L5: Structural loads and internal responses
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Show reaction forces in free body diagram
The system is statically indeterminate with … degrees of
statical indeterminacy
5 unknown support reactions and 3 equations of equilibrium [5-3=2] so 2 degrees so calculation is impossible
How to solve this structure and make it statically determinate
A statically determinate multi-part structure can be obtained if the continuous beam is divided into several members by introducing an appropriate number of hinges. In this way, the system becomes a series of linked beams extended at their ends by cantilevers in alternate spans that are linked to each other by beams supported on the cantilever ends. (Figure 5.2(b)). Such a structure is called a hinged beam or Gerber beam.
At a hinge connection the moment is zero, thus, the introduction of the 2 hinges provides us with two additional equations and the system becomes statically determinate (i.e. 5 unknown support reactions vs the standard 3 equations of equilibrium + 2 additional moment equations taken from the hinged supports [5-5=0]).
![<p>A statically determinate multi-part structure can be obtained if the continuous beam is divided into several members by introducing an appropriate number of hinges. In this way, the system becomes a series of linked beams extended at their ends by cantilevers in alternate spans that are linked to each other by beams supported on the cantilever ends. (Figure 5.2(b)). Such a structure is called a hinged beam or Gerber beam.</p><p>At a hinge connection the moment is zero, thus, the introduction of the 2 hinges provides us with two additional equations and the system becomes statically determinate (i.e. 5 unknown support reactions vs the standard 3 equations of equilibrium + 2 additional moment equations taken from the hinged supports [5-5=0]).</p><p></p>](https://knowt-user-attachments.s3.amazonaws.com/a1fb7413-c6ae-4e6d-9a17-a994eba774ad.jpg)
