Moments Q: Determining EI Beam Distribution

[zahraa1]

The question I'm attempting to do is part (a):

http://www.picpaste.com/struc1-z7FJMCcF.jpg

which translates to: determine distribution of moment, The beam is elastic and has constant EI throughout its entire length. Now part of the solution looks like this:

http://www.picpaste.com/struc2-8VGlrDU7.png

My question is how the moments M_A and M_C replaced with (i.e. equal to) qL^2/18 in this solution?

 

[Simon Bridge]

Welcome to PF;

My question is how the moments M_A and M_C replaced with (i.e. equal to) qL^2/18 in this solution?

Looking at the distribution in the diagram, it certainly looks like the magnitudes of the moments about A and C should be the same (opposite directions).
Have you tried calculating them?

 

[paisiello2]

The cantilevered portions of the beam ends were replaced with equivalent moments Ma and Mc using simple statics.