Every member of a structure will provide three equations of static
equilibrium (ΣF_{x} = 0, ΣF_{y} = 0 and ΣM_{z}
= 0).
(i) If the number of unknown reaction components are equal to the
number of equations of equilibrium, the structure is known as
**statically determinate**.
(ii) If the unknowns are more than the number of equations of
equilibrium the structure is known as **statically
indeterminate**. The difference between unknown reaction
components and the equations of equilibrium is known as degree of
indeterminacy. Therefore the beam shown in the
above figure is statically
indeterminate of degree one as it has 4 reactions and only 3
equations of equilibrium..
(iii) If the unknown reaction
components are less than the number of equilibrium equation, the
structure is known as **unstable**. A structure is also
defined as unstable if all the reaction components are concurrent or
parallel (even if reactions are equal or more than the number of
equations). This is evident from the beam shown in the above figure
that if we change the hinged support at C to a roller support, all
the reactions will be vertical and hence parallel to each other and
this beam will not be able to support any horizontal force.applied
on it.
**Solving Indeterminate Structures**
Most of the structures being used in construction are indeterminate in nature.
Force method of analysis or displacement method of analysis could be used to
solve for indeterminate structures. Some of the common methods to solve for indeterminate structures are; stiffness
method, moment distribution method, flexibility method, Energy theorems,
slope-deflection equations etc.
Please visit the solved
**
Problem 7-1,
Problem 7-2,
Problem 7-4, **to understand better about solving
indeterminate structures
Quiz on Structural Analysis
Quiz on Structural Design
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