How to determine direction of a moment

[dlacombe13]

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?

 

[malemdk]

The direction of the force in the member BD should be reversed and the direction force at the point B is in clockwise

 

[CWatters]

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 F_BD 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)(240F_BD/510) + (+0.135P) = 0

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

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

Some will say it should be obvious that BD is in compression (so F_BD acts downwards and to the left) but the point is if you do things right it doesn't matter if you define F_BD 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.

 

[dlacombe13]

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?

 

[malemdk]

Although the sign of the force doesn't matter much while deciding the cross section of a member it does play big role.

 

[CWatters]

OK sorry I didn't spot that symbol. Yes they are inconsistent.