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Statically Indeterminate Beam



  • In this example we'll solve for the reaction forces and moment for the statically indeterminate beam shown below. The superposition method will be used.



  • A system of five equations will be used to solved for the unknown reactions, Ma, Ra, and Rb. These five equations are placed in a System Solve Cell below.


    The equations are:

    1. Sum of vertical forces
    2. Sum of moments about A
    3. Deflection at B due to distributed load q
    4. Deflection at B due to reaction Rb (without q)
    5. The last equation uses the superposition method to set the total deflection at B (due the combined effects of Rb and q) to zero


    The final field of the System Solve Cell, we specify the unkown variables we want to solve for. Even though we don't need the deflection results, we list those variables as well since it necessary to specify five unknowns for the five equations we're solving for:



  • System =
    Solution =
    Solve for:


  • As can be seen above, all of the solutions are in terms of the beam length l and the distributed load q. We can now evaluate reaction force for a specific distributed load q and beam length l: