Web bend-buckling strength of plate girders with two longitudinal web stiffeners

김병준,박용명,김경식,최병호 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.69 No.4

More than one longitudinal web stiffener may be economical in the design of plate girders that have considerably high width-to-thickness ratio of webs. In this study, the bend-buckling strength of relatively deep webs with two horizontal lines of flat plate-shaped single-sided stiffeners was numerically investigated. Linear eigenvalue buckling analyses were conducted for specially selected hypothetical models of stiffened web panels, in which top and bottom junctions of a web with flanges were assumed to have simply supported boundary conditions. Major parameters in the analyses were the locations of two longitudinal stiffeners, stress ratios in the web, slenderness ratios and aspect ratios of web panels. Based on the application of assumptions on the combined locations of the two longitudinal web stiffeners, simplified equations were proposed for the bend-buckling coefficients and compared to the case of one longitudinal stiffener. It was found that bend-buckling coefficients can be doubled by adopting two longitudinal stiffeners instead of one longitudinal stiffener. For practical design purposes, additional equations were proposed for the required bending rigidity of the longitudinal stiffeners arranged in two horizontal lines on a web.

Stiffness Requirement for Flat-Bar Longitudinal Stiffener of Box-Girder Compression Flanges

Do Dai Thang,구민세,정영도,Asif Hameed 한국강구조학회 2009 International Journal of Steel Structures Vol.9 No.2

In this paper, the moment of inertia requirement of flat-bar longitudinal stiffener of bottom flange in steel box girder is investigated through finite element modeling. The required minimum stiffness for longitudinal stiffeners of box girder flange is given in the AASHTO LRFD Bridge Design Specification and is modified by Yoo. However, this requirement is adopted for T-shape stiffeners. Here, the effect of important parameters on the minimum required moment of inertia of flat-bar stiffener is numerically investigated by examining the anti-symmetric mode of buckling. This study presents the results that are based on 3D finite-element analysis of four hundred hypothetical compression flange models stiffened by varying numbers of flatbar longitudinal stiffeners with realistic dimensions such as the height of stiffener, the thickness of the compression flange, the number of longitudinal stiffeners and the aspect ratio of plate panel. A new proposed equation for required minimum stiffness of the flat-bar longitudinal stiffeners is derived from nonlinear regression analyses. Beside that the study has taken into account the effect of boundary conditions and the effect of inelastic transition on the critical buckling stress of compression flange. Through the evaluation of a design example, the validity and reliability of the new proposed equation is demonstrated. In this paper, the moment of inertia requirement of flat-bar longitudinal stiffener of bottom flange in steel box girder is investigated through finite element modeling. The required minimum stiffness for longitudinal stiffeners of box girder flange is given in the AASHTO LRFD Bridge Design Specification and is modified by Yoo. However, this requirement is adopted for T-shape stiffeners. Here, the effect of important parameters on the minimum required moment of inertia of flat-bar stiffener is numerically investigated by examining the anti-symmetric mode of buckling. This study presents the results that are based on 3D finite-element analysis of four hundred hypothetical compression flange models stiffened by varying numbers of flatbar longitudinal stiffeners with realistic dimensions such as the height of stiffener, the thickness of the compression flange, the number of longitudinal stiffeners and the aspect ratio of plate panel. A new proposed equation for required minimum stiffness of the flat-bar longitudinal stiffeners is derived from nonlinear regression analyses. Beside that the study has taken into account the effect of boundary conditions and the effect of inelastic transition on the critical buckling stress of compression flange. Through the evaluation of a design example, the validity and reliability of the new proposed equation is demonstrated.

수평보강재가 설치된 플레이트거더 복부관의 조밀기준에 관한 연구

이명수(Lee Myung Soo),이두성(Lee Doo Sung),이성철(Lee Sung Chul) 대한토목학회 2010 대한토목학회논문집 A Vol.30 No.6A

