Modeling of inelastic shear in beam or beam-column elements with SINA hysteresis

My name is Juan Jimenez. I am a doctoral student of Earthquake Engineering, at the Polytechnic University of Catalonia. I am interested in the seismic vulnerability of bearing wall buildings of brick masonry. I'm trying to calibrate a 2D model of equivalent frame. To this end, I am using the cyclic pushover of Ruaumoko for simulating the curve of global hysteresis of a quasi-static cyclic test on a full scale prototype (Pavia, 1995). I am using one-component beams for piers and spandrels in my model (although in the future I will test with elements beam-column). I consider flexural plastic hinges at the ends, and inelastic shear deformation. To this respect, Ruaumoko only allows modeling the inelastic shear with SINA hysteresis. And here is where I have problems.

The shear hysteresis of the beam elements of my model (piers and spandrels) must be degrading in strength. In principle, in Ruaumoko is possible to incorporate strength degradation by means of SINA hysteresis, but when I do it, the analysis becomes so unstable that I have not even come to see the degradation in the elements.

Apparently, it's simple. If you are not interested in modeling the flexion-shear interaction (ie, not coupling flexion and shear), the key parameters of degradation are duct1, duct2 and Vres (duct1: shear ductility where the degradation starts, duct2: shear ductility where degradation stops and Vres: residual shear as a proportion of Vy). I have varied these three parameters, and I played with TIME, lengths of plastic hinges, the parameters MAXIT, FTEST, but in all cases, the displacement history imposed in the monitoring point have not reproduced, but rather what I see every time is that eventually the displacements in the monitoring point increase or decrease indefinitely.

Then, If anyone has successfully used Sina hysteresis with strength degradation to modeling inelastic shear in beams or beam-columns elements, likely you encountered these problems. In this case, It would be very helpful your recommendations, suggestions, some guidelines about input parameters, articles or relevant information about it. My email address is jcjimenezp72@gmail.com.

Thank you very much in advance

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We have used this model successfully for the past 12 years. If the system becomes unstable then at some point you must form a mechanism in the structure. What is the post-yield stiffness? You may not strictly have a singularity but do not forget that we are doing approximate finite-precision numerical analysis and as long as the matrix is nearly singular you may have problems. The problem will the stiffness of the softest member that is close to a stiff member. It is for this reason that the rigid links are available in Ruaumoko, we do not need to have people putting in very stiff members to represent a near rigid member with the risks of numerically destroying the analysis.

Thank you, professor Carr. First of all, I must say that I am using Ruaumoko-2D, with manuals dated May 2007.

I want to simulate the cyclic behavior of unreinforced masonry walls. This hysteresis degrades in strength just after reaching Vmax, and degrades up to 75-80% of Vmax, without pinching effect. The ultimate deformation of shear is reached with ductilities between 6 and 12. So I have used with SINA hysteresis duct1 = 1, duct2 = 6 to 12, and Vres = 0.80 (0.80Vmax). Then, consign the properties of one of the masonry piers. The last line corresponds to Sina hysteresis parameters for the beam element. Note the last three values: duct1 = 1.0, duct2 = 8.0, Vres = 0.8

2 FRAME "PILAR CENTRAL-PLANTA BAJA"
1 0 0 16 0 0 0 1 0
1900000 570000 0.455 0.379 0.1256
0.0 0.0 0.25 0.25
0.0 0.0 133.6 -133.6 133.6 -133.6
69.5 48.70 48.00 0.30 0.02 1.0 8.0 0.8

The system (perforated wall with openings for doors and windows), with these parameters of degradation behaves unstable. However, when I remove degradation, cyclic pushover analysis works well for the entire displacement history. In this case, I see that the trilinear factor, R , works as value of post-yielding stiffness of the primary curve, and this value can not be negative or zero (in fact, can only be greater than 0.01: hardening). Complete loops of hysteresis reach the trilinear branches of the primary curve. All this is compatible with Satyarno thesis (2000), where SINA hysteresis is used and strength degradation is defined by a trilinear branch of negative slope. I don´t understand how Ruaumoko incorporates this (Satyarno´s thesis) in the modeling of inelastic shear in beam and beam-column elements.

Should I assume, professor, that in Ruaumoko post-yielding stiffness only can be greater than 0.01 and that the degradation can only be achieved with the three parameters duct1, duct2 and Vres?

Another question: I wonder if the special algorithm is implemented (a phantom step increment method) by Satyarno in the automatic termination of pushover curve in the descending branch of the pushover curve. Existing buildings of unreinforced masonry are degrading systems, so it's important to have that possibility.

Finally, I want to know if there is an updated version of Ruaumoko, and what new capabilities it brings. With my thesis´ director and codirectors are very interested in working with Ruaumoko.

Thank you very much, professor.