Yong-Lin Pi

A FURTHER STUDY OF FLEXURAL-TORSIONAL BUCKLING OF ELASTIC ARCHES

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.

Nonlinear Thermoelastic Buckling of Pin-Ended Shallow Arches under Temperature Gradient

This paper presents a nonlinear thermal buckling analysis of circular shallow pin-ended arches that are subjected to a linear temperature gradient field in the plane of curvature of the arch. The linear temperature gradient produces axial expansion and curvature changes in the arch. The bending action produced by the curvature change and the axial compressive action produced by the restrained axial expansion may lead the arch to buckle suddenly in the plane of its curvature. The end reactions resulting from the restrained axial expansion also produce bending actions that are opposite to that produced by the temperature differential and tend to produce deflections on the convex side of the arch. A geometrically nonlinear analysis for thermoelastic buckling has been carried out based on a virtual work technique, and analytical solutions for the critical temperature gradients for the in-plane limit instability and bifurcation buckling are obtained. It is found that antisymmetric bifurcation is the dominant b...

Elastic flexural-torsional buckling of continuously restrained arches

Arches are often connected to other members which influence the structural behaviour of the arch. These members induce restraining actions during flexural-torsional buckling which restrict the buckled shapes of the arch and may significantly influence its buckling response. This paper uses an energy method to study the elastic flexural-torsional buckling of continuously restrained arches of doubly symmetric open thin-walled cross-section in uniform bending and in uniform axial compression. Closed form solutions for the flexural-torsional buckling moment of restrained arches in uniform bending and for the flexural-torsional buckling load of restrained arches in uniform axial compression are obtained. It is found that the elastic continuous restraints are more effective in increasing the buckling resistance for arches with a large included angle than for arches with a small included angle. The first buckling mode may not correspond to the lowest buckling moment or load for arches restrained by minor axis rotational or lateral-translational restraints. It is also found that the number of half sine waves corresponding to the lowest buckling moment or load increases with the stiffness of the restraints. For restrained arches in uniform axial compression, when the restraining stiffness exceeds a limiting value, the buckling mode may change from flexural-torsional to torsional.

Elasto-plastic buckling and postbuckling of arches subjected to a central load

Abstract This paper presented a rational finite curved beam-element model for 3D nonlinear elasto-plastic analysis of arches. The finite element model incorporates the effects of large twist rotations of the cross-section and has consistent sampling scheme of sampling points over the cross-section and so it can perform the elastic and elasto-plastic flexural–torsional buckling and postbuckling analysis of arches in combined bending and compression actions. Elastic and elasto-plastic flexural–torsional buckling and postbuckling behaviour of arches that are subjected to a central concentrated load has been investigated using the rational finite element model. It has been found that the slenderness, included angle, and the torsional parameter of an arch play important roles in the elastic and elasto-plastic buckling. In addition, the number of the inflexion points is important for the elastic and elasto-plastic buckling of fixed arch. Yielding is a significant factor for the elasto-plastic buckling and postbuckling behaviour. When the included angle of a stocky arch is not large, its elasto-plastic buckling load is much lower than its elastic buckling load. When the included angle a stocky arch is large, the end support condition plays an important role in the buckling and postbuckling behaviour of the arch. The elasto-plastic buckling load of a stocky pin-ended arch with a large included angle is equal to its elastic counterpart. The elasto-plastic buckling load of a stocky fixed arches with a large included angle is lower than its elastic counterpart. For a slender arch, its elasto-plastic buckling load is also equal to its elastic buckling load. In general, the elasto-plastic postbuckling load carrying capacity of an arch decreases when the arch continues to deform while its elastic postbuckling load carrying capacity can increase. For slender shallow arches, the elastic postbuckling response is stiffer because of the relaxation of axial load and moment distribution.

ENERGY APPROACH FOR DYNAMIC BUCKLING OF AN UNDAMPED ARCH MODEL UNDER STEP LOADING WITH INFINITE DURATION

Performing a dynamic buckling analysis of structures is more difficult than carrying out its static buckling analysis counterpart. Some structures have a nonlinear primary equilibrium path including limit points and an unstable equilibrium path. They may also have bifurcation points at which equilibrium bifurcates from the primary equilibrium path to an unstable secondary equilibrium path. When such a structure is subjected to a load that is applied suddenly, the oscillation of the structure may reach the unstable primary or secondary equilibrium path and the structure experiences an escaping-motion type of buckling. For these structures, complete solutions of the equations of motion are usually not needed for a dynamic buckling analysis, and what is really sought are the critical states for buckling. Nonlinear dynamic buckling of an undamped two degree-of-freedom arch model is investigated herein using an energy approach. The conditions for the upper and lower dynamic buckling loads are presented. The merit of the energy approach for dynamic buckling is that it allows the dynamic buckling load to be determined without the need to solve the equations of motion. The solutions are compared with those obtained by an equation of motion approach.

