ANALYTICAL CYCLIC CONSTITUTIVE MODEL FOR CONFINED CONCRETE IMPLEMENTATION IN OPENSEES: CONFINEDCONCRETE02 Abstract This paper presents the new material developed inside the OpenSees by considering constitute model for the concrete subjected to revere cyclic and monotonic loadings. The new material intended to provide the ability of model the cyclic behaviour of concrete subjected to compression in the computational programme. The analytical formulation proposed by the Braga, Gigliotti and Laterza (BGL model, 2006) is used for the envelope and reverse (loading and reloading) action of the material govern by the Yassin (1994) approach, which has given bilinear curve for unloading and loading. The lateral confinement of concrete enhances the strength and durability of the reinforcement concrete significantly. Introducing this uniaxial material inside the OpenSees is capable to model the influence of transverse hoops, ties and/or FRP, external wrapping with the section considered. Many numbers of great researches have been conducted to understand the real compressive and tension behaviour of the reinforced concrete based on the experimental programme and analytical formulations. Research on cyclic response of concrete is becoming a challenge of the earthquake engineering for modelling and capable prediction of hysteretic characters of the reinforced concrete. This research work is devoted to develop the computational methods to model and analyse the reinforced concrete structures subjected to revere cyclic specially by applying the confinement influence to section (Beam, column or joint panel). Key words: Reinforced Concrete, Confinement, Cyclic Load, Axial Stress, Axial Strain Laksiri Pradeep Thanthirige DiCEM - Dipartimento delle Culture Europee e del Mediterraneo: Architettura, Ambiente, Patrimoni Culturali, Via Lazazzera, 75100 Matera. Franco Braga, Rosario Gigliotti DiSG - Dipartimento di Ingegneria Strutturale e Geotecnica, “Sapienza” Università di Roma, Via Eudossiana 18, 00185 Roma. Michelangelo Laterza, Michele D’Amato DiCEM - Dipartimento delle Culture Europee e del Mediterraneo: Architettura, Ambiente, Patrimoni Culturali, Via Lazazzera, 75100 Matera.
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ANALYTICAL CYCLIC CONSTITUTIVE MODEL FOR CONFINED
CONCRETE IMPLEMENTATION IN OPENSEES: CONFINEDCONCRETE02
Abstract
This paper presents the new material developed inside the OpenSees by considering constitute model for the concrete subjected to revere cyclic and monotonic loadings. The new material intended to provide the ability of model the cyclic behaviour of concrete subjected to compression in the computational programme. The analytical formulation proposed by the Braga, Gigliotti and Laterza (BGL model, 2006) is used for the envelope and reverse (loading and reloading) action of the material govern by the Yassin (1994) approach, which has given bilinear curve for unloading and loading. The lateral confinement of concrete enhances the strength and durability of the reinforcement concrete significantly. Introducing this uniaxial material inside the OpenSees is capable to model the influence of transverse hoops, ties and/or FRP, external wrapping with the section considered. Many numbers of great researches have been conducted to understand the real compressive and tension behaviour of the reinforced concrete based on the experimental programme and analytical formulations. Research on cyclic response of concrete is becoming a challenge of the earthquake engineering for modelling and capable prediction of hysteretic characters of the reinforced concrete. This research work is devoted to develop the computational methods to model and analyse the reinforced concrete structures subjected to revere cyclic specially by applying the confinement influence to section (Beam, column or joint panel).
$tag is Integer tag identifying material, $secType is Tag for the transverse reinforcement, $fpc is
Unconfined cylindrical strength of concrete specimen, $Ec is Initial elastic modulus of unconfined
concrete, <-epscu $epscu> OR <-gamma $gamma> is Confined concrete ultimate strain, <-nu $nu>
OR <-varub> OR <-varnoub> is Poisson's ratio, $L1 is section measured respect to the hoop centre
line, ($L2), ($L3) is Additional dimensions when multiple hoops are being used, $phis is Hoop
diameter. If section arrangement has multiple hoops it refers to the external hoop, $S is Hoop spacing
$fyh is Yielding strength of the hoop steel, $Es0 is Elastic modulus of the hoop steel, $haRatio is
Hardening ratio of the hoop steel, $mu is Ductility factor of the hoop steel, $phiLon is Diameter of
longitudinal bars, <-internal $phisi $Si $fyhi $Es0i $haRatioi $mui> is Optional parameters for
defining the internal transverse reinforcement. If they are not specified, they will be assumed equal to
the external ones (for S2, S3, S4a, S4b and S5 typed), <-wrap $cover $Am $Sw $ful $Es0w> are
Optional parameters required when section is strengthened with FRP wraps,
Figure 7 shows the Stress-Strain enveloped by considering S1 type confining fiber section with Hoops
only. The Figure 8 shows the S4a section with Hoops with same parameter.
• The parameters for Figure 7
S1 section fpc=35 MPa, Ec=33721 MPa, epscu=0.03, L1=300 mm, phis=8 mm, S= 75 mm, fyh=450 MPa, Es=206000 MPa, haRatio=0.0, mu=1000, phiLon=18 mm, stRatio=0.85.
• The parameters for Figure 8
S4a section fpc=35 MPa, Ec=33721 MPa, epscu=0.03, L1=300 mm, L2=200 mm, L3=100 mm, phis=8 mm, S= 75 mm, fyh=450 MPa, Es=206000 MPa, haRatio=0.0, mu=1000, phiLon=18 mm, stRatio=0.85.
By concluding results obtained for case of analysed, fully unloading strain is always greater than the
strain of Confined Concrete01 for the same cycle. New parameter (rat) can be used for defining the
required energy dissipation capacity according to unloading and loading stiffness. The energy
dissipation capacity is always represented the area under the Stress-Strain curves for particular
envelope. For same strain of the analysed cases, each loading and unloading cycle of the
ConfinedConcrete02 (See Figure 9 and Figure 10) dissipated more energy than ConfinedConcrete01
as per the results. Hence, this new material can be used in computational modelling to make the
different energy dissipation for same displacement. This new material gives the better opportunity to
model the degradable stiffness depend on the requirement during reverse cyclic loading action.
References
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