Calculating Reactions at a Fixed Support for an L-Shaped Bar

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Discussion Overview

The discussion revolves around calculating the reactions at a fixed support for an L-shaped bar under various loading conditions. Participants explore the necessary equations of equilibrium, including forces and moments, to determine the reactions at the support. The scope includes theoretical and mathematical reasoning related to mechanics and statics.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant outlines the use of three equations of equilibrium to find the reactions at the fixed support, questioning the necessity of additional data provided in the problem.
  • Another participant suggests that torques should also be considered alongside forces to fully analyze the system.
  • A later reply emphasizes the importance of summing moments about the support to find moment reactions, indicating that both translational and rotational equilibrium must be addressed.
  • Discussion includes clarification that in three dimensions, six equations of equilibrium are required, which include moment equations about each axis.
  • One participant explains the concept of moments and how they relate to forces, providing an analogy involving a door to illustrate the concept of torque.
  • There is a concern about the level of information provided, with some participants debating how much guidance to offer without giving away the solution.
  • Another participant acknowledges the need to consider six reactions at a fixed support, indicating a realization of the complexity involved in the problem.

Areas of Agreement / Disagreement

Participants generally agree that both forces and moments must be considered in the analysis, but there is no consensus on how much information should be shared to assist the original poster without leading them to the solution directly.

Contextual Notes

Some participants express uncertainty about the original poster's familiarity with moments and torques, suggesting that the problem may not have been adequately covered in their coursework. The discussion reflects varying levels of understanding regarding the application of equilibrium equations in three-dimensional statics.

Who May Find This Useful

Students and practitioners in mechanics, statics, and engineering who are interested in understanding the analysis of forces and moments in structural systems may find this discussion beneficial.

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Hi all;

An L-shaped bar is constrained by a fixed support at A while the other extreme C is free. Determine the reaction at the point A when the bar is loaded by the depicted forces.

2rcc2mt.jpg


Data:
AB=3m, BC=2m, CD=1m
R_B=3N
R_{Cx}=6N, R_{Cy}=2N, R_{Cz}=3N

Either I'm doing something wrong or there's more than enough data in the problem. I assume we just have to write the three equations of equilibrium:

\sum{R_{ix}}=R_{Ax}-R_B-R_{Cx}=0

\sum{R_{iy}}=R_{Ay}-R_{Cy}=0

\sum{R_{iz}}=R_{Az}-R_{Cz}=0

Then we just calculate their resultant in order to find R_B. If so, then why would we need all those distances? :confused:

Maybe my assumptions are plain wrong, I'm really confused... Help appreciated. Thanks.
 
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This is not really my field, but should you be considering torques as well as forces?
 
Redbelly98 said:
This is not really my field, but should you be considering torques as well as forces?

I'm not sure... That's why I was asking. Are there any other reactions that I didn't consider? Thanks.
 
disclaimer said:
I'm not sure... That's why I was asking. Are there any other reactions that I didn't consider? Thanks.
As per Redbelly98's comment, you need to consider torques.
Your translational equilibrium equations will correctly give you the force reactions at the fixed support, but the loadings also produce moment reactions at that support (also called torques or couples). Thus, you must sum all moments = 0 about the support to find the moment reactions at that support. And you have to look separately at moments about each axis, if they exist.
 
I assume we just have to write the three equations of equilibrium:

When in three dimensions, there are actually six equations of equilibrium (three in 2D). You have moment equations about each axis direction. Note that you can solve mathematically without looking at it about each axis, but it just makes it easier sometimes to break it up into components (like you could break a force into x, y, and z force components).

From your post, I'm guessing you're not too familiar with moments. A moment is simply a twisting force. Like the other guys said, it's also called torque (a couple is slightly different). If you push a door in a straight line, it's still going to swing about the hinge.. right? But you pushed it in a straight line. This is because your force caused a moment about the door hinge. Now if you were to push the same door a few centimeters away from the hinge, it would take a lot more effort to get it to swing at the same speed. This is because the same force creates less of a moment at this distance. The formula is:

Moment = Force * Perpendicular distance.

It's important that you take the perpendicular distance. If you push at right angles to the door (straight on), then the distance would be that along the door between your hand and the hinge.

Moments are positive when counter-clockwise and negative when clockwise.

Sorry if that was confusing or long winded.

As for your problem.. it's simple because each force is is a single plane. It might help you to reset point A to the origin.
 
Last edited by a moderator:
billmccai said:
sum of moments about x-axis = 0
[equations deleted]

Hi,

Presumably the OP has been taught about torques or moments in class (otherwise such a problem would not have been assigned), so beyond giving basic information like this, I wouldn't proceed giving the solution any further than this. People learn more the more they have to do themself.

Regards,

Redbelly
 
Sorry.

It just seemed from his post that he hadn't (or wasn't present when they taught it), so thought doing the first part would help give him the idea.
 
Yeah, it can be a tough call sometimes knowing how much information to give out. I had hoped after post #2 that just hearing the word "torque" would trigger a memory of something that had been covered in class. It's possible moments or torques were not covered by the teacher, but that would make it odd for this question to be assigned in the first place.

Perhaps some clarification from disclaimer would help us know what to do to help out.
 
Right, at the time I didn't realize that there should be six reactions at a fix support. Thanks.
 

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