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Matrix Method of Analysis

Stiffness Method of Analysis

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