How Do You Calculate Deflection in a Simply Supported Overhanging Beam?

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Discussion Overview

The discussion focuses on calculating the deflection of a simply supported overhanging beam with a point load at the end of the cantilever. Participants explore various methods and equations for determining deflection, including the implications of beam stability and the use of different calculation techniques.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant seeks a deflection equation for a simply supported overhanging beam and mentions having trouble finding the deflection between the supports.
  • Another participant points out that a simply supported beam with an overhanging load is statically unstable and questions the validity of the calculations due to missing details.
  • A participant acknowledges a mistake regarding the beam's stability and suggests that the beam is no longer statically unstable after correcting the support conditions.
  • This participant expresses difficulty in obtaining correct units for deflection and requests assistance in calculating deflection at various points along the beam.
  • Another participant suggests solving the beam equation to find displacement as a function of position or using methods like virtual work or finite elements for an approximate solution.

Areas of Agreement / Disagreement

Participants express differing views on the stability of the beam and the validity of calculations. There is no consensus on the best method for calculating deflection, and the discussion remains unresolved regarding the correct approach and calculations.

Contextual Notes

Some calculations and assumptions are not fully detailed, and there are unresolved issues regarding the application of beam theory and the conditions of support. The discussion includes various approaches without a clear resolution on the correct method.

Rhysmachine
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Hey all, first post!

Looking to find a deflection equation for a simply supported overhanging beam with two supports and a point- load at the end of the canteliever. I can determine reactions at the supports but i am having trouble finding deflection between the supports.

Any help is appreciated!

the beam in question looks like (a) in the following picture but if we call L/2 a, instead.

conju2.gif
 
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This is a tricky problem. A simply supported beam with an overhanging load and no other appreciable loading is statically unstable. You have not provided any details about your calculations, so I am unable to comment on their validity. The so-called 'conjugate beam' you show reflects different end conditions from the original beam. The slope and deflection at C for the 'conjugate beam' must both vanish, whereas neither vanish at C for the given beam.
 
Sorry my mistake; the beam is restrained at A, vertically so I guess the triangle needs to be pointing the other way. The beam is no longer statically unstable now, right?

Ive done a number of calcs intergrating something like: P*a*x/LEI, with a number of variations to find slope then deflection, But I always seem to be ending up with an answer that would be mm^2 instead of mm. I was hoping someone might be able to go through finding the answer for me so I can find the deflection at many points along the A-B section.

Oh and the second example shouldn't be there at all. I just had to find a picture that was something like the problem I have as I couldn't upload my own pic.
 
I'd solve the beam equation to find the displacement as a function of x or get an approximate solution using virtual work or finite elements.
 

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