高强钢焊接箱形柱力学性能研究(Ⅱ)：二阶非弹性分析

高强钢的焊接残余应力分布和普通钢材的有较大差异,现有的切线模量和刚度退化函数不适合用于高强钢焊接箱形截面的二阶非弹性分析。而精炼塑性铰模型通过切线模量和刚度退化函数可合理考虑残余应力的影响和塑性渐进发展,达到与塑性区模型相近的精度。基于此,提出适合高强钢焊接箱形截面的二阶非弹性分析方法。通过稳定函数考虑单元二阶效应,基于杆端部转动引起的构件弯曲及其导致的轴向应变,考虑弯曲效应。在精炼塑性铰模型中,采用高强钢焊接箱形截面的残余应力统一分布模型,通过截面分析法构建不同强度等级的焊接箱形截面切线模量计算公式。同时,分析轴力和弯矩共同作用下的渐进屈服对箱形截面刚度退化的影响,从而建立可模拟截面塑性发展的刚度退化函数。结合塑性铰的产生与发展对平衡微分方程解的影响,建立梁柱单元的弹塑性刚度矩阵。结果表明,所提出的二阶非弹性分析方法可准确分析高强钢焊接箱形截面轴压构件的力学性能,可应用于高强钢框架结构设计,为二阶非弹性分析方法的工程应用提供参考。     

A computer method for nonlinear inelastic analysis of 3D semi-rigid steel frameworks

This paper presents an efficient computer method for inelastic and large deflection analysis of steel space frames with non-linear flexible joint connections, based on the most refined type of second order inelastic analysis, the plastic zone analysis. The method employs modeling of structures with only one element per member, which reduces the number of degree of freedom involved and the computational time. Gradual yielding of cross-sections is modeled using the nonlinear inelastic force strain relationships, and then using the flexibility approach the elasto-plastic tangent stiffness matrix and equivalent nodal loads vector of 3-D beam-column element is developed. The method ensures also that the plastic bending moment is nowhere exceeded once a full plastified section develops. A zero-length rotational spring element is used for incorporating the connection flexibility into the element tangent stiffness matrix and equivalent nodal forces. The combined effects of material, geometric and connection behaviour nonlinearity sources are simulated into an object oriented computer program automatically. This program was used to study the ultimate response of several steel frames, which have been studied previously by other researchers. The example of computations and the comparisons made have proved the robustness, accuracy and time saving of the proposed analysis method.     

Implications of using refined plastic hinge analysis for load and resistance factor design

A plastic hinge analysis based on a two-surface stiffness degradation model is outlined for second-order inelastic analysis of steel structures. The analysis approach is based on refinements to the elastic-plastic hinge method and allows for a smooth transition from initial yielding to the full yielding of cross-sections in a beam-column element. This analysis method shows a good representation of the inelastic structural response compared to the conventional elastic-plastic hinge analysis, and it is efficient for use in the analysis design of large-scale structures. Design implications, recommendations and case studies for use of refined plastic hinge analysis for direct frame design considering semirigid connection effects are presented.     

Nonlinear inelastic response history analysis of steel frame structures using plastic-zone method

A beam–column element formulation and solution procedure for nonlinear inelastic analysis of planar steel frame structures under dynamic loadings is presented. The spread of plasticity is considered by tracing the uniaxial stress–strain relationship of each fiber on the cross section of sub-elements. An elastic perfectly-plastic material model with linear strain hardening is employed for deriving a nonlinear elemental stiffness matrix, which directly takes into account geometric nonlinearity and gradual yielding. A solution procedure based on the combination of the Hilber–Hughes–Taylor method and the Newton–Raphson method is proposed for solving nonlinear equations of motion. The nonlinear inelastic time-history responses predicted by the proposed program compare well with those given by the commercial finite element package known as ABAQUS. Shaking table tests of a two-story steel frame were carried out with an aim to clarify the inelastic behavior of the frame subjected to earthquakes generated by the proposed program. A more practical analysis method for seismic design can be developed by comparing it with the presented frames for verification.     

