Statically determinate

Definition

A structure is considered statically determinate when the internal forces and reactions can be determined solely from the equations of equilibrium without needing any additional information. This means that the structure has just the right amount of support and load conditions to allow for a straightforward analysis, making it easier to solve for unknowns without the need for complex calculations or assumptions.

5 Must Know Facts For Your Next Test

1. A statically determinate structure can be analyzed using only static equilibrium equations, which simplifies the problem-solving process.
2. Common examples of statically determinate structures include simple beams, trusses with no redundancy, and certain frames.
3. The number of unknown reactions must equal the number of independent equilibrium equations available for the structure to be considered statically determinate.
4. If additional supports or constraints are added beyond what is necessary, the structure becomes statically indeterminate, complicating its analysis significantly.
5. Statically determinate structures tend to perform predictably under load since their internal force distribution is directly influenced by external loads.

Review Questions

• How can you determine if a given structure is statically determinate?
  • To determine if a structure is statically determinate, you need to compare the number of unknown support reactions with the number of available equilibrium equations. For a planar structure, there are three equilibrium equations: the sum of horizontal forces, the sum of vertical forces, and the sum of moments. If the number of unknowns matches the number of equations, the structure is statically determinate and can be analyzed using these equations alone.
• What are some advantages of using statically determinate structures in engineering design?
  • Statically determinate structures provide several advantages in engineering design, including simpler analysis and predictable behavior under loading conditions. Since their internal forces can be calculated directly from equilibrium equations, designers can easily assess their performance and safety. Additionally, these structures often require less material than their statically indeterminate counterparts, resulting in cost savings and efficiency in construction.
• Evaluate the impact of redundancy in a structure and how it affects its classification as statically determinate or indeterminate.
  • Redundancy in a structure occurs when there are more supports or constraints than necessary to maintain equilibrium. This leads to a classification of the structure as statically indeterminate because additional equations are required to solve for internal forces and reactions. While redundancy can enhance structural safety by providing alternative load paths, it complicates analysis since it requires methods such as compatibility conditions or numerical techniques. Thus, while redundancies might improve resilience under unexpected loads, they hinder straightforward calculations typically associated with statically determinate structures.

Related terms

Equilibrium: A condition where the sum of all forces and moments acting on a body is zero, ensuring that the body remains at rest or in uniform motion.

Redundancy: The existence of more supports or connections in a structure than are necessary to maintain equilibrium, which can complicate the analysis.

Support Reactions: The forces and moments at the supports of a structure that keep it in equilibrium under applied loads.