shape_simple_support.m

function w = shape_simple_support(x,q)
% This function will analytically solve for the shape of the beam and
% return the displacement w(x) given q and x.
% 
% Input:
%   x = Horizontal Distance across the beam beginning on left side [meters]
%   q = Vertical Distributed load along the beam [Newtons/meter]
% Output:
%   w = Vertical displacement of beam [meters]
%

% Length of the beam [meters]:
L = 1; 
% Width of beam [meters]:
b = 0.1;
% Height of beam [meters]:
h = 0.01;
% Second moment of inertia [meters^4]:
I = (b*h.^3)/12;
% Young's Modulus for aluminum [Pascals]:
E = 70e9;

% Derived equation for vertical deflection:
w = (q/(24*E*I)).*x.^4 - ((q*L)/(12*E*I)).*x.^3 + ((q*L^3)/(24*E*I)).*x;


    
end