Understanding Bending Moment Diagrams for Multiple Planes

[pinkcashmere]

can someone explain why this problem would involve two bending moment diagrams, one for the xy plane and another for the xz plane? Also, how are the reaction forces at B and C determined each time?

 

[SteamKing]

can someone explain why this problem would involve two bending moment diagrams, one for the xy plane and another for the xz plane?

I think since the drive force F is applied at an oblique angle, the author thought it would be clearer to the student to decompose this force into its horizontal and vertical components, and work out the reactions and bending moments created by each component separately.

Also, how are the reaction forces at B and C determined each time?

The same equations of static equilibrium apply in each case. The author has resolved F into its components on the overhung end of the shaft. There are two bearings where reactions develop. Write the standard sum of the forces and sum of the moment equations for each case and solve for the unknown reactions.

 

[PhanthomJay]

It is often convenient to break up the forces which cause the moments into its perpendicular components so that the moments about each axis and the axis reactions at the supports can be calculated separately. The reactions are determined from the equilibrium equations. The force reactions in each direction are particularly useful for the bearing bolted connection design.

 

[pinkcashmere]

I think since the drive force F is applied at an oblique angle, the author thought it would be clearer to the student to decompose this force into its horizontal and vertical components, and work out the reactions and bending moments created by each component separately.

So the F_r component for example, it generates a moment about the xy plane because it has a moment arm to the xy plane? But doesn't it also have a moment arm to the yz plane?

 

[SteamKing]

So the F_r component for example, it generates a moment about the xy plane because it has a moment arm to the xy plane? But doesn't it also have a moment arm to the yz plane?

Both moment arms are the same distance from the bearing at C, namely 100 mm.

It's not clear from the attachment what the purpose of this analysis is.