How to determine direction of a moment

In summary: They say anticlockwise is positive but then in the sum of moments equation they have -0.135P. So the solution is correct but the statement is wrong.In summary, the conversation discusses a problem on a pdf and the attempt at solving it. The issue arises when determining the direction of the moment due to the load P, as it seems to contradict the direction of the horizontal force of the member BD. The conversation concludes that the problem is due to a lack of explicitly defining clockwise and anticlockwise moments as positive. The inconsistency is highlighted in the sum of moments equation, which has a negative sign for P despite stating that anticlockwise is positive. This does not affect the solution, but it is an error in the statement.
  • #1
dlacombe13
100
3

Homework Statement


I am following the first problem on this online pdf:
http://www.ce.udel.edu/courses/CIEG212/Homework_1_2007.pdf

Homework Equations


Equilibrium equations for forces and moments.

The Attempt at a Solution


I know how to solve the problem, that part is straight forward. However I can't see how the moment at C due to the load P is going in the clockwise direction as implied by the moment equation. In my mind, it should compliment the counter-clockwise direction due to the horizontal force of the member BD. Is my assumption wrong? If so, why?
 
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  • #2
The direction of the force in the member BD should be reversed and the direction force at the point B is in clockwise
 
  • #3
malemdk said:
The direction of the force in the member BD should be reversed and the direction force at the point B is in clockwise

That's true but...

The real source of the problem is that you didn't explicitly define clockwise or anti clockwise moments to be positive.

In your FBD you have defined the direction of FBD so that positive is up and to the right. There is nothing wrong with that. After all you don't always know the direction of unknown forces. However it means your FBD and your sum of moments equation are inconsistent with each other.

Lets treat your FDB as correct and fix your sum of moments equation so that it is consistent...

First I will arbitrarily define anticlockwise as positive. Then the sum should be..
+(0.450)(240FBD/510) + (+0.135P) = 0

If I were to define clockwise as positive. Then the sum should be..
-(0.450)(240FBD/510) + (-0.135P) = 0

In both cases if you were to solve for FBD you would find it's negative.

Some will say it should be obvious that BD is in compression (so FBD acts downwards and to the left) but the point is if you do things right it doesn't matter if you define FBD so that positive is up and to the right or down and to the left. If you are explicit with your definitions and consistent then it all drops out in the wash.
 
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  • #4
Okay so I will first say this is not my work, I am just studying the problem. They do explicitly define that anticlockwise is positive (it is to the left of the moment equation). I as well defined anticlockwise as positive. Then by judgement, I got the equation that CWatters got:

+(0.450)(240FBD/510) + (+0.135P) = 0

Which is why I am here. Since they do define anticlockwise on this solution, and have:

+(0.450)(240FBD/510) + (-0.135P) = 0

As well as BD being up and to the right, are they incorrect?
 
  • #5
Although the sign of the force doesn't matter much while deciding the cross section of a member it does play big role.
 
  • #6
OK sorry I didn't spot that symbol. Yes they are inconsistent.
 

FAQ: How to determine direction of a moment

What is a moment in relation to direction?

A moment is a measure of rotation around an axis. It is a vector quantity that has both magnitude and direction.

How do you determine the direction of a moment?

The direction of a moment can be determined by using the right-hand rule, where the direction of the moment is perpendicular to both the force vector and the vector from the axis of rotation to the point of application of the force.

What is the right-hand rule?

The right-hand rule is a method used to determine the direction of a vector that is the result of a cross product between two other vectors. It states that if the fingers of the right hand curl in the direction of the first vector, and then the hand rotates towards the second vector, the thumb will point in the direction of the resulting vector.

How do you apply the right-hand rule to determine the direction of a moment?

To apply the right-hand rule to determine the direction of a moment, place your right hand on the plane of rotation with your fingers pointing in the direction of the force vector. Then, curl your fingers towards the axis of rotation. The direction in which your thumb points is the direction of the moment.

Can the direction of a moment change?

Yes, the direction of a moment can change if the direction of the force or the location of the point of application of the force changes. This will result in a different axis of rotation and therefore a different direction for the moment.

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