Determining reaction forces

In summary, the conversation is about solving a problem to find reaction forces for bearings using the equations of sum of forces and moments equal to zero. The person has tried using Gaussian elimination but has encountered difficulties and is seeking help. After some discussion and sharing of details, it is discovered that there was a mistake in the initial matrix. The expert confirms that this is the best way to solve the system of equations and suggests practicing it to be able to do it quickly during exams using a scientific calculator.
  • #1
domabo
32
0

Homework Statement


The problem asks to find the reaction forces for each of the bearings. For such bearings, the reaction forces can be looked up in a textbook, but they just act perpendicular to the shaft.

Homework Equations


Sum of the forces and moments = 0.

The Attempt at a Solution


I understand and have myself reproduced the 6 equations. My problem is now solving for the 6 unknowns. My usual approach in the past has been to just do some simple substitutions. It's not working for me here, and I can't even reproduce the same answer using an online systems of equations calculator. Any help is greatly appreciated.

Here is the problem and the solution: https://imgur.com/a/LrFb8
 
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  • #3
DrClaude said:
You can do it using Gaussian elimination.

Tried it using Gaussian eliminator calculator. Didn’t get the same answer.
 
  • #4
Show some details. What did you put in and what came out ?
 
  • #5
domabo said:
Tried it using Gaussian eliminator calculator. Didn’t get the same answer.
They did mess up the signs, but the magnitudes are correct.
 
  • #6
DrClaude said:
They did mess up the signs, but the magnitudes are correct.
https://imgur.com/a/6LcBv

Do you mind pointing out the mistake here? As you can see, I'm not getting the same answer as the solution has given.
I should add that I've listed the variables in the alphabetical order they appear. That is, Ax = x1, Az = x2, By=x3, Bz=x4, Cx=x5, and Cy=x6.
 
  • #7
BvU said:
Show some details. What did you put in and what came out ?

Please see my reply to Dr Claude
 
  • #8
domabo said:
Do you mind pointing out the mistake here?
Can you show the starting matrix?
 
  • #9
  • #11
DrClaude said:
You forgot the Bz in row 2.
Wow... thanks. Would you say that this is the best way to solve this system of equations? Eventually, I'll be of course asked to do these types of problems in an exam setting where I'll only be able to use a simple scientific calculator.
 
  • #12
domabo said:
Would you say that this is the best way to solve this system of equations? Eventually, I'll be of course asked to do these types of problems in an exam setting where I'll only be able to use a simple scientific calculator.
Yes, try it yourself. You should be able to solve such a system in a few minutes.
 

1. What is the purpose of determining reaction forces?

The purpose of determining reaction forces is to understand the external forces acting on a system or structure. This allows scientists and engineers to design and analyze structures that can withstand these forces and remain stable.

2. How do you calculate reaction forces?

Reaction forces can be calculated using Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. This means that the reaction force at any point is equal in magnitude and opposite in direction to the applied force at that same point.

3. What factors affect reaction forces?

The main factors that affect reaction forces include the magnitude and direction of applied forces, the distribution of weight or load, and the geometry and material properties of the structure.

4. Can reaction forces be negative?

Yes, reaction forces can be negative. This occurs when the applied force and the reaction force are acting in opposite directions. In this case, the reaction force will have a negative sign to indicate its direction.

5. Why is it important to consider reaction forces in structural design?

It is important to consider reaction forces in structural design because they can significantly impact the stability and safety of a structure. By accurately determining reaction forces, engineers can design structures that can withstand these forces and prevent potential failures or collapses.

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