Statically Determinate & Indeterminate Structures: Trusses & Beams

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  • 0:03 Structures & Classifications
  • 1:40 Beams
  • 3:01 Trusses
  • 4:20 Lesson Summary
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Lesson Transcript
Instructor: Hassan Alsaud

Earned my B.S. in Civil Engineering back in 2011. Have two years of experience in oil and gas fields and two year as a graduate research assistant. Earned my Master degree in Engineering from Tennessee State University in 2016.

In this lesson, you are going to learn about statically determinate and statically indeterminate structures and discover how to calculate the degree of indeterminacy. We'll explore beams and trusses as examples.

Structures & Classifications

Have you ever walked under a bridge or a mega structure and seen different joints between the beams and columns in the structure? Perhaps you've seen rollers and hinges and you have wondered if that is enough to support the structure. Isn't a fixed end more stable than a roller or a hinge? Well, the answer is yes. However, sometimes stability creates risk of more exposure to types of stress, such as thermal stress.

Structures are a group of members, such as beams, columns, slabs, foundations, girders, and trusses, that work as a unit to fulfill a purpose. An engineer's duty is to design structures in a professional, safe, and economical manner in order to fulfill the purpose for which it was designed in the first place. Structures as classified into either being statically determinate or statically indeterminate.

Statically determinate structures are structures that can be analyzed using statics equations only, (i.e., equilibrium in all directions). On the other hand, statically indeterminate structures can't be analyzed using statics equations only; they require other material properties, such as deformations, in order to analyze them.

When engineers conduct structural analysis, they calculate the reaction forces due to the external forces applied to the structure as well as internal forces, such as the bending moment, shear force, and normal force. Structural analysis is necessary for structural design in order for the structural engineer to choose the proper sizes and materials so the structure can economically and effectively resist the effects of the possible external loads applied to it.


In regards to beams, if the reaction forces can be calculated using equilibrium equations alone, they are statically determinate. On the other hand, if the reaction force can't be determined using equilibrium equations only, other methods have to be used, and the structure is said to be statically indeterminate.

If the number of unknowns exceeds the number of equations, the structure is statically indeterminate. Otherwise, it is statically determinate.

statically determinate and statically indeterminate

In the above figure, we have three equations for all the cases:

sigma f x

sigma f y

sigma m z

However, the number of unknowns are different; there are three unknowns for beams number 1 and 2, which makes them statically determinate because the number of unknowns is equal to the number of equations. On the other hand, in beams 3 and 4, there are more unknowns than there are equations. Therefore, these structures are statically indeterminate.

In three-dimensional structures, however, there will be six equations, which makes it possible to have up to six unknowns for the beam to be statically determinate. The degree of indeterminacy is equal to the number of unknowns minus the number of equations. When there are fewer reactions than there are equations, however, this makes the beam unstable.

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