I try to solve the ODE shown on the figure. EI and GK are constants related to the beam cross section and properties, and 'm' is a value of an applied distirbuted external torque applied in the middle of a beam that has fixed-fixed conditions (i.e. at z=L/2). I want to obtain the distribution of Circulatory Torque and Warping Torque, as shown in the figure.
The equation to solve is:
Importantly, it has been derived from:
I believe I need to solve the first equation, with the boundary conditions, in order to plot Tc(z) and Tw(z), which is also given here:
The beam starts at z=0 and ends at z=252.
EI = 1.1688e+10
GK, EI and L have all been verified.
I haven't really been able to get very far, as I'm a bit of newbie when it comes to MATLAB. Any help would gratefully be appreciated.
- The Warping Moment is 0 at z=L/4
- The Warping Moment is 0 at z=3L/4
- Theta θ is 0 at z=0
- Theta θ is 0 at z=L
I have also included a figure related to the boundary conditions, if it could help...