A statically indeterminate system is a type of structural system in which the number of unknown reactions or internal forces is greater than the number of available equations of equilibrium. This means that the system cannot be solved using traditional methods of statics.
The degree of indeterminacy in a system can be determined by counting the number of unknown reactions or internal forces and subtracting the number of available equations of equilibrium. The resulting number is the degree of indeterminacy.
Some common methods for analyzing statically indeterminate systems include the slope-deflection method, the moment distribution method, and the force method. These methods involve solving a series of simultaneous equations to determine the unknown reactions and internal forces in the system.
Statically indeterminate systems offer several advantages over statically determinate systems. They can be more efficient in terms of material usage, as they can distribute loads more evenly and reduce the size of individual members. They also have a higher load-carrying capacity and can be more resistant to external forces such as wind or earthquakes.
Thermal expansion can cause significant stresses in statically indeterminate systems. To handle this, engineers often introduce additional supports or use expansion joints to allow the structure to expand and contract without causing damage. Another approach is to design the structure with materials that have a low coefficient of thermal expansion.