# Max Bending Moment of Rigidly Clamped Beam

1. Dec 16, 2009

### eddie135

Dear Experts,

I am a gradute engineer posting here for the first time. I have a query regarding the simple problem to which i cannot seem to get the correct Max bending moment. Here is the problem.

A beam of length L rigidly clamped at both ends with a point load F in the centre, i.e, at location l/2
I calculate the vertical reactions to be f/2 on each end.
Now if we take a section through the beam at a distance x from the left hand side and summing moments about this section, i get the following

M(x) = F(x - L/2) + M + R1x

where R1 is the left hand vertical force which is equal to f/2 and M which is the fixing moment due to LHS of beam being rigidly clamped. From here I get lost. The Max bending moment from various books for this scenario is given to be

Mmax = Fx/2 - FL/8

I am baffled as to where the 8 comes from.

I would really appreciated it if anyone can shed some light on how this max moment is derived.

Looking forward to hearing from you.

Best Regards
Eddie