Trouble Understanding Bending Moments?

[studentoftheg]

I'm having trouble fully understanding bending moments. I get the calculations, the force times distance (lever arm), and how to calculate the bending stress (M*y/I). Its the orientation/direction that I am having trouble picturing in my head. I know this is pretty basic, but I just haven't read or seen something that makes it 'click' in my head. Like say you've got a beam, and along the beam axially is the X axis, vertically Y axis and Z is the lateral direction. The beam is anchored at one end. If I apply a force to the other end, say Fz, how do I know what direction the moment is? Is it the right hand rule? Can someone explain. Thanks

 

[Unrest]

Are you talking about bending moments (within a beam) or applied/reaction moments (at supports/etc)?

Orientation of reaction moment
To find the orientation of the reaction moment in your example I imagine holding the beam where it's fixed and think how I would have to try to turn it to counteract the applied force.

Sign of reaction moment
If you have a feel for the orientation but don't know if it's +ve or -ve, use the right-hand rule as you suggested. In your example the reaction moment is about the Y axis, so put your thumb in the direction of +Y and your curled fingers show the direction of a positive moment.

Sign of bending moment
For bending moments it's less standardized. You can have "sagging is positive" or "hogging is positive". Sagging positive is common for mechanical engineering. When you're feeling positive you're smiling and your face looks like a sagging simply supported beam :P

Since you're bending in the X-Z plane it's more confusing. The "sagging is positive" convention means a positive bending moment is caused by a positive moment at the positive side of the point of interest, and a negative moment on the negative side. In your example the concavity will be in the direction of the +Z axis. So the bending moment about Y would be negative.

However then you can't use stress=My/I, but that's obvious because the stress is independent of the Y-coordinate for bending about Y.

 

[studentoftheg]

Yeah I am talking about the bending moment within the beam as opposed to reactions at supports etc.

 

[studentoftheg]

Anyone point me in the right direction here? Thanks

 

[Unrest]

Anyone point me in the right direction here? Thanks

Maybe my last paragraph was more confusing than anything. You have to first think through the process in a few different cases before you can form a mental image that you trust.

What in particular are you unclear on?
The signs?
Bending in the x-z plane instead of the usual x-y plane?
The meaning of "direction" for a bending moment?

 

[studentoftheg]

Thanks for replying. I know this is pretty basic stuff! Yeah in particular its the resulting direction of the bending moments within a beam. For example, which direction would you need to apply a force to get a moment about Z etc?

 

[Unrest]

Thanks for replying. I know this is pretty basic stuff! Yeah in particular its the resulting direction of the bending moments within a beam. For example, which direction would you need to apply a force to get a moment about Z etc?

I always visualize the deformed beam, then it's obvious how that relates to applied moments.

A smiley face in the XY plane has a bending moment about Z. The direction of that bending moment vector depends on the sign convention - it could be +Z or -Z.

Are you clear that in your example the bending moment would be about Y?

 

[studentoftheg]

Thanks, no that wasnt clear to me, that's what I'm having trouble processing and picturing in my head. So if it bends in XY axis then that is a moment about Z? And so I take it applying a moment about one axis then results in bending in the other two axis'? So if I applied a moment about Y, then it is going to bend in the XZ plane. Resulting in a smiley face laterally.

 

[Unrest]

applying a moment about one axis then results in bending in the other two axis'?

Yes.

 

[Observables]

studentoftheg,

Have a look at these videos.

Bending Beam vids
Part 1: http://www.youtube.com/user/purdueMET#p/u/82/4FBaa82r_7A
Part 2: http://www.youtube.com/user/purdueMET#p/u/81/0yQnAPNwkFc