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The Second-Order Simplified Analysis of the High-rise Steel Structure Double Anti-lateral Force System
**Simplified Analysis of the Order Effect in High-Rise Steel Structures with a Dual Lateral Resistance System**
By Zheng Tingyin, Dong Jun, and Zhu Hui
Department of Civil Engineering, Nanjing Institute of Civil Engineering and Architecture, Nanjing 21000, Jiangsu, China
Nanjing Design Research Institute of China Automobile Corporation, Nanjing 210037, Jiangsu, China
This paper presents a simplified approach for analyzing the order effect in high-rise steel structures that utilize a dual lateral resistance system. A detailed analysis model was established, and the basic differential equations derived from this model closely resemble those from traditional order theory, making them easy to apply. The accuracy of the proposed method is sufficient for engineering design purposes when compared to precise calculation results.
In China, the technical specifications for high-rise steel structures (GB 50011-2010) include various systems such as the steel frame-braced system, steel frame-concrete shear wall system, and the steel moment-resisting frame system. Among these, the core tube system is known as the "Shuangwu" anti-lateral force system due to its unique characteristics. This system is favored for its low cost and fast construction, making it increasingly popular in practical applications. However, due to its large aspect ratio and relatively small member cross-sections, the lateral displacement under vertical loads can be significant. Therefore, order effects must be considered during the structural design process.
Currently, research on the order effect in dual lateral resistance systems remains limited. Existing methods such as the finite shear and finite difference approaches are computationally intensive and often restrict structural rigidity to uniform heights, limiting their applicability. Some studies simplify the model by assuming no variation in stiffness along the height, but they still require iterative calculations for higher accuracy. Another approach, introduced in literature, involves using virtual columns with negative stiffness to represent the order effect, but it only considers extreme cases of shear or bending behavior and neglects axial deformation of columns.
To address these limitations, this paper proposes an improved method that accounts for all key factors, including axial deformation and interaction between different structural components. The method simplifies the analysis process and is particularly suitable for early-stage design calculations. Based on assumptions such as uniform distribution of mass and stiffness, infinite floor plane rigidity, and linear elastic material behavior, the structure is modeled as a combination of shear and bending cantilevers connected by rigid links. Virtual columns with negative stiffness are introduced to simulate the order effect caused by vertical loads.
The equivalent shear and bending stiffness of the system are calculated based on the stiffness matrix equivalence principle. By integrating these elements, the model provides an efficient way to analyze the overall behavior of the dual lateral resistance system. The derived differential equations are solved using standard analytical techniques, allowing for direct computation of displacements and internal forces.
Several examples are presented to validate the method, showing good agreement with existing results. The proposed approach offers a practical and accurate tool for engineers working on high-rise steel structures with complex lateral resistance systems. Future work will focus on incorporating more real-world factors such as varying stiffness and non-uniform load distributions.
References:
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Ye Wenhong, Liang Qizhi. *Simplified Analysis of Frame-Shear Structure Considering Order Effect*. Engineering Mechanics, 1999, 16(12): 634–640.
Kuer, Smith. *High-Rise Building Structure Analysis and Design* (Translated by Chen Yu and Gong Bingnian). Beijing Earthquake Press, 1993.
Liang Qizhi. *Structural Analysis and Design of High-Rise Buildings*. Guangzhou South China University of Technology Press, 1992.
Zheng Tingyin. *High-Rise Building Steel Structure*. Beijing China Building Industry Press, 2000.
Zheng Tingyin. *Equivalent Model of Overall Stability and Order Analysis of High-Rise Steel Frame Support System*. Steel Structure, 2000, Supplement 3.