Deflection of a Cantilever with support

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Discussion Overview

The discussion centers on the theoretical calculation of deflection and bending in a cantilever structure with supporting rods and a connecting plate. Participants explore different configurations of the rods and the implications of the rigidity of the connecting plate on the deflection calculations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant proposes a model of a cantilever rod with two supporting rods and a rigid plate, seeking to calculate deflection under applied force.
  • Another participant questions the assumption of the plate being rigid, suggesting that this may not allow for deflection along the length of the rods.
  • A different participant expresses uncertainty about the configuration of the rigid plate and its implications for the deflection of the rods.
  • One participant suggests using the combined moment of inertia of the rods in the deflection equation for the case where all rods are of the same length.
  • Another participant indicates that for the case where the middle rod is longer, the deflection should be calculated by considering the additional length after the initial deflection calculation.
  • A participant introduces a scenario where the plate is not rigid and asks how to calculate deflection in this case, raising concerns about potential bending of the plate.

Areas of Agreement / Disagreement

Participants express differing views on the rigidity of the plate and its effects on deflection. There is no consensus on the assumptions regarding the plate or the calculations for deflection in the various scenarios presented.

Contextual Notes

Participants have not fully resolved the implications of the plate's rigidity on the deflection calculations, and there are varying interpretations of the plate's configuration. The discussion includes assumptions about the lengths of the rods and the forces applied, which may affect the calculations.

Who May Find This Useful

This discussion may be useful for individuals interested in structural engineering, mechanics of materials, or those studying cantilever beam theory and deflection calculations.

Firzan
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I sketched out a slightly simplified model. It is a cantilever rod with two supporting rods of slightly larger diameter, connected by a plate. (Ignore the weight of the individual parts. For illustration purposes, I draw this to resemble a cantilever beam from the side view but in actual design, this drawing is actually the top view.)
My aim is to theoretically calculate the deflection/bending in the rods (more importantly, the two side/supporting rods) due to the force applied. The plate can be considered rigid.

I'll break down the question into two parts, so that I can understand the concept better:

1. If the three rods were of the same length (the middle rod is not extended and force is applied at the end of the three rods), how do I calculate the forces acting on each rod and then the deflection?

2. With the middle rod being longer than the supporting two rods. How should I approach calculating the deflection in each of the rods?
 

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If you assume the plates are rigid and rigidly attached to the rods, they could not allow any deflection along the full length they are attached to. I think you need to rethink that assumption.
 
After another look, I'm not sure I understand what your rigid plate looks like. I thought it was 500mm x 200mm extending to the support surface, but now I'm thinking it only exist in the plane that is 500mm away from your support surface. If this is the case, the plate constrains all three beams to have the same deflection at 500mm from the support?
 
For #1. I'm pretty sure you can just add the 3 rods moment of inertia and use the total for your deflection equation y = F*L^3/(3*E*Itotal)

For #2. Start with #1 where L = 500. Then just think of the middle beam as starting at the L=500 location and add the additional deflection to the deflection from #1.
 
The plate connects the three rods/beams 500mm away from the support surface. So yes, since assumed to be rigid, the plate would constraint the three to have the same deflection.
 
What if the plate was not rigid? Say, it has a rectangular profile of 125mm*30mm. How would I then calculate the X-axis deflection on the rods?
Also, what other things should I take note of? (ie possible bending of the plate, etc?)
 

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