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Once you know the structural form, the load path, the loads, and that the structure is stable, it is necessary to calculate numerical values for the reactions at the supports and for the forces in the members that make up the structure. To do this we use the principle of equilibrium, that all forces must sum to zero.

After working through this unit and attending the associated lectures and practice classes you should be
able to:

  • understand the concepts of forces and applied moments, and appreciate the need for these to be in equilibrium.
  • apply the mathematical equations for equilibrium of forces and applied moments.
  • calculate the reactions for 2 dimensional determinate structures


A fundamental requirement of a successful structure is that when loaded it resists that load without collapsing. All structures deform when loaded, but they reach stable equilibrium, where the structure supports the applied loads. If this does not occur – if equilibrium is not reached – the structure collapses.

We can consider two types of equilibrium

  • translational (or force) equilibrium
  • rotational (or applied moment) equilibrium