Detroit. Adams, V. and Askenazi, A., (1998) “Building Better Products with Finite Element Analysis,” Santa Fe, New Mexico ASCE Task Committee on Finite Element Analysis of Reinforced Concrete Structures. (1982). State-of-the-Art Report on Finite Element Analysis of Reinforced Concrete, ASCE Special Publications. British Standards Institution (BS8110), (1985) “Code of practice for design and construction.” British Standard Institution, Part 1, London. ANSYS (1998), ANSYS User’s Manual Revision 5.5, ANSYS, Inc., Canonsburg, Pennsylvania. Bathe, K. J., (1996) Finite Element Procedures, Prentice-Hall, Inc., Upper Saddle River, New Jersey. Bangash, M. Y. H. (1989), Concrete and Concrete Structures: Numerical Modeling and Applications, Elsevier Science Publishers Ltd., London, England. Darwin, D. (1993). Reinforced Concrete. In Finite Element Analysis of Reinforced-Concrete Structures II: Proceedings of the International Workshop. New York: American Society of Civil Engineers, pp. 203-232. Ngo, D. and Scordelis, A.C. (1967). "Finite Element Analysis of Reinforced Concrete Beams," Journal of ACI, Vol. 64, No. 3, pp. 152-163. Huyse, L., Hemmaty, Y., and Vandewalle, L. (1994), �Finite Element Modeling of Fiber Reinforced Concrete Beams,� Proceedings of the ANSYS Conference, Vol. 2, Pittsburgh, Pennsylvania, May 1994. Hemmaty, Y. (1998), �Modelling of the Shear Force Transferred Between Cracks in Reinforced
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 44 of 52
and Fibre Reinforced Concrete Structures,� Proceedings of the ANSYS Conference, Vol. 1, Pittsburgh, Pennsylvania, August 1998. Lin, C.S. and Scordelis, A.C. (1975). "Nonlinear Analysis of RC Shells of General Form". Journal of Structural Division, ASCE, Vol. 101, No. ST3, pp. 523-538. MacGregor,J G,;Bartlett, F M., (2000). “Reinforced Concrete: Mechanics and Design”, Prentice-Hall Canada Inc., Scarborough, Ontario Menetrey P. (1998), “Relationships between flexural and punching failure.” ACI Structure Journal, 1998; 95(4), pp. 412-419. Rashid, M (2004), “ The Behavior of Slabs Reinforced with GFRPs”, master thesis, preparing, Faculty of Engineering, Memorial University of Newfoundland, St. John’s, Canada. S. Timoshenko and S. Woinowsky-Krieger, (1987), “Theory of Plates and Shells”. MCGraw-Hill, Inc., New York.
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 45 of 52
Appendix: ANSYS CODE (GSHD1)
/ PREP7
/ TI TLE, The FI NI TE ELEMENT APPLI CATI ON TO SLAB- COLUMN CONNECTI ONS REI NFORCED WI TH
GFRPS
