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NON-LINEAR MODELLING OF FERRO CASTING DUCTILE
SHEAR KEY OF L-SHAPED CONCRETE BLOCKS WITH EPOXY
JOINT USING MIDAS FEA
Putri Ardiyati
Universitas Indonesia, Depok, (Indonesia).
E-mail: Putri.Ardiyati@ui.ac.id ORCID: https://orcid.org/0000-0002-3025-8067
Nuraziz Handika
Universitas Indonesia, Depok, (Indonesia).
E-mail: n.handika@ui.ac.id ORCID: https://orcid.org/0000-0001-9165-9246
Heru Purnomo
Universitas Indonesia, Depok, (Indonesia).
E-mail: heru.purnomo@ui.ac.id ORCID: https://orcid.org/0000-0002-0570-2891
Recepción:
22/06/2021
Aceptación:
01/09/2021
Publicación:
14/09/2021
Citación sugerida:
Ardiyati, P., Handika, N., y Purnomo, H. (2021). Non-linear modelling of Ferro casting ductile shear key of L-Shaped
concrete blocks with epoxy joint using Midas FEA. 3C Tecnología. Glosas de innovación aplicadas a la pyme, 10(3), 101-117.
https://doi.org/10.17993/3ctecno/2021.v10n3e39.101-117
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ABSTRACT
As cast iron with 10-15% of graphite, Ferro Casting Ductile (FCD) Iron material has better mechanical
properties than the ones from Grey Cast Iron. Moreover, it is also close to Carbon Steel’s properties.
Regarding this condition, FCD has the potential to be used as a shear key, specically, as a joint of precast
segmental concrete bridges. The objective of this paper is to study the mechanical behavior of FCD
applied as shear key on a wet precast joint using epoxy. To do so, three-dimensional non-linear numerical
modeling using Midas FEA was conducted on two L-shaped concrete blocks connected by a couple of
FCD shear key representing precast concrete segmental bridge system. Between these two L-shaped
blocks of concrete, epoxy adhesive was ap-plied. Both concrete blocks and FCD shear keys with 50%
scale of original geometries were used. The constitutive behavior of each material was obtained from
previous test results and literatures. Loading applications were performed in two directions, vertical load
to represent load from deck bridge and horizontal load to represent prestressing force. Load bearing
capacity of FCD shear keys increases along with the increase of horizontal load. Non-linear analysis
results show discrepancy comparing to the exper-imental ones, with a deviation reaches more than 7%.
KEYWORDS
Ferro Casting Ductile, Male and Female Shear Keys, Force-Displacement Relations, Numerical
Simulation.
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1. INTRODUCTION
Shear keys are prominently used in the joints of precast segmental concrete bridges. Prior to the use
of metal shear keys, concrete shear keys have been used nowadays. The ultimate strength at the joint
of precast concrete girders depends on the behav-ior of the material of joints between segments. The
behavior of shear key joints, whether using concrete or metal as their primary material, has been a
subject of several experimental studies in the past.
One of the studies is an experimental work by Zhou, Mickleborough and Li (2005). They studied the
behavior of shear strength of joints in precast concrete segmental bridges. Several type of concrete
shear keys such as at shear keys, multiple shear keys, with and without epoxy have been ana-lyzed
experimentally to investigate the shear capacity of each key in dierent kinds of joints. From this study,
it is found that the shear strength of the joints increases with an increase in conning stress. Moreover,
their experimental study stated that dry joints had an ultimate strength of approximately 20 – 40% less
than epoxied joints.
Yuan et al. (2019) studied the shear behavior of epoxy resin joints with plain concrete shear keys,
reinforced shear keys, internal post-tensioned tendon shear keys and concrete shear keys with inclined
design. Following the experimental study that has been conducted by Yuan et al. (2019), several results
found that reinforced shear keys and internal post-tensioned tendon shear keys with epoxy resin joints
generates a superior performance in ductility behavior than any other type of shear keys test-ed in the
experiment.
