## 1 Introduction  
Hollow-section members are used in structural and composite members, for instance, concrete-filled steel tubes (CFTs). In the case of CFTs, the steel tube is used as a base pile or a column, because the steel tube can improve the workability and show its proof strength with the structural member. In contrast, a hollow structural section, non-filled concrete, is lightweight and used in various structural members such as columns, beams, and trusses. In particular, a circular hollow section (CHS) is often used because of its aesthetic and geometrical advantages [1]. The application of high-strength materials could secure the greater usability of CHS members, but most of the current standards [2; 3; 4] restrict the use of high-strength steel in hollow-section members. High-strength steels almost have higher yield ratios than the mild steels which were applied in the construction field until now. These standards are limited for the purpose of preventing the brittle fracture of steel members, however, conservatively evaluated parts should be improved. The shape of hollow-section steel joints can be expressed in a wide variety of ways. In particular, the plate-to-CHS X-joint (XP-joint) can be easily assembled through welding, and the plate and H-steelor branch CHS are joined to form various shapes of joints. To determine the strength of the CHS XP-joint, the ring model [5], which was theoretically analyzed by two-dimensionally idealizing the cross-section of the chord and branch joints, was modified [6]. A number of experimental studies were carried out on the CHS XP-joint in the 1960s in Japan [7; 8; 9; 10]. A design equation based on experimental data and finite element analysis was, thus, proposed [11]. The CHS XP-joint strength formula using the modified ring model by considering the branch chord to longitudinal plate joint was proposed [12]. [PERSON] et al. [13] introduced a total of 220 CHS joints generated in Japan. Based on the results of these studies, the joint strength equation was developed by the International Institute of Welding (IIW) and the Comite International pour le Developpement et l'Etude de la Construction Tubulaire (CIDECT) design guide [14]. The design equation of the American Petroleum Institute [15] was determined based on the nonlinear finite element analysis performed by [PERSON] et al. [16; 17]. The IIW sub-commission XV-E on tubular structures critically affected the design equations [2; 4]. For cold-formed CHS, columns with yield strengths of 700, 900, and 1100 MPa were developed and compared with the design strength [18; 19]. The comparison showed the applicability of high-strength steel. [PERSON] et al. [20] studied the design of steel tube X-joints made of S690 grade high-strength steel which has the yield strength of 690 MPa and showed that some reduction factors were necessary to predict the joint strength using high-strength steels. [PERSON] et al. [21; 22] conducted a study into CHS X-joints using the high-strength steel HSA 800, which has a yield strength of 650 MPa, and showed that the reduction factor of 0.8 used in Eurocode 3 may be conservative for high-strength steels. [PERSON] and [PERSON] [23] verified the applicability of Eurocode and CIDECT for high-strength steels of 960 MPa. [PERSON] et al. [24] suggested that the existing design formula could be applied by performing a variable analysis of CHS X-joints using high-strength steel of S700, S900, and S1100 grades. Studies on CHS XP-joints using the high-strength steel HSB 600, which has a yield strength of 460 MPa [25; 26; 27], were conducted, and a formula for high-strength steels was suggested. [PERSON] and [PERSON] [28] also studied the effect of the increased yield stress and reduced ductility up to the steel grade C450. Although experimental and associated analytical studies on high-strength steel joints were conducted, these were insufficient due to the complexity and the diversity of the joint types.