A simplified method for the analysis of incremental collapse of reinforced concrete arches

An already known, but so far unpublished, remark is considered[10]. According to it the Heyman simplification for the limit design of a masonry arch can be accepted also for the limit design of a reinforced-concrete arch (when some assumptions are satisfied).With these same assumptions, the same simplification can lead to the calculation of the plastic safety factor of a reinforced-concrete arch liable to incremental collapse under the action of several sets of live loads (moving load, temperature change, earthquake) that can be repeated in an arbitrary manner.An example is given showing good agreement with exact theory.     

Effect of strength mismatch on fully plastic fields in dissimilar joints under combined loading

Via detailed finite clement limit analyses, plastic limit loads, rotation factors, and crack-tip stress field are investigated for a combined tension and bending of a plance strain single-edge-cracked bimaterial specimen. Limiting bimaterial specimens are considered, consisting of an clastic/perfectly plastic material bonded to an elastic material having the same elastic properties. The limit loads of bimaterial specimens are shown to be very close to those of homogeneous specimens, so that limit load information for homogeneous specimens can be used even for bimaterial specimens. A tractable, approximate elliptical yield locus is proposed, which first the FE. results within 1% for all ranges of tension-to-bending ratios. The plastic rotation factor of bimaterial specimens can be higher than that of homogeneous specimens as much as 25%, when the specimen is subject to small tensile forces. Results from the present analysis is applied to the analysis of typical fracture testing specimens such as compact tension specimens. For both homogeneous and bimaterial specimens, larger tensile forces are associated with substantial loss of crack-tip constrait. Bimaterial specimens have as much as 2 times higher constraint than homogenous specimens, due to plastic strength mismatch. Tractable closed form approximations for crack-tip stresses are proposed in terms of tension-to-bending ratio.     

Nonlinear in-plane elastic buckling of shallow circular arches under uniform radial and thermal loading

This paper presents a nonlinear in-plane elastic buckling analysis of circular shallow arches that are subjected both to a uniform temperature field and to a uniform radial load field. A virtual work method is used to establish nonlinear equilibrium equations and buckling equilibrium equations, and analytical solutions for the limit instability and bifurcation buckling loads are obtained. It is found that the temperature influences the limit instability, bifurcation buckling and postbuckling behaviour of shallow arches significantly. The limit instability and bifurcation buckling loads increase with an increase of the temperature. A maximum temperature is shown to exist for the occurrence of bifurcation buckling of shallow arches, and when the temperature is higher than this value, bifurcation buckling of an arch is not possible.An arch geometric parameter is introduced to define switches between the limit instability and bifurcation buckling modes, and between buckling and no buckling. Formulae and methods for the calculation of the limiting values of the arch geometric parameter are developed. It is also found that the limiting values of the arch geometric parameter decrease with an increase of the temperature.     

Elastic-plastic analysis of a rolling disk by finite elements

An elastic-plastic finite element method is employed to determine the stress distribution in a circular disk rolling on a rigid track and subjected to hub loads. This model can be assumed to represent a railroad wheel. Of particular interest are the stresses that exceed the initial yield limit near the point of contact. The material constitutive laws considered herein represent elastic-perfectly plastic and strain hardening materials that obey Mises' yield condition. It is shown that unloading of the previously yielded elements due to rotation can be easily handled by the direct stiffness tangent modulus approach. Total and plastic strains, and the plastic work in the disk model are given for the entire rolling history of the disk. It is also demonstrated that the disk will shake down to a purely elastic steady state for load values beyond the initial yield if the material of the disk exhibits even a small amount of strain hardening.     

Limit behaviour of masonry arches in the presence of finite displacements

A procedure is proposed for the calculation of the equilibrium paths of a masonry arch with elastic abutments. The elasticity of the abutments implies the existence of a non-linear, non-trivial equilibrium path, with the development of three hinges from the beginning of the load history. The shape of the equilibrium path suggests that shallow masonry arches should be classified in three different ways according to the nature of their failure load. In the first class a fourth hinge can develop as the live load is increased, and a classical failure load is reached when a four-hinge mechanism occurs. In the second case the equilibrium path shows a limit point, and finally it is possible to have a monotonically increasing equilibrium path, with no limit point or bifurcation point. If the arch is very shallow, only these two latter possibilities must be examined, and the presence of non-rigid abutments can cause instability of the arch. This instability phenomenon could be particularly important for flying buttresses of cathedrals, if they were built along rivers, or more generally on elastic soil.     

