Question 13.4: Illustrate the influence of different hysteresis models on t...

Let mass = 1, stiffness = 39.5, Period = 1 sec, Damping = 0%, step size = 0.02 sec It is subjected to first 10 sec of the North–South component of El Centro earthquake of May 1940. Two hysteresis models are selected: elasto-plastic model and stiffness degrading model.
The elastic response gives the maximum force applied on the system. Yield force is computed corresponding to a reduction factor R = 4, 8 and 16. The concept of reduction factor R was discussed in Chapters 8 and 12. The inelastic response is shown in Figures 13.25(a) and 13.25(b). The maximum ductility demands are as follows:

For elasto-plastic model
For reduction factor = 4, maximum ductility demand = 2.1;
For reduction factor = 8, maximum ductility demand = 4.70;
For reduction factor = 16, maximum ductility demand = 14.95;

For stiffness degrading model
For reduction factor = 4, maximum ductility demand = 1.98;
For reduction factor = 16, maximum ductility demand = 11.20;

The SDOF system with period = 0.5 sec. is again analysed using the elasto-plastic model.

The maximum ductility demands are as follows:
For reduction factor = 4, maximum ductility demand = 2.92;
For reduction factor = 8, maximum ductility demand = 4.94;
For reduction factor = 16, maximum ductility demand = 12.10;

The effect of reduction factors on a SDOF system having a period = 0.5 sec and = 1.0 sec are shown in Figures 13.26(a) and (b).

The following significant observations are made in these results:
• The elastic response oscillates about the mean position while the inelastic response tends to sway on either side of the mean position once the system becomes inelastic.
• The displacement is maximum in the elastic case while it remains within a range with the increase in reduction factor. The maximum displacements (mm) in SDOF system in different cases are as follows:

• The choice of a hysteresis model has a significant influence on the displacement response of the SDOF system.
• The elastic as well as inelastic response depend on the period of the SDOF system.