Analysis of strain hardening creep under random uniaxial loading

Significant advances have taken place in developing methods of analysis of creep and creep rupture under varying stress conditions. However, the attention so far has been focussed on studying creep under deterministic stress histories. Time dependent stress and environmental history of a typical structure element is often definitely not known and it can, at best be described in statistical terms. Idealizing creep as a Markoff process and considering strain hardening theory, a simplified theory is proposed to characterize creep strain under random loading. The random loading refers to statically determinate uniaxial stressing, changing in a stepwise manner with time only and forms an ergodic process. In the light of the feasibility of characterizing the strain distribution under the random loading, an indication is given how a reliability based design approach to creep problems can be developed. The theory and its application are illustrated by a numerical example.     

岩石蠕变对边坡支挡力影响的有限元分析

岩石具有蠕变效应,对砂岩和泥岩岩样分别进行蠕变试验和松弛试验,采用广义Kelvin模型对试验数据作拟合,得到两类岩石在不同压力水平下的蠕变参数,采用有限元程序对重庆地区典型的泥、砂岩互层边坡作数值分析,考虑了边坡开挖卸荷影响区的岩层蠕变效应,分析结果表明,由于泥岩层的剧烈蠕变,支挡锚杆轴力随时间变化明显,最上排锚杆轴力增加幅度达132%,坡顶向外位移也显著增大,建议今后边坡支挡设计时对于上部支挡力增大,对上部尤其第一排锚杆重点加强,加强方法是增加配筋和增大锚固长度。     

Compound-element modeling accounting for semi-rigid connections and member plasticity

A general model of a compound element is proposed in this article to consider the combined influence of semi-rigid connections and plasticity on the non-linear responses of steel frameworks. The stiffness degradation of semi-rigid connections is modeled by a moment–rotation relationship with four parameters, while the plasticity formation of a member end from initial yield to full yield is modeled by an elliptic moment–rotation relationship. The compound element resulting from the combined influence of member plasticity and semi-rigid connection behaviour is used to facilitate the derivation of member stiffness coefficients where the effects of geometrical non-linearity and member shear deformation are also included for the progressive-failure analysis. On the basis of member plasticity behaviour, the categories of semi-rigid connections are investigated. Three semi-rigid steel frameworks are analysed to illustrate the proposed analysis method, and the results are compared with those obtained from experiments and the application of other methods.     

Calculation of the strain hardening behaviour of steel structures based on mill tests

The influence of strain hardening on elastic-plastic frame instability has become more critical since the introduction of modern design codes (e.g. Eurocode 3: part 1.1), which require a much more rigorous treatment of frame instability than was the case with earlier codes. At the same time, it has become apparent that portal frames are much more sensitive to second-order effects than was previously believed. Both the simplicity and economy of plastic design are endangered and there is renewed interest in defining the extent to which advantage can be taken of strain hardening with modern steel qualities and section shapes. This paper provides an up to date assessment of the strain hardening factor that may be incorporated into computer programs for second-order elastic-plastic analysis. A survey of tensile tests (mill tests) is presented which shows that the strain hardening behaviour is independent of material thickness and steel grade. This allows a generalisation of the stress-strain relationship for hot rolled steel to be defined. A modelling technique is presented that allows the non-linear moment-deformation behaviour of beams to be accurately predicted using mill test data. Finally, results from the survey of mill tests are combined with the moment-deformation model to estimate values of the strain hardening factor to be used during elastic-plastic design.     