复杂结构塑性极限分析的修正弹性补偿法

弹性补偿法（ECM）是结构塑性极限载荷分析中一种简单有效的方法,但对复杂结构,其计算结果往往存在较大误差。采用Banach不动点原理,分析了ECM法计算下限极限载荷时存在的收敛性问题,指出只有在弹性模量迭代序列满足压缩映射条件时,才能得到极限载荷的较好的逼近值,从而提出复杂结构极限分析的修正弹性补偿法（KtECM）。该方法采用一种结构主要承载单元的弹性模量迭代序列均满足压缩映射条件的迭代方法,并引入与结构应力集中系数相关的调整因子λ,给出了名义应力的较为合理的定义方法,建立调整因子与应力集中系数之间的关系式。典型复杂结构的极限载荷分析计算表明：KtECM具有简单、高效、易于工程应用等优点,提高了对复杂结构极限载荷的计算精度,调整因子λ的引入可以起到协调计算精度与时间的作用。     

内压及扭矩载荷下无缺陷弯管的塑性极限载荷

弯管在管线中通常是承受应力较大的元件，极限载荷相应较低。为充分发挥结构的塑性极限承载能力，对弯管的塑性极限载荷进行理论分析，利用von Mises屈服准则，推导出内压和扭矩联合载荷作用下等厚弯管、非均匀壁厚椭圆弯管的塑性极限压力。实验验证了理论分析的正确性。     

A FEM study on the mechanical responses of pseudoelastic TiNi alloys to a particle normal loads

In this study, the models of four materials including three sorts of pseudoelastic TiNi alloys and a stainless steel (as a contradistinction) enduring a particle's normal loads were individually simulated based on bilinear strain hardening law by means of finite element method. Owing to the pseudoelasticity, TiNi alloys proved to have high elastic strain limit and low pseudo-Yong's modulus, with which the special mechanical response was created under normal loads. The results shown that pseudoelastic TiNi alloys occurred plastic deformation more difficult than the stainless steel, and the critical load of plastic deformation increased with the increasing elastic strain limit and the decreasing pseudo-Young's modulus. Plastic regions of three TiNi alloys with the elastic strain limit 0.02, 0.04 and 0.06 were 0.60, 0.32, 0.047 times of that of the stainless steel, respectively. When the pseudoelastic TiNi alloys endured a particle's normal loads, the phenomena of decreasing contact stress, von Mises stress and increasing the elastic strain were also observed in this FEM study. In terms of above results, the wear mechanism of pseudoelastic TiNi alloys was discussed finally.     

Elastic flexural-torsional instability of structural arches under hydrostatic pressure

This paper addresses the mechanics of the flexural-torsional buckling instability of pin-ended elastic circular arches, which are acted upon by a hydrostatic loading. This loading arrangement differs from the gravity-based loading usually considered in the literature, in that the load changes its direction with the deformation of the elastic arch during its flexural-torsional buckling, always remaining normal to the contour profile of the arch. The previous treatments of the mechanics of the problem, that assume the load direction remains invariant during flexural-torsional buckling, have been motivated by applications in structural engineering in which this loading regime is valid, but there are a number of applications in more general mechanics where this assumption cannot be made and a solution is needed. Both a mathematically based virtual work principle and a mechanical visualisation of the mechanics of the deformation are considered separately, and they are shown to arrive at the same formulation of the linear differential equations of equilibrium of the buckled arch when the buckling deformations are considered infinitesimal. The differential equations for buckling under radial loading that is distributed uniformly around the circumference of the arch are shown to be solvable in analytic form, resulting in a closed form solution for the elastic buckling load of the arch that hitherto has not been formulated. The buckling equation demonstrates that an arch is stiffer under hydrostatic loading than under gravity loading in its resistance to elastic flexural-torsional buckling.     

New insight into an ancient stone arch bridge—The Zhao-Zhou Bridge of 1400 years old

In this paper an analysis is made for the old Zhao-Zhou Stone Arch Bridge on its carrying capacity based on structural limit analysis. For a stone arch bridge, with a given arch centre line and a given loading condition, there exists a minimum thickness limit for the arch ring. If the actual thickness of the arch ring is less than or equal to that limit, the stone arch will collapse as a result of the development of more than three hinges. The ratio of the actual thickness and the minimum limit characterizes the safety of the arch bridge under that loading condition. A calculation is made in this paper of the minimum thickness limit of the Zhao-Zhou Arch Bridge and its safety factors under a live concentrated load of 10 tons. That ancient bridge with 1400 years of history is shown to be very similar to a modern arch bridge in its appearance and is proved by the calculation to be in good accordance with the modern bridge building science.     

