*5.3. Sti*ff*ness Degradation*

Steel beam-to-column connections will experience stiffness degradation when subjected to cyclic loading. It has conclusively been shown that the stiffness will decrease by increasing the inter-storey drift angle in steel beam-to-column connections [48]. Meanwhile, there is reliable evidence that the metal material behaves differently when subjected to monotonic and impact loading [49]. However, far too little attention has been paid to stiffness degradation of steel material under strong impact loading. Since the available data solely consider the monotonic loading for simulating sudden column

removal, in this study, initial stiffness, *Sj.ini*, and secant stiffness, *Sj.e*ff, were taken into account to evaluate the stiffness degradation. Secant or effective stiffness, *Sj.e*ff, is defined as the ratio of bending moment before substantial loss of strength to the maximum rotation ϕ*u*, as shown in Figure 16.

$$S\_{j\omega f f} = \frac{\mathcal{M}\_{\dot{j}}}{\varphi\_u} \tag{13}$$

Table 6 shows the normalized initial and secant stiffness as well as the connected beam stiffness for all studied specimens before substantial strength degradation. The initial and secant stiffness are normalized with respect to the connected beam stiffness. Table 6 clearly indicates that fully rigid specimens, i.e., SidePlate and I-WB, possess much higher stiffness compared to semi-rigid and flexible specimens. It is also evident that although the initial stiffness in flexible connections is negligible, they can maintain the stiffness where the secant stiffness is almost three times higher than the initial stiffness (consider the web cleat and fine plate specimens).

**Table 6.** Stiffness Properties of the Studied Specimens.


The normalized stiffness degradation versus inter-storey drift angle plots for all specimens are shown in Figures 17–19. Figure 17 generally indicates that by increasing inter-storey drift angles, the normalized stiffness decreases, although the SidePlate connection has considerably higher initial stiffness as well as lower degradation slope. This stiffer behavior is attributed to the distribution of the hinge formation mechanism due to the presence of two side plates wrapping around the shear panel joint region, resulting in increased stiffness of the subassembly. Generally, in this category, flexural action controls the stiffness of the specimens in the early stage of the response.

Figure 18 shows that semi-rigid connections have an irregular pattern for stiffness degradation, where elementary step stiffness experiences degradation, whereas at higher inter-storey drift angle, the stiffness remains constant or even increases before the failure of the specimen. This irregular pattern can be explained by desirable features of extremely high ductility (rotational capacity) and developing catenary action.

Figure 19 indicates that although the flexible connections have considerably lower stiffness compared to fully rigid and flexible connections, they can develop the initial stiffness as the inter-storey drift angle increases. On average, the initial stiffness increases up to 100 percent when the inter-storey drift angles reach around 0.1 rad. This behavior can be explained by the connection geometry that allows rotation at preliminary steps, whereas the tensile capacity of connections' components, i.e., web cleat, bolts, etc., along with stiffness hardening at higher drift angles, resists against rotation and subsequently develops the stiffness.

10

14 16 18

SidePlate

I-W

I-WB

**Figure 17.** Stiffness degradation versus inter-storey drift angle for fully rigid connections.

**Figure 18.** Stiffness degradation versus inter-storey drift angle for semi-rigid connections.

0 0.2 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Interstorey Drift Angle (rad) Stiffness degradation is an important aspect of seismic design since a large deformation leads to P-Delta effects, eventually destabilizing the structure. Several codes and regulations prescribe recommendations for stiffness and strength degradation as a measure in seismic design. For instance, the AISC seismic provisions recommend that the connection must sustain an inter-storey drift angle of at least 0.04 rad, while the flexural resistance at the column face must be equal to at least 0.80 *M<sup>p</sup>* of the connected beam. Overall, according to the results of this study, it is recommended that the stiffness at an inter-storey drift angle of 0.05 rad should be larger than 75% of the initial stiffness to develop a reliable catenary mechanism.

**Figure 19.** Stiffness degradation versus inter-storey drift angle for flexible connections.