하중-저항계수 설계법에서 조밀단면은 휨모멘트에 의하여 특정단면이 소성모멘트에 도달하기 전에 복부판과 플랜지에 국부 좌굴 및 거더의 횡비틈좌굴이 발생하지 않는 단면으로 정의하고 있다. AASHTO LRFD(2007)에서는 수평보강재를 갖지 않는 단면에 관해서만 조밀단면을 만족하는 복부판의 세장비 규정을 제시하고 있다. 복부판에 설치하는 수평보강재의 역할은 휨 좌굴강도를 증가시키는 것이다. 비록 비보강된 복부판이 조밀단면의 기준을 만족하지 못한다고 할지라도, 적당한 수평보강재를 설치한다면 복부판의 좌굴을 방지할 수 있을 것이다. 그러므로 복부판은 소성모멘트에 도달할 수 있을 것이다. 그러나 AASHTO LRFD(2007)에서는 수평보강재를 설치한 복부판이 조밀단면을 민족하지 못하는 이유에 관하여 분명하게 설명하고 있지 않다. 본 연구에서는 수평보강재를 설치한 복부판에서의 휨에 의한 좌굴과 극한강도거통을 선형과 비선형 유한요 소법을 통하여 검토하였다. 비록 조밀단면의 세장비를 만족하지 못하는 복부판이라고 할지라도, 충분한 강성과 적절한 위치에 수평보강재로 보강하면 소성모멘트에 도달할 수 있다는 것을 알아냈다. 비선형해석의 분석을 통해 수평보강재를 갖는 복부판의 조밀단면을 만족하는 새로운 세장비 조건식을 제안하였다. In AASHTO LRFD (2007), a compact section is defined as a section in which no premature failure caused by local buck-of web and flange plate or later buckling occurs before the section reaches the plastic moment, M<SUB>p</SUB>. The current AASHTO LRFD (2007) provides the compact section requirement by limiting the web slenderness only for webs without longitudinal stiffeners. The role of longitudinal stiffener is to increase the web buckling strength caused flexure. Although a web does not satisfy the compactness requirement without longitudinal stiffeners, the web buckling can be prevented by use of valid longitudinal stiffeners. Therefore, the web may be able to reach the plastic moment. However, the reason why a longitudinal stiffener may not be used to satisfy compactness requirement is not cleary explained in AASHTO LRFD (2007). In this study, the buckling and ultimate strength behaviors of stiffened webs subjected to bending are investigated through the linear buckling and nonlinear finite element analysis. It is found that steel plate girders having webs that do not satisfy the compactness requirement are able to reach the plastic moment if the longitudinal stiffeners have sufficient rigidities and are properly located. From a nonlinear regression analysis of the results, a new compactness requirement is suggested for webs stiffened with one longitudinal stiffener.

Elastic Failure of Locally Supported Silos with U-shaped Longitudinal Stiffeners

Arne Jansseune,Wouter De Corte,Jan Belis 대한토목학회 2015 KSCE JOURNAL OF CIVIL ENGINEERING Vol.19 No.4

For practical considerations, thin-walled steel silos are often supported by a limited number of discrete equidistant supports around their circumference. In such cases, large loads are transferred to the limited number of supports, causing locally high axial compressive stress concentrations. A possible solution is to add a partial-height U-shaped longitudinal stiffener above each support. Such stiffeners create a more gradual transmission of vertical loads to the supports, increasing the maximum failure load. This paper aims to map the influence of the dimensions of such longitudinal stiffeners on the failure behaviour of a thin-walled silo. Both the parameters of the cross-section and the height of the stiffeners are discussed. All the results and the findings are based on geometrically and material nonlinear analyses - GMNA - performed with finite element software. The simulations indicate that, in general, thin-walled silos will fail by pure elastic buckling in the unstiffened silo wall above the terminations of the longitudinal stiffeners. However, this is only true if the cross-section of the stiffeners, and to a lesser degree the moment of inertia, is sufficiently large in order that the longitudinal stiffeners can absorb the supporting loads. In contrast, for longitudinal stiffeners with a small cross-section, the silo structure will fail by premature elasto-plastic collapse of the stiffeners itself at significantly lower load levels. Furthermore, the height of the stiffeners and the degree of support - the circumferential width of the supports and the stiffeners is equal to each other - are the most important geometrical parameters which are beneficial to reach a maximum load level for a specific silo. Finally, the buckling behaviour and the failure load are hardly influenced by radial width and the thickness of the longitudinal stiffeners.

