Uniform Radial Load Research Articles

Mechanical property measurement at high temperature based on a new disc-shaped specimen

Three-dimensional digital image correlation (3D-DIC) is frequently used to measure mechanical properties of materials. However, the traditional dumbbell-shapedspecimen has some limitations for measurment of mechanical properties of materials by use of 3D-DIC at high temperature due to two reasons: (1) its transverse dimension is very small and only a small number of valid speckles can be used in 3D-DIC; and (2) only a small amount of valid information, such as the average deformation of the gauge length, can be used to obtain mechanical properties in one direction. In this work, a new test method based on a disc-shaped standard specimen is first proposed. By use of analytical solutions of a disc under a uniform radial load, and measured results of the full-field displacement of the disc-shaped specimen by 3D-DIC in an effective test region at different high temperatures, mechanical properties at different high temperatures are identified.

Out-of-Plane Stability Analysis of the Circular Box Arch with Sinusoidal Corrugated Webs

This paper presents an arch structure called the circular box arch with sinusoidal corrugated webs (CBASCW). This study investigates the out-of-plane elastic buckling behavior and elastoplastic stability capacity of the arch through a combined approach of theoretical derivation and finite element simulation. The section stiffness of the arch, including flexural stiffness, shear stiffness, and torsional stiffness, is achieved through theoretical derivation. Additionally, the elastic buckling load in both pure compression and pure bending states is derived. A simplified model is also introduced, which can conveniently simulate the internal force and deformation of the arch. The elastoplastic instability mechanism and failure mode are studied under various loading conditions, including uniform radial load, end bending moment, vertical load uniformly distributed in full-span, and vertical load uniformly distributed in half-span. Furthermore, the stability curves of the arch under conditions of pure compression and pure bending are graphed by incorporating stability coefficient and regularized slenderness ratio. According to the simulation results obtained from the simplified model and the analysis of stability curves, a design formula for stability capacity is proposed.

Slenderness limit for inner tubes with internal stiffeners in DSSTCC columns

In recent years, composite columns have gained much attention in offshore and marine engineering. This paper, with the motivation of a better design for circular straight double skin steel tubes confined concrete (DSSTCC) columns, theoretically explores the local buckling of the internally stiffened inner skin in this column. Firstly, the force analysis of a DSSTCC stub column was conducted, and its common failure modes were outlined. Based on the similar structural performance of the inner tube and the fixed circular arch, a concise buckling analysis model was built up. Then different buckling modes of clamped circular arches under the uniform radial load were presented. The ultimate load-carrying capacity of internally stiffened inner tubes under different buckling modes was also discussed, which shows relatively high dependence on the structural stability. Next, the calculation method of the expected ultimate hoop compressive stress was given, and the main computational procedure of the cross-sectional slenderness limit for internally stiffened inner skins was illustrated. In addition, a very simple prescriptive equation that considers the elastic modulus, the yield stress, and the formed arch's central angle value was fitted to estimate the cross-sectional slenderness limit for inner tubes with internal stiffeners, with which a slender cross-section can be delineated from an effective one. Meanwhile, the elastic buckling stress of the inner tube was also given. Finally, the applicability of the proposed methodology to materials with the bilinear model, the bilinear plus nonlinear hardening model, the idealized multilinear model, or the Ramberg-Osgood model was investigated, thereby demonstrating its good adaptability to these four common nonlinear constitutive models.

Analysis of the Ultimate Load-Bearing Capacity of Steel-Clad Concrete-Filled Steel Tube Arched Protective Doors under Blast Shock Waves

The mechanism of blast damage to steel-clad concrete-filled steel tube (SCCFST) arched protective doors is studied using the dynamic response characteristics of such loads under the action of blast shock wave loads, and the ultimate blast load-bearing capacity formula is derived based on the “plastic hinge” damage mode of the doors using limit analysis, which explores the effect of the blast shock wave. The effect of the design parameters of each component of the protective door on the load-bearing capacity subjected to blast shock waves is discussed. Results show that the damage mechanism under a uniform radial load on the outer surface of the SCCFST arched protective door is characterized by the plastic hinge lines at the two arch feet, which results in a slip fracture and renders the protective door unstable. The load-bearing capacity of the SCCFST arched protective door depends on the coordinated functioning of the cross-sectional outer cladding steel plate and inner connecting partition, concrete-filled steel tube, and restraining concrete outside the steel tube. The load-bearing capacity of each of the three parts differs with the varying cross-sectional occupancies.

