拱桥的理论极限跨径分析

大跨径拱桥是跨越江河峡谷富有竞争力的桥型之一，近年来，随着施工技术的进步和高性能材料的应用，拱桥正在不断突破自身跨径纪录，研究其理论极限跨径具有重要意义。本文综合考虑强度、面内稳定和面外稳定条件，分别基于抛物线拱轴线和悬链线拱轴线，采用理论推导获得了拱桥的极限跨径的解析公式，并由此考虑高性能混凝土、活性粉末混凝土和高强度钢等新材料的应用，针对混凝土拱桥和钢拱桥，分析其理论极限跨径随矢跨比和材料强度的变化关系。结果表明基于悬链线推导出来的理论极限跨径略小于基于抛物线推导的结果，但结果相差不大。在矢跨比1/5时，混凝土拱桥主拱采用R200活性粉末混凝土时的理论极限跨径可超过2000m，钢拱桥主拱采用Q690高强钢材时的理论极限跨径可超过2500m。

Analysis of Theoretical Ultimate Span for Arch Bridge

Long-span arch bridge is one of competitive types of bridge to cross rives and canyons. Recent years, the record of span length for arch bridge has been continuously broken with the advancement of construction techniques and application of high-performance materials. It is of great importance to study the theoretical ultimate span length of arch bridge. Based on the parabolic and catenary arch axes, the analytical solutions of ultimate span length of arch bridge are solved using theoretical derivation accounting for the strength, in-plane stability and out-plane stability conditions, respectively. Then, the use of high-performance concrete, reactive powder concrete and high-strength steel is considered to study the relationship between theoretical ultimate span length and rise-span ratio as well as material strength for concrete and steel arch bridges. The results show that the theoretical ultimate span length derived by catenary arch axis is slightly smaller than that obtained by parabolic arch axis, but the difference is insignificant. When the rise-span ratio is 1/5, the theoretical ultimate span length for concrete arch bridge using R200 reactive powder concrete can reach 2000m while the main span of steel arch bridge using Q690 high-strength steel can be longer than 2500m.