Int the stiffness
method of analysis it is not essential to select the redundant or to
know whether the structure is determinate or indeterminate.
Base unknowns to be determined in the analysis are the displacement components of various joints.
For calculation of displacement and establishment of equation of equilibrium we develop stiffness matrix.
It is necessary to identify the redundants in force method of analysis.
In stiffness method displacements/ roatation (degree
of freedom) are unknown. In the Kani's method of anlysis, actual end
moment in any member is calculated by superposition of fixed end
moment, moment due to rotation of near end and far end and moment due
to displancement and sway of plane fram.
In stiffness method of analysis joint displacements
are unknown which are equal to the kinematic inderminacy of the
structure.
Stiffness matrix are always symmetrical about its main diagonal due to Maxwell's reciprocal theorem.
Stiffness matrix method is modification of slope
deflection method which uses equilibrium equation to determine the
kinematic (displacement) response of structure and then force response.
Flexibility Method of Analysis
In the flexibility method redundant forces are unknowns.
Flexibility matrix is inverse of stiffness matrix and vice-versa.
Flexibility matrix is square matrix and its element
are symmetrical about diagonal due to Maxwell's reciprocal
theorem.therefor flexibility matrix and it's transpose are equal.
To develop flexibility matrix, structure has to be stable and in equilibrium.
Elements of main diagonal of stiffness matrix and
flexibility are always positive because at a point,displacement will
always occur in the direction of force applied at that point.
Flexibility method is used conveniently to analyze inteterminate structures by force method