! - - - - - - - - - - - - - - - - - - - - - - ( 1) MODEL GENERATI ON- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ANTYPE, STATI C
ET, 1, SOLI D65, , , , , 2, 3 ! Def i ne t he Sol i d65 el ement f or t he concr et e
KEYOPT, 1, 1, 0 ! st r ess r el axat i on af t er cr ack
KEYOPT, 1, 5, 2
KEYOPT, 1, 6, 3
KEYOPT, 1, 7, 1
ET, 2, LI NK8, ! Def i ne t he Li nk8 el ement f or t he r ei nf or cement
ET, 3, LI NK10 ! Def i ne t he Li nk10 el ement f or t he spr i ng suppor t ! *
KEYOPT, 3, 2, 0 ! compr essi on onl y
KEYOPT, 3, 3, 1
MPTEMP, , , , , , , ,
MPTEMP, 1, 0
MPDATA, EX, 3, , 10000000
MPDATA, PRXY, 3, ,
MPTEMP, , , , , , , ,
MPTEMP, 1, 0
MPDE, EX, 3
MPDE, EY, 3
MPDE, EZ, 3
MPDE, NUXY, 3
MPDE, NUYZ, 3
MPDE, NUXZ, 3
MPDE, PRXY, 3
MPDE, PRYZ, 3
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 46 of 52
MPDE, PRXZ, 3
MPDE, GXY, 3
MPDE, GYZ, 3
MPDE, GXZ, 3
MPDATA, EX, 3, , 1E+007
MPDATA, PRXY, 3, , 0
R, 1, ! Def i ne t he r eal const ant f or concr et e
R, 2, 200, ! Def i ne t he ar ea of r ei nf or cement as 200mm̂ 2
R, 3, 2000, 0, , ! Def i ne si ze of t he spr i ng suppor t as 2000mm̂ 2
MP, EX, 1, 26700 ! Def i ne t he modul us of el ast i c i t y of concr et e as 26700 MPa
MP, NUXY, 1, 0. 2 ! Concr et e Poi sson r at i o i s 0. 2
TB, BKI N, 1, 1
TBDATA, 1, 33, 100
! Yi el d st r engt h of concr et e i s 33MPa
TB, CONCR, 1, 1
TBDATA, 1, 0. 2, 0. 9, 3. 5, 33
! t he shear t r ansf er coef f i c i ent of t he open cr ack i s 0. 2
! t he shear t r ansf er coef f i c i ent of t he cl ose cr ack i s 0. 9
! t he t ensi l e st r engt h of concr et e i s 3. 5 MPa
! t he compr essi ve st r engt h of concr et e i s 33 MPa
MPTEMP, , , , , , , ,
MPTEMP, 1, 0
MPDATA, DENS, 1, , 2. 3e- 6 ! Concr et e densi t y i s 2. 3e- 16 kg/ mm̂ 3
MP, EX, 2, 42000 ! Def i ne t he modul us of el ast i c i t y of GFRP as 42000 MPa
MP, NUXY, 2, 0. 3 ! GFRP Poi sson r at i o i s 0. 2
N, 1000, 960, 0, - 50, , , , ! Def i ne t he node f or spr i ng suppor t
N, 1001, 960, 60, - 50, , , ,
N, 1002, 960, 120, - 50, , , ,
N, 1003, 960, 180, - 50, , , ,
N, 1004, 960, 240, - 50, , , ,
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 47 of 52
N, 1005, 960, 300, - 50, , , ,
N, 1006, 960, 360, - 50, , , ,
N, 1007, 960, 480, - 50, , , ,
N, 1008, 960, 600, - 50, , , ,
N, 1009, 960, 720, - 50, , , ,
N, 1010, 960, 840, - 50, , , ,
N, 1011, 960, 960, - 50, , , ,
N, 1012, 0, 960, - 50, , , ,
N, 1013, 60, 960, - 50, , , ,
N, 1014, 120, 960, - 50, , , ,
N, 1015, 180, 960, - 50, , , ,
N, 1016, 240, 960, - 50, , , ,
N, 1017, 300, 960, - 50, , , ,
N, 1018, 360, 960, - 50, , , ,
