find the deflection and rotation for fixed-fixed beam on a point away from the force

I'm trying to get the deflection and rotation of a point located away from the line of force's action, the problem is to fined the deflection and the rotation at x=1m and x=0.5m of a fixed-fixed beam has a force in the middle of it (at x=1), knowing that its length =2m, and the force 240N, I got the answers at x=1 but I'm struggeling for x=0.5, I think I need to do interpolation but I'm not sure.

I need help

here is the code I made and the question figure

syms L;
EI=1;
x1=1;
x2=0.5;
F=240;
%%
for c = 1:2
    if c==1
        L=1;
        %element 1
        k1=  [  12,   6*L,  -12,   6*L;
                         6*L,  4*L^2, -6*L,  2*L^2;
                        -12,  -6*L,   12,  -6*L;
                         6*L,  2*L^2, -6*L,  4*L^2]
        EA_L_k1=(EI / L^3) *k1

        %element 2
        k2=  [  12,   6*L,  -12,   6*L;
                         6*L,  4*L^2, -6*L,  2*L^2;
                        -12,  -6*L,   12,  -6*L;
                         6*L,  2*L^2, -6*L,  4*L^2]
        EA_L_k2=(EI / L^3) *k2
        %Calculate stiffness matrix
        K = sym(zeros(6,6));
        K(1:4, 1:4) = k1;
        K(3:6, 3:6) = K(3:6,3:6) + k2

        % boundary condition inducates that u1=v1=u3=v3=0 , p2x=0 p2y=10 kN
        F=[0; 0; 240; 0; 0; 0]
        k_new=K(3:4,3:4)
        u=inv(k_new)*F(3:4,1)

    else
        %I'm struggeling here I tried this but the answers are wrong
        L=0.5 %at x=0.5
        %element 1
        k1=  [  12,   6*L,  -12,   6*L;
                         6*L,  4*L^2, -6*L,  2*L^2;
                        -12,  -6*L,   12,  -6*L;
                         6*L,  2*L^2, -6*L,  4*L^2]
        EA_L_k1=(EI / L^3) *k1

        %Calculate stiffness matrix
        K = k2;
        p=[0;0;240;0;0;0]
        f=p(3:4,1)
        k_new=K(3:4,3:4)
        u=inv(k_new)*f
    end

end

Answer 1

[Umang Pandey]

Hi Mohammad,

I understand that you want to find the deflection and rotation at the middle of the fixed-fixed beam. You can refer to the Page - 18/23 of following document, which demonstrates the same problem:

https://mae.ufl.edu/nkim/eml5526/Lect05.pdf

Best,

Umang