A fixed beam of span L is subjected to a moment M at the centre of span. The fixed end moment is

Concept:

The fixed end moments generated due to the application of Moment M on a beam fixed at both ends are shown below:

⇒ MAB = \( \frac{{\rm{M}}}{{{{\rm{L}}^{2{\rm{}}}}}} \times \left( {3{\rm{a}} - {\rm{L}}} \right) \times {\rm{b}}\)

When the moment is at the center, a = b = L/2

⇒ MBA = \( \frac{{\rm{M}}}{{{{\rm{L}}^{2{\rm{}}}}}} \times \left( {3{\rm{L/2}} - {\rm{L}}} \right) \times {\rm{L/2}}\)

M_BA = M_AB = M/4

Mistake Points

Here Moment is in Anticlockwise Direction.

MAB = \(- \frac{{\rm{M}}}{{{{\rm{L}}^{2{\rm{}}}}}} \times \left( {3{\rm{a}} - {\rm{L}}} \right) \times {\rm{b}}\)

MBA = \( - \frac{{\rm{M}}}{{{{\rm{L}}^{2{\rm{}}}}}} \times \left( {3{\rm{b}} - {\rm{L}}} \right) \times {\rm{a}}\)

Note: MAB and MBA must have the same sign. a and b, will always be positive which means to have the same sign-on MAB and MBA (3a – L) and (3b – L) must have the same sign.