Statically Determinate and indeterminate Beams

Structure is generally classified into two categories as Determinate and Indeterminate Structures or Redundant Structures for analysis of structures to find forces based on criteria discussed below. Structure is an assemblage of a number of components like slabs, beams, columns, walls, foundations and so on, which remains in equilibrium. It has to satisfy the fundamental criteria of strength, stiffness, economy, durability and compatibility, for its existence. Any structure is designed for the stress resultants of bending moment, shear force, deflection, torsional stresses, and axial stresses. If these moments, shears and stresses are evaluated at various critical sections, then based on these, the proportioning can be done. Evaluation of these stresses, moments and forces and plotting them for that structural component is known as analysis. Determination of dimensions for these components of these stresses and proportioning is known as design.

Determinate structures are analysed just by the use of basic equilibrium equations. By this analysis, the unknown reactions are found for the further determination of stresses. Redundant or indeterminate structures are not capable of being analysed by mere use of basic equilibrium equations. Along with the basic equilibrium equations, some extra conditions are required to be used like compatibility conditions of deformations etc to get the unknown reactions for drawing bending moment and shear force diagrams. Example of determinate structures are: simply supported beams, cantilever beams, single and double overhanging beams, three hinged arches, etc. Examples of indeterminate structures are: fixed beams, continuous beams, fixed arches, two hinged arches, portals, multistoried frames, etc. Special methods like strain energy method, slope deflection method, moment distribution method, column analogy method, virtual work method, matrix methods, etc are used for the analysis of redundant structures.
 
Indeterminate Structures: A structure is termed as statically indeterminate, if it can not be analysed from principles of statics alone, i.e. clip_image001. A statically indeterminate structure may be classified as:
Externally indeterminate, (example: continuous beams and frames)
Internally indeterminate, (example: trusses )
Both externally and internally indeterminate, (example: trussed beams, continuous trusses )