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This paper presents a state-of-the-art discussion of the behavior, strength, and design of steel columns. Demonstrating the progressive improvements which have taken place with respect to understanding the various parameters influencing the strength of columns, current procedures can take into account all major effects and provide for very good correlation with test results. Some new data are discussed regarding the strength of very heavy columns, with potential implications for their use in structures. It is shown that the developments of limit-states design criteria, which have prompted careful examinations of the variability of the strength and the various parameters that play a role, have led to significant improvements in the reliability of members and the overall structures. Future developments are discussed briefly.

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... Secara umum itu dikenal sebagai rumus Secant, yang pada dasarnya adalah kombinasi gaya aksial dan bending momen, yang diakibatkan oleh adanya defleksi lateral akibat beban aksial tersebut (fenomena P-δ). Beberapa kurva perencanaan kolom yang dikenal adalah rumus Tredgold dan Rankine-Gordon (Bjorhovde 1988). Kondisi batas yang umumnya dipakai adalah apabila tegangan telah mencapai kondisi leleh atau kelipatannya. ...

... Pada perencanaannya, kolom dianggap terisolasi dari struktur lainnya sebagai kolom tunggal dengan tumpuan sendi-sendi. Hubungan kolom tunggal tadi terhadap kekakuan elemen struktur lainnya adalah memakai faktor K (panjang tekuk efektif), lihat Gambar 6. Itulah cara yang dipakai dalam AISC Load and Resistance Factor Design Specification, Canadian limit-states design standard, dan banyak lainnya (Bjorhovde 1988). Konsep kolom terisolasi itu tentu hanya ada secara teoritis. ...

... Catatan : AISC Allowable Stress Design Specification -6 th Ed. dari tahun 1963 dan sesudahnya (setelah 1988 perlu diteliti lagi) adalah didasarkan pada rumus Tangent Modulus (Bjorhovde 1988). ...

ABSTRAK Meskipun draft SNI Baja (Puskim 2011) yang mengacu AISC (2010) belum diresmikan, tetapi minimal dapat diketahui acuan keilmuan struktur baja di Indonesia, yaitu American Code. AISC (2010) sendiri memuat dua metode perencanaan, yaitu [1] Effective Length Method (ELM), cara lama sebagai alternatif; dan [2] Direct Analysis Method (DAM), cara baru berbasis komputer yang diunggulkan. Makalah ini akan mengupas secara mendalam : mengapa DAM dan apa keunggulannya dibanding ELM. Makalah akan dibagi menjadi dua bagian, yaitu : [1] Latar belakang teori; [2] Contoh aplikasi praktis.

... Secara umum itu dikenal sebagai rumus Secant, yang pada dasarnya adalah kombinasi gaya aksial dan bending momen, yang diakibatkan oleh adanya defleksi lateral akibat beban aksial tersebut (fenomena P-δ). Beberapa kurva perencanaan kolom yang dikenal adalah rumus Tredgold dan Rankine-Gordon (Bjorhovde 1988). Kondisi batas yang umumnya dipakai adalah apabila tegangan telah mencapai kondisi leleh atau kelipatannya. ...

... Pada perencanaannya, kolom dianggap terisolasi dari struktur lainnya sebagai kolom tunggal dengan tumpuan sendi-sendi. Hubungan kolom tunggal tadi terhadap kekakuan elemen struktur lainnya adalah memakai faktor K (panjang tekuk efektif), lihat Gambar 6. Itulah cara yang dipakai dalam AISC Load and Resistance Factor Design Specification, Canadian limit-states design standard, dan banyak lainnya (Bjorhovde 1988). Konsep kolom terisolasi itu tentu hanya ada secara teoritis. ...

... Catatan : AISC Allowable Stress Design Specification -6 th Ed. dari tahun 1963 dan sesudahnya (setelah 1988 perlu diteliti lagi) adalah didasarkan pada rumus Tangent Modulus (Bjorhovde 1988). ...

ABSTRAK Meskipun draft SNI Baja (Puskim 2011) yang mengacu AISC (2010) belum diresmikan, tetapi minimal dapat diketahui kalau acuan keilmuan struktur baja Indonesia adalah American Code. AISC (2010) sendiri memuat dua cara perencanaan, yaitu [1] Effective Length Method (ELM), cara lama untuk dijadikan alternatif; dan [2] Direct Analysis Method (DAM), cara baru berbasis komputer yang diunggulkan. Makalah ini akan mengupas secara mendalam apa itu DAM, apa keunggulannya dibanding ELM sehingga memahami arti penting mempelajarinya.

