Finite Element Analysis of Bearing Capacity of RC Beams Retrofitted with External Bars
In this paper, results of the nonlinear finite element (FE) analysis of twenty numbers of RC beams are presented and validated using the experimental results reported elsewhere. The nonlinear behavior of RC beams with external bars is quite complicated due to the involvement of heterogenic and crack...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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| Zitieren: | Finite Element Analysis of Bearing Capacity of RC Beams Retrofitted with External Bars / G. Vasudevana, S. Kothandaramanb // Проблемы прочности. — 2014. — № 6. — С. 136-149. — Бібліогр.: 16 назв. — англ. |
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irk-123456789-1732152020-11-26T01:27:14Z Finite Element Analysis of Bearing Capacity of RC Beams Retrofitted with External Bars Vasudevana, G. Kothandaramanb, S. Научно-технический раздел In this paper, results of the nonlinear finite element (FE) analysis of twenty numbers of RC beams are presented and validated using the experimental results reported elsewhere. The nonlinear behavior of RC beams with external bars is quite complicated due to the involvement of heterogenic and cracking behavior of concrete. Also, modeling of external bars at the soffit level anchored at the ends is different from the conventional reinforcing bars due to lack of bonding at the soffit level. The finite element modeling is carried using SOLID65, SOLID45, LINK8, and COMBIN39 elements Одним из экономически эффективных и простых способов повышения прочности при изгибе является укрепление балки с помощью наружных стержней на уровне ее нижней поверхности. Обсуждаются моделирование методом конечных элементов и нелинейный анализ железобетонных балок с дополнительными арматурными стержнями, выполненные на базе программного комплекса ANSYS 12.0. Одним з економічно ефективних і простих способів підвищення міцності при згині є закріплення балки за допомогою зовнішніх стрижнів на рівні її нижньої поверхні. Обговорюються моделювання методом скінченних елементів і нелінійний аналіз залізобетонних балок із додатковими арматурними стрижнями, виконані на базі програмного комплексу ANSYS 12.0. Моделювання методом скінченних елементів залізобетонних балок проводилось на основі дискретного моделювання армування. 2014 Article Finite Element Analysis of Bearing Capacity of RC Beams Retrofitted with External Bars / G. Vasudevana, S. Kothandaramanb // Проблемы прочности. — 2014. — № 6. — С. 136-149. — Бібліогр.: 16 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/173215 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел |
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Научно-технический раздел Научно-технический раздел Vasudevana, G. Kothandaramanb, S. Finite Element Analysis of Bearing Capacity of RC Beams Retrofitted with External Bars Проблемы прочности |
| description |
In this paper, results of the nonlinear finite element (FE) analysis of twenty numbers of RC beams are presented and validated using the experimental results reported elsewhere. The nonlinear behavior of RC beams with external bars is quite complicated due to the involvement of heterogenic and cracking behavior of concrete. Also, modeling of external bars at the soffit level anchored at the ends is different from the conventional reinforcing bars due to lack of bonding at the soffit level. The finite element modeling is carried using SOLID65, SOLID45, LINK8, and COMBIN39 elements |
