problem2_plot.m

% The code uses the central difference approximation used from 2a-c to find
% the max deflection in the beam for each segment split and plot the
% distributed load q against the max deflection dx. 
%For loop for six segments to find max deflection
n=0; 
for q = [1,10,20,30,50]
n=n+1;
x=1/6; %splits up beam into six
b=0.1; %width of beam
E=70E9; %Young's modulus 
h=0.01;%height of beam 
I=(b*(h^3))/12; %Second MOI
z=((x.^4)*q)/(E*I); %differentiation used to solve for displacement

Seg6 =[5,-4,1,0,0;
   -4,6,-4,1,0;
   1,-4,6,-4,1;
   0,1,-4,6,-4;
   0,0,1,-4,5];

Y=[z;z;z;z;z];
B=Seg6\Y;
B_3=B;
max_def3=max(B_3); 
X6(n) = max_def3; 
end
%For loop for ten segments to find max deflection 
n=0;
for q = [1,10,20,30,50]
n=n+1;
x2=1/10; %splits up beam into ten
b=0.1; %width of beam
E=70E9; %Young's modulus 
h=0.01;%height of beam 
I=(b*(h^3))/12; %Second MOI
z=((x2.^4)*q)/(E*I); %differentiation used to solve for displacement

Seg10= [5,-4,1,0,0,0,0,0,0;
   -4,6,-4,1,0,0,0,0,0;
   1,-4,6,-4,1,0,0,0,0;
   0,1,-4,6,-4,1,0,0,0;
   0,0,1,-4,6,-4,1,0,0;
   0,0,0,1,-4,6,-4,1,0;
   0,0,0,0,1,-4,6,-4,1;
   0,0,0,0,0,1,-4,6,-4;
   0,0,0,0,0,0,1,-4,5];

Y=[z;z;z;z;z;z;z;z;z];
B=Seg10\Y;
B_2=B;
max_def2=max(B_2); 
X10(n)=max_def2; 
end 
%For loop for twenty segments to find max deflection 
n=0;
for q = [1,10,20,30,50]
n=n+1;
x3=1/20; %splits up beam into twenty
b=0.1; %width of beam
E=70E9; %Young's modulus 
h=0.01;%height of beam 
I=(b*(h^3))/12; %Second MOI
z=((x3.^4)*q)/(E*I); %differentiation used to solve for displacement

Seg20= [5,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
   -4,6,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
   1,-4,6,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0;
   0,1,-4,6,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0;
   0,0,1,-4,6,-4,1,0,0,0,0,0,0,0,0,0,0,0,0;
   0,0,0,1,-4,6,-4,1,0,0,0,0,0,0,0,0,0,0,0;
   0,0,0,0,1,-4,6,-4,1,0,0,0,0,0,0,0,0,0,0;
   0,0,0,0,0,1,-4,6,-4,1,0,0,0,0,0,0,0,0,0;
   0,0,0,0,0,0,1,-4,6,-4,1,0,0,0,0,0,0,0,0;
   0,0,0,0,0,0,0,1,-4,6,-4,1,0,0,0,0,0,0,0;
   0,0,0,0,0,0,0,0,1,-4,6,-4,1,0,0,0,0,0,0;
   0,0,0,0,0,0,0,0,0,1,-4,6,-4,1,0,0,0,0,0;
   0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1,0,0,0,0;
   0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1,0,0,0;
   0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1,0,0;
   0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1,0;
   0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1;
   0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4;
   0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,5];

Y=[z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z];
B=Seg20\Y;
B_3=B;
max_def3=max(B_3); 
X20(n) = max_def3; 
end

%Plot q vs dx 
setdefaults 
q=[1,10,20,30,50] ; 
title ('Deflection vs Distributed Load')
xlabel('q (N/m)') 
ylabel('dx')
hold on 
plot(q,X6)
plot(q,X10)
plot(q,X20)
legend('6 segments', '10 segments', '20 segments')
hold off