Bracing requirements for inelastic castellated beams

Lateral-torsional buckling can be avoided by properly spaced and designed lateral bracing. Bracings are usually assumed to be elastic, and so may be characterized by their elastic stiffnesses. It is well known that an elastic lateral brace restricts partially the lateral buckling of slender beams and increases the elastic buckling moment. However, a full study of the effect of lateral braces on inelastic buckling has not been made especially for castellated beams, and it is not known whether the limiting stiffness for elastic buckling can be applied to castellated beams that buckle inelastically. This paper develops a three dimensional (3-D) finite-element model using a finite-element program and uses it to investigate the effect of elastic lateral bracing stiffness on the inelastic flexural-torsional buckling of simply supported castellated beams with an elastic lateral restraint under pure bending. It was found that for inelastic castellated beams, the effect of bracing initially is increased to some extent as the lateral unbraced length increases and then decreased until the beam behaves as an elastic beam. In other words, the effect of bracing depends not only on the stiffness of the restraint but also on the modified slenderness of the beam. Also, the results show that Winter’s simplified method to determine full brace requirements cannot be applied to inelastic castellated beams. Therefore, a general equation is proposed to determine the value of optimum stiffness in terms of the beam’s slenderness, applicable to all castellated beams under pure bending.     

Elastic lateral-torsional buckling of tapered I-girder with corrugated webs

This paper deals with the elastic lateral-torsional buckling (LTB) strength of tapered I-girders with corrugated webs under two types of loading conditions: uniform moment and moment gradient with various end restraint conditions. A finite element (FE) program using beam elements is developed to study LTB behaviors. The results from this program are compared with those from the commercial software ABAQUS using shell elements. From the comparisons, it is found that the developed FE program’s results agree well with the results from ABAQUS. For design purpose, the closed-form equations for the critical buckling moment of the tapered I-girder with corrugated webs under uniform moment and moment gradient with four types of end restraint conditions: simply supported, warping fixed, lateral bending fixed, and completely fixed are proposed based on the results from the developed FE program. From the numerical investigations, the new design equations give reasonably accurate results. These equations increase efficiency in bridges and buildings design.     

Lateral-torsional buckling of I-girders with discrete torsional bracings

Discrete torsional bracing systems are widely used in practice to increase the lateral-torsional buckling (LTB) strength of I-girders. However, only limited studies are available on the LTB strength of I-girders with mid-span torsional bracing. In addition, equivalent continuous brace stiffness concept is adopted for general discrete torsional bracing problems. This article presents an analytical solution for LTB strength and stiffness requirements of I-girders with discrete torsional bracings under a uniform bending condition. Firstly, the critical moment and torsional stiffness requirement are derived by using an energy method for an arbitrary number of bracing points. The proposed equations are then compared with the results of finite element analyses and those obtained by previous researchers. From the results, it is found that the proposed solutions agree well with the results of finite element analyses regardless of the number of bracing points, while the results for the equivalent continuous brace stiffness concept are not suitable for multiple discrete torsionally braced beams. Finally, reduced formula for the total stiffness requirement is proposed for the purpose of design, and effects of linear moment gradient loading and geometric imperfections on critical moments and stiffness requirement are also observed.     

Lateral-torsional buckling analysis of cantilever beam with tip lateral elastic brace under uniform and concentrated load

The studies on the lateral-torsional buckling of cantilever steel beam with tip lateral elastic brace are rarely reported. The total potential energy is first established for the lateral-torsional buckling of cantilever steel beam with tip lateral elastic brace under uniform and concentrated load. The modal trial function of the lateral displacement and torsional angle are expressed as trigonometric function combination with six terms. By introducing new dimensionless parameters, the analytical solution of the dimensionless buckling equation for the lateral-torsional buckling of cantilever steel beam with tip lateral elastic brace is obtained. With the help of 1stOpt software which is mathematical optimization analysis software, the non-dimensional critical moment formula of the lateral-torsional buckling of cantilever beam with tip lateral elastic brace is obtained. Then, the accuracy of the formula is verified by ADINA finite element software. The results show that the given critical moment formula is of high accuracy. It provides convenient and simple design method for practical engineering.     

