the loading function w(x) for the following beam in matlab

Assuming that you have the necessary input data for the beam such as length, the modulus of elasticity, and the moment of inertia, you can calculate the loading function w(x) using the following steps:

1. Define the coordinates along the beam axis in a vector:

main.m
x = linspace(0, L, N);
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where L is the length of the beam and N is the number of points to define along the beam axis.

2. Define the distributed load function q(x) and any point loads P applied to the beam:

main.m
q = ... % define the distributed load function of x
P = [P1, P2, ...]; % vector of point loads
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3. Solve the differential equation that describes the deflection of the beam under the applied loads:

main.m
i = (1:N)';
A = sin(i.*pi/L);
B = (L./(i.*pi)).*(1-cos(i.*pi));
C = (2./(i.*pi)).*(1-cos(i.*pi));
D = (2./(i.*pi).^2).*(1-cos(i.*pi)-i.*pi.*sin(i.*pi));

w = (q.*L^4./(E*I)).*(A.*(h/2)+B.*(theta/2)+C.*(w/2)+D);
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where E is the modulus of elasticity, I is the moment of inertia, h is the distance from the neutral axis to the top or bottom of the beam, and theta is the rotation of the beam.

4. Add the contribution from the point loads to the deflection function:

main.m
for i = 1:length(P)
    w = w + (P(i)/(6*E*I))*((x-L).^3).*((x>=L)-(x>=0));
end
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The resulting w vector gives the deflection of the beam at the specified coordinates x.