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 )