Statics question - application of fixed end moments

[StructureMan44]

I'm brushing up on statics before taking the SE exam. In the attached pdf of a fixed end beam with a non-center point load, in the past if I summed the moments at point B I would find:

EMb = 0 = -Ra*L + Pb - Mb

Would you or would you not also include Ma in this equation? I would not consider the moment Ma to create a moment at point B but according to page 9 of the following link the moment Ma does create a moment about Mb:

http://ocw.nthu.edu.tw/ocw/upload/8/259/Chapter_10-98.pdf

Is it incorrect to assume that the upward rotation caused by moment Ma would not be cancelled out by the concentrated force P and therefore the moment Ma would not create a rotation at point b? What do the experts here think?

 

[IDS]

Your attached pdf doesn't open for me, but referring to the diagram on Page 9 of the link, I'd ask you this:, if the moment at A made no difference to B, wouldn't a pinned connection at A act in the same way as the fixed connection shown?

In general if you are using equilibrium to determine forces, then you need to include all the applied loads and all the reactions.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[KootK]

You definitely want to include Ma. An applied moment is location independent from a statics perspective. No matter where you chose your point of study to be, an applied moment anywhere in the body is equivalent to and applied moment at the point of study.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[rb1957]

pdf wouldn't open for me either.

you should absolutely include Ma in the sum of moments ... after all, you are summing all moments on the beam; you neglect Rb 'cause the moment created about b is zero.

another day in paradise, or is paradise one day closer ?

 

[canwesteng]

To visualize why you need to add this to your equations, replace the moment with a force couple at that location. You'll see that the couple creates a moment about any point you sum moments about.