FRPConfinedConcrete

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THIS MATERIAL MODEL IMPLEMENTATION IS KNOWN TO HAVE BUGS

This command is used to construct a uniaxial confined concrete material object (Megalooikonomou et al., 2012) with degraded linear unloading/reloading stiffness according to the work of Karsan-Jirsa and no tensile strength. Confining pressures contributed at each step of deformation by the case of existing transverse and longitudinal steel reinforcement are evaluated considering the stress-strain law of the reinforcing steel. Moreover, compatibility of strain in the lateral direction between the jacketing system and the encased concrete is enforced. Through the described approach the difference in the lateral behavior of the concrete cover (confined with the jacket’s pressure) and the concrete core (confined by both the steel’s and FRP’s pressure) has been considered. This allows the application of the model also in cases of reinforcement repair and FRP retrofit where two different concrete strengths should be considered, one for the new layer of concrete applied externally and the other for the old concrete in the concrete core which may also be cracked due to former seismic loading. Finally, the stress-strain response of FRP-confined concrete is terminated by jacket rupture owing to hoop strains exceeding the strain capacity of the material or to interaction of the jacket with the buckled longitudinal bars. It should be noted that the model can be applied also for the case of concrete-filled FRP tubes.

uniaxialMaterial FRPConfinedConcrete $matTag $fpc1 $fpc2 $epsc0 $D $c $Ej $Sj $tj $eju $S $fyl $fyh $dlong $dtrans $Es $vo $k $useBuck

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$matTag	integer tag identifying material.
$fpc1	concrete core compressive strength.
$fpc2	concrete cover compressive strength.
$epsc0	strain corresponding to unconfined concrete strength.
$D	diameter of the circular section.
$c	dimension of concrete cover (until the outer edge of steel stirrups)
$Ej	elastic modulus of the fiber reinforced polymer (FRP) jacket.
$Sj	clear spacing of the FRP strips - zero if FRP jacket is continuous.
$tj	total thickness of the FRP jacket.
$eju	rupture strain of the FRP jacket from tensile coupons.
$S	spacing of the steel spiral/stirrups.
$fyl	yielding strength of longitudinal steel bars.
$fyh	yielding strength of the steel spiral/stirrups.
$dlong	diameter of the longitudinal bars of the circular section.
$dtrans	diameter of the steel spiral/stirrups.
$Es	elastic modulus of steel.
$vo	initial Poisson’s coefficient for concrete.
$k	reduction factor for the rupture strain of the FRP jacket, recommended values 0.5-0.8.
$useBuck	FRP jacket failure criterion due to buckling of longitudinal compressive steel bars (0 = not include it, 1= to include it).

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NOTES:

• IMPORTANT: The units of the input parameters should be in MPa, N, mm.

• Concrete compressive strengths and the corresponding strain should be input as positive values.

• When rupture of FRP jacket occurs due to dilation of concrete (lateral concrete strain exceeding reduced rupture strain of FRP jacket), the analysis is not terminated. Only a message “FRP Rupture” is plotted on the screen.

• When $useBuck input parameter is on (equal to 1) and the model's longitudinal steel buckling conditions are fulfilled, a message “Initiation of Buckling of Long.Bar under Compression” is plotted on the screen.

• When rupture of FRP jacket occurs due to its interaction with buckled longitudinal compressive steel bars, the analysis is not terminated. Only a message “FRP Rupture due to Buckling of Long.Bar under compression” is plotted on the screen.

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Typical Hysteretic Stress-Strain Relation for FRPConfinedConcrete.

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FRPConfinedConcrete Uniaxial Material Tester:

For Python Interpreter: File:FRPConfinedConcrete Test dot py.pdf

     Please copy the file content to a new file named FRPConfinedConcrete Test.py  to run it with Python Interpreter.

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EXAMPLES:

Example 1: Cantilever FRP-Confined Circular Reinforced Concrete Column under Cyclic Lateral Loading

Cantilever Column Model Definition.

The cantilever column was modeled by a linear beam element with its stiffness corresponding to flexural yielding and by a fiber element at the plastic hinge which is used in order to capture the flexural hysteretic behavior. The length of the fiber element was assumed to be half of the column’s diameter. A rotational spring at the bottom of the column represents the longitudinal bar pullout from the footing and was assumed to have an elastic stiffness. According to FRPConfinedConcrete model, the averaged response of the two different regions - concrete core (confined by both the FRP & the existing reinforcement) and concrete cover (confined only with the FRP wrap) - in the cross-section allows the assignment of a unique stress-strain law (FRPConfinedConcrete) to all the concrete fibers/layers of the circular section.

Input Files:

For Tcl Interpreter: File:ExampleFRP.tcl

For Python Interpreter: File:ExampleFRPpy.doc

     Please change the file type to ExampleFRP.py to run it with Python Interpreter.