| format |
Article |
| author |
Vasudevana, G. Kothandaramanb, S. |
| author_facet |
Vasudevana, G. Kothandaramanb, S. |
| author_sort |
Vasudevana, G. |
| title |
Finite Element Analysis of Bearing Capacity of RC Beams Retrofitted with External Bars |
| title_short |
Finite Element Analysis of Bearing Capacity of RC Beams Retrofitted with External Bars |
| title_full |
Finite Element Analysis of Bearing Capacity of RC Beams Retrofitted with External Bars |
| title_fullStr |
Finite Element Analysis of Bearing Capacity of RC Beams Retrofitted with External Bars |
| title_full_unstemmed |
Finite Element Analysis of Bearing Capacity of RC Beams Retrofitted with External Bars |
| title_sort |
finite element analysis of bearing capacity of rc beams retrofitted with external bars |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2014 |
| topic_facet |
Научно-технический раздел |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/173215 |
| citation_txt |
Finite Element Analysis of Bearing Capacity of RC Beams Retrofitted with External Bars / G. Vasudevana, S. Kothandaramanb // Проблемы прочности. — 2014. — № 6. — С. 136-149. — Бібліогр.: 16 назв. — англ. |
| series |
Проблемы прочности |
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AT vasudevanag finiteelementanalysisofbearingcapacityofrcbeamsretrofittedwithexternalbars AT kothandaramanbs finiteelementanalysisofbearingcapacityofrcbeamsretrofittedwithexternalbars |
| first_indexed |
2025-07-15T09:44:59Z |
| last_indexed |
2025-07-15T09:44:59Z |
| _version_ |
1837705671808647168 |
| fulltext |
UDC 539.4
Finite Element Analysis of Bearing Capacity of RC Beams Retrofitted with
External Bars
G. Vasudevan
a
and S. Kothandaraman
b
a Perunthalaivar Kamarajar Institute of Engineering and Technology, Karaikal, India
b Pondicherry Engineering College, Puducherry, India
ÓÄÊ 539.4
Èññëåäîâàíèå íåñóùåé ñïîñîáíîñòè æåëåçîáåòîííûõ áàëîê, àðìèðîâàííûõ
íàðóæíûìè ñòåðæíÿìè, ñ ïîìîùüþ ìåòîäà êîíå÷íûõ ýëåìåíòîâ
Ã. Âàñóäåâàí
à
, Ñ. Êîòõàíäàðàìàí
á
à Ìåõàíèêî-òåõíîëîãè÷åñêèé èíñòèòóò èì. Ïåðóíòõàëàèâàðà Êàìàðàÿðà, Êàðàèêàë, Èíäèÿ
á Òåõíè÷åñêèé êîëëåäæ ã. Ïóäó÷åððè, Èíäèÿ
Îäíèì èç ýêîíîìè÷åñêè ýôôåêòèâíûõ è ïðîñòûõ ñïîñîáîâ ïîâûøåíèÿ ïðî÷íîñòè ïðè èçãèáå
ÿâëÿåòñÿ óêðåïëåíèå áàëêè ñ ïîìîùüþ íàðóæíûõ ñòåðæíåé íà óðîâíå åå íèæíåé ïîâåðõ-
íîñòè. Îáñóæäàþòñÿ ìîäåëèðîâàíèå ìåòîäîì êîíå÷íûõ ýëåìåíòîâ è íåëèíåéíûé àíàëèç
æåëåçîáåòîííûõ áàëîê ñ äîïîëíèòåëüíûìè àðìàòóðíûìè ñòåðæíÿìè, âûïîëíåííûå íà áàçå
ïðîãðàììíîãî êîìïëåêñà ANSYS 12.0. Ìîäåëèðîâàíèå ìåòîäîì êîíå÷íûõ ýëåìåíòîâ æåëåçî-
áåòîííûõ áàëîê ïðîâîäèëîñü íà îñíîâå äèñêðåòíîãî ìîäåëèðîâàíèÿ àðìèðîâàíèÿ. Ïîëó÷åííûå
äàííûå ñðàâíèâàëèñü ñ ðåçóëüòàòàìè ýêñïåðèìåíòàëüíûõ èññëåäîâàíèé 20 îáðàçöîâ áàëêè ïðè
÷åòûðåõòî÷å÷íîì èçãèáå. Äëÿ ìîäåëèðîâàíèÿ áàëêè ìåòîäîì êîíå÷íûõ ýëåìåíòîâ èñïîëü-
çîâàëèñü ýëåìåíòû SOLID65, SOLID45 è LINK8. Íàëè÷èå óïðóãèõ ýëåìåíòîâ COMBIN39 ïîçâî-
ëèëî ñìîäåëèðîâàòü êîíòàêò òðåíèÿ ìåæäó íèæíåé ïîâåðõíîñòüþ áàëêè è íàðóæíûìè
ñòåðæíÿìè. Ðåçóëüòàòû èññëåäîâàíèé èçîãíóòîé ôîðìû áàëêè, èçìåíåíèÿ äåôîðìàöèè ïî åå
äëèíå è ãëóáèíå, à òàêæå ðàñïðîñòðàíåíèå òðåùèíû íà ðàçíûõ ñòàäèÿõ íàãðóæåíèÿ ïðåä-
ñòàâëåíû â âèäå øèðîêîäèàïàçîííîãî ãðàôè÷åñêîãî äèñïëåÿ ñ ïîìîùüþ êîìàíäíîãî ôàéëà ñ
èñïîëüçîâàíèåì êîìïëåêñà ïàðàìåòðè÷åñêîãî ïðîåêòèðîâàíèÿ ANSYS.
