Modeling an Accelerating Structure as Static

[Alex Mondal]

Hello all,

I am calculating the loads on an unconstrained structure in space that is accelerating. There is a constant known force (T) being applied to it at one end (point A). The structure is a rocket with distributed mass but let's assume it is a uniform beam with constant density. I would like to know the load and bending moments across the length of this beam structure. The force of the weight acts at the center of mass (L/2 for an uniform beam). For a classic rigid beam problem, the force applied would be constant throughout. However, because the system is unconstrained, point A sees the magnitude of the force applied while point b, at the other end, sees a zero load. I also don't understand how to couple the fact that the structure is accelerating. If the structure experiences 3 g's (3 times the acceleration Earth's gravity) it will experience a load that is higher then the applied load T. Is my logic correct?

In the end I would like to have mass points along this vehicle with rough moments of inertia of the vehicle. Then if I determine linear and angular acceleration, I can determine the load and moment distribution.

Thank you in advance.

Regards,
-Alex M.
Austin, Tx

 

[SteamKing]

Hello all,

I am calculating the loads on an unconstrained structure in space that is accelerating. There is a constant known force (T) being applied to it at one end (point A). The structure is a rocket with distributed mass but let's assume it is a uniform beam with constant density. I would like to know the load and bending moments across the length of this beam structure. The force of the weight acts at the center of mass (L/2 for an uniform beam). For a classic rigid beam problem, the force applied would be constant throughout. However, because the system is unconstrained, point A sees the magnitude of the force applied while point b, at the other end, sees a zero load. I also don't understand how to couple the fact that the structure is accelerating. If the structure experiences 3 g's (3 times the acceleration Earth's gravity) it will experience a load that is higher then the applied load T. Is my logic correct?

In the end I would like to have mass points along this vehicle with rough moments of inertia of the vehicle. Then if I determine linear and angular acceleration, I can determine the load and moment distribution.

Thank you in advance.

Regards,
-Alex M.
Austin, Tx

In problems like these, start with a simple sketch of your body and all the external forces (or accelerations) acting on the body, i.e., make a free body diagram. For example, it is the thrust of the rocket motor which is causing the rocket to accelerate at 3 g's, so you can replace the thrust of the motor with inertia loads acting on the internal structure of the rocket (at least in the direction of travel), because that's the dynamic loading the structure sees. After all, F = ma, even for rockets.

 

[OldEngr63]

To find the variation of force along the length of the structure, make an FBD of just one end (say the end opposite the applied force). The internal force shows up in this FBD as an external force on the cut surface (where you cut through the complete body to sever one end).

 

[Chestermiller]

What is the orientation of the force relative to the axis of the rocket?

 

[Chestermiller]

What is the orientation of the force relative to the axis of the rocket? Is the rocket rotating in a plane, and, does the force also lie within that plane?