Resistance of steel I-sections under axial force and biaxial bending

The plastic criteria for the verification of steel cross-sections resistance are usually based on some basic hypotheses such as the development of plastic hinges, which depend on the interaction between the internal forces and the cross-section shape; therefore, specific equations are required for each type of cross-section.This paper presents new alternative interaction criteria for the analysis of steel I-sections subjected to an axial force and biaxial bending moments, at the elastic or the plastic limit states (as long as buckling phenomena are not involved).The plastic interaction criteria are presented, in a first step, for some particular combinations of the internal forces, such as axial loading with bending about a main axis, and biaxial bending without axial loading. In these cases, they are given by exact equations (within the frame of the hypotheses adopted in this study). All these plastic interaction criteria are compared with the corresponding plastic criteria adopted in the Eurocode 3 (EC3).Afterwards, a simplified global criterion is proposed for the simultaneous combination of an axial force and bending moments about both the main axes of inertia. This new simplified plastic criterion and the corresponding plastic criterion adopted in the EC3 are compared with the exact solution, obtained by a mixed numerical and analytical integration procedure. This comparison shows that this simplified criterion usually leads to results closer to the exact solutions. Some suggestions are then presented to improve the results given by the EC3.     

Coupled instability of thin-walled members under combined bending moment, axial and shear force

In this paper we analyse the behaviour of thin-walled steel members with an I-shaped cross-section, in the presence of phenomena of coupled instability as overall-local type and combined state of stress of bending moment, axial and shear force. The analysis has been made by the ‘column model method’ and it has been used for bending moment-curvature-axial force diagrams, modified by the presence of local instability for web buckling of steel beams.

The previous analysis allows one to define interaction diagrams M_Imax−λ−N, which can be used to check the steel members in relation to the overall slenderness and the local slenderness of the web panel.     

轴力和弯矩共同作用下盾构隧道纵向非线性等效抗弯刚度研究

实际工程中,盾构隧道纵向弯矩和轴力可能同时存在,若按传统的纯弯等效抗弯刚度计算可能会带来较大误差。考虑轴力和弯矩共同作用对纵向弯曲变形的影响,提出5种弯曲模式,在经典的志波模型的基础上,建立盾构隧道纵向等效抗弯刚度计算模型,基于该模型开发了计算程序,以成都地铁3号线盾构隧道为实例,对其纵向等效抗弯刚度和管环张开量随轴力和弯矩的发展规律进行分析,并讨论弯曲模式的实用判别方法,求出变形过程的临界弯矩,最后给出纵向弯曲变形为线性和非线性的内力条件。研究发现:盾构隧道纵向变形随弯矩的发展过程可按轴力分为4类,各过程下管环张开量和等效抗弯刚度随弯矩的发展规律十分不同;轴力对等效抗弯刚度有显著影响,一般呈现压弯纯弯拉弯的规律。研究成果可应用于盾构隧道结构纵向力学分析、抗弯刚度分析等方面。     

Partially stiffened RHS sections under transverse bearing force

Concentrated force applied to rectangular hollow sections (RHS) members at loading or reaction points can lead to web crippling of the members. This paper investigates the possibility of improving the web crippling behaviour of RHS sections using internal stiffeners. Tests of RHS sections partially filled with concrete and with wood plus a bolt through the web are described. Both end-bearing and interior-bearing forces were applied. Design models are established for the four failure modes identified in the tests. The parameters varied include section aspect ratio (D/B) which ranges from 1.5 to 3.0, web depth to thickness ratio (D/t) which ranges from 15 to 75, and bearing length to section width ratio (γ=N/B) which ranges from 0.5 to 1.0.     

Ultimate strength formulations for stiffened panels under combined axial load, in-plane bending and lateral pressure: a benchmark study

This paper develops advanced, yet design-oriented ultimate strength expressions for stiffened panels subject to combined axial load, in-plane bending and lateral pressure. The collapse patterns of a stiffened panel are classified into six groups. It is considered that the collapse of the stiffened panel occurs at the lowest value among the various ultimate loads calculated for each of the collapse patterns. The panel ultimate strengths for all potential collapse modes are calculated separately, and are then compared to find the minimum value which is then taken to correspond to the real panel ultimate strength. The post-weld initial imperfections (initial deflection and residual stress) are included in the developed panel ultimate strength formulations as parameters of influence. The validity of the developed formula is confirmed by comparing with the mechanical collapse tests and nonlinear FEA. A comparison of the present method is also made with theoretical solutions from the Det Norske Veritas classification society design guideline. Important insights developed are summarized.     