Êëþ÷åâûå ñëîâà: íàðóæíûå ñòåðæíè, ïðîãðàììíûé êîìïëåêñ ANSYS, ýëåìåíò
COMBIN39.
Introduction. Strengthening of existing reinforced concrete (RC) structures is of
prime importance in the current scenario due to the reasons such as to safeguard the
non-engineered buildings, and upgrade the vulnerable buildings to current seismic codes,
Retrofitting of existing buildings is always preferred over demolition and reconstruction so
as to reduce the consumption of raw materials and mitigate the global warming problems.
The existing strengthening methods, such as section enlargement, bonded steel plating,
external post-tensioning and fiber reinforced polymer (FRP) composites wrapping, have
demerits, such as high cost, loss of aesthetics, increase in self-weight, need for careful
surface preparation, unexpected delamination failure, etc. The external reinforcement
technique proposed by the authors [1] has advantages such as speed and simplicity of
installation; minimal disruption during installation; use of cost effective materials; greater
cross-sectional area of external bars when compared to prestressed tendons makes it less
susceptible to corrosion, vandalism and sabotage; minimal surface preparation of concrete
substrate; no delamination failure problems, as experienced in bonded plates and FRP
laminates [2, 3]. In this paper, results of the nonlinear finite element (FE) analysis of twenty
© G. VASUDEVAN, S. KOTHANDARAMAN, 2014
136 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 6
numbers of RC beams are presented and validated using the experimental results reported
elsewhere. The nonlinear behavior of RC beams with external bars is quite complicated due
to the involvement of heterogenic and cracking behavior of concrete. Also, modeling of
external bars at the soffit level anchored at the ends is different from the conventional
reinforcing bars due to lack of bonding at the soffit level. The finite element modeling is
carried using SOLID65, SOLID45, LINK8, and COMBIN39 elements [4].
1. Review of Literature. Experimental testing on the flexural behavior of RC beams
has been carried out by Buckhouse [5], and the critical results were compared with
analytical values. Wolanski [6] has carried out the finite element analysis (FEA) using
ANSYS for the experimental beams provided by Buckhouse [5] and validated the results.
He has used SOLID65, SOLID45, and LINK8 elements to model concrete, steel cushion at
the supports and loading points using one quarter of the beam model. The steel
reinforcements were incorporated in the concrete elements through the nodes created by the
mesh of the concrete volume. Boundary conditions were applied at points of symmetry, and
at the supports. Kachlakev et al. [7] studied the behavior of RC beams with externally
bonded carbon fiber reinforced polymer (CFRP) fabric using ANSYS. They followed
smeared cracking approach for FE modeling using SOLID65 for concrete, LINK8 for
rebar, SOLID46 for FRP composites and SOLID45 for steel plates at the supports and
loading points. Fanning [8] conducted FEA on 3.0 m RC beams and 9.0 m post-tensioned
concrete beams with ANSYS V5.5 using smeared crack model to allow for concrete
cracking with the option of modeling the reinforcement in a distributed or discrete manner.
