ConfinedConcrete01 Material

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---

This 
command 
is 
used 
to 
construct 
an 
uniaxial
 material 
object 
of 
confined
 concrete 
in 
according 
to
 the
 work 
of 
Braga, 
Gigliotti
 and 
Laterza
 (2006). 
The
 confined
 concrete 
model
 (BGL
model) 
has 
not
 tensile
 strength 
and 
degraded
 linear 
unloading/reloading
 stiffness
 as 
proposed
 by 
Karsan 
and 
Jirsa
 (1969).
 The 
BGL 
model 
accounts 
for 
confinement
 effects 
due
 to 
different 
arrangements 
of 
transverse
 reinforcement 
and/or
 external 
strengthening
 such
 as 
steel 
jackets 
or 
FRP 
wraps. 
The 

confinement 
effect 
along
 the 
column is described 
as 
well.
 In
 order 
to 
obtain 
th e
compressive 
envelope 
curve a
 non
 linear 
approach 
is 
performed
 at 
each
 increment
 of 
column
 axial
 strain.
The
 sougth
 curve 
is 
obtained
 crossing 
different 
stress‐strain
 relationships,
 each 
of 
which
 corresponding
 to 
a 
different
 level 
of 
confinement.
 Currently,
 the
 Attard
 and
 Setunge’s
 model
 is
 implemented
 in
 calculating
 each
 active
 curve
 of
 the
 confined
 concrete.


uniaxialMaterial ConfinedConcrete01 $tag $secType $fpc $Ec (<-epscu $epscu> OR <-gamma $gamma>) (<-nu $nu> OR <-varub> OR <-varnoub>) $L1 ($L2) ($L3) $phis $S $fyh $Es0 $haRatio $mu $phiLon <-internal $phisi $Si $fyhi $Es0i $haRatioi $mui> <-wrap $cover $Am $Sw $fuil $Es0w> <-gravel> <-silica> <-tol $tol> <-maxNumIter $maxNumIter> <-epscuLimit $epscuLimit> <-stRatio $stRatio>

---

$tag	integer tag identifying material
$secType	tag for the transverse reinforcement configurations. See NOTES 1.
$fpc	unconfined cylindrical strength of concrete specimen.
$Ec	initial elastic modulus of unconfined concrete.
$epscu	confined concrete ultimate strain. See NOTES 2.
$gamma	value between 0 and 1.0. See NOTES 2.
$nu	Poissons Ratio.
$L1	concrete core dimension of square section or diameter of concrete core section measured respect to the hoop center line.
$L2	dimensions of multiple hoops for S4a section type measured respect to hoop center line. See NOTES 4.
$L3	dimensions of multiple hoops for S4a and S4b section types measured respect to hoop center line. See NOTES 4.
$phis	hoop diameter. If section arrangement has multiple hoops it refers to the external hoop.

NOTES:

1) The following section types are available:

S1	square section with S1 type of transverse reinforcement with or without external FRP wrapping;
S2	square section with S2 type of transverse reinforcement with or without external FRP wrapping;
S3	square section with S3 type of transverse reinforcement with or without external FRP wrapping;
S4a	square section with S4a type of transverse reinforcement with or without external FRP wrapping;
S4b	square section with S4b type of transverse reinforcement with or without external FRP wrapping;
S5	square section with S5 type of transverse reinforcement with or without external FRP wrapping;
C	circular section with or without external FRP wrapping;
R	rectangular section with or without external FRP wrapping.

2) The confined concrete ultimate strain is defined using -epscu or -gamma. If -gamma option, $gamma specified is the ratio of the strength corresponding to ultimate strain to the peak strength of the confined concrete stress-strain curve. If $gamma cannot be achieved in the range [0, $epscuLimit] then $epscuLimit (optional, default: 0.05) will be assumed as ultimate strain.

3) Poisson's Ratio is specified by one of 3 methods: a)providing $nu using the -nu option. b)using the -varUB option in which Poisson’s ratio is defined as a function of axial strain by means of the expression proposed by Braga et al. (2006) with the upper bound equal to 0.5; or c) using the -varNoUB option in which case Poisson’s ratio is defined as a function of axial strain by means of the expression proposed by Braga et al. (2006) without any upper bound.

EXAMPLES:

REFEERENCES:

1. Attard, M. M., Setunge, S., 1996. “Stress-strain relationship of confined and unconfined concrete”. Material Journal ACI, 93(5), 432-444
2. Braga, F., Gigliotti, R., Laterza, M., 2006. “Analytical stress-strain relationship for concrete confined by steel stirrups and/or FRP jackets”. Journal of Structural Engineering ASCE, 132(9), 1402-1416.
3. D’Amato M., February 2009. “Analytical models for non linear analysis of RC structures: confined concrete and bond-slips of longitudinal bars”. Doctoral Thesis. University of Basilicata, Potenza, Italy.
4. Karsan, I. D., Jirsa, J. O., 1969. “Behavior of concrete under compressive loadings”, Journal of Structural Division ASCE, 95(12), 2543-2563.

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Code Developed by: Michele D'Amato, University of Basilicata, Italy