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Statics - other methods for determining reactions of supported beam

Engineering Asked on March 12, 2021

Question: Because the question regards the statics, I am going to pose it as well.

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  1. Are there other methods to solve equilibrium problems other than the method of sections, when dealing with pivots. In the situation, there usually are more equations than unknown variables, hence we split the construction into two and learn about equilibrium at different parts and then solve all equations (splitting the pivot). Method of sections is applicable to constructing the diagrams of the bending moment in the beam.
  2. I have learnt about how to draw 3D diagrams of bending moment in the beam and how to solve the equilibrium problem in 3D for simple cases. However, I would like to ask if anyone has attempted to draw 3D diagrams of the beam (bending moment and shear forces) into different planes (xy, xz and yz planes), in other words, construct it on three screens. No need for that, because it is uncomplicated to draw one in 3D without doing so, but still curious as to whether it is possible. The same questions about statics problem. Would we be able to solve equilibrium 3D probleem by working with three planes (xy, xz and yz), where write equilibrium equations for each plane separately. After that, we put equations together and solve them. My guess is no because the load is connected to the point. Were the answer to be yes, then I would be able to skip the definition of torque about an axis via a point (I cannot realise that), since I can determine the moment of a force (or torque) in 2D system. Despite that, I can definite the torque in 3D about an axis. However, I am still curious!

I study civil engineering and hereby declare having no wish to break the laws of the forum; hence, should the question be not normal or disrespecting the members of the forum, then I would love to be apprised of it. Much obliged!

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