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Structure analysis and its basic approaches

Short answer

Structural analysis determines reactions, internal forces, stresses and displacements so structures can be designed safely and economically. Every method satisfies equilibrium, compatibility and force-displacement relations. The force method uses redundant forces and compatibility; the displacement method uses joint displacements and equilibrium. Force method suits few redundants; displacement method suits few degrees of freedom and computer implementation.

What is structure analysis? Explain the basic approaches of structural analysis.

Structural analysis is the process of determining the reactions, internal forces (axial force, shear force, bending moment, torsion), stresses and displacements of a structure under given loads, so that it can be designed safely and economically.

Basic approaches

Every method of analysis must satisfy three conditions: equilibrium, compatibility (continuity of displacements) and the force-displacement (constitutive) relation. Depending on the unknown chosen, two approaches exist.

1. Force (flexibility) method

  • Unknowns: redundant forces.
  • Remove redundants to get a statically determinate (released) structure, then apply compatibility equations.
  • Examples: method of consistent deformation, three-moment theorem.

2. Displacement (stiffness) method

  • Unknowns: joint displacements (rotations and translations).
  • Write joint equilibrium equations using stiffness coefficients.
  • Examples: slope-deflection, moment distribution, matrix stiffness method.

The force method suits structures with few redundants; the displacement method suits structures with few degrees of freedom and is used in computer programs.

✓ Answer checked by Claude Opus 5.5 (high effort)

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