截面轴力与弯矩屈服面在钢框架动力弹塑性分析中的应用

为了在现行规范下考虑轴力与弯矩的相互作用,并兼顾计算精度与计算效率,研究了截面屈服面在钢框架动力弹塑性分析中的新应用。首先选用截面组合思想构建轴力与弯矩的屈服面。接着,基于经典塑性理论建立截面恢复力模型,并给出了截面状态确定方法。然后阐述了基于力的梁柱单元状态确定过程及其对截面恢复力模型的调用。最后采用alpha-OS积分算法,对一个四层两跨钢框架开展了动力弹塑性分析。结果表明：截面轴力弯矩屈服面能很好地考虑轴力存在及变化对截面弯矩承载力的影响,基于屈服面的恢复力模型在计算精度上远高于塑性铰模型并逼近纤维模型,在效率上远高于纤维模型,可以用于钢框架的动力结构弹塑性分析。     

Ultimate strength of stiffened plates with a square opening under axial and out-of-plane loads

The high strength to weight ratio and high stiffness to weight ratio of stiffened plates find wide application in aircraft structures, ship structures, offshore oil platforms and lock gates. The strength and stability of stiffened plates is highly influenced by openings and initial imperfections. The main objective is to study the behaviour of stiffened steel plates with openings up to collapse and to trace the post-peak behaviour under axial and out-of-plane loads. Four stiffened steel plates with a square opening were fabricated for testing. Angle sections were used as stiffeners. Imperfections in the plate, stiffener and overall imperfection of the whole panel were measured. All fabricated panels were tested to failure. A finite element (FE) model was developed for the analysis of stiffened plates with initial imperfections and validated with the test results. Parametric studies were conducted using the developed FE model, and interaction curves and equations were developed for the design of stiffened plates with initial imperfections and openings. The interactive effect for stiffened panels with a square opening was found to be linear, with proportional reduction of the ultimate axial load carrying capacity due to the constant out-of-plane load.     

The design of perforated cold-formed steel sections subject to axial load and bending

The uprights in a typical pallet rack are typically singly-symmetrical cold-formed sections subject to axial load together with bending about both axes. They usually contain arrays of holes in order to enable beams to be clipped into position at heights that are not pre-determined prior to manufacture. Their slenderness is such that their behaviour may be influenced by the three generic forms of buckling, namely local, distortional and global (lateral torsional). In practice, these members have generally been designed on the basis of expensive test programmes. This paper addresses the problem of how they might be designed analytically. The basis of the investigation is a comprehensive set of test results on upright sections in compression which embraces both stub column tests, in which the load position was varied along the axis of symmetry, and longer columns. The test results were analysed using both finite elements and a version of “Generalized Beam Theory” (GBT) which incorporated systematic imperfections. Consideration was also given to the design procedures proposed by the “Federation Europeene de la Manutention” (FEM) and recent research into the influence of perforations on the performance of cold formed steel sections. It is shown that GBT can be modified to take account of perforations so that the lower bound results give a sufficiently accurate column design curve, which takes account of local, distortional and global buckling, thus making extensive testing unnecessary.     

An experimental study on steel-caged RC columns subjected to axial force and bending moment

Among the different methods of strengthening RC columns, steel caging is one of the most extensively used, for square or rectangular cross-section columns. Few studies have been carried out on steel caging and most of these have focused on axially loaded strengthened columns, without taking the effects of bending moments into account. This paper presents the results of a series of experimental tests on full-scale specimens strengthened with steel caging including simulation of the beam-column joint under combined bending and axial loads. Capitals were applied to all the specimens to connect the caging with the beam-column joint either by chemical anchors or steel bars to improve the transmission of forces. In all the specimens tested it was observed that steel caging increases both the ultimate load and ductility of the strengthened columns. The specimens fitted with steel bars reach higher ductility and strength than those with chemical anchors. The laboratory results were compared with three design proposals and the degree of fit with each one was analysed.     