... For the case of steel columns, the current level of knowledge reflects the fact that much effort has been devoted to evaluating practical applications of the strength and performance data that are available (Beer and Schulz 1970;Bjorhovde 1972Bjorhovde , 1978Bjorhovde , 1988Galambos 1998;Ziemian 2010). It is a matter of record that the present amount of data and other information very significantly exceeds the size of the data base that was used to establish earlier column formulas. ...

... The more column strength parameters that are incorporated into the model, the closer will be the values of the theoretical and the physical strengths. Thus, column models (iii) and (iv) of the preceding chapter of this paper are generally capable of producing results that are within 5 percent of the experimental data (Bjorhovde 1972(Bjorhovde , 1988Galambos 1988Galambos , 1998Ziemian 2010). ...

... It reflected the tangent modulus solution for a perfectly straight column with residual stress. The three SSRC Curves that were developed by Bjorhovde (1972Bjorhovde ( , 1988 were maximum strength solutions, taking into account residual stress as well as initial out-of-straightness, and also incorporated the random nature of all of the column strength parameters. These curves were a perfect fit for a code that would be based on limit states principles, which was done for the US in the late 1970-s and early 1980-s (Johnston 1976;Galambos 1988Galambos , 1998Ziemian 2010). ...

The strength and stability of steel columns have been the subjects of a great many studies since the original work of Leonhard Euler in 1744 and 1759. Numerous examinations of elastic buckling of perfectly straight columns were conducted during the 19th century, the most famous being the studies of Engesser and Considère, with several series of column tests attempting to find agreement between theory and physical behavior. The research work continued in the 20th century, examining the influence of material and member imperfections, including the famous tangent modulus work of Shanley, and the resolution of the effects of material non‐linearity, residual stress and column out‐of‐straightness. The definitive solutions were only obtained in the 1970‐s, when modeling and numerical solutions allowed for the incorporation of all nonlinear effects. Since that time reliability and probabilistic solutions have provided state‐of‐the‐art criteria for limit state treatment of the column problem. These principles are now the bases of the design standards for columns in all of the countries in the world. The paper focuses on the major evolutions that have taken place, but especially the work over the past 40 years. Realistic treatment and representation of the strength of columns in actual structures have now been achieved by the engineering profession.

... According to all the former expressions, the relationship between the co-rotational displacements and the global ones, which means differentiate q α with respect to p i , is given by: (22) In which ϕ d is the rigid body rotation, with α = 1 to 3, and i = 1 to 6, what determines the called Instantaneous Change of Coordinates Matrix B(ϕ d ), expressed by: (23) Making ϕ d = 0 in the last equation, it's found the Kinematical Incidence Matrix just seen before B 0 on Eq. (20b), that is following: (24) Now can be determined the FE's Stiffness Matrix referred to the global system, by derivation of Eq. (20a) with relation to a global displacements p i , remembering that exists additionally some part from rigid body motion, joined to geometrical compatibility. By this way, can be found the equation: (25) The term in parenthesis of Eq. (25) is found by differentiating Eq. (21) with respect to q β : (26) in which: ...

... Liew et al. [24] recommended L/1500, adopted by ECCS [6]. Bjorhovde [25] by statistical way found the same mean value. ...

This paper presents a little study about the necessary steps to qualify a second- order inelastic analysis as advanced one.
Plastic-zone approach is applied to steel plane frames (portals) and the numerical formulation is based on finite element
model of a Bernoulli-Euler beam-column member using the called “slice technique”. This element is set on a Lagrangian updated
co-rotational system. The nonlinear problem is solved using Newton-Raphson iterative strategy and a new axial force iterative
integration is shown. This process was implemented on a computer program PPLANAV* and the minimum requirements of advanced
analysis (initial geometrical imperfections and residual stress) are automatically generated. Two examples show good agreement
with other researcher’s answers, but there’s a great elapsed computing time.

... Liew et al. (1993) recomendam, entretanto, o valor adotado pelo ECS3 (1993: H/1500. Bjorhovde (1988) obteve por meios estatísticos o mesmo valor médio. ...

Este artigo fornece os fundamentos necessários para que as análises inelásticas de segunda ordem com plasticidade distribuída (método da zona plástica) em estruturas metálicas planas sejam qualificadas como uma Análise Avançada. Utiliza-se uma formulação de elementos finitos para barras à flexo-compressão segundo a teoria de Bernoulli-Euler, baseada em pequenas deformações. O elemento finito é descrito em um sistema Lagrangiano corrotacional e o problema não-linear é resolvido de forma incremental usando a técnica iterativa de Newton-Raphson. É apresentado um novo processo para integração do esforço normal, que é calculado agora de forma iterativa e que permite um bom comportamento do modelo. Esta formulação é empregada para avaliar dois exemplos de colunas à flexo-compressão, com perfis I. Esses exemplos incluem alguns requisitos importantes da Análise Avançada, ou seja: tensões residuais, curvatura inicial das barras e fora de prumo da estrutura. Os resultados mostram que a formulação é acurada ao determinar a carga limite, esforços e deslocamentos, porém com elevado tempo de processamento.