In-Plane Failure Mechanism and Strength Design of Plate-Tube-Connected Circular Steel Arches

The in-plane elastoplastic failure mechanism of plate-tube-connected steel circular arches with inverted triangular cross sections is investigated in this study by using theoretical derivation and numerical simulation. First, the in-plane elastic buckling load formula of the arch under full-span uniform radial load (FSURL) is presented. Then, the limited conditions of avoiding the connecting plate and chord local failure before global elastic instability are derived. Lastly, the elastic–plastic failure mechanisms of arches are studied under FSURL, full-span uniform vertical load (FSUVL), and half-span uniform vertical load (HSUVL). It is found that the arch will experience global failure, chord local failure, combined connecting plate and chord failure, and connecting plate local failure under FSUVL and HSUVL. The failure mode is mainly related to the stiffness of the connecting plate. The corresponding design formulas are proposed for the global failure of arches and local failure of the chord. The proposed formulas and FE results are in good agreement.

Out-of-plane dynamic parametric instability of circular arches with elastic rotational restraints under a localized uniform radial periodic load

Out-of-plane dynamic instability of a circular arch with elastic rotational constraints under localized uniform radial periodic load is studied in this paper which has not been yet reported in the literature. In the out-of-plane dynamic instability analysis, the coupled equation of motion associated with lateral displacement and twist angle is derived by using an energy method and Hamiltonian principle. Then the mode shape functions of arches with different elastic rotational restraints are deduced and analytical solution for unstable regions with a period of 2T are obtained by using Bolotin’s method. Finite element numerical analysis is employed to justify the dynamic unstable regions by frequency sweeping simulation and the results show a desirable agreement. It is found that when the flexibility of out-of-plane elastic rotational restraints decreases, the unstable region moves towards the direction of higher frequencies owing to the increase in rigidity of the arch, with the out-of-plane dynamic stability of the arch being improved. The load localized parameter significantly impacts the dynamic stability for the arches with various flexibility of out-of-plane restraints. These results give us a deep understanding of the instability mechanism of engineering structures with arches and provide insight into the effective design of arch structures.

Nonlinear in-plane thermal buckling of rotationally restrained functionally graded carbon nanotube reinforced composite shallow arches under uniform radial loading

Nonlinear in-plane thermal buckling of rotationally restrained functionally graded carbon nanotube reinforced composite shallow arches under uniform radial loading

Axisymmetric buckling of annular plate with internal source of heat

In this article, the axisymmetric stability of an elastic annular plate with distributed internal heat source under uniform constant compressive radial loading at the outer edge is investigated. The governing and compatibility equations of the annular plate are taken from modified Karman’s equations, which are solved by the shooting method. The effect of the density of distributed internal heat source on critical load is investigated and discussed in detail. Numerical results of the plate without an internal heat source are in good agreement with the results from the literature, validating the effectiveness and advantages of the current method. The critical buckling load increases with a rise of the density of distributed internal heat sources. Moreover, an increase of wave number increases the critical buckling loads of the plate. The results of this research can be considered as benchmark solutions for buckling of the annular plates with an internal heat source.

Critical limit of diameter-to-thickness ratio for inner tubes of DSSTCC columns

To improve the confinement efficiency of steel tubes to the sandwiched concrete, the concept of double skin steel tubes confined concrete (DSSTCC) columns was proposed. This paper aims to theoretically investigate the local stability of inner steel tubes in DSSTCC columns. Firstly, considering that the stress state and failure mode of the inner steel tube are similar to those of the fixed circular arch subjected to a uniform radial load, the arc section of the inner steel tube was simplified into a circular arch for stress analysis. Secondly, the expected value of the in-plane elastic ultimate axial compressive stress of the circular arch was solved by the Monte Carlo method, and the ratio of its value to the yield stress was used to characterize the stable state of the inner tube. Then, the influence of the maximum included angle corresponding to the formed circular arch on the result was discussed, and an empirical formula was given to obtain a reasonable estimation of the critical limit of diameter-to-thickness ratio. Finally, it can be seen from the analysis that the method proposed in this paper is suitable for inner tubes made of the material with an elastic perfectly-plastic model, a bilinear model, or a bilinear plus nonlinear hardening model. These results are a contribution to the buckling analysis of inner tubes.

