Coordinate System (Sign Convention)
Internal forces are defined as:
The positive direction of internal forces is evident from the following figure:
The principal moments and directions of principal axes are provided by:
The meaning of individual variables is the following: internal forces can be transformed from the (x, y) coordinate system to the (x', y') coordinate system by rotating the (x, y) plane through a certain angle about the z-axis. The angle α, in particular, corresponds to a rotation angle for which the transformed mx'y' moment attains a zero value whereas the mx' and my' moments attain their maximum and minimum values m1 and m2, respectively.
The maximum shear force is obtained similarly:
and the angle between vmax and the x-axis:
The sign convention of the applied force and moment load is evident from the following figure:
It is worth to point out a different sign convention applied to the load moment M (at a point or along a line) and to internal moment m. While the Mx moment rotates about the x-axis (as usual for beams), the internal moment rotating about the x-axis is denoted as my.