A series of tests resulted in a dierent epoxy resin joint failure mode for each design parameters. Epoxy
joint with plain concrete shear keys exhibited typical shear o along the key base, reinforced shear keys
demonstrated concrete covers crushed o over the reinforcing bar, meanwhile internal post-tensioned
shear keys revealed cracks propagated deeply into the male and female specimens. The Japanese stand-
ard (Japan Society of Civil Engineering, 2007) recommends the use of FCD (ferro casting ductile) metal
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with grade 450 as a material for FCD shear keys. The Japa-nese standard’s recommendation was veried
by Purnomo et al. (2017) in their ex-periment.
Purnomo et al. (2017) found that shear keys with grade 450 have higher shear strength with the smallest
displacement than any other FCD metal with grade range from 265-274 MPa (Compression yield
stress). Purnomo et al. (2018) have conducted experiments with specic geometry shear key and dierent
geometry shear keys. The geometry shear key used in this paper is also one of the types of shear keys
which has been used by Purnomo and others in previous experiments. The methodology of the non-
linear models closely resembles the methodology in Purnomo and others’ experimental study.
In this numerical study, non-linear analysis is performed by using two L-shaped concrete blocks
representing precast concrete segmental bridge system. These two blocks are connected by male shear
key in top of concrete blocks and female shear keys in bottom of concrete blocks. One layer of epoxy
with thickness 1 mm is ap-plied between concrete blocks as representative of epoxy connection type
in joint of concrete blocks. Pinned support is placed at the bottom of concrete blocks as its boundary
condition. Afterwards, increment vertical load is mounted at top of upper concrete block to represent
load which occur on top joint segmental concrete gird-ers. The horizontal load is applied at left of
upper concrete blocks as representative of prestress force. The constitutive law applied for the nonmetal
materials are the Total Strain Crack Model (T-S Crack Model).
2. METHODOLOGY
2.1. NON-LINEAR APPROACH
The non-linear analysis is made to simulate similar experimental test setup in pre-vious studies (Purnomo
et al., 2017; 2018). The conguration of the test setup of precast concrete girder uses two concrete
blocks as shown in Figure 1. The two con-crete block itself are set in a test frame which is equipped
with two hydraulic pumps. One of the two hydraulic pumps is placed above the concrete blocks with
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vertical orientation to represent the incremental load which compresses the concrete block. Another one
is placed in the center, beside the concrete block, with horizontal orien-tation to represent the equivalent
prestress force. Four digital gauges are located uniformly in the vertical direction to record the vertical
displacements in front and at the back of the concrete block. The correlation between the load and
displace-ment is obtained from the recording of the load cell placed above the concrete block to represent
incremental load and from the average of result from the four digital gauges to represent displacement.
Figure 1. Laboratory Test Set-Up.
Source: own elaboration.
2.2. SHEAR KEY GEOMETRY AND MATERIAL PROPERTIES
The male and female shear keys are made of Ferro casting ductile with material grade of FCD 450.
The concrete blocks are made of reinforced concrete with a 28-days compressive strength of 41.2 MPa,
which is representative of the conned compressive strength of precast concrete girders.
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The geometry of the shear keys modeled in Midas FEA is presented in Figure 2. The male shear key is
described in blue color. On the right side of Figure 2. is the female part of the shear key joint.
Figure 2. Geometry of the Male and Female Shear Keys (K1) in Midas FEA.
Source: own elaboration.
The dimensions of the concrete blocks and shear keys used in the test are shown in Figure 3. The
numerical analysis uses a model of concrete blocks and shear keys with fty percent downscaling in
geometry. The geometry of the concrete blocks and shear keys are modeled using Autodesk inventor
separately. The joint, made of ferro casting ductile shear keys, are located at the vertical midpoint of the
upper concrete block and are casted into the female shear keys and bottom concrete block. The upper
concrete block is mounted 10 mm higher than bottom concrete block. The vertical gap in between the
concrete blocks is lled with epoxy joint with a thickness of 1 mm.
Corresponding to the experimental study, vertical loads are applied as incremental load while the
horizontal load needs to be maintained as linear load throughout the duration of the experiment. Due
to limitations in the loading application setting in Midas FEA, the program cannot distinguish the two
loads with dierent step of loading.
