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Two basic approaches of structural analysis

Short answer

The force/flexibility method takes redundant forces as unknowns and solves compatibility equations; it suits structures with few redundants. The displacement/stiffness method takes joint displacements as unknowns and solves joint equilibrium equations; it suits structures with few kinematic degrees of freedom and is the basis of computer programs. Examples include consistent deformation/three-moment and slope-deflection/moment distribution.

What are the two basic approaches of structural analysis? Explain them briefly.

Structural analysis is carried out by one of two basic approaches, depending on which quantity is taken as the unknown. Both satisfy equilibrium, compatibility and force-displacement relations.

1. Force method (flexibility method)

  • The unknowns are redundant forces (reactions or internal forces).
  • The structure is made statically determinate by removing redundants, and compatibility conditions at the removed points are written in terms of flexibility coefficients.
  • Used mainly for structures with a low degree of static indeterminacy.
  • Examples: consistent deformation, three-moment equation, Castigliano's second theorem.

2. Displacement method (stiffness method)

  • The unknowns are joint displacements (rotations and translations).
  • Equilibrium equations of joints are written in terms of stiffness coefficients and solved for displacements, then member forces are found.
  • Used when the degree of kinematic indeterminacy is small, and it is easy to programme.
  • Examples: slope-deflection method, moment distribution, matrix stiffness method.
PointForce methodDisplacement method
UnknownsRedundant forcesJoint displacements
Conditions writtenCompatibilityEquilibrium
CoefficientsFlexibilityStiffness
Suitable forFew redundantsFew degrees of freedom

✓ Answer checked by Claude Opus 5.5 (high effort)

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