Force method for Indeterminate continuous Beam - Matrix Approach

In force method of structural analysis,

  • the first step is to find the Redundancy/indeterminacy of the structure. For example for the given beam in the following example there are total five number of support reactions, therefore the redundancy is 2.
  • Second step is to convert the indeterminate structure into a basic determinate by replacing the the two of the unknown support reactions with redundants.  
  • Third step is to find out the displacements of the basic determinate structure along the redundants due to the given loading conditions. 
  • fourth step is to find out the flexibility matrix by applying the unit loads along the redundants and finding out the corresponding displacements at these two places.
  • Next, form the equations as per the compatibility conditions and form the matrices. 
  • Solve the matrix problem to find out the unknown reaction forces.
Example: Let us consider a continuous beam with a total span of 10m, EI constant, udl acting on the first half and a couple acting at 7.5m from the left. There are hinge and roller support at B and C, while beam is fixed at the left end A. Find out the support reactions at B and C using the force method (matrix approach.)


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