%
%Subroutine with the constraint functions
% file name column_conf.m
% constraints
% Prof. Reyolando Brasil May 2021
function [g,h]=column_conf(x)
% renaming design variables
x1=x(1);x2=x(2);
%data
P=50000; % vertical compressive load (N)
E=210e9; % elastic modulus (Pa)
L=5.0; % column length (m)
Sy=250e6; % allowable stress (Pa)
Delta=0.25; % allowable displacement at column top
% geometric characteristics
A=2*pi*x1*x2; % section area
W=pi*x1^2*x2; % bending modulus
I=pi*x1^3*x2; % moment of inertia
e=0.02*x1; % load eccentricity
%inequality constraints
g(1)=P/A*(1+e*A/W*sec(L*sqrt(P/E/I)))/Sy-1; % allowable stress
g(2)=1-pi^2*E*I/4/L^2/P; % buckling
g(3)=e*(sec(L*sqrt(P/E/I))-1)/Delta-1; % displacement at column top
g(4)=x1/x2/50-1; % Radius/thickness ratio
% equality constraints (none)
h=[];