Study On Second-Order Design Method For Reinforced Concrete Rib Arch

In recent years, the design method of long-span arch bridge is based on the second-order elasto-plasticity theory, which considers the effect of geometry and material nonlinear on the structure of long-span arch bridge. However, for mid-span and small-span arch bridges the second-order effect is generally analyzed by using simple approximate method according to the design codes. That is, arch rib is considered as eccentric compression member and eccentric magnified factor η is used to analyze the effect of arch rib deflection on internal force. In design codes, eccentric magnifier factor approach originates from classical elastic stable theory and is deduced from eccentric compression column without lateral loads and its flexural stiffness is modified by experiment results. Eccentric magnifier factor approach can't reflect the characteristics and mechanic behavior of arch structure, thus the effect of arch rib deflection on internal force can't be accurately presented. Eccentric magnifier factor of arch is associated with many factors and interrelationship is complex. Study on eccentric magnifier factor is of practical significance for the design of reinforce concrete rib arch. However, only a few studies about this field can be found. Research focusing on R.C. rib arch aims to meet the needs and propose a simple available second-order design method of R.C. rib arch. In this dissertation, catenary, parabola and circinal fixed arch is investigated. The main contents are as follows.Given some assume, the elastic limit state of parabola bar with different support condition and loading condition was analyzed, furthermore, the expression of moment magnifier factor on key section of Parabola bar was deduced, which has an analogy form with the moment magnified factor of eccentric compression column. Based on the deflection theory and some assume, the expressions of moment magnifier factor on foot of parabola fixed arch and crown of parabola two-pinned arch were deduced. Moment magnified factor increases with axial force, and is associated with support condition and loading condition. Moment magnified factor of arch is different with eccentric compression column.Using nonlinear finite element method and taking deflection as disturbance variable, the whole loading course was traced. Considering pre-buckling nonlinear displacements, the effects of rise-to-span, span and the ratio of rise to radius of gyration on buckling loads of arch structure were analyzed. It can be concluded that the ratio of elastic buckling loadsto nonlinear buckling loads increases with the increasing of span and the ratio of rise to radius of gyration and decreases with the descend of rise-to-span. Furthermore, the effects of the ratio of rise to radius of gyration on the buckling form of shallow arches are analyzed. For non-shallow arches the buckling mode is characterized by anti-symmetric bifurcation, but the post-buckling loads of pin-ended arches increase slightly while the post-buckling loads of fixed arches decrease slightly.The effective length in elastic stable theory differs from that in the r\-/o method. Buckling mode of arch usually differs from its deformation under loads; the result may be inaccuracy when using the effective length in elastic stable theory to calculate second-order moment. As a substitutive way, equivalent length of rib arch was put forward. Equivalent length is associated with rise-to-span, the ratio of actual horizontal force to critical horizontal force (H/Hc) and the ratio of developed length to radius of gyration(5/rH,). For catenary's fixed-ended arches with the same rise-to-span and archaxis coefficient, equivalent length factor of rib arch remains constant so long as the ratio of developed length to radius of gyration(5/rw) unchanges. After nonlinear finite element analysis for 1,080 rib arches model, functional expression between equivalent length factor and the ratio of developed length to radius of gyration is derived, which is similar in shapeMerits and disadvantages were pointed out by comparing with several design codes and some studies on effective flexural stiffness (El) calculating in reinforce concrete eccentric compression member. On the basis of the merits of studies and curve fitting to existent experimental data, a new calculating approach on effective flexural stiffness was presented. Combining the equivalent length calculating formula, second-order internal force method on reinforce concrete rib arch was presented.Based on Artificial Neural Network (ANN) theory, using self-adaptive error BP algorithm, a forecast system on eccentric magnified factor of reinforce concrete rib arches was founded. The solving ability was tested by two examples and it proved that the forecast system is accurate and available. ANN also provides a new solving approach for determining parameter on the basis of experimental data.