How Can You Solve Reaction Forces in Bearings Using Basic Calculations?

[domabo]

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

 

[DrClaude]

You can do it using Gaussian elimination.

 

[domabo]

You can do it using Gaussian elimination.

Tried it using Gaussian eliminator calculator. Didn’t get the same answer.

 

[BvU]

Show some details. What did you put in and what came out ?

 

[DrClaude]

Tried it using Gaussian eliminator calculator. Didn’t get the same answer.

They did mess up the signs, but the magnitudes are correct.

 

[domabo]

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.

 

[domabo]

Show some details. What did you put in and what came out ?

Please see my reply to Dr Claude

 

[DrClaude]

Do you mind pointing out the mistake here?

Can you show the starting matrix?

 

[domabo]

Can you show the starting matrix?

It's attached as the second image

Or, here: https://imgur.com/pRhoxor

 

[DrClaude]

It's attached as the second image

Or, here: https://imgur.com/pRhoxor

You forgot the Bz in row 2.

 

[domabo]

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.

 

[DrClaude]

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.