Load on a beam: More unknowns than equations?

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SUMMARY

The discussion centers on analyzing a propped cantilever beam, which is classified as statically indeterminate. The key to solving the problem lies in applying additional equations that account for the deflection and slope conditions at points A and B. Specifically, the deflection at B must equal zero, and both the deflection and slope at A must also equal zero. The presence of a hinge between points A and B allows for the bending moment to be zero at that location, providing the necessary equation to determine the reaction forces.

PREREQUISITES
  • Understanding of statically indeterminate structures
  • Knowledge of beam deflection and slope conditions
  • Familiarity with Free Body Diagrams (FBD)
  • Basic principles of structural analysis
NEXT STEPS
  • Study the principles of propped cantilever beam analysis
  • Learn about additional equations for statically indeterminate structures
  • Explore methods for calculating beam deflection and slope
  • Review the concept of hinges in structural mechanics
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Structural engineers, civil engineering students, and anyone involved in the analysis of beam structures will benefit from this discussion.

Marvin94
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Homework Statement



IMG_20150802_193659.jpg


Homework Equations


FBD and all forces and moments = 0

The Attempt at a Solution


Sketched in the image.

So, I don't know how to go on with my analysis of the load, since I can't determine the reaction forces. Can someone please help me? Thanks in advance!
 

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This beam is what is known as a "propped cantilever". It is statically indeterminate.

You will have to write additional equations, knowing that the deflection = 0 at B and the deflection and slope of the beam at A are both equal to zero.
 
There seems to be a hinge between A and B. This makes it statically determinate. At the hinge, the bending moment would be zero, and this gives you the additional equation you need to solve the problem.
 

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