Derivation directly using CST for the derivation in Appendix III(C).

% Derive the force

clc; clear;

syms alpha r F_e M_e l_t GJ EI GA EA M_y M_z F_y F_z Delta_theta_h M_a;

assume([alpha r F_e M_e l_t GJ EI GA EA M_y M_z F_y F_z Delta_theta_h M_a], 'real')

pi = sym(pi);

K = diag([ EI, EI, GJ, GA, GA, EA]) % this is the K matrix

K = 

W =[ 0;

F_e*r*sin(alpha) - M_e*cos(alpha);

- M_e*sin(alpha) - F_e*r*cos(alpha);

0;

-F_e*cos(alpha);

-F_e*sin(alpha);]

W = 

% This negative sign is due to the definition of D_l

U = 1/2*l_t*(W'*K^-1*W);

D_l = collect(diff(U,F_e), [F_e, l_t* M_a])

D_l =