... Welded I-sections undergo a different manufacturing process than the hot-rolled I-sections are 133 subjected to. Unlike hot-rolled I-sections, in which it was observed that the larger the section, the greater the 134 intensity of the residual stresses, the welding process has a greater influence on the distribution and intensity 135 of the residual stresses of light I-sections [31,39,[45][46][47]. Nagarajo Rao et al. [48], Alpsten and Tall [31] and 136 Dwight and White [49] studied the distribution form and the factors that influence the residual stress values 137 of welded I-sections. ...

The structural imperfections, namely, the residual stresses, are generated during most manufacturing processes involving material deformation, heat treatment, machining or processing operations. The intensity and distribution of residual stresses are dependent on the techniques used in the production of steel sections (welding, rolling or cold formed techniques) and their dimensions. An appropriate evaluation of residual stress is of great importance for the structural performance of steel I-beams. Residual stresses can have a significant impact on the stability of structural members. In the case of I-section beam elements, such stresses can impact lateral torsional buckling (LTB) strength, particularly in the inelastic range. For the development of post buckling numerical analyses, the consideration of residual stress distribution models is fundamental for the correct determination of the LTB strength of I-beams. However, there are several models that attempt to represent the distribution and intensity of residual stresses. These models have a different influence on the LTB behavior of I-beams in numerical analysis. Therefore, this paper aims to investigate, through the development of post buckling numerical analyses with the ABAQUS software, the influence of the different residual stress distribution models on the LTB strength of I-beams. Seven different residual stress models were analyzed on simply supported I-beams subject to uniformly distributed loading applied in the shear center and in the upper flange. The results were compared with standard procedures. It was verified considerable divergences in LTB strength depending on the residual stress model applied. In addition, this paper presents a synthesis of the main residual stress distribution models. The analyses showed in this work shall help the choice of the residual stress distribution model on future numerical simulations.

... Unlike hot-rolled I-sections, in which it was observed that the larger the section, the greater the 276 intensity of the residual stresses, the welding process has a greater influence on the distribution and intensity 277 of the residual stresses of light I-sections [62,63,[77][78][79]. Nagarajo Rao et al. [80], Alpsten Dwight and White [81] studied the distribution form and the factors that influence the residual stress values 279 of welded I-sections. ...

The behavior of structural steel frames is significantly influenced by the presence of structural and geometric imperfections. The structural imperfections, namely, the residual stresses, are generated during most manufacturing processes involving material deformation, heat treatment, machining or processing operations. As the residual stresses, the geometric imperfections are fundamental in the analysis of critical buckling and post-buckling behavior of thin-walled structures. These initial imperfections can be captured using the second order inelastic analysis, also known as advanced analysis. In the modern steel design codes, e.g., European code EC3, Australian code AS4100, North American Code AISC360-16 and Chinese code GB50017 the development of advanced numerical analyses is allowed to predict the behavior of steel and composite frames. However, the random nature of the shapes and magnitudes of the initial imperfections results in difficulties in developing these analyses. Therefore, this paper presents an assessment of the influence of structural imperfections, namely, the residual stresses, and geometric imperfections on the Lateral Distortional Buckling (LDB) strength of steel-concrete Composite Beams (SCCB). The basis of the research is a thorough comparison between numerical and experimental results. Several residual stress patterns found in the literature have been implemented in numerical simulations of four different tests on SCCB subjected to uniform hogging moment. In addition, a sensitive analysis of the geometric imperfection values, namely, the initial bending, was developed. The post buckling numerical analyses were developed with the ABAQUS software. The analysis shown in this work shall help the choice of the initial imperfections on future numerical simulations on SCCB.

... Then, the simulations of the models of geometrical imperfections were performed, as previously presented and the results are shown in Fig. 5. Finally, the imperfections were combined, generating a model with both physical and geometrical imperfections, therefore Fig. 6 presents the results for the columns analyzed with the combination of the five residual stress models presented in Table 1 with a geometric imperfection of / 1,000 L . This value of geometric imperfection was adopted because it is the maximum tolerated value in structural profiles ( Kala and Valeš [18], Bjorhovde [19]). Therefore, the following results relate the ratio between the critical buckling load ( cr P ) and the ) to the different slenderness ratios of the column, which has the HP250x85 profile as the geometrical section. ...