N, 1019, 480, 960, - 50, , , ,
N, 1020, 600, 960, - 50, , , ,
N, 1021, 720, 960, - 50, , , ,
N, 1022, 840, 960, - 50, , , ,
N, 2000, 960, 0, - 60, , , ,
N, 2001, 960, 60, - 60, , , ,
N, 2002, 960, 120, - 60, , , ,
N, 2003, 960, 180, - 60, , , ,
N, 2004, 960, 240, - 60, , , ,
N, 2005, 960, 300, - 60, , , ,
N, 2006, 960, 360, - 60, , , ,
N, 2007, 960, 480, - 60, , , ,
N, 2008, 960, 600, - 60, , , ,
N, 2009, 960, 720, - 60, , , ,
N, 2010, 960, 840, - 60, , , ,
N, 2011, 960, 960, - 60, , , ,
N, 2012, 0, 960, - 60, , , ,
N, 2013, 60, 960, - 60, , , ,
N, 2014, 120, 960, - 60, , , ,
N, 2015, 180, 960, - 60, , , ,
N, 2016, 240, 960, - 60, , , ,
N, 2017, 300, 960, - 60, , , ,
N, 2018, 360, 960, - 60, , , ,
N, 2019, 480, 960, - 60, , , ,
N, 2020, 600, 960, - 60, , , ,
N, 2021, 720, 960, - 60, , , ,
N, 2022, 840, 960, - 60, , , ,
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
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t ype, 3 ! Const r uct t he spr i ng el ement s
r eal , 3
* do, i , 0, 22
n1=1000+i
n2=2000+i
E, n1, n2
* enddo
wpst yl e, 10, 100, 0, 1000, 10, 0, 0, , 5 ! wor kpl ace st at us
Bopt , Numb, of f
K, 1, 0, 0, 0, ! Def i ne key poi nt s f or GFRP r ei nf or cement
K, 2, 960, 0, ,
K, 3, 0, 960, , ,
LSTR, 1, 2
LSTR, 1, 3
FLST, 3, 2, 4, ORDE, 2 ! Def i ne l i nes f or GFRP r ei nf or cement
FI TEM, 3, 1
FI TEM, 3, - 2
FLST, 3, 1, 4, ORDE, 1
FI TEM, 3, 2
LGEN, 9, P51X, , , 120, , , , 0
FLST, 3, 1, 4, ORDE, 1
FI TEM, 3, 1
LGEN, 9, P51X, , , 0, 120, , , 0
FLST, 2, 18, 4, ORDE, 2
FI TEM, 2, 1
FI TEM, 2, - 18
LOVLAP, P51X
LATT, 2, 2, 2, , , , ! Def i ne t he l i nes wi t h GFRP at t r i but es
ESI ZE, 120, 0, ! Mesh and const r uct t he GRFP el ement s
FLST, 5, 54, 4, ORDE, 49
FI TEM, 5, 19
FI TEM, 5, - 20
FI TEM, 5, 22
FI TEM, 5, - 23
FI TEM, 5, 25
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 49 of 52
FI TEM, 5, - 27
FI TEM, 5, 29
FI TEM, 5, - 31
FI TEM, 5, 34
FI TEM, 5, 38
FI TEM, 5, 42
FI TEM, 5, 46
FI TEM, 5, 49
FI TEM, 5, 53
FI TEM, 5, - 55
FI TEM, 5, 57
FI TEM, 5, - 59
FI TEM, 5, 62
FI TEM, 5, 66
FI TEM, 5, 70
FI TEM, 5, 74
FI TEM, 5, 77
FI TEM, 5, 80
FI TEM, 5, 84
FI TEM, 5, - 86
FI TEM, 5, 91
FI TEM, 5, 93
FI TEM, 5, 97
FI TEM, 5, - 98
FI TEM, 5, 103
FI TEM, 5, - 104
FI TEM, 5, 109
FI TEM, 5, - 110
FI TEM, 5, 115
FI TEM, 5, - 116
FI TEM, 5, 121
FI TEM, 5, - 122
FI TEM, 5, 127
FI TEM, 5, - 128
FI TEM, 5, 133
FI TEM, 5, - 134
FI TEM, 5, 139
FI TEM, 5, - 140
FI TEM, 5, 145
FI TEM, 5, - 146
FI TEM, 5, 151
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 50 of 52
FI TEM, 5, - 152