Bending behavior of concrete-encased composite I-girder with corrugated steel web

A partially encased composite I-girder with flat or corrugated web has been proposed to improve the structural performance of continuous composite girder under hogging moment. The flexural behavior of such structure under two points symmetric loading has been experimentally and analytically investigated. Static flexural loading tests showed that the partially encased girder improved bending strength in comparison to steel I-girder, as local bucking of steel flange was restricted by encased concrete. Especially for the corrugated web girder, the ultimate bending strength was improved about 20%, and the ductility also increased about 3 times. In addition, the limitation of width-to-thickness ratios for steel and concrete-encased composite I-girders with corrugated web were suggested to prevent premature failure due to local buckling of compressive flange. Moreover, the analytical methods of flexural strength under service and ultimate state for partially encased composite girder were proposed and verified with experimental results. It was found that the analytical bending strengths agreed well with the experimental ones at both service and ultimate state, which means the proposed analytical equations can be applied in predicting flexural strength accurately for such encased composite girder with flat or corrugated web.     

部分混凝土外包波形钢腹板组合工字梁的抗剪性能试验研究

针对提高负弯矩作用下连续梁的结构特性提出了一种新型的部分混凝土外包波形钢腹板组合工字梁。对这种混凝土外包组合工字梁在对抗荷载下的抗剪性能进行试验分析研究。试验结果显示与普通的工字梁相比,混凝土外包组合工字梁的剪切屈曲因受外包混凝土的限制而有了更好的抗剪强度。由于组合截面的抗剪刚度是基于波形钢腹板和破裂前外包混凝土平均厚度的总和,且其抗剪强度决定了由钢腹板和外包混凝土共享的抗剪强度比。此外,根据试验中的破坏模式和应变分布,提出部分混凝土外包波形钢腹板组合工字梁的预估抗剪强度。试验结果验证了之前分析得出的弹性阶段的抗剪刚度和抗剪比。且之前计算得出的钢腹板与组合梁的抗剪强度也与试验结果一致。通过对比可知文中提到的分析方法可以应用到部分混凝土外包波形钢腹板组合工字梁结构的抗剪刚度预估和抗剪强度设计中去。     

Moment modification factor of I-girder with trapezoidal-web-corrugations considering concentrated load height effects

Moment modification factors of the I-girder with trapezoidal web corrugations subjected to concentrated load, applied at different heights on the cross section and various end restraint conditions, are investigated. The moment modification factors are obtained by finite element buckling analyses. The new FEM program is developed by using beam elements and new general formulas of cross-section properties as well as a new warping constant of the I-girder with trapezoidal web corrugations. The theoretical results of moment modification factors are compared with commercial finite element software (ABAQUS) using shell elements. A series of finite element analyses with different corrugation profiles and lengths is performed. Through comparative numerical studies, the theoretical results are successfully verified. The moment modification factors from the SSRC Guide are compared with present FEM results. The new values of the variable C_b, the moment modification factor, in the SSRC Guide are proposed as the variable C_b,c to improve the accuracy of lateral-torsional buckling strength.     

有平面外支撑的工形截面圆弧钢拱弹性稳定性能及支撑刚度设计

采用有限元特征值屈曲数值方法，对平面外支撑工形截面圆弧拱弹性屈曲荷载及其刚度取值进行研究。在考虑各种荷载条件与拱脚条件下，研究了支撑刚度，约束类型、数量以及作用位置对钢拱平面外屈曲性能的影响，对于设置等间距侧向支撑的情况，给出了侧向支撑弹性门槛刚度的拟合式，并提出了支撑点间拱段不发生平面外弹性失稳的条件。研究结果表明：平面外支撑越靠近拱顶，其防止平面外失稳的工作效率越高；设置侧向支撑的钢拱屈曲时，随着支撑刚度的增大其屈曲半波数逐渐增加，而仅在拱顶设置扭转约束时始终呈现1个半波失稳模式；从均匀受压圆弧拱的情况获得的等间距侧向支撑门槛刚度，应用在其他组合荷载作用下，同样可以获得足够的支承刚度；当工形截面钢拱的支撑点间拱段长度满足所提出的要求时，钢拱平面外失稳不先于平面内反对称整体失稳。     

