Prof.Kodali Srinivas

A beam with both ends fixed is called as Fixed Beam. Fixed beams are statically indeterminate to the 2 nd  degree, and any structural analysis method applicable on  statically indeterminate  beams can be used to calculate the fixed end moments.   The  moment distribution method ,  slope deflection method  and the  matrix method  make use of the fixed end moments. Fixed End Moments in standard loading 

Example : 1 Analyse the statically indeterminate beam shown in the figure Members AB, BC, CD have the same length  . Flexural rigidities are EI, 2EI, EI respectively. Concentrated load of magnitude   acts at a distance   from the support A. Uniform load of intensity   acts on BC. Member CD is loaded at its midspan with a concentrated load of magnitude  . Note: In the following calcuations, clockwise moments and rotations are positive. Fixed end moments Slope deflection equations Joint equilibrium equations Joints A, B, C should suffice the equilibrium condition. Therefore Rotation angles The rotation angles are calculated from simultaneous equations above. Member end moments Substitution of these values back into the slope deflection equations yields  the member end moments (in kNm):