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Two numerical models are created in Midas FEA. The rst model is a linear analy-sis model with
only horizontal load is applied. This rst model is used to identify the eects of horizontal load, which
represents the prestressing force on the concrete block. The horizontal load is modeled in a linear model
where its shear stress is ex-tracted and applied as additional shear stresses of the epoxy joint and concrete.
The second model is a non-linear analysis model with incremental vertical displace-ments. The non-
linear model considers the additional shear stress from the rst model which is applied to shear stress of
epoxy joint and concrete.
Figure 3. Dimensions of the Concrete and Shear Key Models. (a) Front view, (b) Cross Section View.
Source: own elaboration.
The engineering data of each of the materials in the joint precast concrete girders have been measured
in the laboratory. The compressive stress-strain relationship of concrete obtained from cylindrical
compressive strength test are acquired from the internal data of Structural and Material Laboratory
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of Universitas Indonesia (“Ma-terials Test Result Internal Data of Structural Laboratory at Universitas
Indone-sia”, 2020). The tensile strength of concrete model uses the formula obtained from Hu, Lin and
Jan (2004). In addition, the shear strength of concrete and the com-pressive, tensile and shear strength
of epoxy are obtained from the internal data of Structural and Material Laboratory of Universitas
Indonesia (“Materials Test Re-sult Internal Data of Structural Laboratory at Universitas Indonesia”,
2020). The compressive and tensile stress-strain relationship of ferro casting ductile are also obtained
from the laboratory. The stress -strain relation for FCD Material of each behavior is shown in Figure
4. The Poisson’s ratio of concrete, ferro casting ductile and epoxy use the values 0.2, 0.28, and 0.35,
respectively.
The constitutive law for nonmetal material of numerical models uses Total Strain Crack model which
is provided by Midas FEA. Meanwhile, failure behavior of each material uses dierent constitutive law.
The maximum shear strength of the joint is measured by either the tensile failure of the concrete or the
yielding of the shear keys. The epoxy joint can increase the shear capacity of the joint if applied with
a proper thickness. The tensile failure of the concrete is assumed to be the maximum principal stress or
Rankine’s theory (Boresi & Schimdt, 2003). Rankine’s theory is assumed to occur when the maximum
principal stress at any point reaches a value equal to the tensile stress of a simple tension specimen
at failure. Correspondingly, the tensile failure at the upper concrete block occurs when the maximum
principal stress reaches the tensile strength of concrete. Meanwhile, the failure criterion of ferro casting
ductile shear key use the Von Mises criterion. Based on the Von Mises criterion, the yielding of the shear
key occurs when the equivalent stress of a mate-rial under load is equal or greater to its yield limit (Boresi
& Schimdt, 2003).
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Figure 4. Stress-Strain Relationship for FCD Material.
Source: own elaboration.
In the following Table 1, stress representing prestress applied on the system as hori-zontal load is
presented. Two dierent horizontal forces were used to examine and to nd the adequate conguration
of shear key and concrete block which produces the maximum shear capacity. These values are applied
in the 1st numerical model-ling.
Table 1. FEA Analysis Variation.
Variation Initial Stress (MPa)
K1P3 0.345
K1P6 0.69
Source: own elaboration.
The nite element model uses three-dimensional simulation in Midas FEA. Solid element with Total
strain crack mode was used as the consecutive model of three primary materials. Contact between the
concrete-shear key and the epoxy was de-ned as rigid contact with symmetric condition. Rigid contact
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is considered to be the contact between the shear key and concrete. Pinned boundary condition for the
transversal axis is applied to the base of bottom concrete block. The upper concrete block was set free
with no boundaries. Vertical displacements were applied above the upper concrete block. The vertical
displacements are assigned in a 150x150 mm2 area incrementally. The horizontal load area is located
on the left side of the upper concrete block. Two models of numerical analysis are schematically shown
in Figure 5.
Figure 5. Linear and Non-Linear Models on Midas FEA. (a) 1st Model for Linear Analysis with Horizontal Load, (b) 2nd Model for
Non-Linear Analysis with Vertical Load.
Source: own elaboration.
