FRPConfinedConcrete

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This command is used to construct a uniaxial Megalooikonomou-Monti-Santini concrete material object with degraded linear unloading/reloading stiffness according to the work of Karsan-Jirsa and no tensile strength.

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

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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 edge of steel stirrups)
$Ej	elastic modulus of the fiber reinforced polymer (FRP) jacket.
$Sj	clear spacing of the FRP strips - zero if it's 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.
$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..

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.

Typical Hysteretic Stress-Strain Relation for FRPConfinedConcrete.

EXAMPLES:

Example: 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 the stiffness corresponding to flexural yielding and a fiber element used to capture the flexural hysteretic behavior at the plastic hinge. 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.

File:ExampleFRP.tcl

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

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REFEERENCES:

• 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.

• 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.

• PAPAVASILEIOU G.S., MEGALOOIKONOMOU K.G., “Numerical Simulation of FRP-Confined Circular Bridge Piers Using Opensees”, In Proceedings of: Opensees Days Italy (OSD), Second Italian Conference, University of Salerno, Fisciano, Salerno, Italy, June 10-11, 2015.

• 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.

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Code Developed By:

Konstantinos G. Megalooikonomou, Onassis Foundation Scholar, University of Cyprus.