Shear behavior of partially encased composite I-girder with corrugated steel web: Experimental study

A new type of partially encased composite I-girder with corrugated steel web has been proposed to improve the structural performance of continuous girders under hogging moment. The shear behavior of such partially encased composite I-girders under anti-symmetric loading has been experimentally and analytically investigated. Experimental results show that the partially encased composite girders has superior shear strength compared to steel I-girders, since shear bucking of steel web is restricted by concrete encasement. The shear stiffness of the composite section is based on the total summation of corrugated web and concrete encasement with average thickness before cracking, and the ratio of shear resistance shared by the steel web and the concrete encasement depends on their shear stiffness. In addition, predicted shear strength of the partially encased composite girder with corrugated web is proposed according to the experimental failure mode and strain distribution. The analytical shear stiffness and shear resistance ratio at the elastic stage are verified by experimental results. And the calculated shear strength for steel and composite girders agree well with the experimental results. The comparison shows that the proposed analytical methods can be applied in predicting elastic shear stiffness and design shear strength for such partially encased composite girders with corrugated web.     

Elastic lateral stability of I-shaped cellular steel beams

In this paper, the lateral stability of cellular steel beams is numerically investigated. The study is carried out using three-dimensional finite element modeling of simply supported I-shaped cellular steel beams with a broad spectrum of cross-sectional dimensions, span lengths and web perforation configurations. Stability analyses are carried out for beams subjected to equal end moments, mid-span concentrated loads and uniformly distributed loads. Finite element results reveal that, unlike the case of conventional beams with solid webs, the moment-gradient coefficient C_b is significantly influenced by the beam geometry and slenderness. In addition, the C_b coefficient of cellular beams depends on the web perforation configuration. Moment-gradient coefficient values that fluctuate closely to those values recommended by design codes are associated with pure elastic lateral torsional buckling (LTB) deformations. As the beam slenderness decreases, the web distortion increases, leading to the lateral distortional buckling (LDB) mode, which is associated with lower C_b values than code-recommended ones. Severe reduction in the C_b coefficient to values less than 1.1 is noticed for shorter-span beams where the response is dominated by non-lateral local buckling modes.A simplified approach is developed to enable accurate prediction of a moment modification factor κ_LB for cellular beams. The proposed κ_LB factor is provided by an empirical formula that is derived based on the best fit of the finite element results related to lateral buckling (LTB and LDB) modes only. The proposed approach allows for accurate and conservative evaluation of the critical moment associated with the lateral torsional/distortional buckling of cellular beams. Several numerical examples are worked out to illustrate the application of the proposed procedure.     

Innovative steel bridge girders with tubular flanges

I-shaped steel girders with tubular flanges have been studied for application in highway bridges because of their large torsional stiffness compared to conventional I-shaped steel plate girders (I-girders). For straight girder bridges, the large torsional stiffness of a tubular flange girder (TFG) results in significantly greater lateral–torsional buckling strength compared to a corresponding I-girder. For horizontally curved girder bridges, the large torsional stiffness of a TFG results in much less normal stress, vertical displacement and cross-sectional rotation compared to a corresponding I-girder. The paper presents experimental and finite element analysis results for straight and horizontally curved TFG bridges. The results show the advantages of TFGs in comparison to conventional I-girders. A TFG demonstration bridge constructed in the USA is described.     

