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studentoftheg

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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.

- #1

studentoftheg

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- #2

Unrest

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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.

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.

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.

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.

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- #3

studentoftheg

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

- #4

studentoftheg

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Anyone point me in the right direction here? Thanks

- #5

Unrest

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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?

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studentoftheg

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- #7

Unrest

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studentoftheg said:

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?

- #8

studentoftheg

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- #9

Unrest

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

Yes.

- #10

Observables

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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

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.

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.

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.

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.

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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