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
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Slope deflection equations
- Joint equilibrium equationsJoints A, B, C should suffice the equilibrium condition. ThereforeRotation anglesThe rotation angles are calculated from simultaneous equations above.
Member end moments
Substitution of these values back into the slope deflection equations yieldsthe member end moments (in kNm):
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