Second-order distributed plasticity analysis of steel frames with semi-rigid connections

This paper proposes an accurately and efficiently numerical procedure for distributed plasticity analysis of semi-rigid steel frames. Both geometric and material nonlinearities are included in the proposed analysis. Geometric nonlinearities due to the large and small P-Delta effects are respectively captured using the corotational formulation and curvature-based displacement procedure. Material nonlinearities due to residual stresses and inelastic behaviour of materials are taken into account using a fibre model. The nonlinear semi-rigid behaviour of beam-to-column connections is simulated using a zero-length connection element. The validity of the present analysis is verified by comparing the obtained predictions with existing solutions. A case study of a very large-scale steel frame indicates that the present analysis is very reliable and computationally efficient and thus would be a valuable tool for daily use in office engineering design.     

考虑时变因素修正的混凝土斜拉桥换索前初态模型

为准确掌握混凝土斜拉桥换索施工前的索力和主梁受力状态,建立的换索施工前的初态分析模型,需要对其运营期间混凝土收缩徐变、预应力索应力松弛、恒载性超载等因素产生的影响进行评估。而混凝土弹性模量、徐变、收缩及预应力筋松弛等因素具有与时间历程和应力历史紧密关联的材料非线性特征,采用有限元增量分析是合理的选择。为此,在时间历程划分的基础上,推导了考虑材料徐变、松弛、收缩影响的弹塑性有限元求解方程,建立了时间增量步内单元计入徐变、收缩、松弛影响的数值函数表达式,给出了斜拉索损伤刚度修正的具体措施和恒载性超载影响计入的分析方法,建立的初态模型分析技术进一步改善了混凝土斜拉桥运营期的桥梁状态评估方法。     

Elastic-plastic analysis of internally pressurized torispherical shells

The constitutive equation for an elastic-plastic material model was derived using the von Mises yield criterion and assuming isotropic strain hardening. A layered finite element permitting geometrically linear and geometrically nonlinear elastic-plastic analysis of thin shell structures is presented. The effect of linear strain hardening on the size of plastic regions and the distribution of internal forces in an internally pressurized torispherical shell was analyzed. At sufficiently high pressures a significant difference in the distribution of internal forces was observed between elastic, perfectly plastic and strain hardening material. The effect of the size of plastic regions on the difference in the magnitude of internal forces obtained by geometrically linear and geometrically nonlinear computations of the torispherical shell was studied. An increase in the size of the plastic region was found to produce greater differences in the computation of meridional bending moments than in the computation of hoop stress resultants.     

TIME EFFECTS IN CONCRETE-FILLED STEEL BOX COLUMNS IN TALL BUILDINGS

This paper considers the time dependent effects of creep and shrinkage of concrete in a fabricated steel box column typically used in tall building construction. The effects of creep and shrinkage on the behaviour of the steel box are considered using the age adjusted effective modulus method. The analysis has been undertaken to include incremental loading to simulate the construction of individual floor levels in a building. A parametric study has been developed to consider the effects of various material and geometric properties as well as the number of constructed levels of the building. A study of the strain and stress distribution is undertaken and a numerical model for the determination of the axial shortening is developed. Recommendations for further research to be undertaken including full-scale experiments and material property testing are suggested in order to augment the minimal research data available. © 1997 John Wiley & Sons, Ltd.     

Lateral buckling strengths of cold-formed Z-section beams

This paper is concerned with the inelastic lateral buckling strengths of cold-formed Z-section (CFZ) beams. The point symmetry of the cross-section of a CFZ beam introduces characteristics that are not encountered in a doubly symmetric I-beam. Firstly, the effective section rotates after yielding, so that a CFZ beam under in-plane bending about the geometrical major principal axis is subjected to bending moments about the effective minor axis and bimoments. Secondly, the minor axis bending and warping strain distributions and therefore the lateral inelastic buckling behaviour and strengths of CFZ beams are related to the twist rotation and minor axis displacement directions. The stress–strain curves, residual stresses, initial imperfections, and lipped flanges of CFZ beams are all different to those of hot-rolled I-beams. This paper develops a realistic finite element model for the analysis of CFZ beams and uses it to investigate the elastic lateral-distortional buckling, inelastic behaviour, and strengths of CFZ beams with residual stresses and initial imperfections. The results of the study are used to develop improved design rules which are suitable for CFZ beams. The effects of moment distribution and load height on the lateral buckling strengths are also studied.     

