renanrr3
Structural
- Aug 18, 2020
- 1
Dear colleagues,
I have been working with SAP2000 API for Python in the context of Dynamic Analysis and I need to get the stiffness and mass matrix from the TKX and TKM files generated by SAP2000.
In order to check if I correctly understood the way these matrices are constructed, I am running a modal analysis on a 1-span simply supported beam, getting the mode shapes, stiffness and mass matrices, and trying to compute the modal stiffness (Ki) and modal mass (Mi), and then the squared eigenvalues (Ki/Mi), and checking against SAP2000 outputs. The model I use is composed of just 3 frame elements, and the UY, RX, and RZ global DOFs are deactivated in order to produce a simply 2D beam behaviour. The local axis of each joint are aligned to the global axis, so to avoid the need for any transformation.
My problem is: After my computations, only the modal stiffnesses and masses, and eigenvalues, of some modes are equal to those informed by SAP2000 analysis outputs, obtained under the "Show Table" option. More specifically, I am just able to get these values correctly for modes related to axial deformation on the simply supported beam. Modes related to bending provide very wrong values.
I have searched around about documentation regarding the construction of such matrices, how they relate to Joints' local DOFs and displacement outputs, but I am stuck. Does anyone know something that may be leading to this odd behaviour?
Further information to help tackling the problem:
[ul]
[li]As far as I understand, since all Joints' local axis in my model are aligned to the global axis, such problem may not seem to be related to any incompatibility between mode shape displacement direction and stiffness and mass matrices DOFs entries.[/li]
[li]I have already built the mode shapes with displacements accordingly to mass and stiffness matrices entries, i.e. I consulted the TXE file to know what is the DOF that each row/column on those matrices refer to, and then built the mode shapes vectors accordingly to these organization.[/li]
[li]I am computing modal stiffness and modal mass by multiplying each matrix, on each side, by the appropriate mode shape of a given mode. Is that correct in this case?[/li]
[li]The modal stiffnesses and eigenvalues I get for the bending modes (the first and second modes in the structure I am working with) are way higher than they should be.[/li]
[li]The structure, by being a simply supported beam discretized in three frames, has only 5 possible modes, since its mass matrix has only 5 non-zero elements in the diagonal. The first two modes are beam bending, and the last three modes (third, fourth, and fifth) are axial modes. Therefore, for the third mode onwards, the modal stiffness, mass and eigenvalues seems to be correct. Only the first and second modes provide odd results.[/li]
[li]I am running a Eigenvector analysis and retrieving the stiffness and mass matrix from the MODAL case.[/li]
[/ul]
Thanks in advance for your help.
I have been working with SAP2000 API for Python in the context of Dynamic Analysis and I need to get the stiffness and mass matrix from the TKX and TKM files generated by SAP2000.
In order to check if I correctly understood the way these matrices are constructed, I am running a modal analysis on a 1-span simply supported beam, getting the mode shapes, stiffness and mass matrices, and trying to compute the modal stiffness (Ki) and modal mass (Mi), and then the squared eigenvalues (Ki/Mi), and checking against SAP2000 outputs. The model I use is composed of just 3 frame elements, and the UY, RX, and RZ global DOFs are deactivated in order to produce a simply 2D beam behaviour. The local axis of each joint are aligned to the global axis, so to avoid the need for any transformation.
My problem is: After my computations, only the modal stiffnesses and masses, and eigenvalues, of some modes are equal to those informed by SAP2000 analysis outputs, obtained under the "Show Table" option. More specifically, I am just able to get these values correctly for modes related to axial deformation on the simply supported beam. Modes related to bending provide very wrong values.
I have searched around about documentation regarding the construction of such matrices, how they relate to Joints' local DOFs and displacement outputs, but I am stuck. Does anyone know something that may be leading to this odd behaviour?
Further information to help tackling the problem:
[ul]
[li]As far as I understand, since all Joints' local axis in my model are aligned to the global axis, such problem may not seem to be related to any incompatibility between mode shape displacement direction and stiffness and mass matrices DOFs entries.[/li]
[li]I have already built the mode shapes with displacements accordingly to mass and stiffness matrices entries, i.e. I consulted the TXE file to know what is the DOF that each row/column on those matrices refer to, and then built the mode shapes vectors accordingly to these organization.[/li]
[li]I am computing modal stiffness and modal mass by multiplying each matrix, on each side, by the appropriate mode shape of a given mode. Is that correct in this case?[/li]
[li]The modal stiffnesses and eigenvalues I get for the bending modes (the first and second modes in the structure I am working with) are way higher than they should be.[/li]
[li]The structure, by being a simply supported beam discretized in three frames, has only 5 possible modes, since its mass matrix has only 5 non-zero elements in the diagonal. The first two modes are beam bending, and the last three modes (third, fourth, and fifth) are axial modes. Therefore, for the third mode onwards, the modal stiffness, mass and eigenvalues seems to be correct. Only the first and second modes provide odd results.[/li]
[li]I am running a Eigenvector analysis and retrieving the stiffness and mass matrix from the MODAL case.[/li]
[/ul]
Thanks in advance for your help.