Suggested that for RC beams internal reinforcement should be modeled discretely and for
post-tensioned beams the post-tensioning tendons should be modeled discretely with any
other additional reinforcement modeled in a distributed manner. Also stated that, the Young
modulus and concrete tensile strength used in the numerical models can be calculated using
the existing rules of thumb from the known compressive strength of concrete.
Dahmani et al. [9], studied the crack propagation in RC beams using ANSYS modeled
with SOLID65 element with smeared reinforcement approach, in which the concrete and
the reinforcing were incorporated into elements with the same geometrical boundaries and
the effects of reinforcing were averaged within the pertaining element. Based on the results,
they stated that, in spite of the relative simplicity of the employed models, satisfactory
predictions of the response were obtained. Travarez [10] discussed the merits and demerits
of discrete model, embedded model and smeared model for incorporating reinforcements
depending on the type of system. Advantages ANSYS parametric design language (APDL)
and batch mode approach for conducting multiple analysis was studied and discussed by
Vasudevan and Kothandaraman [11]. Sallam et al. [12] presented the numerical simulation
of peeling failure of FRP strengthened flexural beams using ANSYS and stated that the
discrete crack approach was more accurate than smeared crack approach in simulating the
peeling crack. Elavenil and Chandrasekar [13] presented the numerical models to predict
the flexural behavior of RC beams strengthened with ferro-cement. The general behavior of
the FE models represented by the load–deflection plots at mid-span showed good
agreement with the experimental and theoretical results. The FE models showed slightly
more stiffness than the test data ranges due to the exclusion of bond slip (between the
concrete and steel reinforcing) and micro cracks occurring in the actual beams in the model.
Santhakumaret et al. [14] presented numerical study on unretrofitted and retrofitted
reinforced concrete beams subjected to combined bending and torsion using ANSYS and
revealed that the CFRP composites with � �45 fiber orientations were more effective in
retrofitting the RC beams subjected to combined bending and torsion for higher torque to
moment ratios. A detailed parametric study on nonlinear FEA on RC beams was conducted
by Vasudevan and Kothandaraman [15] with regard to mesh density, material modeling,
effect of excluding shear reinforcements in flexural behavior, inclusion of steel cushion at
the supports and loading points.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 6 137
Finite Element Analysis of Bearing Capacity …
2. Beam Specimens under Study. Six control beams (RF-N-X, RF-H-X) and
fourteen retrofitted beams (ER-N-X-Y, ER-H-X-Y) with external bars at the soffit level are
used for the FEA and the results are compared with test results. Beam specimens of size
2000 250 200� � mm with an effective span of 1800 mm for two grades of concrete
designated as N and H with targeted cube compressive strength of 30 and 40 MPa was used
for the investigation. The clear cover of 25 mm for the experimental testing and effective
cover 31.25 mm for FE modeling was used for beams. The beams were tested for
four-point bending with loading at a distance of 550 mm from either end of the support, so
as to have a moment span of 700 mm. The detailed report on the experimental investigation
on the behavior of RC beams with external bars at the soffit is to be reported elsewhere.
The details and other parameters used for the study are shown in Fig. 1 and Table 1.
3. Finite Element Modeling and Analysis Using ANSYS. RC beam specimens were
modeled using eight nodes SOLID65 element with three degrees of freedom at each node
(translations in the nodal x, y, and z directions), capable of handling nonlinear behavior,
cracking in three orthogonal directions due to tension, crushing in compression and plastic
deformation. The reinforcing bars were incorporated in the concrete model using two nodes
LINK8 spar element with three degrees of freedom at each node (translations in the nodal
x, y, and z directions), capable of handling plasticity, creep, swelling, stress stiffening and
large deflection. The supports and loading points were modeled as steel cushion to avoid
stress concentration problem using eight nodes SOLID45 element with three degrees of
freedom at each node (translations in the nodal x, y, and z directions), which handles
plasticity, creep, swelling, stress stiffening, large deflection and strain. The contact between
external bars and the soffit of the beam is modeled using COMBIN39, a unidirectional
element with nonlinear generalized force-deflection capability. One-quarter of the beam
was modeled for the FEA due to symmetry as shown in Fig. 2. Material model for concrete
used for the study is derived from IS 456: 2000 [16] with a partial safety factor of 1.0.
