# Trouble Understanding Bending Moments?

• studentoftheg
In summary, the orientation of the reaction moment is determined by trying to turn the beam so that the applied force is in the opposite direction of the reaction moment. For bending moments, the sign convention is usually "sagging is positive" but it can also be "hogging is positive". The direction of the bending moment is determined by the location of the point of interest on the beam and the direction of the force applied.
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

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.

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

Anyone point me in the right direction here? Thanks

studentoftheg said:
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?

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?

studentoftheg said:
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?

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.

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

Yes.

## 1. What are bending moments?

Bending moments refer to the internal forces or moments generated within a structural element, such as a beam or column, due to external loads or forces applied to it. These moments cause the element to bend or deform.

## 2. How do bending moments affect structures?

Bending moments play a critical role in determining the structural integrity and stability of a building or other structure. High bending moments can lead to excessive deflection and potential failure of the structure, while low bending moments can result in a weaker structure that is unable to support its intended load.

## 3. What factors influence bending moments?

The magnitude and distribution of bending moments are influenced by several factors, including the type and magnitude of external loads, the type and shape of the structural element, and the material properties of the element. The geometry and support conditions of the structure also play a role in determining bending moments.

## 4. How are bending moments calculated?

Bending moments can be calculated using the principles of statics and structural analysis. This involves determining the external loads acting on the structure, analyzing the geometry and supports of the structure, and applying equations and formulas to calculate the internal forces and bending moments within the structural elements.

## 5. What are some common challenges in understanding bending moments?

One common challenge in understanding bending moments is the complex nature of structural analysis and the calculations involved. Another challenge is the need to consider various factors and assumptions, such as the distribution of loads and the material properties of the structure, which can affect the accuracy of the results. Additionally, the interpretation of bending moments and their significance in relation to the overall structural design can also be challenging.

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