Fixed end moment (FEM) is important to determine the reaction forces in statically indeterminate beam, such as propped cantilever and fixed end beam. In this video, we look into the derivation of FEM for fixed end moment using force method.
Since the beam is having three degree of indeterminacy, we may make three reaction forces redundant. However, horizontal reaction can be neglected as it does not pose any effect on the beam deflection.
Two compatibility equations are formed, to solve for vertical reaction and moment separately. Both of them focus on vertical deflection and beam rotation respectively. After solving for deflection and rotation for each case, the unknown reaction forces are determined by using simultaneous equations we made out of the compatibility equations.
The following introduces the derivation of fixed end moment formula using force method. Watch the video above for full details.
Beam overview
Analysis cases for force method
Solution for primary structure with original loading
Solution for primary structure with redundant By
Solution for primary structure with MB
Solution for redundant By and MB
Final result
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