Funicularity of conics

Funicular structures can resist a given load with pure axial forces and therefore tend to use material very efficiently. One main challenge in their design is form finding, which often requires advanced numerical methods. In this article, we show analytically that a very common family of curves, conics, is funicular for a particular load case: a uniform radial load emanating from a focus. The result is a generalization of the well-known funicularity of parabolas and arcs of circles, respectively, under uniform vertical load and constant normal pressure. It can be used to design self-stressed structures by hand without the need for calculations. Portions of conics can be combined to obtain original shapes.

Nonlinear in-plane buckling of fixed shallow arches with an orthotropic thin-walled section under uniform radial and thermal loading

This paper presents a comprehensive investigation of nonlinear in-plane buckling of fixed shallow arches with an orthotropic thin-walled section under uniform radial and thermal loading. For convenience of analysis, the stretching–bending coupling within section internal forces is decoupled by utilizing a neutral plane concept. The principle of minimum total potential energy in conjunction with the first-order shear deformation theory is used to derive the differential equation of equilibrium and the buckling equation and a modified slenderness ratio is proposed to govern the buckling behaviors of laminated arches. The closed-form solutions for the limit point buckling and bifurcation buckling are obtained. Effects of environment temperature increases and the stacking sequences on the buckling load are discussed in detail. Comparisons with finite elements results show that the presented analytical solution can precisely predict the nonlinear behaviors of thin-walled laminated arches.

A theoretical study on nonlinear in-plane buckling of shallow angle-ply laminated arches with elastic supports

This paper presents, for the first time, an analytical study on the nonlinear in-plane buckling of angle-ply laminated shallow arches with elastic supports under a uniform radial loading. To decouple internal forces and facilitate theoretical derivations, the nonlinear equilibrium path and buckling equation are established based on neutral plane formulation by using a virtual work method, from which the closed-form solutions for limit point buckling and bifurcation buckling are determined. The buckling mode of the laminated arch is characterized by introducing the modified slenderness ratio. The present analysis is verified through direct comparisons with finite element results. The effects of radial and circumferential stiffnesses of the elastic supports on the buckling behaviors are discussed in detail. It is found that the laminated arch may buckle in either a limit point mode or a bifurcation mode and its buckling behavior is highly sensitive to the support stiffness. The effects of ply-angle on the critical buckling load are also researched. It is found that the buckling loads of laminated arches decrease with an increase of flange and web ply-angles, and the influence of flange ply-angle on buckling load is more pronounced than that of web ply-angle.

Thoracic aortic parallel stent-graft behaviour when subjected to radial loading

To manage complex aortic arch disease using minimally invasive techniques, interventionalists have reported the use of multiple stent-graft devices deployed in a parallel configuration. The structural device-device and device-artery interactions arising during aortic arch parallel endografting, also known as chimney thoracic endovascular aortic repair (ch-TEVAR), is not well understood. Through the use of a radial force testing system we sought to characterise both the loading and deformation behaviour of parallel endografts in representative ch-TEVAR configurations. Four commercially available devices (Bentley BeGraft, Gore TAG, Gore Viabahn, and Medtronic Valiant) were subjected to uniform radial load individually, and in six combinations, to quantify loading profiles. Image data collected during testing were analysed to evaluate mechanical deformations in terms of gutters, chimney and main endograft compression, as well as graft infolding. Parallel endografting was found to increase radial loads when compared to standard TEVAR. Chronic outward force during ch-TEVAR was dependent on main endograft manufacturer, with TAG combinations leading to consistently higher loads than Valiant, but independent of chimney graft type. Endograft deformations were dependent on chimney graft type, with Viabahn combinations presenting with lower gutter areas and increased lumen compression than BeGraft. Chimney graft deformations were also influenced by deployment arrangement in the case of double ch-TEVAR. This study emphasizes the significant variability in both radial loads and mechanical deformations between clinically relevant ch-TEVAR configurations.

