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 W_{a} 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 W_{t})
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, W_{r}, about the x axis in the y - z plane.

David J Grieve, 9th November 2001.