Buckling of interbraced beam systems

Analyses of parallel beam floor support systems under both uniform beam moment and uniform spread load are carried out. The beams are braced by lines of braces which provide torsional and lateral support and which may be attached eccentrically. Charts illustrate the variation of the buckling load of this interconnected structure under different brace stiffnesses and eccentricities and, in particular, show the levels of stiffness at which ‘full bracing’ is achieved. The matrix equation which allows the uniform moment calculations to be quickly made is presented. Other cases employ a beam-column finite element.     

偏心支撑压弯构件稳定性分析

对压弯构件在跨中设置侧向支撑和扭转支撑时的稳定性进行研究 ,先就一般情况建立平衡微分方程 ,推导出压弯构件的稳定临界方程 ,在此稳定临界方程的基础上对偏心支撑压弯构件进行详细的分析 ,得到了使压弯构件计算长度减半的扭转支撑临界刚度表达式和侧向支撑临界刚度表达式 ,导出了判断支撑是否能使压弯构件计算长度减半的临界荷载偏心。此外还分析了非完全支撑时支撑刚度和构件承载力的关系 ,以及侧向支撑、扭转支撑及两者联合作用对构件承载力的影响 ,推出了上面所有分析的解析式     

Shear strength of horizontally curved steel I-girders — finite element analysis studies

This paper presents the results of finite element analysis (FEA) studies of four curved steel I-girder shear components tested experimentally in previous research, as well as parametric extensions of these tests. These studies focus on the influence of horizontal curvature on the maximum strength of transversely stiffened members with web slenderness D/t_w approximately equal to the largest value permitted in AASHTO [AASHTO LRFD bridge design specifications. 3rd ed. In: 2005 Interim Provisions, Washington (DC): American Association of State and Highway Transportation Officials; 2004], and with panel aspect ratios of d_o/D=1.5 and 3.0. These ratios are larger than previously considered in experimental tests of curved I-girders with similar or larger slenderness. The girders studied have subtended angles between their bracing locations of L_b/R=0.05 and 0.10, and web panel d_o/R values ranging from 0.03 to 0.10. The FEA models incorporate the measured material stress-strain relationships and section dimensions from the physical tests, detailed modeling of the test boundary conditions, residual stresses due to flame cutting and welding, and initial geometric imperfections in the form of buckling mode shapes. The load transfer mechanisms of the test girders are investigated via elastic buckling and full nonlinear analyses. The parametric studies are performed to investigate the effects of residual stresses and geometric imperfections, the behavior of equivalent straight girders, and the influence of reduced flange size on the peak shear capacity and moment-shear interaction.     

拱墙结构平面外失稳机理与设计研究

拱墙是一种由拱、立柱、横梁组合而成的竖向平面结构，横梁上的竖向平面内荷载通过立柱传递到大跨度拱体中。为研究拱墙结构的失稳机理，采用有限元分析方法，对拱墙模型在弹性和弹塑性条件下的稳定性能进行了研究。分析结果表明：立柱侧向刚度及横梁侧向支撑刚度是影响拱墙稳定性能的主要因素，当横梁侧向支撑刚度小于其门槛刚度时，拱墙的屈曲模式表现为拱墙整体平面外失稳；当横梁侧向支撑刚度大于其门槛刚度而立柱的侧向刚度小于其门槛刚度时，拱墙的屈曲模式表现为拱体的平面外失稳；当横梁侧向支撑和立柱的侧向刚度均大于各自的门槛刚度时，拱墙的屈曲模式表现为拱墙整体平面内失稳。结合某火车站站房工程，建立了横梁位置施加侧向弹簧支撑和带纵向桁架的两种拱墙模型，分析了该拱墙结构的平面外稳定承载力。结果表明，纵向桁架为拱墙横梁提供的平面外支撑刚度远大于拱墙的侧向支撑门槛刚度，提高拱墙的平面外稳定承载力需通过增大立柱的侧向刚度和加强立柱两端的可靠连接实现。     

Analytical and parametric investigations on lateral torsional buckling of European IPE and IPN beams