The influence of stiffness coefficient of steel support on supporting effect and its optimization

The stiffness coefficient of steel support plays an important role in controlling the deformation of foundation pit, but the influence of various parameters in the stiffness coefficient on the supporting effect of foundation pit is still unclear, resulting in the unreasonable value of the stiffness coefficient. By means of theoretical analysis and numerical simulation, this paper makes a comprehensive and in-depth study on the influence law and optimization of the stiffness coefficient of steel support on the supporting effect. Based on the calculation of the stiffness of steel support, the calculation formula of the stiffness of steel support under the uniform radial load is derived by using the basic definition of stiffness calculation; the change rules of horizontal displacement and surface subsidence of the support structure under different parameters were analyzed by numerical simulation method, and the original scheme was optimized. The results show that: (1) in the stiffness coefficient, the steel support spacing and wall thickness have a great influence on the supporting effect; (2) with the increase of the rigid support spacing and the decrease of the steel support wall thickness, the horizontal displacement value and surface settlement value of the support structure both become larger. However, when the steel support spacing is 3.00-3.10m and the steel support wall thickness is 14mm-16mm, the horizontal displacement value and surface settlement value of the support structure do not change much, and they are all within the monitoring and warning value; (3) the original design scheme was optimized from 3.00m steel support spacing and 16mm steel support wall thickness to 3.10m steel support spacing and 14mm steel support wall thickness in the original scheme, which reduced the engineering cost and improved the construction efficiency.

In-plane failure mechanisms and strength design of circular steel tubular Vierendeel truss arches with rectangular section

This paper investigates the in-plane failure mechanisms and strength of circular steel tubular Vierendeel truss arches with a rectangular section by using the finite element models. Firstly, the analytical solution for the in-plane elastic buckling load of pin-ended circular steel tubular Vierendeel truss arches with a rectangular section under a uniform radial load is obtained. Then, limiting conditions of avoiding chord local buckling before the global elastic buckling of the arch are also derived. Lastly, the in-plane instability mechanisms and failure modes of the arch under a uniform radial load, a full-span uniform vertical load (FSUVL) and a half-span uniform vertical load (HSUVL) are investigated. It is found that the arch may undergo a global failure mode or three local failure modes under FSUVL and HSUVL. Based on the theoretical and finite element results, a design equation for the global strength of arches subjected to uniform compression is proposed. Strength design equations for global failure and local failure of arches subjected to FSUVL and HSUVL are also proposed. There is a good agreement between the prediction of the proposed design equations and the FE results.

Elastic lateral-torsional instability of monosymmetric shear deformable fixed arches under a localized uniform radial load

This paper investigates the elastic lateral-torsional instability of shear deformable fixed arches having a monosymmetric cross-section when subjected to a localized uniform radial load. Hitherto, this topic has not been addressed in the open literature. The complex in-plane internal actions in a fixed arch with a monosymmetric section are produced by a localized uniform radial load and are affected by the arc length of localized load segment. When the in-plane internal actions reach certain magnitudes, the fixed arch may fail suddenly in a lateral-torsional instability mode. The lateral-torsional instability loads of such arches considering shear deformations under a localized uniform radial load are difficult to obtain and are investigated in this paper. The strain-displacement relationships for the longitudinal normal axial and shear strains in the arch with a monosymmetric section are derived. In-plane analyses for the internal forces produced by the localized uniform radial load are firstly carried out. The analytical solution for the lateral-torsional instability load accounting for shear deformations and monosymmetry is then obtained using the principle of stationary potential energy together with the Rayleigh-Ritz method and compared with ANSYS numerical results. It is found that the monosymmetry parameter, the shear deformations, the slenderness ratio and the arc length of the localized load segment have considerable effect on the lateral-torsional instability load of fixed arches with a monosymmetric section.

