What is three moment theorem?,Three moment theorem,claparons theorem 2021

 What is three moment theorem?

     Three moment theorem express the relationship between the moment at three successive supports. The supports "moments" can be determined by the Three moment equation. It is mostly suitable for continuous beam. 

According to this theorem the supports moments Ma, Mb, Mc are evaluated by using the equation.

       

Civil engineering study nots
Three moment theorem equation

               


Where:-


a1 = area of free Bending moment diagram of span AB


a1 = area of free Bending moment diagram of span BC


X1 = distance of centroid of Bending moment diagram (AB) from side A (left)


X1 = distance of centroid of Bending moment diagram (BC) from side C (right)


For example:-


Numericals page 1

Numericals page 2

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Numericals page 5


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