Second-Order Pre-Camber Analysis of Steel Tube Concrete Arch Bridges Considering Temperature Effects

Literature Overview

The paper by Xie Xiaoli, Zhao Guofan, Hu Anni, and Zou Cunjun, published in "Engineering Mechanics" (2005, Vol. 22, No. 4, pp. 62-66), investigates the pre-camber (pre-elevation) calculation of steel tube concrete (STC) arch bridges during construction, with particular attention to temperature effects and second-order (P-delta) effects. The work is supported by the National Natural Science Foundation of China (Grant 50068001) and the China Postdoctoral Science Foundation (Gui Ke Pei 0135008). The authors adopt the moment balance principle to derive the cable force expressions for the temporary hanger system used in the segmental erection method, and then incorporate second-order effects into the temperature analysis to establish the relationship between pre-camber and cable deformation. The study is illustrated through a case study of the Yongjiang Bridge in Yongning County, Guangxi, China.

Core Technical Content

The construction method under consideration is the jack-and-cable segmental erection technique, in which prefabricated steel tube concrete arch segments are lifted by hydraulic jacks and temporarily supported by cables (hangers) before being connected to form the complete arch ring. The pre-camber is the deliberate vertical offset applied to each segment during erection to compensate for the elastic and inelastic deformations that will occur as the arch is loaded progressively during construction and service.

The authors derive the cable tension expressions using the principle of moment equilibrium at each erection stage. This is a classical but essential step, as the cable forces directly govern the temporary support conditions and the resulting deformation pattern. The key innovation lies in incorporating second-order effects into the temperature analysis. Temperature variations during construction cause differential thermal expansion of the steel tube and the concrete infill, leading to axial forces and bending moments that can significantly alter the deformation profile.

The case study of the Yongjiang Bridge demonstrates that while large temperature differentials do have a measurable influence on the pre-camber values, the second-order effects are relatively small and can be neglected in most practical cases. This is an important and somewhat counterintuitive finding, as second-order effects are often assumed to be significant in slender arch structures. The conclusion is that for the typical temperature ranges encountered in southern China, first-order thermal analysis provides adequate accuracy for pre-camber determination.

Engineering Practice and Quality Control Implications

For practitioners involved in the construction of STC arch bridges, this study offers practical guidance on pre-camber determination. The pre-camber must be calculated before erection begins and applied precisely during segment positioning. Any error in pre-camber calculation translates directly into residual deformations after the arch ring is closed, potentially leading to excessive stresses, geometric imperfections, and serviceability issues.

From a welding quality perspective, the segment joints in STC arch bridges are critical. The longitudinal butt welds connecting adjacent steel tubes must be full-penetration welds with complete radiographic inspection (RT) in accordance with standards such as GB/T 11345 or ISO 17636. The weld quality directly affects the continuity of the arch ring and the accuracy of the pre-camber application. Thermal effects from welding can also cause local distortions that must be accounted for in the erection sequence.

The temperature effect analysis is particularly relevant for construction in regions with large diurnal or seasonal temperature variations. During hot summer days, the steel tube may expand significantly more than the concrete infill, creating compressive stresses in the steel and tensile stresses in the concrete. If the segments are erected at a different temperature than the design reference temperature, the resulting thermal mismatch can alter the pre-camber requirements.

Study Insights and Reflections

The finding that second-order effects can be neglected for pre-camber calculation is practically valuable, as it simplifies the construction planning process. However, this conclusion should be interpreted with caution. The study examines specific temperature ranges and bridge geometries, and the neglectability of second-order effects may not hold for very slender arches with high rise-to-span ratios or for extreme temperature environments. The multiple temperature segment analysis provides a more realistic representation of the thermal conditions during construction, which is a methodological improvement over single-temperature analyses.

The moment balance approach for cable force derivation is straightforward and well-suited for the segmental erection method. However, it assumes rigid segment connections and does not account for the flexibility of the temporary support system. In practice, the cables and jacks have finite stiffness, and the actual cable forces may differ from the idealized calculations. A more refined analysis incorporating the flexibility of the temporary works would provide additional safety margins.

Summary

This study provides a practical framework for pre-camber calculation of STC arch bridges during segmental erection, incorporating temperature effects through a second-order analysis. The key conclusion that second-order effects are negligible for typical temperature ranges simplifies construction planning without compromising accuracy. Engineers should nonetheless verify this assumption for their specific project conditions and ensure that weld quality at segment joints meets the required standards to maintain arch ring continuity.