# Study of Effective Length Factor of Frame-Core Wall Structure with Cross-Layer Columns
###### Abstract  
The aim of this study was to examine the effective length factor of frame-core wall structures with cross-layer columns, which are relevant for current high-rise building construction. Using the finite element method, improved inflection point method (D-value method), and GB50017-2017, the study investigated how the height and distribution of cross-layer columns affect the lateral stiffness ratio, natural vibration period, member internal force, maximum interlayer displacement angle, and effective length factor of the column in the frame-core wall structures. However, the force acting in the frame in the weak axis direction that is considered in GB50017-2017 does not reflect the actual mechanical behavior. Therefore, when determining the effective length factor of cross-layer columns, the interaction between the remaining frames' sub-structure and cross-layer columns is considered and the effective length factor is modified accordingly. A simplified model of a 140 m frame-core wall structure was established for analysis, and it was assumed that rigid links connect the frame and core wall hinged at both ends. The results show that increasing the height and number of cross-layer columns decreased the lateral stiffness ratio of the structure, and increased the maximum interlayer displacement angle and natural vibration period. Furthermore, the effective length factor of the structure decreased with an increase in height and the number of cross-layer columns. The modified effective length factor agrees well with the results obtained by the finite element method. These findings provide a useful reference for calculating the load-carrying capacity of cross-layer columns in engineering. frame-core wall structure; cross-layer column; effective length factor; mechanical behavior; FEM analysis +
Footnote †: journal:  
with and without lateral shifts based on the modified formula of AICC 360-16 standard codes. [PERSON] [16; 17] studied the effective length factors of the stepped columns, revealed the interaction mechanism between the allowed side-shift stepped columns, and proposed the formula for calculating the side-shift stiffness and verified its validity. In modern buildings, such as commercial, office, and hotel buildings, the beams and columns of the frame are partially reduced due to the layout needs of the large local space at the bottom of the building, and columns are formed of more than two stories in height, or so-called slender columns. Cross-layer columns can be combined with the frame, frame-shear wall, and frame-core wall structures, which are widely used in engineering. Since the frame-core wall structure is the most common form of high-rise and super high-rise hybrid structure, the frame-core wall structure with cross-layer columns has great research value. For the building with cross-layer columns in the frame-core wall structure, as shown in Figure 1, the structure can be divided into the cross-layer column part and the remaining frames' sub-structure part. There are many studies on the load-bearing performance and stability performance of cross-layer column members [18; 19; 20]. Since the load-carrying capacity of slender columns is affected by the effective length, [PERSON] et al. [21] proposed a new method to calculate the effective length of the column based on the equivalent model and used the finite element for eigenvalue buckling analysis. However, most of the studies have mainly focused on the member level, and fewer studies have been conducted at the structural level. The frame-core wall structure is a double-layer lateral force-resisting system; the core shear wall is usually the main lateral force-resisting structure in engineering, and the frame is used as the second line of defense for structural seismic resistance. For the structural columns in the double lateral force resisting system, due to the support of the shear wall or core, the effective length factor is often between the laterally shifted frame with hinged ends and the non-lateral shifted frame with rigid ends.