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FEA_LTB.m
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FEA_LTB.m
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function Mcr = FEA_LTB(E,vv,h,tw,bT,tT,bB,tB,L,Nel,vz0,vz1,uz0,uz1,phiz0,phiz1,qy,Py,Mx0)
%%% Output
% Mcr = [Amp z]
%%% Secondery Input
G = E / (2 * (1+vv)); % G
Le = L / Nel; % Lenth of an element
Nnd = Nel + 1; % Nodes numbers
NdDOFs = 4; % Num. of Nodes DOFs [LTB] u u' phi phi'
%%% Moment and Shear Distribution, Mxmax
[Mx, Mxmax] = FEA_Moment(E,vv,h,tw,bT,tT,bB,tB,L,Nel,vz0,vz1,qy,Py,Mx0); % N m
Me1 = Mx(1 : Nel);
Me2 = Mx(2 : Nel+1);
Vy = (Me2 - Me1) / Le;
%%%%%%%%%%%%% Geometric Parameters %%%%%%%%%%%%%%
%%% yc = 0 at the section coordinate
ys = Section_Shear(h,tw,bT,tT,bB,tB)*10^-3; % m
Iy = Section_Iy(h,tw,bT,tT,bB,tB)*10^-12; % m^4
It = Section_It(h,tw,bT,tT,bB,tB)*10^-12; % m^4
Iw = Section_Iw(h,tw,bT,tT,bB,tB)*10^-18; % m^6
By = Section_By(h,tw,bT,tT,bB,tB)*10^-3; % m
%%%%%%%%%%%%% Element Matrix %%%%%%%%%%%%%%
KKLE = Ele_Stiff_Mat_KLE(Le,NdDOFs,E,G,Iy,It,Iw);
% KKGE is defined at total matrix
%%%%%%%%%%%%% Total Matrix %%%%%%%%%%%%%%
%%% Stiffness Matrix [K](2*Nnd)x(2*Nnd)
KKL = Global_Stiff_Mat(KKLE,Nnd,NdDOFs);
KKG = Global_Stiff_Mat_KG(Le,Nnd,NdDOFs,By,Vy,Me1,qy,Py,L);
%%%%%%%%%%%%% Total Matrix with BCs %%%%%%%%%%%%%%
% the Node DOFs Num. for all BCs
BCsNdDOF = Mat_BCs_NdDOF_LTB(uz0,uz1,phiz0,phiz1,Le,NdDOFs);
% [K] and [Q] with BCs for solving
KKLsl = Mat_BCs(KKL,BCsNdDOF);
KKGsl = Mat_BCs(KKG,BCsNdDOF);
%%%%%%%%%%%%% Solve %%%%%%%%%%%%%%
[VV, DD] = eig(KKLsl,KKGsl);
DD = diag(DD);
ucr = min(DD(DD>0));
Mxmax(1) = ucr * Mxmax(1) * 10^-3;
Mcr = Mxmax;
end