%subroutine constraint equations
%file name = port_wood_con.m
%optimization of redundant wood planar portal frame
%Prof. Reyolando Brasil - May 2021
function [g,h]=port_wood_con(x,h,L,b,P)
%
%design variables
x1=x(1);%column section d dimension, m
x2=x(2);%beam section d dimension, m
Ac=b*x1;%column section area, m²
Av=b*x2;%beam section area, m²
Wc=b*x1^2/6;%column section flexural modulus, m³
Wv=b*x2^2/6;%beam section flexural modulus, m³
Ic=b*x1^3/12;%column section moment of inertia, m^4
Iv=b*x2^3/12;%beam section moment of inertia, m^4
%wood parameters
E=15e6;%efective Young's Modulus, KN/m²
fcd=20e3;%design resistance, KN/m²
%axial forces and bending moments
X=(P*L^2*h/8/Iv)/(2*h^3/3/Ic+L*h^2/Iv);
Nc=P/2;%KN
Mc=X*h;%KNm
%
FE=pi^2*E*Ic/h^2;%Euler's buckling load
e=(Mc/Nc+h/300)*(FE/(FE-Nc));
Mc=Nc*e;
%
Nv=X;%KN;
Mv=P*L/4-X*h;%KNm
%
FE=pi^2*E*Iv/L^2;%Euler's buckling load
e=(Mv/Nv+L/300)*(FE/(FE-Nv));
Mv=Nv*e;
%
%inequlitiy constraints
g(1)=(Nc/Ac+Mc/Wc)/fcd-1;
g(2)=(Nv/Av+Mv/Wv)/fcd-1;
%equality constraints (none)
h=[];