Lateral torsional buckling is one of the main failure modes controlling the strength of the slender thin-walled members. A transversely or transversely and axially combined loaded member that is bent with respect to its axis of greatest flexural rigidity may buckle laterally and twist as applied load reaches its critical value unless the beam is provided with a sufficient lateral support. This study intends to present a unique convenient equation that it can be used for calculating critical lateral-torsional buckling load of simply supported European IPE and IPN beams. First, an analytical model is introduced to describe lateraltorsional buckling behavior of beams with monosymmetric cross-section. The analytical model includes first order bending distribution, load height level and monosymmetry property of the section. Then, parametric study is carried out using the analytical solutions in order to establish a simplified equation with dimensionless coefficients. The effect of slenderness and loading positions on lateral-torsional buckling behavior of IPE and IPN beams are studied. The proposed solutions are compared to finite element simulations where thin-walled shell elements and beam elements including warping are used. Good agreement between the analytical, parametric and numerical solutions is demonstrated. It is found out that the lateral-torsional buckling load of European IPE and IPE beams can be determined by presented equation and can be safely used in design procedures.

     

偏心受压铝合金构件稳定的试验研究

以长细比和荷载偏心率为主要参数,测试了19个H形截面铝合金挤压型材偏心受压试件的稳定承载力,13个试件在受弯平面内发生了整体弯曲屈曲,6个试件在受弯平面外发生了弯扭屈曲。对试验结果进行了分析,并将试验结果与国家标准《铝合金结构设计规范》(报批稿)以及《欧洲铝合金结构设计规范》(EN9)进行了比较。研究表明,对于弯曲屈曲两规范与试验结果均吻合较好,对于弯扭屈曲两规范都偏于安全,且两种情况下我国规范与试验结果均更为接近。     

门式刚架中隅撑轴力强度的ANSYS分析

研究受到檩条和隅撑支撑作用的梁的弯扭,首先对檩条-隅撑体系提供结果的侧向支撑刚度进行了推导,然后考虑梁的初始侧移,研究了使梁的临界弯矩达到屈服弯矩时隅撑中的内力,这个内力即是对隅撑的强度要求。通过4个算例表明,隅撑轴力不到下翼缘屈服轴力侧向分量的1%,远小于《门式刚架轻型房屋钢结构技术规程》(CECS 102∶2002)中规定的支撑力。     

门式刚架梁隅撑设计的强度要求

研究了受到檩条和隅撑侧向支撑的梁的弯扭失稳问题。首先对檩条-隅撑体系对梁提供的侧向支撑刚度进行了推导,然后考虑檩条位置和隅撑支撑作用的特点,对梁的弯扭失稳临界弯矩与支撑刚度的关系进行了有限元分析,考虑梁的初始侧移和初始扭转,研究了使梁的临界弯矩达到屈服极限时隅撑中的内力,这个内力即是对隅撑的强度要求。通过4个算例表明,侧向支撑力小于下翼缘屈服轴力的1%,远小于《门式刚架轻型房屋钢结构技术规程》(CECS 102∶2002)中规定的支撑力。     

Numerical validation of the general method in EC3-1-1 for prismatic members

Part 1-1 of Eurocode 3 includes a general method for lateral and lateral-torsional buckling of structural components that uses a Merchant-Rankine type of empirical interaction expression to uncouple the in-plane effects and the out-of-plane effects. In this paper, the safety of this approach is assessed for prismatic members subjected to compression, bending and bending and axial force by comparison of both with advanced nonlinear numerical simulations (GMNIA) using beam and shell elements and the other Eurocode 3 approaches based on the European buckling curves. Analytical expressions are derived for columns, beams and beam-columns that show the variation of resistance with varying slenderness. A parametric study is carried out whereby cross-sectional shape, type of loading, slenderness and steel grade are varied. It is concluded that the method gives similar levels of safety as the methods prescribed in clauses 6.3.1 to 6.3.3 of Eurocode 3, part 1-1.