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Statically Determinate: Definition, Equation & Examples

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  • 0:04 Structural Analysis
  • 0:26 Statically Determinate…
  • 1:52 Some Examples
  • 3:14 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, we are going to learn about two categories of structure; one can be analyzed using statics, and the other cannot be analyzed using statics only. We are going to learn about statically determinate structures, and we will give equations and examples for them.

Structural Analysis

Structural analysis is the calculation of: reaction forces, internal forces, stresses (shear and normal), bending moments, deflection, angle of rotation, etc. on a given structural member, provided different forces are determined. Structural engineers make structural analysis in order to design structures to withstand the effects of possible forces on structures.

Statically Determinate Structures

In some cases, statics, which means the sum of forces in any direction is zero, and hence, no acceleration is experienced; this means it's enough to analyze a structure. These structures are referred to as statically determinate. In other cases, however, statics is not enough to analyze the structure, in which case it is called statically indeterminate.

In two dimensional statics, the summation of forces in the x and y directions, and the summation of moments in the z direction all must equal zero. In three dimensional statics, the summation of forces in x, y and z directions, and the summation of moments in x, y and z directions all must equal zero. For each case, a mathematical equation is formed.

If the number of equations = the number of unknowns, then the structure is statically determinate. If, on the other hand, number of equations < the number of unknowns, the structure is statically indeterminate, and hence, other methods need to be used to analyze it.

The unknown forces are in the direction of restriction motion for each support. For instance, in the case of hinges, motion is restricted in both x and y directions, but the member is free to rotate. The moment in the z direction has a zero value, but the forces in x and y are nonzero. For a roller, there is a force in the y direction, but zero in x-direction and zero at the moment z. And finally, fixed ends cause forces in the x and y direction, as well as a moment in the z direction.

Some Examples


statically d


In the figure above, the beams number 1 and 2 are statically determinate structures due to the following reasons:

1- Beam number 1: the number of unknown forces is 3 = the number of equations is 3.

2- Beam number 2: the number of unknown forces is 3 = the number of equations is 3.

The equations are as follows:


sigma f x


sigma f y


sigma m z


ex s d


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