Tangent stiffness in elastic frame element
Tangent stiffness in elastic frame element
I was running some dynamic time history analyses for bridge column considering elastic frame elements with nonlinear link at bottom. I tried both the tangent and initial stiffness proportional damping options while using Raleigh damping. But unexpectedly both the results provide 100% similar outcome. I am confused about whether the results are correct for tangent or initial damping and why are they similar?
Re: Tangent stiffness in elastic frame element
He newaj88.
It sounds like the hysteretic behavior of the nonlinear link at the base of the structure is dominating the response. Does the link get loaded well beyond yield for your analyses? If so, it could be that the energy dissipation from the link is much, much larger than the energy dissipation from the Rayleigh damping.
It is not uncommon for a link to effectively add 30% or more of critical damping to a system. If your Rayleigh damping percentages are small, then they may be relatively insignificant when compared to the energy dissipation of the link.
For example, suppose the effective Rayleigh damping at the response frequency was 2% of critical based on the initial stiffness model and 1% based on the tangent stiffness based model. Suppose further that the hysteretic link behavior imparted, effectively, 30%. Then the total system damping is 32% for one model and 31% for the other, hardly any difference.
Are your Rayleigh percentages in fact producing small damping at the frequencies of interest in the structure? You could run an eigenvalue analysis or do some hand calculations - it sounds like your structure is simple enough to do so - and compute the Rayleigh damping contribution at the natural frequency with the link un-yielded and with the link yielded.
Is the link, in fact, loaded well beyond yield? If so you could estimate the equivalent effective damping contributed by hysteretic behavior of the link.
Note that the energy dissipation from hysteretic behavior of the link is implicit in SeismoStruct, but there is plenty of literature available giving expressions for the effective damping of nonlinear links.
You could assign an artificially high yield level force to the link such that it never yields during the ground shaking. Then the entire system damping would be due to the Rayleigh component and there would be an appreciable difference in response for the two cases, I suspect.
Another thought is that local, element-level damping will override the global settings. I doubt if you have done it, but you may have changed the damping settings on the element level when you defined the element classes.
These are just thoughts, newaj88. Best of luck.
It sounds like the hysteretic behavior of the nonlinear link at the base of the structure is dominating the response. Does the link get loaded well beyond yield for your analyses? If so, it could be that the energy dissipation from the link is much, much larger than the energy dissipation from the Rayleigh damping.
It is not uncommon for a link to effectively add 30% or more of critical damping to a system. If your Rayleigh damping percentages are small, then they may be relatively insignificant when compared to the energy dissipation of the link.
For example, suppose the effective Rayleigh damping at the response frequency was 2% of critical based on the initial stiffness model and 1% based on the tangent stiffness based model. Suppose further that the hysteretic link behavior imparted, effectively, 30%. Then the total system damping is 32% for one model and 31% for the other, hardly any difference.
Are your Rayleigh percentages in fact producing small damping at the frequencies of interest in the structure? You could run an eigenvalue analysis or do some hand calculations - it sounds like your structure is simple enough to do so - and compute the Rayleigh damping contribution at the natural frequency with the link un-yielded and with the link yielded.
Is the link, in fact, loaded well beyond yield? If so you could estimate the equivalent effective damping contributed by hysteretic behavior of the link.
Note that the energy dissipation from hysteretic behavior of the link is implicit in SeismoStruct, but there is plenty of literature available giving expressions for the effective damping of nonlinear links.
You could assign an artificially high yield level force to the link such that it never yields during the ground shaking. Then the entire system damping would be due to the Rayleigh component and there would be an appreciable difference in response for the two cases, I suspect.
Another thought is that local, element-level damping will override the global settings. I doubt if you have done it, but you may have changed the damping settings on the element level when you defined the element classes.
These are just thoughts, newaj88. Best of luck.
Tim Huff
Re: Tangent stiffness in elastic frame element
Hi Huffte,
Thank you for your time. It was helpful. I have not defined any element level damping. I should try changing the link element yield level to monitor the Rayleigh damping effect.
Thank you.
Thank you for your time. It was helpful. I have not defined any element level damping. I should try changing the link element yield level to monitor the Rayleigh damping effect.
Thank you.