# Macro-Modelling Approach for the In-Plane Cyclic Response of Cold-Formed Steel Partition Walls
## 4 Validation of the Proposed Analytical Model
### Validation of the Proposed Analytical Model  
#### 4.2.1 Force-displacement Hysteretic Curves Assessment  
The analytical models are subjected to the displacement history record that is the same one used for the experiments of the CFS partition wall specimens. Figure 13 comparing the analytical and experimental force-displacement curves shows that the analytical model captures the experimental response such as the overall strength and stiffness degradation and pinching behavior well. The specimens are first loaded in the positive direction, hence the strength capacity of specimens in the negative direction becomes experimentally weaker due to the deteriorations experienced during positive directional loading. Unlike this non-symmetric nature of the experimental results, the suggested analytical model assumes symmetric behavior. Since the construction details, such as gaps between GBs and slabs and studs and runners are hard to exactly relate to those prescribed on the specification, a small variation in force-displacement curves is also inevitably observed. For direction comparison of cycle-by-cycle hysteresis, Figure 14 compares several hysteresis loops of analytical and experimental results of the ST600 and ST450 specimens. The figure confirms that the analysis is in good agreement with the test results.  
Figure 14: Cycle-by-cycle comparison between analytical and experimental hysteresis loops: (**a**) ST600; (**b**) ST450.  
Figure 13: Force–displacement relations of the analytical model and experimental results: (**a**) ST600; (**b**) ST450.  
In order to evaluate the variability during the entire loading cycles, a more rigorous error assessment was conducted. Two error indicators are adopted, namely errors in maximum force and in cumulative energy dissipation. Using the maximum force envelop of experiment and analysis as shown in Figure 15, it is observed that the analytical model estimates that the maximum force values show a good agreement for the first two steps of the hysteresis loop. Before contact between GBs and the concrete slab occurs, the estimated maximum forces of the analytical model do not differ more than 10% compared to those of the experimental results. After the eight loading step in which corner crushing of GBs is experimentally initiated, the analytical model estimates the maximum force values in the positive direction of the hysteresis loop with an average error of 11% and more precise estimation is recorded in the negative direction. In particular, due to the contact between studs and tracks, enhanced maximum forces of the ST600 specimen are accurately estimated by the analytical model with an error of 2%.  
Figure 16 shows the analytical and experimental cumulative energy dissipated by the specimens. The cumulative energy dissipation obtained from analytical model is slightly underestimated compared to the corresponding experimental results. Since the specimens remain elastic during several initial loading cycles, the model cannot simulate dissipation of energy. However, a small amount of energy dissipation is observed in the experimental results since the friction mechanism could be developed at the test frame. At those displacement ranges, the difference between analytical and experimental results is negligible. The underestimation of the analytical model becomes increased during the last cycles after the maximum force of the screw connections has been reached. This mainly results from the difference of the hysteresis loop in which pinching effects of the screw connection are observed as shown in Figure 14.  
Figure 16: Comparison of analytical and experimental cumulative energy dissipation: (**a**) ST600; (**b**) ST450.  
Figure 15: Comparison of analytical and experimental backbone curves: (**a**) ST600; (**b**) ST450.