## 8 Recent Advances in the Design of IPB Braced Frame
### Discussion of Modes of Buckling  
Braces in IPB systems are expected to buckle in-plane when the compressive force demand exceeds their buckling capacity. This is ensured by introducing knife plates in the end connections. However, past studies (e.g., [10; 31]) have shown that IPB braces may undergo out-of-plane buckling (Figure 2a). Traditionally, the detailing of end connections of OOPB braced systems involves the provision of linear or elliptical clearance in the gusset plates. This facilitates the out-of-plane buckling of braces with low stress demand on the interface connection. However, there is no clarity on how a brace performs when the end clearance is not provided in the gusset plate. It is shown in Figure 4a that despite no or low clearance, out-of-plane buckling of braces has been observed in the IPB braced system due to bending and subsequent yielding of gusset plates [31] (Figure 4b). The undesired out-of-plane brace buckling would impose additional flexural demand on the interface weld of the gusset plates. Since these welds are often not designed to take into account this additional demand, this may lead to their failure prior to the in-plane buckling of the brace. Out-of-plane buckling was found to be one of the major problems that prevent the use of the IPB connection. The gusset and knife plate's inherent orientation facilitates two different buckling modes. These modes are observed to be closely spaced modes and highly sensitive to geometry and mass/stiffness distribution present along the length of the member. The OOPB mode is formed when the plastic hinges are formed in the gusset plates and in the middle of the brace. In contrast, the IPB mode is formed when the plastic hinges are formed in the knife plates and the middle of the brace. It can also be interpreted that the minor-axis bending of the gusset plate and knife plate facilitate OOPB and IPB modes, respectively. The illustration of the plane of buckling and the orientation of the plate to facilitate the modes is shown in Figure 5. Based on the deformed configuration, associated hinge zones are formed in the respective plates. In both cases, the hinge at the brace member is formed at the center. In general, it can be concluded that the modes of buckling primarily depend on the effective buckling length and characteristics of the end connections. Here, the tendency of the brace member to buckle is unbiased for both directions (sections including Hollow Square Section (HSS) and Hollow Circular Section (HCS)). Figure 5: Illustration of plane of buckling and detailing of end connection including hinge zone. (\(\mathrm{t_{kp}}\)—thickness of knife plate, \(\mathrm{t_{gp}}\)—thickness of gusset plate, \(\mathrm{n}\)—any rational number). The clearance of the gusset plate is denoted based on the design philosophy considered while detailing the end connection. To ensure uniform nomenclature for the gusset plate, the area on the gusset plate is broadly classified into three regions: no clearance zone (NCZ), elliptical clearance zone (ECZ), and linear clearance zone (LCZ), as shown in Figure 6. Based on the insertion of the knife plate, the clearance zone and its associated value in terms of thickness can be expressed. The clearance in each zone is quantified based on the associated partition line. For the ECZ and NCZ, the clearance is measured along the centreline of the brace member toward the center of the brace. For the NCZ, it is measured along the centreline of the brace and away from the center of the brace. The nomenclature is used to quantify the extent of the insertion and clearance of the gusset plate. In structural design, stability calculations are critical because of the uncertain behavior of its components that arises from the fabrication and manufacturing process. Figure 7 shows the list of uncertainties that may be involved in predicting the direction of buckling. These uncertainties can be broadly divided into two types, i.e., local-level uncertainties and global-level uncertainties.