Geometrically nonlinear buckling of graphene platelets reinforced dielectric composite (GPLRDC) arches with rotational end restraints

This paper presents an analytical investigation on the nonlinear buckling behavior of graphene platelets reinforced dielectric composite (GPLRDC) arches with rotational end restraints under applied electric and uniform radial load. The effective materials properties of GPLRDC, including the elastic modulus and dielectric permittivity, are estimated by employing effective medium theory (EMT). The analytical solutions for nonlinear equilibrium, critical load of limit point buckling and bifurcation buckling of the GPLRDC arch are derived according to the principle of virtual work. The critical geometric parameters and electric voltage governing the buckling mode switching behavior are also identified and discussed. The effects of graphene platelets (GPLs) weight fraction, size and geometry, applied DC voltage, AC frequency, as well as geometry of the arch on the buckling behavior are examined comprehensively. It is found that the dielectric property of the GPLRDC has significant effects on the buckling behavior of the GPLRDC when the GPLs concentration exceeds the percolation threshold. The nonlinear buckling behavior of the GPLRDC is quite sensitive to the AC frequency within a certain range. Furthermore, the change of the applied voltage can switch the buckling mode and even the number of limit points of the GPLRDC arch.

Nonlinear in-plane buckling of shallow laminated arches incorporating shear deformation under a uniform radial loading

This paper is concerned with the nonlinear in-plane buckling of shear deformable laminated composite shallow arches under a uniform radial loading. The virtual work method is used to establish both governing differential equations and buckling equilibrium equations based on the first order shear deformation theory to include the effect of shear deformation for which analytical solutions for both limit point buckling and bifurcation point buckling are derived. A specific parameter that defines the switch between buckling and pre-buckling, limit point buckling and bifurcation buckling is proposed and defined. The effect of shear deformation on the buckling load is discussed in detail. It is observed from typical equilibrium paths of the arch that the shear deformation decreases the critical buckling load of laminated arches and this effect becomes more important and cannot be neglected for fixed arches with slenderness ratio S/rx < 150 and pinned arches with S/rx < 100. Direct comparisons with finite element results demonstrate that the proposed analytical solutions can provide a good prediction for the nonlinear buckling of shallow laminated arches under a uniform radial loading.

Nonlinear dynamics of loaded visco-hyperelastic spherical shells

In this paper, the nonlinear dynamic behaviors, especially, limit cycles and chaos, are investigated for the spherical shell composed of a class of visco-hyperelastic materials subjected to uniform radial loads at its inner and outer surfaces. To include the thickness effect, a more general model compared with the membrane and thin plate is proposed to investigate the dynamic characteristics of the visco-hyperelastic structure. Then, the coupled integro-differential equations describing the radially symmetric motion of the spherical shell are derived in terms of the variational principle and the finite viscoelasticity theory. Due to both the geometrical and physical nonlinearities, there exists an asymmetric homoclinic orbit for the hyperelastic structure. Particularly, under constant loads, the system converges to a stable equilibrium point, and the convergence position and speed are closely related to both the initial condition and the viscosity because of the existence of different basins, while under periodic loads, some complex phenomena, such as the limit cycles and chaos, are found, and the chaotic phenomena are analyzed by the bifurcation diagram and Lyapunov exponent. Moreover, by numerical analyses, parametric studies are carried out to illustrate the effects of viscosity, load amplitude, external frequency and initial condition.

Long-term lateral-torsional buckling behavior of pin-ended CFST arches under uniform radial loads and temperature field

In this paper, analytical solutions of the long-term lateral-torsional buckling behavior for the concrete filled steel tubular (CFST) arch with pin ends subjected to uniform radial loads and temperature field are presented. First, an accurate pre-buckling analysis considering both the temperature effect and the creep of concrete is proposed to obtain the time-dependent internal forces of the CFST arch. Then, based on the principle of stationary potential energy and the Rayleigh-Ritz method, the analytical solutions corresponding to the elastic lateral torsional buckling load of the arch and the time-dependent internal force are derived. The variation of buckling load of a CFST arch with time and temperature under uniform radial load and temperature field is analyzed. Good agreements are founded between the analytical solutions and the finite element analysis results, and both of them show that the buckling load of CFST arch subjected to uniform radial load and temperature field decreases significantly as the time and temperature increase. These results are useful for guiding a safer design of CFST arches.