How to add applied moments
In order to add applied moments it is necessary to be consistent in describing the direction that an applied moment acts in. In these notes an applied moment will be positive if it follows the right hand screw rule. This works as follows (refer also to Appendix A),
- select the axis that you are going to sum applied moments about (ie the axis about which you are checking for rotational equilibrium)
- wrap your right hand around this axis, with your thumb extended along the positive axis direction
- the direction defined by your fingers is the positive applied moment direction
In 2 dimensional models of structures applied moments can be represented as a curved arrow in the direction of the applied moment. For 3 dimensional models this representation does not work, so in this case we often represent applied moments as double headed arrows. The direction of the double headed arrow gives the direction of the applied moment in accordance with the right hand screw rule.
Note that when a structure is in equilibrium, there is no rotation about any axis, irrespective of where that axis is. This leaves you with a free choice of the point about which you will “take moments”.
The sign convention for adding forces and applied moments
- forces are positive in the positive axis direction applied moments are positive if they follow the right hand screw rule (wrap your right hand around
- the axis with your thumb in the positive axis direction)