高强钢焊接箱形截面压弯构件局部稳定试验研究

为研究高强钢压弯构件的局部稳定性能,对5个Q460C和5个Q690D钢焊接箱形截面构件进行了单向偏压试验,分析了其破坏形式、局部稳定性能以及承载力;将实测承载力与欧洲规范EN 1993-1、我国标准GB 50017—2017和美国规范ANSI/AISC 360-16相关公式计算结果相比较,以验证各规范对Q460C钢和Q690D钢焊接箱形截面压弯构件屈曲后强度计算的适用性。研究结果表明：所有高强钢焊接箱形截面压弯构件均在柱中附近发生局部屈曲破坏;由轴向压力-轴向压缩变形或轴向压力-水平位移曲线可知,其为极值点失稳;构件的轴向压力-水平位移或轴向压力-应变曲线的形状和局部屈曲模式有关;在翼缘宽厚比为28.1～56.3、腹板高厚比为40.2～80.4、偏心距为20～50 mm范围之内,EN 1993-1和GB 50017—2017中的屈曲后强度计算公式仍然适用于Q460C和Q690D钢焊接箱形截面压弯构件,而ANSI/AISC 360-16中的相关公式需要进一步修正。     

Behaviour of semi-rigid steel beam-to-beam joints under bending and axial forces

This paper presents an analysis of semi-rigid beam-to-beam end-plate bolted joints that are subjected to bending and tension or a compression axial force. Usually the influence of axial force on joint rotational stiffness is neglected. According to EC3, the axial load, which is less than 10% of plastic resistance of the connected member under axial force, may be disregarded in the calculation of characteristics of a joint. Actually, the level of axial forces in joints of structures can be significant and has a significant influence on characteristics of semi-rigid joints. One of the most popular practical methods permitting the determination of rotational stiffness and moment resistance of a joint is the so-called component method. The extension of the component method for evaluating the influence of bending moment and axial force on the rotational stiffness and moment resistance of a joint are presented in the paper. The numerical results of calculations of characteristics of joints and calculations of steel framework are presented in this paper as well.     

轴向力作用下岩柱抗弯刚度的数值解

基于平截面假定,利用MATLAB程序编写了岩柱在不同轴向力作用下的弯矩曲率计算程序,以得到地下工程中岩（矿）柱抗弯刚度的计算方法和其弹性区和软化区数值特征,最后分析了轴向力对岩柱抗弯刚度和岩爆的影响,结果表明,随着轴向力的增加,岩柱的抗弯刚度基本不变,但抵抗极限弯矩的能力随之加强,而岩柱在岩爆中释放的弯曲应变能也愈大。     

Elasto-plastic response of orthotropic pipes under bending, pressure and axial force

An elasto-plastic analysis of circular thin-walled pipes in the non-buckled configuration subjected to bending moment, pressure and axial loads is presented. Plastic stress-strain relationships based on Drucker's postulates, Hill's yield criterion and the deformation theory are utilized. The analysis includes orthotropic behaviour with the assumption of a linear strain-hardening material. Results are presented for both isotropic and orthotropic materials.     

超大轴力及弯矩钢管砼柱柱脚设计方法

本文主要介绍双向倾斜的巨型框架柱在超大轴力、超大弯矩荷载作用下的柱脚结构形式的优化选用及钢管柱柱脚计算方法,归纳重型钢管混凝土柱柱脚设计要点及合理选型原则,为类似工程提供参考。     

Ultimate strength and ductility of stiffened steel tubular bridge piers

This paper presents the ultimate strength and ductility of steel tubular bridge piers with the inner cruciform plates, the stiffener plates, the concrete-filled sections and the outer tube subjected to monotonic and cyclic horizontal loads. Numerical analyses were carried out using the finite element package MARC. Firstly, to check the validity of the numerical analysis, the analytical results of the steel tubular columns with the inner cruciform plates, the concrete filled sections and the outer tube were compared with the previous experimental results. Secondly, the effects of the radius-to-thickness ratio parameter and the slenderness ratio parameter on seismic performance (the ductility, the ultimate strength etc.) of these steel tubular piers were examined. Numerical results indicated that the steel column with inner cruciform plates was able to improve the ultimate strength and ductility of the steel tubular piers.     