Other parameters used for the modeling is furnished in Tables 1 and 2. Parameters which
are not stated in this report were taken as program default. The FE modeling was carried
out in batch mode in sequence using KEYPOINTS, LINES, LESIZE, VOLUME, VMESH
and VSWEEP commands. The rebar elements were introduced in the nodes of the concrete
Fig. 1. Details of beam specimen.
138 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 6
G. Vasudevan and S. Kothandaraman
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Finite Element Analysis of Bearing Capacity …
elements using discrete reinforcement modeling which is most preferred for RC elements
with well defined reinforcement locations using E and EGEN commands. The support
conditions were created using displacement (D) boundary conditions. The entire process of
the nonlinear finite element analysis, such as geometrical modeling, material modeling,
parameters for nonlinear analysis, creation of load-steps, graphical post processing of
results, generation of various graphs and images and output in the form of text file was
generated using a single input file developed using the APDL [4]. The FE model with
discrete reinforcement model is shown in Fig. 3.
4. Modeling of Frictional Contact between the External Bar and Soffit of the
Beam. The external bars behave in a hybrid of flexural and tied arch action, in addition to
the frictional bonding by the soffit level external reinforced beams. The external bars also
follow the deflected shape of the beam due to loading and frictional bonding increases due
to load increase. This is one of the additional advantages of providing external bars at the
soffit level when compared to the methods proposed by earlier researchers, in which the
external bars were provided by the sides of the beam. The above behavior is incorporated in
the model by the use of COMBIN39 element between the external bar and the soffit of the
beam. COMBIN39 is a unidirectional element with nonlinear generalized force-deflection
capability. The element has longitudinal or torsional capability. The longitudinal option is a
uniaxial tension-compression element with up to three degrees of freedom at each node
such as translations in the nodal x, y, and z directions (ANSYS [4]). Displacement along
X and Y axes were activated for the longitudinal and transverse COMBIN39 spring
elements and all other options were set to default values. For incorporating the frictional
bonding of longitudinal COMBIN39 elements, 5 percent of the bond strength of the fully
bonded bar is assumed using IS 456: 2000 [16] nodal values. Since the external bars
T a b l e 2
Materials Properties for Concrete and Steel
Property Value Property Value
Yield strength of hanger bars (MPa) 556 Shear transfer coefficient for open crack 0.3
Yield strength of stirrups (MPa) 550 Shear transfer coefficient for closed crack 1.0
Tangent modulus for steel (MPa) 20 Uniaxial crushing stress value �1.0
Poisson’s ratio of concrete 0.2 Stiffness multiplier constant (Tc) 0.6
Poisson’s ratio of steel 0.3
Fig. 2. Quarter beam model.
140 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 6
G. Vasudevan and S. Kothandaraman
restrained to displace independently along the transverse direction by the contact of
concrete elements a full stiffness using the modulus of elasticity of concrete is used for
transverse COMBIN39 elements.
5. Results and Discussion.
5.1. Load–Deflection Behavior. Plots of load versus mid-span deflections obtained
from experiment and FEA are depicted in Fig. 4 for beams in N and H series. The shape of
the load–deflection plots are trilinear and immediately after the first crack formation, there
is a small kink in the FEA plot, which is due to sudden loss of moment of inertia after the
first crack formation. The comparison with experimental and FEA curves indicated that the
experimental and FEA results are in good agreement.
