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Geometric and loading conditions affect stability and strength of arch frameworks. Prestressed arches that are made by buckling of flat struts into shape are more sensitive to these parameters. Most studies on prestressed arches are limited to the initial buckling path, not accounting for the looping response. This paper investigates the effect of arch rise-to-span ratio, support fixity, tapering of the arch section and various loading conditions on the complete response of prestressed arches. A corotational formulation augmented with a two-parameter path finding technique is developed to effectively trace the snap-through, snap-back, and looping paths of the arch. Results indicate that symmetric limit loads increase almost proportionally to the steepness ratio of the arch, whereas the asymmetric bifurcation loads asymptote around the rise-to-span ratio of 0.5. Clamped arches are more stable than their equivalent pinned arches, and do not demonstrate any looping behavior. A tapered-out prestressed arch with a taper angle of less than 2° 12′ is more stable than its equivalent prismatic or tapered-in arch. Prestressed arch is least stable when a point load acts within 12%–27% of its span length from the crown, or when only three-quarters of the span is loaded with a uniform load.

Intentional buckling as a fabrication technique for arch frameworks results in prestrains at every section of the arch, which in turn affect its strength and stability. A nonlinear corotational straight beam element with elastic, linear strain hardening material has been developed to study the elasto-plastic buckling of prestressed arches. The study indicates that for prestressed arches there is an interdependence between the slenderness and steepness ratios of the arch with the ratio of prestresses to the yield strength of the material, all of which control the magnitude and shape of buckling mode. While steeper arches are generally more stable in their elastic range, the effect of steepness ratio is reduced as the prestress exceeds 55% of the yield strength. Effects of loading and support conditions have also been considered. Although fixed supports result in more stable arches, their effectiveness depends on the steepness ratio and the level of prestresses. Finally, the effect of strain hardening on the plastic buckling of the arch is more pronounced for lower values of the plastic tangent modulus.

This paper uses both a virtual work approach and a static equilibrium approach to study the elastic flexural-torsional buckling of circular arches under uniform bending, or under uniform compression. In most studies of the elastic flexural-torsional buckling of arches under uniform compression produced by uniformly-distributed radial loads, the directions of the radial loads are conventionally assumed not to change but to remain parallel to their initial directions during buckling. In practice, the uniform compression may be produced by hydrostatic loads or by uniformly-distributed radial loads that are directed to a specific point during buckling. In addition, there are discrepancies between existing solutions for the elastic flexural-torsional buckling moment and load of arches under uniform bending or under uniform compression which need to be clarified. Closed form solutions for the buckling moment and load are developed. The discrepancies among the existing solutions for the elastic flexural-torsional buckling moment and load of arches are clarified and the sources for the discrepancies are identified. It is found that the lateral components of hydrostatic loads and of uniformly-distributed radial loads that are always directed toward the center of the arch increase the flexural-torsional buckling resistance of an arch under uniform compression. It is also found that first-order buckling deformations are sufficient for static equilibrium approaches for the flexural-torsional buckling analysis of arches. The rational static equilibrium approach for the flexural-torsional buckling in the present study is effective.

This paper considers the nonlinear in-plane behaviour of a circular arch subjected to thermal loading only. The arch is pinned at its ends, with the pins being on roller supports attached to longitudinal elastic springs that model an elastic foundation, or the restraint provided by adjacent members in a structural assemblage. By using a nonlinear formulation of the strain-displacement relationship, the principle of virtual work is used to produce the differential equations of in-plane equilibrium, as well as the statical boundary conditions that govern the structural behaviour under thermal loading. These equations are solved to produce the equilibrium equations in closed form. The possibility of thermal buckling of the arch is addressed by considering an adjacent buckled equilibrium configuration, and the differential equilibrium equations for this buckled state are also derived from the principle of virtual work. It is shown that unless the arch is flat, in which case it replicates a straight column, thermal buckling of the arch in the plane of its curvature cannot occur, and the arch deflects transversely without bound in the elastic range as the temperature increases. The nonlinear behaviour of a flat arch (with a small included angle) is similar to that of a column with a small initial geometric imperfection under axial loading, while the nonlinearity and magnitude of the deflections decrease with an increase of the included angle at a given temperature. By using the closed form solutions for the problem, the influence of the stiffness of the elastic spring supports is considered, as is the attainment of temperature-dependent first yielding of a steel arch.

This paper intends to study the train-induced vibration of a parabolic tied-arch bridge using an analytical approach. The train loads over the bridge are regarded as a sequence of equidistant moving loads with identical weights. The tied-arch bridge considered is modeled as the combination of a parabolic flat-rise arch with two-hinged supports and a simple beam suspended by densely distributed vertical cables connected to the arch rib. Using the normal coordinate transformation method, the coupled equations of motion of the arch rib and suspended beam are converted into a set of uncoupled equations. Then, one can derive closed form solutions for the response of the tied-arch beam to successive moving loads, by which the resonant conditions of higher modes of the suspended beam can be identified. According to the present study, the critical position for the maximum acceleration on the suspended beam depends upon the vibration shape that has been excited. Moreover, the numerical results indicate that the lower the rise of the arch rib, the larger the acceleration response of the main beam suspended by the arch.