Response of Cantilever FRP-Confined Circular Reinforced Concrete Column under Cyclic Lateral Loading.

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Example 2: Inelastic Time-History Analysis of FRP-Retrofitted Bridge Column Subjected to Horizontal and Vertical Excitation

Bridge Column Model Definition.

The above Figure presents the test specimen model using Beam with Hinges (BWH) element to represent the column. Two rigid elements (rigid offsets) at the top and the base are used for the top block and the footing, respectively. A rotational spring is added below the rigid element at the base. A hysteretic material that follows the bilinear moment-curvature response of the reinforced concrete section of the column under study based on FRPConfinedConcrete is employed for the section aggregator object in OpenSees. The latter aggregates previously-defined UniaxialMaterial objects into a single section force-deformation model inside the plastic hinge length of the BWH element.

Input Files:

For Tcl Interpreter:

File:SP1.tcl

File:Accelerations All.tcl

    Please change the file type to Accelerations_All.txt.

File:Accelerations Vertical All.tcl

    Please change the file type to Accelerations_Vertical_All.txt.

Inelastic Time-History Response of FRP-Retrofitted Bridge Column Subjected to Horizontal and Vertical Excitation.

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OpenSees Seminar on FRPConfinedConcrete Material Model

Please click on the following link: https://www.youtube.com/watch?v=kGiHERNnfTM

References in the Literature to the Performance of 'FRPConfinedConcrete' (Megalooikonomou et al. 2012) Uniaxial Concrete Material Model

• Ahmed M. Ismail, Mohamed F.M. Fahmy, Zhishen Wu (2017), Simulating the lateral performance of FRP-confined RC circular columns using a new eccentric-based stress-strain model, Composite Structures, Vol.180, pp.88-104, https://doi.org/10.1016/j.compstruct.2017.07.075

• Lin, Guan (2016). Seismic performance of FRP-confined RC columns : stress-strain models and numerical simulation. Ph.D. Thesis, Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, https://theses.lib.polyu.edu.hk/handle/200/8695

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REFERENCES:

• MEGALOOIKONOMOU K.G., MONTI G., SANTINI S., “Constitutive Model for Fiber –Reinforced Polymer - and Tie – Confined Concrete”, ACI Structural Journal, Vol. 109, No. 4, July 2012, pp. 569-578. https://doi.org/10.14359/51683876

• KARSAN, I.D., JIRSA, J.O., “Behaviour of concrete under compressive loadings”, Journal of Structural Division ASCE, Vol. 95, No. 12, 1969, pp. 2543-2563. https://doi.org/10.1061/JSDEAG.0002424

• MEGALOOIKONOMOU K.G., "Seismic Assessment and Retrofit of Reinforced Concrete Columns", Cambridge Scholars Publishing, ISBN (10): 1-5275-2785-9, ISBN (13): 978-1-5275-2785-0, 2019, p. 387. https://www.cambridgescholars.com/product/978-1-5275-2785-0

• MEGALOOIKONOMOU K.G., MONTI G., "Numerical Modeling of FRP-Retrofitted Circular RC Columns Including Shear", In Proceedings of: 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2015), Crete Island, Greece, May 25 - 27, 2015. https://doi.org/10.7712/120115.3663.400

• MEGALOOIKONOMOU K.G., "Modeling the behavior of shear-critical reinforced concrete columns under lateral loads", Ph.D. Thesis, Department of Civil and Environmental Engineering, Faculty of Engineering, University of Cyprus, Nicosia, Cyprus,December 2019,https://doi.org/10.12681/eadd/47504

• MEGALOOIKONOMOU K.G., PAPAVASILEIOU G.S., “Analytical stress-strain model for FRP-confined rectangular RC columns.”, Front. Built Environ. Journal, Vol. 5, Article. 39, April 2019, https://doi.org/10.3389/fbuil.2019.00039

• MEGALOOIKONOMOU K.G., "Inelastic Time-History Analyses of FRP-Retrofitted Bridge Columns Subjected to Near-Field Ground Motions", In Proceedings of: 9th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2023), Athens, Greece, June 12 - 14, 2023. https://doi.org/10.7712/120123.10754.20021

• GALLARDO – ZAFRA R., KAWASHIMA, K., “Analysis of CFRP RC Bridge Columns under Lateral Cyclic Loading”, Journal of Earthquake Engineering, Vol. 13, 2009, pp. 129-154. https://doi.org/10.1080/13632460802347455

• KUMAR P., MOSALAM K. M., "Shaking Table Evaluation of Reinforced Concrete Bridge Columns Repaired Using Fiber-Reinforced Polymer Jackets", Journal of Bridge Engineering, ASCE, Vol.20; No.12 ,December 2015, p. 04015025, https://doi.org/10.1061/(ASCE)BE.1943-5592.0000780