5.2. Load versus Concrete Compressive Strain Behavior. Compressive strain values
at the top compression face at mid-span section obtained from FEA are plotted and
compared with experimental values and is depicted in Fig. 5 for beams in N and H series.
The load versus compressive strain for the top compression face of the beams obtained by
FEA is in good agreement with the experimental results.
5.3. Load versus Rebar Strain Behavior. The strain variations of the internal and
external bars noted from FEA are compared with experimental values and are presented in
Figs. 6 and 7. From the experimental investigations, it was noted that the strain observations
of the internal bars were not recorded up to ultimate failure due to damage of the electrical
strain gauges caused by crack formation and yielding of internal bars. The comparison of
the plots shown in Figs. 6 and 7 indicated that the results of the FEA and experimental
testing are in good agreement. The strain variation of the external bars showed that the
yielding of the external bars occurs slightly at higher load when compared to internal bars.
Hence, it is observed that even after the yielding of internal bars, the load carrying capacity
was substantially increased due to the contribution by the external bars.
5.4. Rebar Strain Variation along the Length of the Beam at Various Loading
Stages. Graphical display of axial strain variation along the length of the beam in internal
and external bars for the beam specimens RF-H-10 and ER-H-10-10 at each load
increments are depicted in Fig. 8. The strain in internal bars varies along the length of the
beam with zero at the supports to maximum at the mid-span section in variation with
bending moment values. Whereas, the strain in external bars remains uniform almost all
along the length of the external bar due to lack of proper bonding along the length of bar.
Fig. 3. FE model with reinforcement.
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Finite Element Analysis of Bearing Capacity …
However, a small increase in external bar strain was noted towards the mid-span section of
the beam due to frictional bonding. A small strain variation in the compression bar also
depicted in Fig. 8. Similar observations were obtained for all the reference and retrofitted
beams.
5.5. Cracking Behavior. Crack patterns developed during the experimental testing
were keenly observed and marked on the beam and compared with cracking regions
generated by FEA and are presented in Fig. 9. It is to be noted that the crack patterns
generated by ANSYS are not the actual cracks but, the possible cracking regions. The loads
at initial crack formation are keenly observed during the experimental testing and from
FEA. The corresponding bending moment values calculated at initial crack formation in
test and FEA are compared as indicated in Fig. 10 for all the beam specimens. It is to be
noted that for the conventional beams (without external bars) the load at first crack
essentially depends upon the strength of concrete. On the contrary, the provision of external
Fig. 4. Comparison of load versus mid-span deflection.
142 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 6
G. Vasudevan and S. Kothandaraman
bars has contributed significantly to enhance the load at initial crack formation. Improvement
in the initial cracking behavior is mainly due to the hybrid of flexural and tied arch action
in addition to the frictional bonding by the soffit level external reinforced beams. This is
one of the additional advantages of providing external bars at the soffit of the beam. For the
beam ER-H-16-16 with higher internal and external reinforcements the experimental initial
cracking moment was higher by 64%.
Fig. 5. Comparison of load versus concrete compressive strain.
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Finite Element Analysis of Bearing Capacity …
5.6. The Ultimate Behavior. The ultimate load values obtained from FEA and
experiments are compared as the ultimate moment as indicated in Fig. 11. The percentage
increase in the ultimate capacity also varies with respect to grade of concrete, percentage of
internal bars and external bar to internal ratio. It is also noted that the percentage increase in
the ultimate moment capacity is higher for beams with lesser percentage of internal
reinforcement. This clearly indicates that the external bars are more effective for lightly
reinforced section than the heavily reinforced ones. The comparison between the
experimental values and FEA results are in good agreement.
Fig. 6. Comparison of load versus rebar strains (N-series).
144 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 6
G. Vasudevan and S. Kothandaraman
Conclusions. Based on the above nonlinear finite element analysis, six reference
beam specimens and fourteen RC beam specimens retrofitted with external bars at the soffit
level using ANSYS 12.0 and comparison with experimental results, the following
conclusions are made.