Effect of transient creep on the behaviour of reinforced concrete columns in fire

Concrete experiences transient creep when subjected to elevated temperatures, which is believed to be the result of thermo-mechanical interactions within the cement paste microstructure. Transient creep occurs in compression under first time heating. Although it is particularly relevant to the behaviour of columns, which most of the time are under a state of compression, its systematic effects on their performance and stability under fire have not been well elucidated. Indeed, current design of reinforced concrete columns is based at worst on tabulated data, which bear no resemblance to real fires, or at best, on codes of practice that consider transient creep through the deformation properties of concrete. Using a previously developed finite element code, which is capable of considering transient creep either explicitly as an additional strain rate component, or implicitly through the deformation properties of concrete, a systematic study of its effects on the behaviour of an unrestrained column is presented. It was found that transient creep gives rise to additional compressive stresses in the column magnifying any bending moments, and therefore precipitating its failure.     

Nonlinear inelastic analysis of building frames with thin-walled cores

A second-order inelastic analysis by combining the theories of stability and plasticity is proposed for studying frames with thin-walled cores. In the proposed approach, steel frameworks surrounding the cores are modelled by using the plastic hinge beam-column approach, and core walls modelled by using the thin-walled beam-column approach. Transformation procedures are proposed to consider the kinematic relationship between beams, columns, core walls and floor diaphragm. Nonlinear solution procedures are incorporated for the incremental analysis. The proposed inelastic analysis is used to investigate the inelastic behaviour and ultimate strength of core-braced frames.     

Pile Capacity in Nonhomogeneous Softening Soil

Closed form solutions for vertically loaded piles in elastic-plastic, nonhomogeneous soil have been established recently using an ideal elastic-plastic load transfer model. However, in some cases, the load transfer from piles to the surrounding soil shows softening behaviour. In this paper, the established solutions are extended to account for this behaviour using a simplified strain softening soil model. The solutions are recast in non-dimensional forms, and expressed via modified Bessel functions. The effect of non-homogeneity and the degree of softening on pile capacity is explored.     

Simulation of the behaviour of stiffened box girders with and without shear lag

A finite element program with large deformations and plasticity is used to analyse the behaviour of stiffened compression flanges of box girders. Simulations are performed for pure bending and for bending with shear in order to investigate the diminishing of the shear lag effect at collapse. It is concluded that at the actual ultimate load, shear lag has largely disappeared but that a design at ultimate load without consideration of the shear lag may entail an inelastic behaviour under service load. First yielding occurs in the centre of the stiffened panel for pure bending and in the middle of the unloaded edges when elastic shear lag becomes important. A substantial increase of the ultimate load can be expected from an increase of the stiffener rigidity.     

Practical nonlinear analysis of steel–concrete composite frames using fiber–hinge method

A fiber–hinge beam–column element considering geometric and material nonlinearities is proposed for modeling steel–concrete composite structures. The second-order effects are taken into account in deriving the formulation of the element by the use of the stability functions. To simulate the inelastic behavior based on the concentrated plasticity approximation, the proposed element is divided into two end fiber–hinge segments and an interior elastic segment. The static condensation method is applied so that the element comprising of three segments is treated as one general element with twelve degrees of freedom. The mid-length cross-section of the end fiber segment is divided into many fibers of which the uniaxial material stress–strain relationship is monitored during analysis process. The proposed procedure is verified for accuracy and efficiency through comparisons to the results obtained by the ABAQUS structural analysis program and established results available from the literature and tests through a variety of numerical examples. The proposed procedure proves to be a reliable and efficient tool for daily use in engineering design of steel and steel–concrete composite structures.