Structural Analysis
The three moments equation is applicable only when

The beam is prismatic
There is no discontinuity such as hinges within the span
There is no settlement of supports
The spans are equal

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Structural Analysis
To generate the j th column of the flexibility matrix

a unit displacement is applied at co-ordinate j and the forces are calculated at all coordinates
a unit force is applied at coordinate j and the forces are calculated at all coordinates
a unit displacement is applied at co-ordinate j and the displacements are calculated at all co-ordinates
a unit force is applied at coordinate j and the displacements are calculated at all coordinates

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