Calculation Model Analysis of Dumbbell-Shaped Cross-Section Steel-Concrete Composite Members

Literature Overview

This paper by Zhou Shuixing, Xiong Hongbin, and Zhang Min, published in Civil Construction and Environmental Engineering (Vol. 31, No. 2, 2009, pp. 105-109), addresses the structural analysis of steel-concrete composite members with dumbbell-shaped cross-sections. Funded by the Western Transportation Science and Technology Project (200631881422), the research develops a computational model based on the concept of spatial composite beam elements and proposes a corrected lattice column method for calculating axial forces in the upper and lower chords of the dumbbell section. The work is particularly relevant to bridge engineering, where such composite sections are used in arch ribs and other load-bearing members.

Structural Characteristics of Dumbbell-Shaped Sections

The dumbbell-shaped cross-section is a composite structural form that consists of two parallel steel tubes (chords) connected by a web plate, with concrete filling the interior of both the steel tubes and the web cavity. This configuration provides several advantages over conventional circular or rectangular steel-concrete composite sections:

• High bending stiffness: The wide spacing between the chords creates a large moment of inertia.
• Efficient material utilization: Concrete is confined within steel tubes, preventing premature concrete crushing.
• Constructability: The modular nature of the section facilitates fabrication and assembly.
• Aesthetic appeal: The open-web design offers architectural advantages in bridge applications.

However, the structural behavior of this section is more complex than conventional composite sections due to the interaction between multiple components operating at different stress levels and deformation modes.

Computational Model Development

The authors develop the computational model through the following systematic approach:

1. Component discretization: The dumbbell section is decomposed into discrete components: the steel tubes, the concrete within the tubes, the web plate, and the concrete within the web cavity.
2. Element formulation: Each component is modeled as a conventional spatial beam element, utilizing the plane section assumption (Bernoulli-Euler hypothesis) for each individual component.
3. Master-slave node coupling: A transformation matrix is established between master nodes and slave nodes to enforce compatibility conditions between the different components. This coupling ensures that the deformation of each component is consistent with the overall section behavior.
4. Composite element assembly: The individual spatial beam elements are assembled into a single spatial composite beam element through the transformation matrix, creating a unified computational entity that captures the interaction between all components.
5. Program implementation: A Fortran-based calculation program is developed for the analysis of dumbbell-section arch ribs.

The following table summarizes the key aspects of the computational model:

Key Results and Engineering Implications

The numerical examples presented in the paper reveal several important findings:

1. Axial force dominance: The steel tubes and the concrete within the tubes primarily carry axial forces, with bending moments being relatively small. This observation validates the assumption that the dumbbell section behaves predominantly as an axial-force-carrying member in arch rib applications.
2. Web contribution: The web plate primarily transfers shear forces between the chords and provides lateral stability, but contributes minimally to the overall axial capacity.
3. Lattice column method correction: The authors propose a corrected formula for the lattice column method that accounts for the actual load distribution between the upper and lower chords. The corrected results show good agreement with the finite element analysis results, providing a practical hand-calculation method for engineers.

The corrected lattice column method formula adjusts the conventional approach by incorporating the actual stiffness ratio between the chords and accounting for the P-delta effect that becomes significant in slender arch ribs. This correction is particularly important for long-span bridges where the arch rise-to-span ratio is low.

Reflections on the Methodology

The approach of decomposing a complex composite section into simpler beam elements and coupling them through transformation matrices is elegant and computationally efficient. It avoids the need for a full three-dimensional finite element model while still capturing the essential structural behavior. The master-slave node coupling technique is particularly useful because it allows each component to be modeled with its own material constitutive law while maintaining kinematic compatibility.

From a practical engineering standpoint, the confirmation that the dumbbell section behaves predominantly as an axial-force member is reassuring. It means that the design can be simplified by focusing on axial capacity checks, with secondary checks for shear and local buckling. The corrected lattice column method provides a valuable tool for preliminary design and code compliance checks, complementing more detailed finite element analyses for final design verification.

This paper serves as a useful reference for engineers designing composite steel-concrete structures with non-conventional cross-sections, and the methodology can potentially be extended to other composite section geometries such as I-shaped or box-shaped sections.