## tangent-stiffness proportional damping

04-Future developments & requests
mattfox
Posts: 9
Joined: 19 Sep 2012, 13:16

### tangent-stiffness proportional damping

Dear Seismosoft,

In future versions of the programme could you please try to incorporate tangent stiffness proportional damping for constant ductility spectra. It appears at the moment that it is initial stiffness proportional.

Matt.
seismosoft
Posts: 1056
Joined: 06 Jul 2007, 04:55

### Re: tangent-stiffness proportional damping

Hi Matt,

Yes, SeismoSignal does indeed consider initial stiffness proportional damping in its constant ductility response spectrum calculations.

We will keep note of your suggestion for the possibility of using also tangent stiffness proportional damping to be included in future versions of the program.

Thanks for the interest and support,

Seismosoft Support
huffte
Posts: 942
Joined: 22 Jul 2011, 10:19
Location: Cookeville, Tennessee, USA
Contact:

### Re: tangent-stiffness proportional damping

In the meantime, it may be possible to mimic a tangent-stiffness-based solution with the initial-stiffness-based algorithm in SeismoSignal (and most inelastic spectra programs).

The reference below suggests specifying an artificially low viscous damping ratio in an initial-stiffness-based algorithm as an attempt to mimic a tangent-stiffness-based solution to the equations of motion. The reduced damping ratio is:

x* = x[1-0.1(m-1)(1-a)]/sqrt[m/(1+am-a)]

x is the actual damping ratio for the linear range, typically 3-5%
x* is the value to be specified in order to emulate tangent-stiffness-based analysis
m is the displacement diuctility
a is the post-yield stiffness ratio

So, for example, with x = 0.05, m = 6, and a = 0.05, the equation gives:

x* = .05[0.525]/sqrt[4.8] = 0.012

In SeismoSignal, the user may thus specify 1.2% damping instead of the default 5% as an effort to approximate a tangent-stiffness-based solution. Note that this feature is not available in SeismoSpect - when inelastic spectra are generated in SeismoSpect the damping is automatically set to 5% (you may try to change it, but once you specify the ductility values it will revert back to 5%).

Priestley, M. J. N.; Calvi, G. M.; Kowalsky, M. J.,"Displacement-Based Seismic Design of Structures", IUSS Press, Pavia Italy, 2007, pp. 210.

Good stuff.
Tim Huff