Bending in Shafts With Helical Gears

Reactions at A and B in the x and y directions are found by summing forces in the x direction and taking moments about the y axis, then by summing forces in the y direction and taking moments about the x axis.
All the reaction to the axial force Wa will be carried at one end, depending upon the bearing arrangements. The axial force will cause tension or compression in the shaft and as it is not acting co-axially with the shaft centre line, it will also cause a bending moment about the x axis, in the y - z plane, see diagram below:

The general form of the bending moment diagram due to the transmitted load (which is replaced by an equal parallel force acting through the shaft centre and a torque rotating the shaft equal to R Wt) causes bending about the y axis in the x - z plane, see below:


This is also the general diagram for the bending moment caused by the radial force, Wr, about the x axis in the y - z plane.

David J Grieve, 9th November 2001.