Free vibration of partially supported piles with the effects of bending moment, axial and shear force

The pile parts above the soil and embedded in the soil are called the first region and the second region, respectively. The fourth order partial differential equations of both regions for free vibration of partially supported pile subjected to bending moment, axial force and shear force are obtained using the small-displacement theory and the Winkler model. It is assumed that the behavior of the material is linear-elastic, and that axial force along the pile length and modulus of subgrade reaction for the second region to be constant. Shear effect is included in the partial differential equations by the second derivative of the elastic curve function with respect to shear deformation. Natural circular frequencies and relative stiffness of the pile are calculated for non-trivial solution of linear homogeneous system of equations obtained due to the values of axial forces acting on the pile, the shape factors, and the boundary conditions of the pile with both ends free and both ends simply supported; the results are presented in graphs.     

Finite element analysis of CFT columns subjected to an axial compressive force and bending moment in combination

Proper material constitutive models for concrete-filled tube (CFT) columns subjected to an axial compressive force and bending moment in combination are proposed and verified in this paper by using the nonlinear finite element program ABAQUS compared against experimental data. In the numerical analysis, the cross sections of the CFT columns are categorized into three groups, i.e., ones with circular sections, ones with square sections, and ones with square sections stiffened with reinforcing ties.It is shown that the steel tubes can provide a good confining effect on the concrete core when the axial compressive force is large. The confining effect of a square CFT stiffened by reinforcing ties is stronger than that of the same square CFT without stiffening ties but weaker than that of a circular CFT. Nevertheless, when the spacing of reinforcing ties is small, a CFT with a square section might possibly achieve the same confining effect as one with a circular section.     

Full plastic capacity of equal angle sections under biaxial bending and normal force

Steel angle members are usually designed by elastic methods, which may lead to uneconomical design. In order to make use of the plastic reserves of the section, the knowledge of its exact failure surface is important. In this study, it is shown that idealizing the section with lines of no thickness, which is common in the literature, entails a significant error when the neutral axis intersects a leg at a small angle. A simple interaction formula is proposed, which is shown to be very accurate based on an exhaustive analysis of all common angle sections listed in the tables. Further increase in accuracy is achieved through analytical relations for the cross-sectional properties, both elastic and plastic, that are derived. The proposed analysis forms the base of inelastic design and does not address stability issues.     

Limit analysis of strain softening steel frames under pure bending

The present paper extends the classical limit analysis approach for steel structures to account for local strain softening behavior. As is well-known, the bound theorems underpinning the collapse load estimation of ductile structures require an assumption of perfect plasticity. They are invalid for the class of structures, such as those being considered here, that exhibit local softening. We propose a method, based on the same conditions governing the path-independent state problem, for capturing the maximum load multiplier characterizing the one parameter proportionally applied loading regime. The problem is cast as a special instance of the notoriously difficult to solve class of problems known as a mathematical program with equilibrium constraints (MPEC). Various solution approaches, all based on solving the MPEC as a standard nonlinear programming problem, are briefly presented. One of them, namely the penalty scheme, is used to solve the three numerical examples provided to highlight application of the proposed limit analysis approach.     

Ultimate load-carrying capacity of cold-formed thin-walled columns with built-up box and I section under axial compression

The use of cold-formed thin-walled steel structures has increased in recent years, and some built-up section members are motivated and also widely used for their excellent structural behaviors. In this paper, a series of axially-compressed tests on built-up box section members composed of two C-section by self-drilling screws at flanges are conducted. The differences of global, local and distortional buckling behaviors between members with built-up and single sections are investigated at first. Then the effects of installation error and fastener spacing on ultimate load-carrying capacity of built-up members are analyzed. A strength estimation method for built-up members under axial compression is proposed based on the experimental investigation in this paper, as well as some existing experiments, and corresponding numerical analysis studies. Finally, the predicted capacity obtained by using the proposed strength estimation method is compared with experimental results and the nominal axial strength determined according to the AISI provisions, by which the suitability and accuracy of the proposed strength estimation method have been established.