Design Method and Finite Element Analysis of a New Prefabricated Steel Special-shaped Lattice Column

A new steel special-shaped lattice column (SSLC) was proposed, which can be used in prefabricated steel structure residence. The finite element models of four SSLC with different cross-section (L-shaped, T1-shaped, T2-shaped and X-shaped) were established under cyclic loading by using ABAQUS, in which the strength, lateral resist capacity and hysteretic behavior were analyzed. The results indicate that SSLC has adequate strength, stiffness and safety redundancy. Among the four SSLC, the SSLC with Xshaped has the best structural performance and seismic behavior.


Introduction
Special-shaped columns mainly exist in the residential buildings with reinforced concrete frame structure [1]. Scholars at home and abroad have done extensive research on special-shaped columns. Joaquin Marin [2] carried out force-deformation analysis on L-shaped special-shaped columns, and a practical design calculation diagram was provided. Chen Qian and Feng Jianping [3,4] conducted an eccentric compression test of L-shaped column. The calculation formulas for the bearing capacity of L-shaped and T-shaped specialshaped columns were proposed. Huang chengkui [5,6] researched the shear performance of the special-shaped columns. The results show that the flange has a greater horizontal bearing capacity and has a greater impact on the shear bearing capacity of special-shaped columns. Zhang Ailin, Xu Min et al. [7][8][9] studied the seismic performance of X-shaped steel special-shaped columns, in which the hysteretic behavior and ductility performance of the special-shaped column are analysed. The combined limit of flange width-thickness ratio and web height to thickness ratio is proposed.
The special-shaped column has some shortcomings such as low bearing capacity and poor seismic resistance, which makes its use range limited. In this paper, a new prefabricated steel special-shaped lattice column was proposed as a solution, in which the strength, lateral resist capacity and hysteretic behaviour were analysed.
2 Steel special-shaped lattice column (SSLC) structure 2.1. Design of SSLC SSLC ( Fig. 1) is composed of channel steel and square steel tube columns. The channel steel is connected by lace bars. The cross section is shown in Fig. 2. SSLC can be divided into T-shaped SSLC, L-shaped SSLC and Xshaped SSLC according to the shape of the section.

SSLC connection design
The channel steels is connected by lace bars, as shown in Figure 3. In Figure 4, the square steel tube column and the channel steel web are connected by high-strength bolts.

Establishment of finite element model
The SSLC proposed in this paper is an elastic-plastic structure. The bilinear Kinematic ( Figure 5) is selected.

Fig. 5. Material constitutive relation
Q235 steel is used for channel steel and square steel tube column, and Q345 steel is used for lace bars. The mechanical properties of the materials are shown in Table 1. During finite element analysis, the lace bar is bound to the channel steel by the Tie command so that no slip occurs between the contact surfaces. The loading methods include monotonic loading and cyclic loading, which are controlled by displacement.

Analysis of lateral resistance of SSLC
L-shaped SSLC, T-shaped SSLC and X-shaped SSLC models were established by finite element software ABAQUS. Due to the different force directions of Tshaped model, the T-shaped SSLC is defined as T-SSLC-1 when the force is applied along the symmetric axis and the T-shaped SSLC when the force is applied along the asymmetric axis is defined as T-SSLC-2. Four SSLC models were loaded in a monotone horizontal manner. The load-displacement curve of the SSLC model is shown in Figure 6.  It can be seen from the above chart that the loaddisplacement curves of the four models have obvious rising and strengthening section. In the two models of Tshaped SSLC, T-SSLC-1 has greater lateral stiffness than T-SSLC-2. The yield displacement and ductility coefficient of T-SLC-1 and T-SLC-2 are similar. The ultimate bearing capacity of X-shaped SSLC model is the highest. The X-shaped SSLC model has the highest ultimate bearing capacity, better plastic deformation capacity and more obvious energy dissipation capacity.

Hysteresis performance
The displacement control method was used to load the model, and the loading system was shown in Figure 7. In order to study the hysteretic behavior of SSLC, four groups of models were cyclically loaded to obtain hysteretic curves (Figure 8). The skeleton curves (Fig. 9) were obtained by selecting the positive and negative peak values.  Fig. 8. Comparison of hysteretic curves Analysis of hysteretic curve: the hysteretic curves of each SSLC were relatively full. The initial stiffness of Xshaped SSLC is the largest, and the forward bearing capacity reaches 1372KN, the reverse ultimate bearing capacity is 1446KN. In the elastic stage and the plastic development stage, the stiffness decreases uniformly.

Fig. 9. Comparison of skeleton curves
The analysis of skeleton curve shows that the forward ultimate bearing capacity of L-shaped SSLC is 773KN, and the reverse ultimate bearing capacity is 812KN, which is 43.65% and 43.84% lower than Xshaped SSLC. T-SSLC-1 and T-SSLC-2 decreased by 6% and 7.2% respectively compared with X-shaped SSLC. SSLC has high stability in positive and negative directions and is suitable for use as fabricated frame columns.

Conclusion
The finite element models of four SSLC were established under the horizontal and cyclic loading by using ABAQUS, in which the lateral resist capacity and hysteretic behavior were analyzed. The following conclusions were drawn: (1)SSLC has adequate strength, stiffness, ductility, and safety redundancy. It is suitable to be used as frame seismic column.
(2)When the SSLC reaches the yield ultimate bearing capacity, there is an obvious plastic strengthening stage, which is beneficial to structural energy dissipation.
(3)Among the four types of SSLC, the SSLC with Xshaped has the best structural performance and seismic behavior. The stress direction of T-shaped SSLC has E3S Web of Conferences , 03012 (2020) ISCEG 2020 https://doi.org/10.1051/e3sconf/202019803012 little effect on the plastic deformation, but has a great influence on the bearing capacity.