Static moment for a continous beam!

[dcredskins]

Could you guys talk a look at the attachment and comment on this? I have been told that total static moment, for a continuous beam with uniformly distributed load throughout the beam length, is always constant. Is there any book or article I can look at to proove this?

 

[Dinosaur]

Yes, the difference between the average end moments and the max mid-span moment is always w x L^2 / 8.

 

[csd72]

Everyone wants a reference these days, no-one has the patience to justify things themselves.

Verifying this is 1st year beam analysis type stuff.

Basically:
1. The total shear is the same and the shear diagram is the same (well nearly, different end moments will attract slightly different shears)
2. The change in moment across the span is caused by the shear diagram.
3. The result is that the moment diagram is raised up by the end moments(i.e. the dashed line across the top), but the shape is the same.

Do the numbers and you will see what I mean.

 

[Lion06]

Yes, it is true. Prove it to yourself by doing a few shear and moment diagrams for beams of varying span length. It can also be for a single span beam with one or both ends fixed. The midspan moment minus the average of the end moments is always (wl^2)/8; You could also say that the midspan moment is (wl^2)8 - (the average of the two end moments). If you have no end moments (simple span case), you can say that the midspan moment is (wl^2)/8 - 0.

 

[rb1957]

'cause it's the moment due to the distributed load ... (w*L/2)*L/4

 

[Denial]

Strictly speaking, your diagram needs to have its green wL²/8 arrows drawn vertically, not perpendicular to the blue dashed line.

 

[dcredskins]

Thanks for the inputs.

I do not understand why people are always looking for reasons to blame others. If you do not like it, do not participate in the discussion. The main purpose of this forum is we discuss and share our concerns and experiences here so that we do not have to spend hours try to figure out ourselves. Do not tell me to go back and use manual calculations if a computer software can do it in seconds. In this case, I have already done some calculations to see if it is true. I just wanted to make sure, I am correct. There is always exception...

:))