Upper Concrete Block
Bottom Concrete Block
Horizontal Load
Shear Keys
Pinned B.C
Pinned B.C
Shear Keys
Bottom Concrete Block
Upper Concrete Block
Vertical Displacements
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3. RESULTS
3.1. MAXIMUM LOAD CAPACITY OF JOINTS
Figure 6. Von Mises Stress Contour in Male (Upper) and Female (Bottom) Shear Keys.
Source: own elaboration.
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Figure 6 displays the contour of Von Mises stress of each shear key with dierent initial stresses prior to
reaching its maximum vertical load. Following the displayed contour of Von Mises stress, it can be seen
that the male shear keys in every initial stress condition demonstrate the highest concentration of stress
at the outer ring of the shear key. The highest concentration of stress of the female shear keys follows
the male shear keys. The highest Von Mises stress of shear key is generated by vari-ation K1P3 with 331
MPa and K1P6’s Von Mises Stress is 274, Meanwhile Female shear key of K1P6 exhibit greater stress
than K1P3’s Female shear key. The max-imum value of Von Mises Stress for each model exceeded the
yield stress of ferro casting ductile shear key. The comparation of stress- strain relationship between
two models is shown in below Figure 7. Based in graphic in Figure 7 maximum loads occurred in K1P6
greater than K1P3. The deviation between two models maximum load reach 37%.
Figure 7. Load-Displacements Relationship of Shear Keys.
Source: own elaboration.
In Figure 7, K1P3 exhibit the lowest maximum vertical load which can be received by the concrete
block. K1P6 exhibit ductile behaviour while K1P3 demonstrated brittle behaviour after reaching its
maximum value, the graphic shows the load plunges after reaching the maximum load. In K1P6, the
loads are decreasing after reaching its maximum value with displacement almost twice the displacement
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of maximum value. In accordance with these results, horizontal forces can aect the joint system. The
maximum load demonstrates better value along with the in-creased horizontal force.
3.2. COMPARISON BETWEEN EXPERIMENT RESULTS AND NUMERICAL ANALYSIS
Figure 8. Comparison of Load-Displacement Relationship between Experiment Results and Nu-merical Analysis.
Source: own elaboration.
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Referring to Figure 8, comparing the graphic of load-displacement relation from experiment results
and numerical analysis, the results are very disparate. For both models, failure occur due to brittleness.
Therefore, the loads drop after reaching their maximum value. The dierent results between the
experimental results and numerical analysis are due to several occasions that happened during the experi-
ment. For example, an equal application of epoxy thickness between the concrete blocks is quite hard to
achieve in experiment. Meanwhile, in the numerical model, thickness of epoxy can be arranged equally.
The percentage value of deviation for each model are shown in Table 2. The minimum deviation occurs
in the K1P6 model.
Table 2. Comparison of Results between Experiment and Numerical Analysis.
Source: own elaboration.
4. CONCLUSIONS
Based on the numerical modelling of shear key and precast concrete block joint, it can be concluded
that the maximum load capacity of the joint system occurs ac-cordingly with the increase of horizontal
force. Following the contour of Von Mises stress, it can be seen that the highest stress is localized at the
counter part of female shear keys of model K1P6. The results of experiment and numerical studies show
dierent results due to limitation of application on experiments study and limita-tions of numerical
study program. The load vs displacement curves obtain from numerical study are compared with the
result of the experimental study. The choice of tensile stress-strain model for the concrete in the TS
Crack Model aect the maximum load obtained by the numerical simulation. The experimental and
nu-merical curves matched suciently up to before the rupture of epoxy layer, to be precise at the elastic
linier region. Once it behaves non-linearly, passing 1000 kg of loading application, only K1P3 sample
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could exhibit close mechanical behavior to the experimental results. Furthermore, in case of K1P3,
passing 2200 kg of loading application, the result of experiments and simulations are very dierent. It
seems the damage in the system concrete blocks and shear key occurred largely. In the future works, the
modelling can be improved, such as consideration of damage con-dition after the post peak of loading
application.
ACKNOWLEDGEMENTS
We gratefully thank for Midas FEA to supporting this numerical study.
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