Design Research on Hyperbolic Double-Torque Steel Pipe Grid Shell Structure

Literature Overview

This paper, published in the Journal of Architecture and Civil Engineering in 2018, presents a comprehensive structural analysis of a hyperbolic double-torque steel pipe grid shell roof system designed for the Linxia National Grand Theater. Authored by Wang Xiuli, Chen Qingqing, and Wu Xiaoyan from Lanzhou University of Technology and Gansu Construction Investment Steel Structure Co., Ltd., the study employs ANSYS finite element analysis to evaluate seismic nonlinear time-history performance and wind load response of the grid shell structure. The research further investigates the plastic development and buckling behavior of critical nodes by comparing hyperbolic double-torque rectangular steel tube joints with conventional straight rectangular tube joints.

Structural System Description and Design Rationale

The hyperbolic double-torque steel pipe grid shell is a single-layer space structure that combines the geometric complexity of hyperbolic paraboloid surfaces with the structural efficiency of grid shell systems. Unlike conventional spherical or cylindrical grid shells, this geometry provides dual curvature in two orthogonal directions, which enhances structural stiffness and load-carrying capacity while allowing for distinctive architectural expressions. The "double-torque" designation refers to the torsional deformation characteristics inherent in the hyperbolic geometry, where members experience coupled bending and torsion under load.

The Linxia National Grand Theater project required a roof system that could span a large interior volume while accommodating complex architectural forms and strict seismic performance requirements. The selected steel pipe grid shell system utilizes rectangular hollow sections (RHS) as primary members, connected through welded or bolted nodes. The choice of rectangular steel tubes offers advantages in terms of material efficiency, ease of fabrication, and aesthetic integration with modern architectural design.

Typical Structural Parameters

Seismic Nonlinear Time-History Analysis

The seismic analysis conducted in this study represents a rigorous approach to evaluating the dynamic response of the grid shell structure under earthquake loading. The nonlinear time-history analysis accounts for both geometric nonlinearity (large displacements and P-delta effects) and material nonlinearity (plastic deformation of steel members), which is essential for accurately predicting the structural behavior under severe seismic events.

The analysis results identified critical members within the grid shell system that are most susceptible to yielding and potential damage during seismic events. These critical members are typically located at regions of high stress concentration, such as boundary supports, geometric discontinuities, and areas where the curvature changes abruptly. The identification of these critical members provides essential input for detailed design and construction quality control, particularly regarding welding procedures and material selection at these locations.

Seismic Performance Indicators

Wind Load Analysis and Aerodynamic Considerations

The wind load analysis for the hyperbolic double-torque grid shell addresses the complex aerodynamic characteristics of this non-conventional geometry. Unlike simple cylindrical or spherical shells, the hyperbolic geometry creates varying wind pressure distributions across the surface, with regions of both suction and pressure that can be highly localized. The analysis accounts for mean wind pressure, gust effects, and potential vortex shedding phenomena that may induce dynamic responses.

The wind load results demonstrate that the grid shell structure possesses good wind resistance performance, attributable to its inherent structural stiffness derived from the dual curvature geometry. The hyperbolic form provides continuous stiffness variation across the surface, which helps distribute wind-induced forces more uniformly compared to structures with abrupt geometric changes. This is particularly important for large-span cultural facilities where wind-induced vibration could affect occupant comfort and structural integrity.

Node Performance Analysis and Buckling Behavior

A significant contribution of this paper is the comparative analysis of node performance between hyperbolic double-torque RHS joints and conventional straight RHS joints. The study establishes full-scale finite element models of both node types with identical member specifications to isolate the effects of geometric curvature on joint behavior.

Comparative Node Performance

The analysis reveals that the hyperbolic double-torque nodes exhibit different buckling modes compared to straight tube joints. The combined torsional and bending deformation in the curved geometry leads to more complex buckling patterns, including torsional-flexural buckling modes that are not present in straight tube joints. This finding has direct implications for welding procedure specification, as the stress concentrations at these nodes require careful control of welding parameters, preheat, and post-weld heat treatment to prevent weld defects and ensure adequate joint toughness.

From a fabrication standpoint, the hyperbolic geometry introduces additional challenges in member cutting, fitting, and welding. The members must be fabricated with precise curvature profiles, and the joint geometry requires careful fit-up to minimize residual stresses. The welding sequence must be planned to control distortion, particularly given the complex three-dimensional geometry of the nodes.

Engineering Practice Implications

The findings of this study have several practical applications for engineers involved in the design and construction of steel pipe grid shell structures. First, the seismic analysis results provide a basis for identifying critical structural elements that require enhanced quality control during fabrication and erection. Second, the node performance comparison offers guidance for welding procedure development and inspection protocols at curved joints. Third, the structural analysis methodology demonstrates the importance of considering both geometric and material nonlinearities in the design of complex spatial steel structures.

The study also highlights the need for close coordination between structural design and fabrication engineering. The complex geometry of hyperbolic double-torque grid shells requires detailed shop drawings, precise cutting tolerances, and skilled welding operations. The welding quality at these nodes is critical to overall structural performance, and comprehensive non-destructive testing should be specified for all welded connections in critical members.

Construction Quality Control Recommendations

Based on the analysis results, the following quality control measures are recommended for similar projects:

1. Material verification: Confirm that RHS steel tubes meet specified grade requirements (typically Q345 or Q235 per GB/T 6728) with appropriate impact toughness at service temperatures.
2. Cutting precision: Implement CNC cutting with tolerance control to ensure proper member curvature and joint fit-up.
3. Welding procedure qualification: Develop and qualify welding procedures specifically for the curved joint geometry, considering the elevated stress concentrations.
4. Weld inspection: Apply ultrasonic testing (UT) or magnetic particle testing (MT) to all critical welds, with acceptance criteria per GB/T 11345 or equivalent.
5. Distortion control: Implement pre-bending or post-straightening procedures to maintain geometric accuracy within specified tolerances.
6. Erection sequence: Plan the erection sequence to minimize temporary loading and ensure progressive structural stability during construction.

Study Insights and Conclusions

This paper demonstrates the successful application of advanced finite element analysis to the structural design of complex steel pipe grid shell systems. The integration of seismic nonlinear time-history analysis, wind load assessment, and detailed node performance comparison provides a comprehensive engineering approach that ensures both structural safety and architectural expression.

The comparative analysis of curved versus straight RHS joints offers particularly valuable insights for fabrication and welding engineers. The findings indicate that while the hyperbolic geometry provides enhanced structural performance, it also introduces additional complexity in terms of buckling behavior and fabrication requirements. This necessitates a holistic engineering approach that integrates structural design, material selection, fabrication planning, and quality assurance from the earliest stages of project development.

The study contributes to the growing body of knowledge on steel pipe grid shell structures and provides a practical reference for engineers designing similar large-span cultural facilities. The emphasis on node-level analysis and the identification of critical structural elements represent best practices that should be adopted in all complex steel structure projects. The successful implementation of this project demonstrates that advanced steel pipe grid shell systems can achieve both structural excellence and architectural distinction when supported by rigorous engineering analysis and meticulous construction quality control.