I am involved in a task where we are to obtain the maximum response of an elasto-plastic SDOF due to a rectangular pulse load. For this, we started by looking at the book: Introduction to Structural Dynamics by John M Biggs, 1964.
In this book they provide tables that gives out the maximum response in terms of Mu (ratio of the maximum and the elastic response of a SDOF subjected to a rectangular pulse load). The maximum response depends only on the ratio between the duration of the pulse (td) and the structure's natural period (T) and the ratio between the the system maximum load capacity (Rm) and the maximum load (F1). See a snip of the table below:
Since we would like to conduct sensitivity analysis, using the table is not very practical for the number of analysis we will conduct. Therefore we solved the problem analytically. However, the maximum response we obtained didn't match the table. So we took a step back and look at an example in the book itself:
Other parameters:
In this case the load has infinite duration. So we look at the table for a large value of td/T. In this case Rm/F1 is 1.5, which for a large value of td/T results in a ductility ratio of 2.0 from the Figure/Graph. However, as shown in the figure with the complete response of the system un the example in the book, the ductility ratio is 0.806/0.543, which is ~1.5. Using different values for td/T and Rm/F1 and solving the complete response analytically results in even bigger differences with the graph results.
I am wondering whether I am using the right parameters on this table or what is the reason for the difference between results?
Thank you for any input.
In this book they provide tables that gives out the maximum response in terms of Mu (ratio of the maximum and the elastic response of a SDOF subjected to a rectangular pulse load). The maximum response depends only on the ratio between the duration of the pulse (td) and the structure's natural period (T) and the ratio between the the system maximum load capacity (Rm) and the maximum load (F1). See a snip of the table below:
Since we would like to conduct sensitivity analysis, using the table is not very practical for the number of analysis we will conduct. Therefore we solved the problem analytically. However, the maximum response we obtained didn't match the table. So we took a step back and look at an example in the book itself:
Other parameters:
In this case the load has infinite duration. So we look at the table for a large value of td/T. In this case Rm/F1 is 1.5, which for a large value of td/T results in a ductility ratio of 2.0 from the Figure/Graph. However, as shown in the figure with the complete response of the system un the example in the book, the ductility ratio is 0.806/0.543, which is ~1.5. Using different values for td/T and Rm/F1 and solving the complete response analytically results in even bigger differences with the graph results.
I am wondering whether I am using the right parameters on this table or what is the reason for the difference between results?
Thank you for any input.
