Structural Dynamics by Mario Paz & Young Hoon Kim

Author:Mario Paz & Young Hoon Kim
Language: eng
Format: epub
ISBN: 9783319947433
Publisher: Springer International Publishing

12.6 Transformation of Coordinates

The stiffness matrix , Eq. (12.9), as well as the consistent and the lumped mass matrices in Eqs. (12.11) and (12.14), respectively, are in reference to the local system of coordinates. Therefore, it is necessary to transform the reference of these matrices to the global system of coordinates before their assemblage in the corresponding matrices for the structure. As has been indicated, the z axis for the local coordinate system coincides with the Z axis for the global system. Therefore, the only step left to perform is a rotation of the coordinates in the x-y plane. The corresponding matrix for this transformation may be obtained by establishing the relationship between components of the moment at the nodes expressed in these two systems of coordinates. In reference to Fig. 12.3, these relations when written for node ① are

Fig. 12.3Components of the nodal moments in local and global coordinates

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