Oving5

tic

L = 40;             %length of beam in m
b = 10;             %distance between forces in m
P_1 = 200;          %force in kN
P_2 = 300;          %force in kN

%x-coord of P_1 in m
x = linspace(-b,L,500);

%deflection * EI at the middle of the beam due to P_1
d_1 = zeros(1,length(x));

%d_1*EI when P_1 is located before the middle of the beam
d_1( (x<L/2) & (x>=0)) = P_1 .* x( x<L/2 & x>=0) .* (L/2) .* ...
    (L^2-x( x<L/2 & x>=0 ) .^2 -(L/2)^2) ./ (6*L);

%d_1*EI when P_1 is located at or after the middle of the beam
d_1(x>=L/2 & x<=L) = P_1 .*(L-x(x>=L/2 & x<=L)) .* (L/2) .* ...
    (L^2 - (L - x(x>=L/2 & x<=L)).^2 -(L/2)^2) ./ (6 .* L);

%deflection * EI at the middle of the beam due to P_2
d_2 = zeros(1,length(x));

%d_2*EI when P_2 is located before the middle of the beam
d_2( (x+b<L/2) & (x+b>=0)) = P_2 .* (x( x+b<L/2 & x+b>=0)+b) .* (L/2) .* ...
    (L^2-(x( x+b<L/2 & x+b>=0 )+b) .^2 -(L/2)^2) ./ (6*L);

%d_2*EI when P_2 is located at or after the middle of the beam
d_2(x+b>=L/2 & x+b<=L) = P_2 .*(L-(x(x+b>=L/2 & x+b<=L)+b)) .* (L/2) .* ...
    (L^2 - (L - (x(x+b>=L/2 & x+b<=L)+b)).^2 -(L/2)^2) ./ (6 .* L);

%deflection*EI of the beam at the center if there was no support at B
d_3 = d_1 + d_2;

%Support B is added back in as an upward force that makes the deflection zero
%at the centre of the beam
B_z = 48 .* d_3 ./ L^3;

plot(x,B_z,'-b')
hold on

[a,I] = max(B_z);

%the value of x that gives the max value for B_z
max_x = x(I)

plot(max_x,a,'xk','MarkerSize',15)

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