Modeling the Internal Forces Exerted on a Catapult Arm while Throwing

I am currently creating a MATLAB script to determine the internal forces present in a uniform beam as it is accelerated by a torsional spring. I was able to derive the equation for the axial force present in the beam, but I am not sure how to determine the shear force of bending moment at any time. My setup is approximated by this image:

My intuition tells me that there should be a nonlinear shear force across the radius of the beam, with the largest shear occurring near the rotational axis. I believe the bending moment should follow a similar distribution.

I was able to simulate the dynamics of the system, so I know the angular velocity, acceleration, and spring force at any point, but I am not sure how to translate this to the shear and moment. I attempted an integral of the force required to accelerate each point of the beam, but I don't believe that my result is accurate. If I could see the derivation process to determine the shear and moment distributions, that would be invaluable. Thank you!

• I guess your analysis is assuming the beam is massless. Your intuition is not. Commented Apr 3, 2023 at 22:18