Linear Elastic Theory And Ultimate Load Carrying Capacity Analysis Of Thin-walled Curved Beams

Curved girders of streamline shape have been applied widely in highway bridges and interchange facilities. This is due primarily to the ever-increasing emphasis on aesthetics coupled with transportation alignment restrictions. The use of curved beams in industrial buildings is also not uncommon. They can be found in circular cast houses of blast furnace, in oil-sealed dry gasholders and in workshops with curved cranes. Cross sections of these curved members are of various types, such as Il-shaped, I-shaped, channel, box and H section without any symmetrical axis.Compared to their straight counterparts, the behaviors exhibited by curved beams are far more complex. Curved beams will deflect biaxially and twist simultaneously when subjected to general loadings. Numerous studies have been undertaken to investigate the behavior of curved beams and various theories were produced since the 50's in last century. The discrepancies between these theories have prevented the development of reasonable analysis and design methods on such types of structures. Adopting the conceptions of thin-walled member theory, studies on linear elastic analysis and ultimate strength behaviors of curved I-beams are presented in this paper, which may give helps to a deeper understanding of the behavior of curved beams and provide a reasonable design guideline.Starting from two well-accepted assumptions in theory of thin-walled beams, a general theory for linear analysis of curved beams with any open sections is established in this paper by using the principle of virtual work. The equations of equilibrium and natural boundary conditions are given. Simplified theories are also presented for curved beams with commonly used sections, such as I-shape, channel and H section without any symmetrical axis. Linear analysis is also performed in combination with finite element method.Following the linear analysis, a new nonlinear theory for curved members with I-shaped sections is presented according to the theory of finite deformation, in which the effect of transverse stress is also incorporated. Focuses are then put on the flexural torsional buckling analysis of mono-symmetry I-section arches. Closed form solutions are obtained for arches subjected to uniformly distributed radial load and to equal and opposite end moments. Effects of different laying positions and of asymmetry of cross-section on buckling loads are included. The solutions are compared with previous theoretical results. Conditions of inextensibility and negligible prebuckling in-plane deformation usually adopted in arch buckling analysis are also discussed.A curved beam element is proposed for the elastic and elasto-plastic large-displacement analysis of thin-walled curved beams based on the new developed nonlinear theory. Using polynomial displacement functions, the proposed element includes the second order effect associated with geometric and material nonlinearities. The increment-iteration solution strategy is adopted in the nonlinear finite element analysis. Arc-length method and the incremental plastic reversibility procedure are used to find the complete load-deflection curve and deal with elastic unloading occurring in elasto-plastic analysis.Relatively little experimental studies are available on the ultimate strength of curved beams, 18 simple-supported welded beams subjected to a concentrated force at the mid-span are tested. The load displacement curves and the ultimate strength of each member are presented. Effects of beam length, radius of curvature and flexural-torsional rigidity on ultimate are considered. Test results for deformations and ultimate strength are found to be in good agreement with the corresponding values predicted by the elasto-plastic finite element analysis when warping boundary constraints are accounted of.The developed finite element program is then used to investigate the ultimate behaviors of horizontally curved beams with a specified I-shaped cross-section. These curved members are assumed to be simple-supported and subjected...