FI TEM, 5, 157
FI TEM, 5, - 158
CM, _Y, LI NE
LSEL, , , , P51X
CM, _Y1, LI NE
CMSEL, , _Y
! *
LESI ZE, _Y1, 60, , , , , , , 1
! *
FLST, 2, 144, 4, ORDE, 2
FI TEM, 2, 19
FI TEM, 2, - 162
LMESH, P51X
wpof f , 0, 0, - 50 ! Def i ne t he vol umes f or concr et e sl ab and col umn st ub
BLC4, 0, 0, 360, 360, 200
BLC4, 360, 0, 600, 360, 200
BLC4, 0, 360, 360, 600, 200
BLC4, 360, 360, 600, 600, 200
wpof f , 0, 0, 200
BLC4, 0, 0, 120, 120, 600
FLST, 2, 4, 6, ORDE, 2
FI TEM, 2, 1
FI TEM, 2, - 4
VGLUE, P51X
WPSTYLE, , , , , , , , 0
nummr g, al l
numcmp, al l
VATT, 1, 1, 1, 0 ! Def i ne t he vol umes wi t h concr et e at t r i but es
FLST, 5, 4, 4, ORDE, 4 ! Mesh and const r uct t he concr et e el ement s
FI TEM, 5, 5
FI TEM, 5, 8
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
Page 51 of 52
FI TEM, 5, 170
FI TEM, 5, 173
CM, _Y, LI NE
LSEL, , , , P51X
CM, _Y1, LI NE
CMSEL, , _Y
! *
LESI ZE, _Y1, 60, , , , , , , 1
! *
FLST, 5, 1, 4, ORDE, 1
FI TEM, 5, 159
CM, _Y, LI NE
LSEL, , , , P51X
CM, _Y1, LI NE
CMSEL, , _Y
! *
LESI ZE, _Y1, , , 4, , , , , 1
! *
MSHAPE, 0, 3D
MSHKEY, 1
! *
FLST, 5, 5, 6, ORDE, 2
FI TEM, 5, 1
FI TEM, 5, - 5
CM, _Y, VOLU
VSEL, , , , P51X
CM, _Y1, VOLU
CHKMSH, ' VOLU'
CMSEL, S, _Y
! *
VMESH, _Y1
! *
CMDELE, _Y
CMDELE, _Y1
CMDELE, _Y2
! *
nummr g, al l
numcmp, al l
FE application to slab-column connections reinforced with GFRPs By Qi Zhang
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FLST, 2, 6, 5, ORDE, 6 ! Def i ne t he symmet r y boundar y condi t i on
FI TEM, 2, 3
FI TEM, 2, 5
FI TEM, 2, 11
FI TEM, 2, 13
FI TEM, 2, 18
FI TEM, 2, 21
DA, P51X, SYMM
FLST, 2, 23, 1, ORDE, 2 ! Def i ne t he spr i ng f i xed i n t he end
FI TEM, 2, 24
FI TEM, 2, - 46
! *
/ GO
D, P51X, , 0, , , , ALL, , , , ,
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ( 2) SOLUTI ON- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
/ sol u
cnvt ol , f , , 0. 05, 2 ! Def i ne f or ce as t he conver gence l i mi t , 0. 05
nsubst , 1000, 2000 ! Load st eps ar e 1000, t he maxi mum l oad st ep ar e 2000
out r es, al l , al l ! Out put al l t he dat a t o t he r esul t f i l e
aut ot s, 1 ! Set aut o st eppi ng on
l nsr ch, 1 ! Set l i ne sear ch on
ncnv, 2 ! Fi ni sh but not exi t i f not conver gent
neqi t , 50 ! Maxi mum i t er at i on i n each st ep i s 50
pr ed, on ! Set pr edi ct i on opt i on on
t i me, 25 ! Set t i me 25 second
FLST, 2, 1, 5, ORDE, 1 ! Appl yi ng t he di spl acement 25mm al ong - UZ
FI TEM, 2, 10
! *
/ GO
DA, P51X, UZ, - 25
ACEL, 0, - 9. 81, , ! Appl y t he gr avi t y of model
sol ve
f i ni sh