# Simplified Deflection Model

In the simplified deflection model, the same assumptions adopted for the strength model were made, except that the sheathing panels were not considered to be rigid. In contrast, the sheathing panels were defined as isotropic and deformable in terms of material properties; hence, the shear strain was assumed to be uniform over a whole panel. The purpose of the deflection model was to predict the deflection of the wall, Anety, corresponding to the yield strength, Sy (or yield load capacity Sywan). The total displacement of the steel frame can be determined by considering the rotation of the frame and the bottom slippage on the support (Eq. 2).

 1 1 F + ~GLt+ ^baseslip1 ^ ^baseslip2 + ід A W H N N I x? I yi V i=1 i=1 J .1 2 J uplift1 ^uplift 2)*- L
 1 2 A walltop ~~T FH *

 (Eq. 2)

Where k is the stiffness of the individual sheathing connector (Tables 2&4), F is the applied shear force obtained from Eq. 1, H and L are the dimensions of the wall, G is the shear modulus of the wood sheathing, t is the thickness of the wood sheathing, A represents the base slip and uplift displacements, x and y are the position of the fasteners and N is the number of sheathing connections..

The final two components in Eq. 2 can be affected by many factors, such as the type of frame-to – support connections/anchorage, the shear modulus of these connections, the friction between a wall and its support, extension and slippage of the hold-down connections and the deformation of the steel frame. Although these factors have an impact on the behaviour of a tested wall, their inclusion would overly complicate the model, and hence they were not considered. Therefore, the deflection model used herein to predict the net lateral deflection was as shown in Eq. 3; which is similar to that presented by Kallsner & Lam (1995) for predicting the deflection of wood framed shear walls.

Comparison of Predicted and Tested Shear Wall Deflection

Comparisons between the deflections measured during testing and the predictions made with Eq. 3 were performed to verify the accuracy of the model introduced above. Meanwhile, in order to verify that Kallsner’s & Lam’s elastic model is more appropriate for the prediction of shear wall deflection than other models, Easley’s model and McCutcheon’s model were included in the comparison. The results of the Kallsner & Lam model are presented in Table 6; the remaining test-to-predicted deflection ratios were tabulated by Chen (2004). The same connection property cases, as described in the comparison of strength models, were incorporated in the deflection models. However, additional combinations were necessary because the deflected position of the wall depends on the estimated force, which was determined with Eq. 1 and the different connection strength values (Tables 2&4). Each combination of the listed deflection models and loading cases included all 16 wall configurations; a total of 103 individual shear wall test specimens. Only the combined ratio of the full-scale test-to-predicted deflection in each combination is listed in Table 6. More detailed information is provided by Chen (2004).

For the most part, the prediction of lateral deflections was not as accurate as that of the lateral shear wall resistance. This can likely be attributed to the strong nonlinear behaviour of the sheathing-to-frame connections, as well as the overall nonlinear load vs. resistance performance of the shear walls (Fig. 2). The predictions based on the initial stiffness, ke, of a connection tend to underestimate the lateral deflection under monotonic loading. In contrast, the predictions that incorporate the stiffness based on the ultimate load, ks, can significantly overestimate the wall deflection. Kallsner’s & Lam’s elastic model can provide a reasonable estimate of the shear wall deflection if the EEEP 25 load level and initial stiffness, ke, connection properties are used. It should be noted, however, that the base slip and uplift of the wall have been ignored in the calculation of deflection. A variation in the type of holddowns and anchor bolts used for the full-scale shear wall tests could result in a change to the actual deflection of a wall.

Table 6. Full-scale shear wall test-to-predicted shear deflection (Chen, 2004).

 Monotonic Loading Cases Kallsner & Lam Elastic Model Ratio SD COV EEEP 12.5 & ke 2.236 0.380 0.170 EEEP 25 & ke 1.441 0.303 0.210 Max. Load 12.5 & ke 1.923 0.339 0.176 Max. Load 12.5 & ks 0.431 0.075 0.174 Max. Load 25 & ke 1.263 0.301 0.238 Max. Load 25 & ks 0.307 0.096 0.313 Kallsner & Lam Cyclic Loading Cases Elastic Model Ratio SD COV EEEP 25 & ke 0.886 0.124 0.139 Max. Load 25 & ke 0.775 0.133 0.171 Max. Load 25 & ks 0.293 0.092 0.313