Local and Global Co-ordinates

In the previous section the element stiffness for a tension - compression bar element was derived; for simplicity the x-axis was arranged to coincide with the longitudinal axisa of the bar. In framework problems the various members will exhibit this derived stiffness matrix in their own "local axis co-ordinate systems". However to combine members a common co-ordinate system is required, this is called the "global" co-ordinate system.

Translation of Nodal Displacements

Using similar notation to the previous section the displacements are:

And by geometry: