## Compute the compressive strength of confined concrete

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parasismique
Posts: 56
Joined: Tue Dec 13, 2016 7:14 am
Location: University of Tlemcen-Algeria

### Compute the compressive strength of confined concrete

Dear all,

I’m trying to validate a fibre FE model that analyse the cyclic pushover response of 415 RC column of Lehman et al. [1]. In a general way, I followed the modelling strategy proposed by Wang et al. [2].
To model the confined concrete, I used Mander et al. model [3] to compute the compressive strength given by eq. 29. The obtained value is equal to 42 MPa, which gives ɛcc of 0.66% and ɛcu of 1.56%.
Strangely, the obtained values are different to that obtained by Wang et al. [2] (compressive strength of 61 MPa and ɛcc of 1.36% and ɛcu of 1.85%).
Moreover, the FE model does not work in OpenSees when using my values!
The MATLAB script used to compute the compressive strength of confined concrete is given bellow.

[1] D. Lehman, J. Moehle, S. Mahin, A. Calderone, and L. Henry, “Experimental Evaluation of the Seismic Performance of Reinforced Concrete Bridge Columns,” J. Struct. Eng., vol. 130, no. 6, pp. 869–879, 2004.
[2] Z.-H. Wang, L. Li, Y.-X. Zhang, and S.-S. Zheng, “Reinforcement model considering slip effect,” Eng. Struct., vol. 198, p. 109493, 2019.
[3] J. B. Mander, M. J. N. Priestley, and R. Park, “Theoretical stress-strain model for confined concrete,” J. Struct. Eng, vol. 114, no. 8, pp. 1804–1826, 1988.

The matlab script:
% Compute of Compressive Strength of Confined Concrete, f'cc by Mander eq
%f'cc=f'c0(-1.254+2.254*sqrt(1+((7.94*f'l)/f'c0))-2*f'l/f'c0)
s=0.032; %spacing (Column Lehman 415)
Dcol=0.6096;
cover=0.03302;
dbar=0.01588;
dbarT=0.006;
fyh=607;
numBar=22;
Hcol=2.44;
fc0=30.3; % f'c0: unconfined concrete compressive strength
%Vcore=Score*Hcol
%-------------------------------------------
% Ke coefficient given by eq. 14 or 15
% s : center to center spacing or pitch of spiral or circular hoop
% s': clear vertical spacing between spiral or hoop bars
% s : spiral spacing or pitch
s1=s-dbarT;
% ds: diameter of spiral between bar centers
ds= Dcol-2*cover-dbarT;
% Rhocc : ratio of area of longitudinal reinforcement to area of core of section
%------
% Acc: the area of concrete core eq.12
% Area of longitudinal reinforcement
Areinf=(pi*dbar^2)/4*numBar;
% Effectively confined core Diameter (fig.2)
DeffCore=ds-s1/2;
% Ae : the area of an effectively confined concrete core eq. 12
%Ae=(pi/4)*ds^2*(1-(s1/2*ds))^2;
Ac=(pi*ds^2)/4;
Rhocc= Areinf/Ac
% spiral spacing or pitch
Ke=(1-(s1/2*ds))/(1-Rhocc)
%--------------------------------------------
% RhoS: ratio of the volume of transverse confining steel to the
% volume of confined concrete core eq.17
%----------
% Asp: area of transverse reinforcement bar (Formule of Tore in google)
% Asp=4*pi^2*(dbarT/2)*(Dcol/2-cover-dbarT/2);
Asp=(pi*dbarT^2/4);
RhoS=(4*Asp)/(ds*s)
%--------------------------------------------
% fyh : yield strength of the transverse reinforcement
%--------------------------------------------
% f'l: lateral confining pressure on concrete
% f'l is given by eq. 19
f1l=1/2*Ke*RhoS*fyh
%---------------------------------------------
% fc0: Compressive Strength of unconfined Concrete (Experimental value)(MPa)
% Compute of Compressive Strength of Confined Concrete, f'cc (eq. 29)
ratio=(-1.254+2.254*sqrt(1+(7.94*f1l)/fc0)-2*f1l/fc0)
fcc=fc0*ratio