井筒在孔隙压力和渗流作用下的统一极限分析

采用统一强度理论,考虑井筒周围岩石的孔隙压力和渗流作用,对井筒进行弹塑性分析,求出保持井壁稳定的弹性极限载荷和塑性极限载荷的统一解析式。以往基于Mohr-Coulomb强度理论和双剪强度理论的解均为该解的特例。所得的统一解可以用于适合不同强度理论的各类岩石材料的极限分析。     

Buckling and collapse of cylinders with one end open and one end simply supported with varying axial restraint

This paper examines the buckling and collapse of cylindrical shells under axial load with one end radially and tangentially fixed, with varying axial fixity, and the other end free. The bifurcation loads are found for elastic cylinders, while collapse loads are found for both elastic and elastic-perfectly plastic cylinders. The varying axial restraint is applied in the form of linear springs. The eigenvalue buckling loads are calculated with conditions matching those of a classical analysis. Bifurcation loads are shown to be a function of the axial restraint; as the axial restraint is increased, the bifurcation load increases dramatically, until it reaches that of a semi-infinite, open ended cylinder. A non-dimensional form of the axial spring stiffness is proposed, and shown to be applicable across a range of geometries.The collapse load and imperfection sensitivity of cylinders with the boundary conditions examined here is also found to be a function of the axial restraint. Cylinders with low axial restraint are shown to be imperfection insensitive, with collapse loads above, or close to, the bifurcation load. As the amount of axial restraint increases, the collapse behaviour displays a degree of imperfection sensitivity associated with more usual boundary conditions.     

Limit load solution for electron beam welded joints with single edge weld center crack in tension

Limit loads are widely studied and several limit load solutions are proposed to some typical geometry of weldments.However,there are no limit load solutions exist for the single edge crack weldments in tension(SEC(T)),which is also a typical geometry in fracture analysis.The mis-matching limit load for thick plate with SEC(T) are investigated and the special limit load solutions are proposed based on the available mis-matching limit load solutions and systematic finite element analyses.The real weld configurations are simplified as a strip,and different weld strength mis-matching ratio M,crack depth/width ratio a/W and weld width 2H are in consideration.As a result,it is found that there exists excellent agreement between the limit load solutions and the FE results for almost all the mis-matching ration M,a/W and ligament-to-weld width ratio(W-a)/H.Moreover,useful recommendations are given for evaluating the limit loads of the EBW structure with SEC(T).For the EBW joints with SEC(T),the mis-matching limit loads can be obtained assuming that the components are wholly made of base metal,when M changing from 1.6 to 0.6.When M decreasing to 0.4,the mis-matching limit loads can be obtained assuming that the components are wholly made of base metal only for large value of(W-a)/H.The recommendations may be useful for evaluating the limit loads of the EBW structures with SEC(T).The engineering simplifications are given for assessing the limit loads of electron beam welded structure with SEC(T).     

Resolving the contradiction of asperities plastic to elastic mode transition in current contact models of fractal rough surfaces

The paper suggests a revision to the asperities plastic to elastic mode transition in the elastic–plastic contact model of fractal rough surfaces, offered by Majumdar and Bushan [A. Majumdar, B. Bushan (MB model) J. Tribol. 113 (1991) 1–11.]. According to the MB model, the contact mode of a single fractal asperity transfers from plastic to elastic when the load increases and the growing contact area exceeds a certain critical value, which is scale independent. This surprising result of the MB model is in contrast with classical contact mechanics where increasing contact area due to increased load is associated with a transition from elastic to plastic contact. The present study describes a revised elastic–plastic contact model of a single fractal asperity showing that, contrary to the MB model prediction, the critical contact area is scale dependent. The revised model also shows that a fractal asperity behaves as would be expected from classical contact mechanics namely, as the load and contact area increase a transition from elastic to plastic contact mode takes place in this order.     

