Shear force in a frame due to torsion?

[boganaut]

The orange thing is a gear being turned by a motor, which is intended to move the frame the shaft is fixed to. I realize the applied torque is going to create support reactions, but I can't quite figure out how to calculate the needed material strength so that the frame won't shear.

All helps greatly appreciated.

Edit: I should probably add that there's a load attached to the frame in the z direction relative to the bottom right picture.

 

[Chestermiller]

Is this a homework problem?

 

[boganaut]

Is this a homework problem?

No, it's for a project.

 

[JBA]

The torque induced shear stress at each plate connection should be 1/2 of the shear stress from an applied torque calculated for a shaft of your dimensions using standard textbook/online available equations.