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FrameElement.m
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classdef FrameElement < handle
properties
uniqueID_etabs
nonUniqueID_etabs
% BEAMS:
% iNode is on LEFT, jNode is on RIGHT
% COLUMNS:
% iNode is on BOTTOM, jNode is on TOP
% in XZ/YZ plane right is +X/+Y direction
iJoint_etabs
jJoint_etabs
iNode_opnss
jNode_opnss
storyName
length
length_clrSpn % l_n parameter in ACI: length of clear span, measured face to face of supports
section
isOnOpenseesFrame = 0;
minBarDistance = 25;
Ls % 0.5 * frame element's clear span
rho_sh
alpha_sl = 1; % bond-slip %steel columns wont need nor use this
% d_b
AWeb = 0;
nWebTorsLongBarsOnOneSide = 0;
nWebHorTransBars = 0;
webBarsDiamArr
% AvOnS
transReinf
% nonlinear model parameters
elasticElmnt
hystereticMat
ImodFac
% MyPos % N.m
% MyNeg % N.m
% Mr = 0;
% Ky
% Kstf
% thetapPos
% thetapNeg
% thetapcPos
% thetapcNeg
% lambda
% McPos
% McNeg
end
methods
function this = FrameElement(etabsUniqueID,etabsNonUniqueID,storyName,iJoint,jJoint,length)
this.uniqueID_etabs = etabsUniqueID;
this.nonUniqueID_etabs = etabsNonUniqueID;
this.storyName = storyName;
this.iJoint_etabs = iJoint;
this.jJoint_etabs = jJoint;
this.length = length;
end
function calcRhoSh(this)
m2mmFactor = 1000;
this.rho_sh = (this.transReinf.AvOnS/m2mmFactor)/this.section.b;
end
function [db, AsBot, AsTop] = getLongReinfParams(~)
db = 0;
AsBot = 0;
AsTop = 0;
fprintf('\nWARNING!\n')
fprintf('no GetLongReinfParam method has been defined in Column/Beam class')
end
function calcHystereticModelParams(this,tag,fc,Ec,fy,Es,HYSTERETIC_MODEL_FLAG,isOnBasement)
KN2N = 1000;
Nmm2Nm = 0.001;
tag = strcat('40',tag);
d = this.section.d;
dPrime = this.section.dPrime;
b = this.section.b;
h = this.section.h;
Ag = this.section.Area;
Ig = this.section.I33_etabs;
s = this.transReinf.spacing;
N = -1 * (this.P) * KN2N; % unit: Newtons
% in my code, compression is - , in Fardis formulation and in other
% formulae, compression is + , so the P value is multiplied by -1
nFac = Domain.stfnsModFac;
[db, AsBot, AsTop] = this.getLongReinfParams();
% hystereticModelIsPinching = (HYSTERETIC_MODEL_FLAG == 3);
% if hystereticModelIsPinching
% FprPos = 0.25;
% FprNeg = 0.25;
% A_Pinch = 0.25;
% end
frmElmntRotStfns = (6*Ec*Ig/this.length_clrSpn) * Nmm2Nm;
% frequently used params in equations
sn = (s/db)*sqrt(fy/100);
nu = N/(Ag*fc);
rhoSh = this.rho_sh;
if isOnBasement
kstf = FrameElement.calcKstf(N,Ag,fc,this.Ls,h);
this.ImodFac = kstf;
k0 = (kstf * frmElmntRotStfns);
% disp('*********************************************************')
% fprintf('ID: %s\nStory: %s\n',this.nonUniqueID_etabs,this.storyName)
% disp(this.elasticElmnt.openseesTag)
% disp(kstf)
else
ky = FrameElement.calcKy(N,Ag,fc,this.Ls,h);
k0 = (ky * frmElmntRotStfns);
this.ImodFac = ky;
% disp('*********************************************************')
% fprintf('ID: %s\nStory: %s\n',this.nonUniqueID_etabs,this.storyName)
% disp(this.elasticElmnt.openseesTag)
% disp(ky)
end
% in MyPos, beam's bottom reinforcement is in tension
MyPos = FrameElement.calcMy(fc,Ec,fy,Es,d,dPrime,b,AsBot,AsTop,this.AWeb,N);
MyNeg = FrameElement.calcMy(fc,Ec,fy,Es,d,dPrime,b,AsTop,AsBot,this.AWeb,N);
McPos = 1.3 * MyPos;
McNeg = 1.3 * MyNeg;
thetapPos = FrameElement.calcThetaP(this.alpha_sl,nu,rhoSh,fc,fy,sn,AsBot,AsTop,b,h);
thetapNeg = FrameElement.calcThetaP(this.alpha_sl,nu,rhoSh,fc,fy,sn,AsTop,AsBot,b,h);
asPos = (McPos - MyPos)/(thetapPos * k0);
asNeg = (McNeg - MyNeg)/(thetapNeg * k0);
thetapcPos = FrameElement.calcThetaPC(nu,rhoSh,AsBot,AsTop,b,h,fc,fy);
thetapcNeg = FrameElement.calcThetaPC(nu,rhoSh,AsTop,AsBot,b,h,fc,fy);
thetayPos = MyPos/k0;
thetayNeg = MyNeg/k0;
thetauPos = thetayPos + thetapPos + thetapcPos;
thetauNeg = thetayNeg + thetapNeg + thetapcNeg;
lambda = FrameElement.calcLambda(nu,s,d);
bigLambda = lambda * min(thetapPos,thetapNeg);
% if arguments seem wrong, it's because you are :D
% acoording to joint2D nodes axes, the material params should
% be altered like this (*Pos and *Neg values are used instead
% of one another):
this.hystereticMat = HystereticModel(HYSTERETIC_MODEL_FLAG,...