1. Various plots constructed during FEA, such as load versus deflection behavior, load
versus concrete compressive strain behavior, load versus axial strain in internal and
external bars, axial strain variation along the length of internal and external the bars and
crack patterns gives a broader view of the nonlinear behavior of RC beams with external
bars at the soffit level.
Fig. 7. Comparison of load versus rebar strains (H-series).
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Finite Element Analysis of Bearing Capacity …
Fig. 8. Axial strain in internal, external, and compression bars.
Fig. 9. Crack pattern from tests and FEA.
146 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 6
G. Vasudevan and S. Kothandaraman
2. Modeling of frictional contact between the external bars and the soffit of the beam
using COMBIN39 spring elements along longitudinal and lateral direction provides
reasonable results, which are in good agreement with test results.
3. The moment at initial crack formation and the ultimate moment obtained using FEA
are in good agreement with test results.
4. The analysis procedure used in this paper and various output plots constructed by
FEA has provided useful and deep insight for future application of finite element software
for the nonlinear analysis of RC beams with external bars at the soffit level.
Fig. 9 (continued). Crack pattern from tests and FEA.
Fig. 10. Calculated and experimental moments at the initial crack formation instant.
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Finite Element Analysis of Bearing Capacity …
Ð å ç þ ì å
Îäíèì ç åêîíîì³÷íî åôåêòèâíèõ ³ ïðîñòèõ ñïîñîá³â ï³äâèùåííÿ ì³öíîñò³ ïðè çãèí³ º
çàêð³ïëåííÿ áàëêè çà äîïîìîãîþ çîâí³øí³õ ñòðèæí³â íà ð³âí³ ¿¿ íèæíüî¿ ïîâåðõí³.
Îáãîâîðþþòüñÿ ìîäåëþâàííÿ ìåòîäîì ñê³í÷åííèõ åëåìåíò³â ³ íåë³í³éíèé àíàë³ç
çàë³çîáåòîííèõ áàëîê ³ç äîäàòêîâèìè àðìàòóðíèìè ñòðèæíÿìè, âèêîíàí³ íà áàç³
ïðîãðàìíîãî êîìïëåêñó ANSYS 12.0. Ìîäåëþâàííÿ ìåòîäîì ñê³í÷åííèõ åëåìåíò³â
çàë³çîáåòîííèõ áàëîê ïðîâîäèëîñü íà îñíîâ³ äèñêðåòíîãî ìîäåëþâàííÿ àðìóâàííÿ.
Îòðèìàí³ äàí³ ïîð³âíþâàëèñü ³ç ðåçóëüòàòàìè åêñïåðèìåíòàëüíèõ äîñë³äæåíü 20 çðàç-
ê³â áàëêè ïðè ÷îòèðèòî÷êîâîìó çãèí³. Äëÿ ìîäåëþâàííÿ áàëêè ìåòîäîì ñê³í÷åííèõ
åëåìåíò³â âèêîðèñòîâóâàëèñü åëåìåíòè SOLID65, SOLID45 òà LINK8. Íàÿâí³ñòü
ïðóæíèõ åëåìåíò³â COMBIN39 äîçâîëèëà çìîäåëþâàòè êîíòàêò òåðòÿ ì³æ íèæíüîþ
ïîâåðõíåþ áàëêè ³ çîâí³øí³ìè ñòðèæíÿìè. Ðåçóëüòàòè äîñë³äæåíü ç³ãíóòî¿ ôîðìè
áàëêè, çì³íè äåôîðìàö³¿ ïî ¿¿ äîâæèí³ ³ ãëèáèí³ òà ïîøèðåííÿ òð³ùèíè íà ð³çíèõ
ñòàä³ÿõ íàâàíòàæåííÿ ïðåäñòàâëåíî ó âèãëÿä³ øèðîêîä³àïàçîííîãî ãðàô³÷íîãî äèñï-
ëåÿ çà äîïîìîãîþ êîìàíäíîãî ôàéëà ç âèêîðèñòàííÿì êîìïëåêñó ïàðàìåòðè÷íîãî
ïðîåêòóâàííÿ ANSYS.
