Cantilever Bracket Calculations

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Discussion Overview

The discussion revolves around the calculations related to a cantilever bracket fixed at one end and subjected to a downward load. Participants explore the forces acting on the bracket, particularly the force attempting to pull the top fixing from the wall, and whether the bottom fixing acts as a pivot point for torque calculations. The context includes technical calculations and considerations for structural integrity in a plasterboard wall application.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant describes the setup of a cantilever bracket and poses questions about the forces acting on the top fixing and the role of the bottom fixing as a pivot point for torque calculations.
  • Another participant suggests searching for "prying action" or "prying calcs" as relevant concepts in civil/structural engineering.
  • A participant mentions using two torque calculations to determine the load on the top fixing and expresses concern about the failure rate of the plasterboard wall.
  • One participant provides a correction regarding the units of force, emphasizing the need to express force in Newtons and the importance of proper unit notation.
  • Another participant acknowledges the correction and discusses the need for a physical test to determine the pull-through force of the plasterboard wall.
  • A participant expresses agreement with the calculations for the force on the top fixing but questions the method used for another force calculation, suggesting a potential misunderstanding about the presence of a brace.
  • One participant shares a link to a previous discussion involving a finite element analysis (FEA) model related to similar calculations, indicating a desire to provide additional resources for understanding.

Areas of Agreement / Disagreement

Participants generally agree on the need for accurate calculations and the importance of unit notation. However, there are differing opinions on the methods used for calculating certain forces, and the discussion remains unresolved regarding the specifics of the torque calculations and the presence of a brace.

Contextual Notes

Participants express uncertainty about the pull-through force for the plasterboard wall and the implications for the bracket's loading capacity. There are also unresolved questions about the calculations related to the forces acting on the bracket.

rich866
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I have a cantilever bracket, fixed at one end, free at the other.
One vertical element AB, 330mm long with a fixing at either end to a wall.
One horizontal element CD, 375mm long.
CD is fixed at 90deg to AB, 130mm from the top.
A constant, downward load W=30kg, is applied to the end of CD, l=375mm.

What is the force trying to pull the top fixing from the wall?
Does the bottom fixing work as a pivot point making this a torque calculation?

Assumptions:
The strength of the bracket will well exceed the failure rate of the top fixing, so no flex in the 40mm box sections will occur.

This bracket has been installed on a plaster board wall. The chemical fixings will take 9Kn but the plaster board will fail before this point, long before!

Before a set up a chemical anchour in the mock up of the wall to test the fixing/ board to failure I would like to know at what point I exceed my working force of the bracket/ anchour interface??
 
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Can you please give us a diagram. It's kinda hard to see what's going on. We shouldn't have to assume what it looks like.
 
appoligoies, left the pdf at work :confused: will attach tomorrow. Think I've solved it with two torque calculations but will attach them too just double check the math!
 
rich866 said:
What is the force trying to pull the top fixing from the wall?
Does the bottom fixing work as a pivot point making this a torque calculation?

Yes, I would consider the bottom fixing work as a pivot point in making your calculation. Try a quick google for "prying action" or "prying calcs". Thats a pretty common term used in civil/structural engineering for that type of action.
 
attached drawing of calculation. Want to know Fb, load to top fixing, when a given load is applied to the end of the cantilever arm F
Hope that makes more sense!
Given torque calculations a try, assuming that the loads I'm applying are well under the bracket components failure rating of over 1Kn, the weak link is the top fixing into the plaster board. If I know the loading on that fixing I can then move to the likely failure rate of the material
Used two torque calculations: 1. from the end of the arm to the bottom pivot point, 2. and from the torque at the pivot point back up to the top of the arm to the top fixing for pry force Fb.
 

Attachments

rich866: Your answer for Fb is currently correct, except force is measured in units of Newtons (N). Therefore, multiply your current value for Fb (and load F) by g = 9.81 m/s^2, to obtain Newtons (N). Therefore, Fb = 334.4 N.

By the way, always leave a space between a numeric value and its following unit symbol. E.g., 375 mm, not 375mm. See the international standard for writing units[/color] (ISO 31-0[/color]).
 
Thanks nvn
Thats goood news, on the finished document I had converted the Fb load to Newtons, as the fixings tension loads are listed in KN, also added a safety factor of 1.4.

What I haven't been able to get is a pull though force for the construction of plaster board wall the bracket is to be mounted on, so I will have to construct a demo wall and physically pull the fixing out to make a statement about the maximum weight the bracket can be loaded too.

Thanks for the pointer on units, I am using this and a number of other parts of this as a project report so would be nice to be accurate. Been in the electrical industry using units for 30years and never come across that before! learning all the time.

Thanks again
 
yep, just checked the standard link you attached and can't fault your point of fact. I will revise my documentation to refect this. Most useful fact of the week!
 
I checked your calculations and get the same for Fb doing it another way. I don't understand why you did Ta that way, is there a brace there? If there wasn't Ta would equal Fb in the opposite direction.

Here's a link of something I did similar and nvn helped me with it. It might give you some ideas. I did an FEA model to determine the stresses at the wall.

https://www.physicsforums.com/showthread.php?t=625739
 

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