How Do You Draw an Equivalent System for a Given Moment?

[Oblivion77]

Homework Statement

Here is the problem I am stuck on, need some advice

Homework Equations

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The Attempt at a Solution

I found the moment to be -19.282 for the system shown (not sure if it correct) but I am confused about how to drawing will look for the equivalent system. (- is added for the moment since it is clockwise)

 

[LowlyPion]

Homework Statement

Here is the problem I am stuck on, need some advice

2. Homework Equations

Sum of Fx =0, Sum of Fy = 0, Sum of M(about a point) = 0

3. The Attempt at a Solution

I found the moment to be -19.282 for the system shown (not sure if it correct) but I am confused about how to drawing will look for the equivalent system. (- is added for the moment since it is clockwise)

The question doesn't suggest that there is no net moment or force about O.

To calculate the Force couple you want to separate the forces into their x,y components. To calculate moments then you want to take the x,y components and sum their moments about the point of reference.

 

[Oblivion77]

Whoops I was thinking of something different for that.

Anyways, once I find the moment acting on O, would it be the same for the equivalent system right?

 

[LowlyPion]

Whoops I was thinking of something different for that.

Anyways, once I find the moment acting on O, would it be the same for the equivalent system right?

Yes. And the Force Couple too. Otherwise it wouldn't be equivalent would it?

 

[Oblivion77]

Ok, did I do this right so far?

Sum of Fx, 1.3 + 1.477 = 2.777kN
Sum of Fy, 1.196kN
Sum of the Moment about point O, -78 + 58.718 = -19.282kN-M

I know the sum of the forces and moment about O in the equivalent system needs to be the same, but I am not sure if the couple will be the same in both.

 

[LowlyPion]

Ok, did I do this right so far?

Sum of Fx, 1.3 + 1.477 = 2.777kN
Sum of Fy, 1.196kN
Sum of the Moment about point O, -78 + 58.718 = -19.282kN-M

I know the sum of the forces and moment about O in the equivalent system needs to be the same, but I am not sure if the couple will be the same in both.

I think there should be 3 terms in your moment equation. There are the coupled x component moments acting in opposition at 60m on each side of O and there is the negative moment contribution from the y component acting at 25m to O. I get -19.315 which I guess is close enough.

Edit: As for the couple, why wouldn't it be? Whatever equivalent system is in the x,y plane because that's where those forces are acting.

 

[Oblivion77]

I think there should be 3 terms in your moment equation. There are the coupled x component moments acting in opposition at 60m on each side of O and there is the negative moment contribution from the y component acting at 25m to O. I get -19.315 which I guess is close enough.

Edit: As for the couple, why wouldn't it be? Whatever equivalent system is in the x,y plane because that's where those forces are acting.

Thanks for all the help? Would the answer to the problem be -19.282/-19.315?

 

[LowlyPion]

Thanks for all the help? Would the answer to the problem be -19.282/-19.315?

Well of course I like my number better. But yours or mine is likely within the precision of the grading system.

So long as you were calculating the moment from the components of Fb, I think that is what the exercise is about.