5.9 : Constraints and Statical Determinacy

In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium equations.

Statically determinate systems are the easiest to analyze and design, as all the forces acting on the system can be determined using a specific number of equations of equilibrium. Typically, the equations of equilibrium involve the sum of all the forces acting on a system and the sum of all the moments equal to zero.

However, if additional redundant supports are added to the system to maintain equilibrium, it becomes statically indeterminate. This means that more constraints are acting on the system than there are equations of equilibrium available for their solution. In statically indeterminate systems, the additional supports restrict the motion of the system, but they also create additional equations. These additional equations are usually obtained by the deformation of the system, which is dealt with under the mechanics of materials. The challenge with statically indeterminate systems is finding the correct number of redundant supports to add to the system so that equilibrium is maintained without overconstraining the system.

In addition, improper constraints refer to a situation in which all the reactive forces either meet at a single point, pass through a common axis, or become parallel. Such a condition may cause instability in the structure and should be avoided in engineering practice. When reactive forces intersect at a single point or follow a common axis, they can push the body out of balance and cause it to topple over. Similarly, forces that are parallel to each other may not be able to maintain equilibrium and can lead to structural failure. It is essential to avoid improper constraints to prevent unstable conditions and potential hazards.