What is the difference between statically determinate and indeterminate structures in structural analysis?

1 Statically determinate structures

A statically determinate structure is a structure that can be fully analyzed using only the equations of equilibrium. These are the equations that state that the sum of forces and moments acting on a structure must be zero. For example, a simple beam supported by two pin joints is a statically determinate structure, because you can find the reactions at the supports by applying the equations of equilibrium to the beam. A statically determinate structure has a unique solution for the internal forces and displacements, regardless of the material properties or deformation behavior of the structure.

2 Statically indeterminate structures

A statically indeterminate structure is a structure that cannot be fully analyzed using only the equations of equilibrium. This is because there are more unknowns than equations, and the structure has some redundancy or excess rigidity. For example, a beam supported by two fixed ends is a statically indeterminate structure, because you cannot find the reactions at the supports by applying the equations of equilibrium alone. You also need to consider the compatibility of displacements and the constitutive relations of the material. A statically indeterminate structure has multiple possible solutions for the internal forces and displacements, depending on the material properties and deformation behavior of the structure.

3 Degree of indeterminacy

The degree of indeterminacy of a structure is a measure of how much more information is needed to analyze the structure beyond the equations of equilibrium. It is equal to the number of unknowns minus the number of equations. For example, a beam supported by two fixed ends has four unknown reactions (two forces and two moments at each end) and three equations of equilibrium (sum of forces in x and y directions and sum of moments about any point). Therefore, its degree of indeterminacy is 4 - 3 = 1. A higher degree of indeterminacy means a more complex and challenging analysis.

4 Methods of analysis

There are different methods of analysis for statically determinate and indeterminate structures. For statically determinate structures, the most common methods are the method of sections, the method of joints, and the method of free body diagrams. These methods involve cutting the structure into segments or joints and applying the equations of equilibrium to each part. For statically indeterminate structures, the most common methods are the force method, the displacement method, and the stiffness method. These methods involve introducing additional unknowns or equations to solve for the internal forces and displacements using compatibility and constitutive relations.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?