Force method of analysis | Structural Analysis

The force method (also called the flexibility method or method of consistent deformation ) is used to calculate reactions and internal forces in statically indeterminate structures due to loads and imposed deformations.

We have two methods of analysing structures, one is the force method (Flexibility method) and the rest one is the displacement method (displacement method). In the force method the unknowns are forces, moments and in case of displacement method, unknowns are deflection, rotation. So in the force method we find the Degree of indeterminacy (DS) and in the displacement method we find out the degree of freedom (DK) value.


In both the methods, we write down the force displacement equation. The force method is used when the DS<DK, if not we use the displacement method.


Force method includes unit load method, Castigliano’s method, Strain energy method and flexibility matrix method, etc.


Procedure of force method of analysis


The general procedure of force method is discussed using the examples.

Then we choose a redundant force and remove it. Here taking the vertical reaction at the prop (B point) as the redundant force, remove it. Use the compatibility equation after, which says the net deflection at B is zero.


Here we will use the principle of superposition. 1st we have removed the redundant and find the deflection at point B (𝛅B), due to load P. In the next step, we will find out the deflection due to the reaction RB.


Once we obtain the reaction/redundant force, we can simply use the equilibrium equations to get the rest of the unknowns. We use the term called flexibility in the analysis. Flexibility(fBB) is the deflection caused by unit load.


The deflection caused by reaction RB is



Flexibility will have a unit of m/kN.


Summarizing the steps of the force method of analysis


  1. Convert the indeterminate structure to a determinate one by removing some unknown forces / support reactions and replacing them with (assumed) known / unit forces.

  2. Using superposition, calculate the force that would be required to achieve compatibility with the original structure.

  3. Unknowns to be solved for usually redundant forces.

  4. Coefficients of the unknowns in equations to be solved are "flexibility" coefficients.

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