%% Function name
%        principalstresses

%% Revised: 
%       16 January 2014

%% Author
%       Adam Wolfe, Trey Moore, & Autar Kaw
%       Section: All
%       Semester: Fall 2012

%% Purpose
%       Given the global stresses acting on the lamina, output the 
%       longitudinal, transverse and in plane principal stresses of a lamina

%% Usage
%       function [ps1,ps2,tmax] = principalstresses(stress_glo)
% Input variables
%       stress_glo=vector of global stress applied to unidirectional lamina
%       [stress_glo]=[sx;sy;txy]
%       sx=longitudinal global stress
%       sy=transverse global stress
%       txy=in-plane shear stress
% Output variables
%       ps1=principal stress in direction 1 [pricipal stress 1, angle]
%       ps2=principal stess in direction 2 [pricipal stress 2, angle]
%       tmax=maximum shear stress
%       thetaps=angle at which principal stress occurs
%       thetass=angle at which maximum shear stress occurs
% Keyword
%       global stresses
%       principal stresses

%% License Agreement
%       http://www.eng.usf.edu/~kaw/OCW/composites/license/limiteduse.pdf

%% Code
function [ps1,ps2,tmax,thetaps,thetass] = principalstresses(stress_glo)
% Stress in the x direction
sx=stress_glo(1);
% Stress in the y direction
sy=stress_glo(2);
% Stress in the x-y plane
txy=stress_glo(3);
% Longitudinal and Transverse Stresses
ps_1=((sx+sy)/2)+sqrt((((sx-sy)/2)^2)+((txy)^2));
ps_2=((sx+sy)/2)-sqrt((((sx-sy)/2)^2)+((txy)^2));
thetaps=atand((2*txy)/(sx-sy))/2;
if ps_1 > ps_2
    ps1=ps_1;
    ps2=ps_2;
else
    ps1=ps_2;
    ps2=ps_1;
end
% Shear Stresses
tmax=sqrt((((sx-sy)/2)^2)+(txy^2));
thetass=atand(-(sx-sy)/(2*txy))/2;
end