tag,k0,asNeg,asPos,MyNeg,MyPos,bigLambda,thetapNeg,...
thetapPos,thetapcNeg,thetapcPos,thetauNeg,thetauPos,nFac);
end
end
methods (Static)
function My = calcMy(fc,Ec,fy,Es,d,dPrime,b,tensionAs,compressionAs,AWeb,N)
Nmm2Nm = 1e-3;
n = Es/Ec;
rho = tensionAs/(b*d);
rhoPrime = compressionAs/(b*d);
rhoNu = AWeb/(b*d);
deltaPrime = dPrime/d;
A_stlYld = rho + rhoPrime + rhoNu + N/(b*d*fy);
B_stlYld = rho + rhoPrime*deltaPrime + ...
0.5*rhoNu * (1 + deltaPrime) + N/(b*d*fy);
Ky_stlYld = sqrt(n^2*A_stlYld^2 + 2*n*B_stlYld) - n*A_stlYld;
phiY_stlYld = fy/(Es*(1-Ky_stlYld)*d);
A_concCmprs = rho + rhoPrime + rhoNu - N/(1.8*n*b*d*fc);
B_concCmprs = rho + (rhoPrime*deltaPrime) + 0.5*rhoNu * (1 + deltaPrime);
Ky_concCmprs = sqrt(n^2*A_concCmprs^2 + 2*n*B_concCmprs) - n*A_concCmprs;
phiY_concCmpr = 1.8*fc/(Ec*Ky_concCmprs*d);
if phiY_stlYld < phiY_concCmpr
phiY = phiY_stlYld;
Ky = Ky_stlYld;
else
phiY = phiY_concCmpr;
Ky = Ky_concCmprs;
end
term1 = 0.5*Ec*Ky^2*(0.5*(1+deltaPrime)-Ky/3);
term2 = 0.5*Es*((1-Ky)*rho + (Ky-deltaPrime)*rhoPrime+(rhoNu*(1-deltaPrime))/6)*(1-deltaPrime);
My = phiY * (term1 + term2) * b * d^3;
My = My * Nmm2Nm;
end
function Ky = calcKy(N,Ag,fc,Ls,h)
Ky = -0.07 + 0.59*N/(Ag*fc) + 0.07*Ls/h;
lowerLimit = 0.2;
upperLimit = 0.6;
Ky = FrameElement.applyUpperAndLowerLimits...
(Ky,lowerLimit,upperLimit);
end
function Kstf = calcKstf(N,Ag,fc,Ls,h)
Kstf = -0.02 + 0.98*N/(Ag*fc) + 0.09*Ls/h;
lowerLimit = 0.35;
upperLimit = 0.8;
Kstf = FrameElement.applyUpperAndLowerLimits...
(Kstf,lowerLimit,upperLimit);
end
function thetaP = calcThetaP(alpha_sl,nu,rhoSh,fc,fy,sn,tensionAs,CmprsnAs,b,h)
rho = tensionAs/(b*h);
rhoPrime = CmprsnAs/(b*h);
thetaP = 0.12*(1+0.55*alpha_sl)*(0.16^nu)*(0.02+40*rhoSh)^0.43*...
(0.54)^(0.01*fc)*0.66^(0.1*sn)*2.27^(10*rho);
numerator = max(0.01,rhoPrime*fy/fc);
denomerator = max(0.01,rho*fy/fc);
fardisTerm = (numerator/denomerator)^0.225;
thetaP = thetaP * fardisTerm;
% if showInfo
% disp('****************************************')
% fprintf('nu = %f\n',nu)
% fprintf('rhoSh = %f\n',rhoSh)
% fprintf('f''c = %f\n',fc)
% fprintf('fy = %f\n',fy)
% fprintf('sn = %f\n',sn)
% fprintf('rho = %f\n',rho)
% fprintf('rho'' = %f\n',rhoPrime)
% fprintf('thetaP = %f\n',thetaP)
% end
end
function thetaPC = calcThetaPC(nu,rhoSh,tensionAs,CmprsnAs,b,h,fc,fy)
thetaPC = (0.76)*(0.031^nu)*(0.02+40*rhoSh)^1.02;
rho = tensionAs/(b*h);
rhoPrime = CmprsnAs/(b*h);
numerator = max(0.01,rhoPrime*fy/fc);
denomerator = max(0.01,rho*fy/fc);
fardisTerm = (numerator/denomerator)^0.225;
thetaPC = thetaPC * fardisTerm;
lowerLimit = 0; % it's always a positive value
upperLimit = 0.1;
thetaPC = FrameElement.applyUpperAndLowerLimits...
(thetaPC,lowerLimit,upperLimit);
end
function lambda = calcLambda(nu,s,d)
lambda = 170.7 * (0.27^nu) * (0.10)^(s/d);
end
function revisedValue = applyUpperAndLowerLimits(value,lowLim,upLim)
if value < lowLim
revisedValue = lowLim;
elseif value > upLim
revisedValue = upLim;
else
revisedValue = value;
end
end
end
end