Static approach for analysis 'Force method'

If the static degree of indeterminacy (Ds) of the structure is less than the kinematic degree of indeterminacy (Dk) of the structure, the application of static approach will give much faster results than kinematic approach. The statically determinate structures (when Ds = 0) the process become much much easier as just by the application of equilibrium equations of forces and moments in the orthogonal coordinates will give the value of support reactions. Then these support reactions will be used to evaluate the variations of internal forces and moments within the structural body and that will be use to estimate the values of stresses and strains.

    The force method was originally developed by James Clerk Maxwell in 1864 and later refined by Otto Mohr and Heinrich Müller-Breslau.*

    The equation can be written in two forms. First for relating displacements with forces and second for relating rotations with moments.

∆ = f  * F

Ө = f  * M

where; 

∆ is displacement;

Ө is displacement;

 f is flexibility coefficient;

 F is force and;

M is moment. 
   To counteract the static degree of indeterminacy of the structure the addition equations are generated by substituting the values for displacements and rotations by splitting the structure in a determinate structure and same structure with the redundant reactions and then superimposing the results, in this way redundant support reactions workout. In next step the remaining support reactions are evaluated by using equilibrium equations of forces and moments. 

*page number 385, sixth edition, R. C. Hibbeler, Structural Analysis, Pearson publication.