Plastic mechanism and elastic-analytical approaches applied to estimate the strength of an axially compressed-thin-walled channel steel section beam

This paper presents the study of an analytical model to estimate the strength of a thin-walled channel steel section beam subjected to axial-compressive loads. The model is based on two different methods of analysis, which are performed by analysing a plastic failure mechanism and elastic behaviour of the beam. These analytical methods can be used to establish plastic-unloading and elastic-inclining-theoretical load-deflection behaviour of the beam. Meanwhile, the axial-compressive strength of the beam is estimated by directly measuring the value of load at an intersection point between two different curves of the theoretical load-deflection behaviour. The accuracy of using this analytical model is also verified by comparing its estimated data of the strength to the one obtained from a number of tests on 38 specimens of thin-walled channel steel section under the test loads of axial compression. It is clearly shown that deviation of the analytical data from the experimental one is still scattered within acceptable limits of ±20%. A statistical analysis of the scattered data indicates that its mean value is 1.03 with standard deviation of 0.058. This certainly means that the estimated strength, on average, displaces from the actual one by 3% and mostly tends to be conservative.     

Effect of hard and stiff overlay coatings on the strength of surfaces in repeated sliding

Most work on the strength of coated surfaces has assumed that there are no residual stresses and that the load is applied only once. Both these assumptions are incorrect. The manufacturing process itself may develop large residual stresses in the surface and repeated sliding causes the load to be applied many times, leading to the development of residual stresses. These residual stresses are protective in nature so that a load which causes yielding in the first pass may be supported purely elastically in the steady state. The load limit for elastic steady state is known as the shakedown limit and is the rational design criterion in bearing industries. In the present paper, the effect of coating thickness, coating stiffness and the friction coefficient on the shakedown limit has been investigated and the results are presented in the form of non-dimensional maps.     

Shakedown theory for elastic-perfectly plastic bodies revisited

Yield criteria for elastic-perfectly plastic solids, in particular, the Mises and Tresca ones, permit unlimited hydrostatic stresses, leading to some singularity in the classical Melan–Koiter shakedown theory. Classical shakedown theory is re-examined regarding this problem. It is shown that the complete proofs of both static and kinematic theorems require restrictions on the hydrostatic stresses. A modified shakedown kinematic theorem using a fictitious material that can yield in bulk tension and compression has been constructed for subsequent treatment of real engineering materials, which cannot yield but fail under high hydrostatic stresses. The kinematic theorem should have vanishing hydrostatic plastic strain rate solution for the safety of the body against hydrostatic fracture. In this way, the modified kinematic formulation including the limits on hydrostatic stresses are suggested for application. The modifications are also naturally added into the plastic limit theory, which is a limiting case of the shakedown one. Also in the paper, the kinematic approach is used to deduce some simplified estimates for specific non-shakedown collapse modes of elastic plastic structures.     

Load capacity of components with initial point contact

Formulas have been derived for the critical loads corresponding to the onset of plastic deformation in different loading stages. Likewise, a formula has been obtained for the limiting load corresponding to sharp deviation of the size of the surface impression from the values predicted by the Hertz equations, which describes elastic behavior. A means of increasing the load capacity with initial localized contact is considered.     

Limit analysis of strain-hardening viscoplastic cylinders under internal pressure by using the velocity control: Analytical and numerical investigation

The paper aims to assess plastic limit loads of thick-walled hollow cylinders of strain-hardening viscoplastic materials under internal pressure. Particularly, the problem concerned features in the interaction between strengthening and weakening behavior during the deformation process. Therefore, the relating onset of instability and the stability condition also deserve to be further investigated. Analytical and finite-element limit analysis efforts are both made for complete and comparative investigation. By the concept of sequential limit analysis, the plastic limit loads were acquired by solving a sequence of limit analysis problems via computational optimization techniques. Applying the velocity control as a computational strategy to simulate the action of pressure, the paper investigates analytically and numerically the plastic limit load, the onset of instability and the stability condition of plane-strain circular cylinders. Especially, analytical solutions of the onset of instability were solved explicitly by the fixed point iteration. Validation of the present analytical and finite-element efforts was made completely with good agreement between the analytical solutions and the numerical results.     

Studying magnetic stray field at the surface of elastostrained extensive object

Application of metal magnetic memory effect to revealing stress-concentration zones (SCZ) that occur in a specimen due to cyclic loads within the elastic deformation domain is considered. Experimental data are provided on the search for a correlational dependence between the magnetic stray field of a hot-rolled no. 6 channel bar and the stresses in the domains of elastic and plastic deformation.