1. S. Kothandaraman and G. Vasudevan G, “Flexural retrofitting of RC beams using
external bars at soffit level – An experimental study,” Constr. Build. Mater., 24, No. 11,
2208–2216 (2010).
2. T. Hassan and S. Rizkalla, “Investigation of bond in concrete structures strengthened
with near surface mounted carbon fiber reinforced polymer strips,” J. Compos.
Construct., 7, No. 3, 248–257 (2003).
3. H. Thomsen, E. Spacone, S. Limkatanyu, and G. Camata, “Failure mode analyses of
reinforced concrete beams strengthened in flexure with externally bonded fiber-
reinforced polymers,” J. Compos. Construct., 8, No. 2, 123–131 (2004).
4. ANSYS Commands Reference, ANSYS, http://www.ansys.com (2005).
5. E. R. Buckhouse, External Flexural Reinforcement of Existing Reinforced Concrete
Beams Using Bolted Steel Channels, Master’s Thesis, Marquette University,
Milwaukee, WI (1997).
6. A. J. Wolanski, Flexural Behavior of Reinforced and Prestressed Concrete Beams
Using Finite Element Analysis, Master’s Thesis, Marquette University, WI (2004).
Fig. 11. Comparison of the ultimate moment.
148 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 6
G. Vasudevan and S. Kothandaraman
7. D. Kachlakev, T. Miller, S. Yim, et al., Finite Element Modeling of Reinforced
Concrete Structures Strengthened with FRP Laminates, Final Report, SPR 316,
Oregon Dept. of Transportation, Washington, DC (2001).
8. P. Fanning, “Nonlinear models of reinforced and post-tensioned concrete beams,”
Electr. J. Struct. Eng., 2, 111–119 (2001).
9. L. Dahmani, A. Khennane, and S. Kaci, “Crack identification in reinforced concrete
beams using ANSYS software,” Strength Mater., 42, No. 2, 232–240 (2010).
10. F. A. Tavarez, Simulation of Behaviour of Composite Grid Reinforced Concrete
Beams Using Explicit Finite Element Methods, Master’s Thesis, University of
Wisconsin-Madison, Madison, WI (2001).
11. G. Vasudevan and S. Kothandaraman, “Behaviour prediction of RC beams –
Comparison of experimental, FEA and analytical methods,” in: Proc. of the IEEE-Int.
Conf. on Advances in Engineering, Science, and Management (Nagapattinam, India)
(2012), pp. 365–370.
12. H. E. M. Sallam, A. A. Badawy, M. M. Balaha, et al., “Finite element analysis of
peeling failure in strengthened RC beams by CFRP plates,” The Egyptian Int. J. Eng.
Sci. Technol., 12, No. 2, 25–36 (2009).
13. S. Elavenil and V. Chandrasekar, “Analysis of reinforced concrete beams strengthened
with ferrocement,” Int. J. Appl. Eng. Res., 2, No. 3, 431–440 (2007).
14. R. Santhakumar, E. Chandrasekaran, and R. Dhanaraj, “Behaviour of retrofitted
reinforced concrete beams under combined bending and torsion: A numerical study,”
Electr. J. Struct. Eng., 7, 1–7 (2007).
15. G. Vasudevan and S. Kothandaraman, “Parametric study on nonlinear finite element
analysis on flexural behaviour of RC beams using ANSYS,” Int. J. Civil Struct. Eng.,
2, No. 1, 98–111 (2011).
16. IS 456: 2000. Indian Standard: Plain and Reinforced Concrete – Code of Practice,
Bureau of Indian Standards, New Delhi (2000).
Received 03. 06. 2013
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