... The maximum out-of-straightness permitted in the AISC COSP [44] is effectively L b /1000. Bjorhovde [45,46] determined that wide-flange section members in North America tend to have values near this maximum tolerance, with an average of approximately L b /1500 and a coefficient of variation of 10%. However, Dux and Kitipornchai [11] and Essa and Kennedy [47] measured out-ofstraightness values of L b /3300 and L b /2000 respectively in their studies. ...

The lateral torsional buckling (LTB) resistance equations of the unified design provisions under-lying the current AISC and AASHTO Specifications are a fit to a large body of experi¬mental test data for light to medium weight rolled and welded I-section members. The resulting nominal LTB resistances differ considerably from those of the Eurocode provisions, which tend to provide a lower-bound fit to experimental and simulation data. It is observed that finite element test simula¬tions conducted with defacto standard practices commonly predict lower capacities than indicated by experimental tests. This disconnect is shown to be partly due to the use of simple deterministic resid¬ual stress patterns and geometric imperfections in test simulations that are conservative approx¬i¬mations of the true values occurring in physical tests. This paper aims to resolve this dis¬con¬nect by employ¬ing an “inverse solution” approach, wherein appropriate simplified residual stresses and geomet¬ric imperfections to model in test simulations are determined based on correla¬tion with experi¬mental data. In addition, the paper presents the results of extensive sensitivity studies on I-section members subjected to uniform moment. These studies justify the use of as low as one-half the magnitudes of common nominal residual stresses and geometric imperfections in test simulations. In addition, these comparisons justify reductions in the “plateau length,” Lp, used in the AISC and AASHTO flexural resistance calculations, as well as in the stress limit FL in AISC and Fyr in AASHTO corresponding to the applicability of the theoretical elastic LTB equations.

The strength and stability of columns have been the subjects of numerous studies since the original work of Euler in 1744 and 1759. Elastic buckling of perfectly straight columns was examined during the 19th century, with landmark theories developed by Engesser and Considère. Several series of column tests were conducted to establish the correlation between theory and physical behavior. Research in the 20th century examined the influence of material and member imperfections, including the tangent modulus study of Shanley. These efforts provided the resolution of the effects of material non-linearity, residual stress and out-of-straightness. The definitive solutions were developed in the 1970-s, when modeling and numerical procedures allowed all nonlinear effects to be included. Since that time reliability and probabilistic solutions have provided state-of-the-art limit states criteria for steel columns. Such approaches are now the bases for columns in all advanced design codes in the world. © (2010) by COPPE - Federal University of Rio de Janeiro All rights reserved.

The strength and stability of steel columns have been the subjects of a great many studies since the original work of Leonhard Euler in 1744 and 1759. Numerous examinations of elastic buckling of perfectly straight columns were conducted during the 19th century. The most important of these were the studies of Engesser and Considère, with several series of column tests attempting to find agreement between theory and physical behavior. The research work continued in the 20th century, examining the influence of material and member imperfections, including the seminal tangent modulus work of Shanley, and the resolution of the effects of material non-linearity, residual stress and column out-of-straightness. The definitive solutions were only found in the 1970-s, when modeling and numerical procedures allowed for the incorporation of all nonlinear effects. Since that time reliability and probabilistic solutions have provided state-of-the-art criteria for limit state treatment of the column problem. These principles and approaches are now the bases of the design standards for columns in all countries.

Design codes are essential for all construction projects, but especially in the international market. Materials, elements, structural systems and analysis techniques differ somewhat between geographical regions, although computational equipment and other tools of the design profession have become remarkably similar over the past decade. Thanks to globalization and efficient means of communication, the different design and construction teams may be located in widely separated areas. However, professionals rely on codes and standards to be able to execute the assignments properly. Since the requirements and especially the forms of expression of such documents tend to vary from region to region, it is critical to understand the basic code philosophies and practical approaches. The paper focuses on some of the criteria of various steel design standards, and evaluates the resulting strength and serviceability requirements. It is found that safety and reliability are never in question, and that the real structural differences are limited. Construction economy is another matter all together.

A problem of the influence of residual stresses together with the material and geometry parameters on the resistance of a selected type and size of the hot rolled HEA wide-flange columns is elaborated. Two parallel approaches are used to define the nominal and design resistances. The two methods used for the study include the method of modified column deflection curve with the first-order-reliability-method (FORM) application and the approach based on the FEM with the Monte Carlo simulation for stochastic analysis. The compliance of die differences in resulting strengths with assignment of the cross-section to one column strength curve is also evaluated.