Experimental Investigation into Flexural-Torsional Ultimate Resistance of Steel Circular Arches

AbstractThis paper deals with experimental investigations into flexural-torsional ultimate resistance of in-plane-pinned circular steel arches. Three I-section arches with the same span but different rise-to-span ratios were tested under different loading conditions. A test rig comprising loading frames and lever beams was used to apply symmetrical three-point loads over the full span and unsymmetrical two-point loads over half the span to the arch rib. These concentrated loads are directed toward fixed points during flexural-torsional buckling of the arches. The arches are supported in such a way that their ends in plane are pinned and out of plane are semirigidly restrained. Geometric imperfections are measured before loading. The test results show that when the test arches reach their load-carrying capacity, plastic zones form in the arch rib, and the out-of-plane flexural-torsional deformation is significant. It is found that the pinned arches buckle in an asymmetric double-wave S-shaped flexural-tors...

In-Plane Failure Mechanism and Strength of Pin-Ended Steel I-Section Circular Arches with Sinusoidal Corrugated Web

AbstractThis paper investigates the global in-plane failure and local web shear failure mechanism and strength of steel I-section circular arches with a sinusoidal corrugated web. In reference to a flat web that can resist both the shear and axial forces, the sinusoidal corrugated web can resist the shear force only. As a result, the sinusoidal corrugated web may fail in an elastic-plastic shear buckling mode. This study considers pin-ended circular steel arches with a sinusoidal corrugated web under a uniform radial load or a uniform vertical load to elucidate numerically their different failure modes. It is found that local web failure occurs suddenly without warning, and all aspects pertaining to the local web shear failure are investigated thoroughly with an equation for the ultimate shear-carrying capacity of nonuniformly sinusoidal corrugated webs being proposed. It is also found that the effects of the shear deformations of corrugated web on global in-plane buckling and the strength of steel arches...

Nonlinear Equilibrium and Buckling of Fixed Shallow Arches Subjected to an Arbitrary Radial Concentrated Load

This paper is concerned with an analytical study of the nonlinear in-plane equilibrium and buckling of fixed shallow circular arches that are subjected to an arbitrary radial concentrated load. The structural behavior of an arch under an arbitrary radial concentrated load is quite different from that of an arch under a central concentrated load. It is shown that a fixed arch under an arbitrary radial concentrated load can buckle in a limit point instability mode, but cannot buckle in a bifurcation mode, which is different from that of a fixed arch under a central concentrated load that can buckle in a bifurcation mode or in a limit point instability mode. Analytical solutions for the nonlinear equilibrium path and limit point buckling load of shallow circular arches under an arbitrary radial concentrated load are derived. It is found that the load position influences the buckling load significantly and the influence is much related to the modified slenderness of the arch defined in the paper. It is also found that when the modified slenderness of an arch is smaller than a specific value, the arch has no typical buckling behavior. The analytical solution for the relationship of the specific modified slenderness with the load position is also derived. Comparisons with finite element (FE) results show that the analytical solutions can accurately predict the nonlinear equilibrium and buckling load of shallow fixed arches under an arbitrary radial concentrated load.

Flexural-Torsional Buckling and Ultimate Resistance of Parabolic Steel Arches Subjected to Uniformly Distributed Vertical Load

AbstractThis paper focuses on the flexural-torsional buckling and ultimate resistance of parabolic steel arches with box sections subjected to full-span uniformly distributed vertical load by using finite-element numerical analyses. First, analyses on prebuckling internal forces and flexural-torsional buckling loads are performed and compared with the existing theories. They show that parabolic arches under uniformly distributed vertical load are actually subjected to combined axial compressive and in-plane bending actions, rather than pure compression in the classic theory. Because the bending moment is substantial for shallow arches, the classic theory with the assumption of pure compression does not predict exactly the flexural-torsional buckling load. Second, the flexural-torsional ultimate resistance of parabolic arches is explored based on extensive finite-element numerical results, resulting in a design method based on a modified slenderness. The rise-to-span ratio is found to have a great effect o...

Lateral-Torsional Buckling Analysis of Arches Having In-Plane Rotational End Restraints under Uniform Radial Loading

AbstractIn many cases, an arch may have in-plane elastic end restraints provided by the connected structures or elastic foundations, which may influence the elastic lateral-torsional buckling of the arch. However, little research of the lateral-torsional buckling of arches with elastic end restraints has been reported in the open literature. This paper analytically investigates the lateral-torsional buckling of pin-ended circular arches having in-plane elastic rotational end restraints under a uniform radial load. The analytical solutions for the prebuckling behavior of such an arch show that the uniform radial load produces combined axial compressive and bending actions in the arch and that the axial compressive force produced by the uniform radial load is approximately uniform along the arch axis. It is found that the stiffness of elastic rotational end restraints has significant effects on the magnitude and distribution of the axial compressive forces and bending moments. The axial compressive force de...