Appendix A
The Stiffness Matrix
Stiffness Matrix
The degrees of freedom of the structure are first identified. It is referred to as the
number of independent joint displacements of the structure.
The intersections or interconnections between individual elements of the structure are called joints or nodes. Displacements corresponding to each degree of
freedom, referred to as nodal displacements, are numbered, and positive directions
are assumed.
In order to evaluate the elements of the stiffness matrix, the structure is assumed
to deform corresponding to a unit value of one of the nodal displacements, while all
other displacement is restrained. The forces at all the required points are evaluated.
The process is repeated for a unit value for each nodal displacement. The formation
of the stiffness matrix is explained with the help of an example.
The continuous beam of Fig. A.1 has two degrees of freedom numbered δ 1 and δ 2 .
Referring to Fig. A.1b, joint B is allowed to rotate by unity in the counter clockwise
direction (i.e. positive direction, see Fig. A.2), while joint C is kept fixed. The moment
Fig. A.1 A continuous beam
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Switzerland AG 2021
M. Mukhopadhyay, Structural Dynamics,
https://doi.org/10.1007/978-3-030-69674-0
607
The Stiffness Matrix
Stiffness Matrix
The degrees of freedom of the structure are first identified. It is referred to as the
number of independent joint displacements of the structure.
The intersections or interconnections between individual elements of the structure are called joints or nodes. Displacements corresponding to each degree of
freedom, referred to as nodal displacements, are numbered, and positive directions
are assumed.
In order to evaluate the elements of the stiffness matrix, the structure is assumed
to deform corresponding to a unit value of one of the nodal displacements, while all
other displacement is restrained. The forces at all the required points are evaluated.
The process is repeated for a unit value for each nodal displacement. The formation
of the stiffness matrix is explained with the help of an example.
The continuous beam of Fig. A.1 has two degrees of freedom numbered δ 1 and δ 2 .
Referring to Fig. A.1b, joint B is allowed to rotate by unity in the counter clockwise
direction (i.e. positive direction, see Fig. A.2), while joint C is kept fixed. The moment
Fig. A.1 A continuous beam
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Switzerland AG 2021
M. Mukhopadhyay, Structural Dynamics,
https://doi.org/10.1007/978-3-030-69674-0
607