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Coordinate System (Sign Convention)

Internal forces

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:

Load

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.