Tubular members are used extensively in offshore structures, which are installed to facilitate offshore oil and gas production. Member damage, in the form of dents, can be caused by supply workboat collisions, dropped heavy objects, and minor mishaps during offshore structure construction, loadout or installation. To avoid costly repair and construction delay, a fitness-for-purpose evaluation may be performed to ascertain whether a repair is necessary. The ultimate strength, and sometimes the pre- and post-ultimate strength behavior, of a dented member may be required to conduct the fitness-for-purpose evaluation.A moment-thrust-curvature (MPΦ) approach for calculating the behavior and ultimate strength of dented tubular members is presented. A new set of MPΦ expressions for dented or undented tubular members, presented previously by the authors, is used. A computer program, BCDENT, was developed, whose capabilities include analysis of single or multiple-dent tubular members subjected to axial compression, end bending moments, and laterally distributed and concentrated loads. In order to capture accurately the tubular member behavior for the multiple-dent and biaxial bending cases, BCDENT employs a three-dimensional beam-column analytical method. In this paper, the validity and accuracy of the MPΦ approach for the behavior analysis of dented tubular members are verified by comparing BCDENT predictions to existing test results from several references.

Design guidance for structural steel members under combined axial and transverse loads, or beam-columns, has evolved from very simple assumptions to the present ultimate-strength approaches. The change in design recommendations have paralleled the state of knowledge of the behavior of these structural elements. Early elastic models have given way to an understanding of inelastic behavior. This paper follows the advances in design recommendations for these members from the late 19th century to the present specifications, including load and resistance factor design. An example of the application of these methods to a typical steel beam-column is shown. This information on past design methods will be of assistance to structural engineers involved with rehabilitation of vintage structures.

The American Institute of Steel Construction was founded in 1921 and issued the first US structural steel design code in 1923.11The steel design code in the US is officially called the Specification for Structural Steel Buildings. In this paper the words specification and code are used interchangeably, meaning the same thing. It was 10 pages long and based on the principles of allowable stress design (ASD). The ASD code was subsequently published in various editions, through the ninth in 1989. No substantive changes have been made to this document since the eighth edition (1978). Limit state design, or Load and Resistance Factor Design (LRFD) as it is called in the United States, was officially introduced by the first (1986) edition of the LRFD Specification. It was based on extensive research and development carried out over 15 years. This code has since been revised twice; the current version is the third edition (1999).The presence of two design codes has created difficulties for US designers and industry. The AISC Committee on Specifications therefore undertook to develop a single, unified structural steel design code, which has just been approved (April 13, 2005). The paper describes the key concepts of the new code, including the use of nominal strength criteria in combination with appropriate measures of reliability. Among many other developments, significant additions have been made in the requirements for stability and bracing design for framing systems, including novel methods using inelastic criteria.

This paper develops exact and approximate probabilistic characteristics of the buckling strength of end-restrained metal columns The exact probability density function of the strength is developed from the transcendental equation that governs the buckling condition by nonlinear transformation of random variables It can only be evaluated by numerics On the other hand closed-form solutions can be obtained if the transcendental equation is approximated by a smooth and differentiable analytic function A simple analysis procedure based on this approximation is proposed to predict the strength of metal columns with uncertain end restraints The procedure uses the conventional effective length factor for columns and incorporates the mean and standard deviation of the end restraint in formulation The end restraint is modeled with two identical rotational springs at the ends of the column The spring constant for these springs is assumed to be a Weibull-distributed random variable with known parameters Results in this work show that the characteristics of the column strength such as the mean and standard deviation vary significantly with the degree of uncertainty of the end restraint It is assumed in this work that the column is slender and free of imperfections and residual stresses.

The paper presents the results of a study on the maximum strength and behavior of wide-flange steel columns of large cross-sectional dimensions. Thus, hot-rolled and welded built-up shapes of flange thickness up to 150 mm and web thickness up to 75 mm were examined, using a variety of steel grades and manufacturing methods. It was found that there is a clear correlation between the relative maximum strength and the flange thickness for heavy hot-rolled wide-flange shapes. Specifically, the capacity drops by as much as 10 to 15% as the flange thickness goes from 25 to about 75 mm. As the thickness increases further, the relative maximum strength goes up, and it regains its full value when the flange is 125 to 150 mm thick. The effect is a function of the slenderness ratio of the column; it is most pronounced in the intermediate range. Welded built-up shapes appear to be less heavily influenced by the flange thickness variation, especially for short and long members. However, the welded shape database was limited, and further studies need to be conducted to verify the findings for these shapes. The results are currently being evaluated for design code recommendations.

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