수평보강재로 1단 보강된 강재 거더의 웨브 세장비와 보강재 강성 변수에 대한실험 연구

박용명,김병준,김희순,만경록 한국강구조학회 2018 韓國鋼構造學會 論文集 Vol.30 No.6

The AASHTO LRFD Bridge Design Specifications stipulates two requirements for the bending rigidity of the longitudinal stiffeners; formation of a buckling nodal line and securing the buckling strength of the T-section composed of a stiffener and a part of the web. Therefore, the required rigidity of the stiffener is related to the web slenderness ratio(D/tw) and yield strength of steel. In this study, an experimental study was carried out on the steel girders stiffened with single stiffener considering the web slenderness ratio and the rigidity of stiffeners as variables. Two cases of web slenderness ratios 331 and 247 were selected and total six girders were tested for the unstiffened and stiffened webs with two different stiffener rigidity for each slenderness ratio. Based on the tests, a required rigidity of the stiffener to reach the yield moment according to the web slenderness ratio was investigated. In addition, the stiffener rigidity requirements of AASHTO and Eurocode 3 were compared and possible shortcomings were analyzed by taking into consideration the web slenderness ratio, yield strength of girder and stiffener. AASHTO LRFD 교량 설계 기준에서는 수평보강재의 휨강성 요건으로서 좌굴 nodal line의 형성과 보강재와 웨브 일부분으로 구성된 T-단면의 좌굴강도 확보의 두 가지를 규정하고 있다. 따라서, 보강재의 필요 강성은 웨브 세장비(D/tw)와 강재의 항복강도와 연계가 된다. 본연구에서는 웨브를 1단 보강한 강재 거더에서 웨브 세장비와 보강재 휨강성 변수에 대한 실험 연구를 수행하였다. 웨브 세장비는 331과 247의두 경우를 고려하였으며, 각 세장비에 대해 비보강 및 두 가지 보강재 강성을 고려하여 총 6개의 거더에 대해 실험을 수행하였다. 실험 결과로부터웨브 세장비에 따라 항복모멘트에 도달하기 위해 필요한 보강재의 휨강성을 분석하였다. 아울러 웨브 세장비, 거더와 보강재의 항복강도 변수를고려하여 AASHTO 및 Eurocode 3 기준의 보강재 강성 요건을 비교하고 문제점을 분석하였다.

1단 수평보강 강재 거더의 보강재 휨강성 규정 제안을 위한 연구

박용명,김병준,성택룡,박찬희 한국강구조학회 2019 韓國鋼構造學會 論文集 Vol.31 No.1

In the longitudinally stiffened steel girders, AASHTO LRFD Bridge Design Specifications stipulates the requirements for the bending rigidity of the stiffeners: 1) formation of a buckling nodal line, 2) ensuring column buckling strength of T-section composed of the stiffener and a part of the web. On the other hand, Eurocode 3 is based on the elastic buckling strength of the T-section considered as an elastically-supported column by the web. The first requirement of the AASHTO is somewhat irrational because the size of the stiffener should increase as the web slenderness ratio decreases. Meanwhile, since the longitudinal stiffeners are usually installed on one side, an eccentric effect of compressive force is inevitable, but these criteria do not consider such effect in the buckling strength. In this study, an equation for the bending rigidity of the stiffener based on the buckling strength of the T-section, which includes web slenderness ratio and yield strength of steel, was proposed. The proposed equation adopts the column strength of the AISC standards and the eccentric effect was considered as the effective buckling length of the T-section. 수평보강 강재 거더에서 수평보강재의 휨강성 요건으로 AASHTO LRFD 교량 설계 기준에서는 1) 좌굴 nodal line 형성과2) 보강재와 웨브 일부분으로 구성되는 T-단면의 기둥으로서의 좌굴강도를 토대로 하고 있다. 반면 Eurocode 3는 T-단면을 웨브에 의해 탄성지지된 기둥으로 간주한 탄성좌굴강도를 기준으로 하고 있다. AASHTO의 첫 번째 요건은 웨브 세장비가 감소함에 따라 보강재의 제원이 커져야 하는 다소 비합리적인 면이 있다. 한편, 수평보강재가 편측에 설치됨으로 인해 T-단면에는 압축력의 편심효과가발생하나 이들 기준에서는 좌굴강도에 이를 고려하지 않고 있다. 본 연구에서는 웨브 세장비와 강재의 항복강도를 포함하여 T-단면의좌굴강도를 토대로 한 보강재 휨강성 요건식을 제안하였다. 제안 식은 AISC 기준의 기둥 강도를 적용하고 편심 효과를 T-단면의 유효좌굴길이로 고려하였다.

Patch loading resistance prediction of plate girders with multiple longitudinal stiffeners using machine learning

Carlos Graciano,Ahmet Emin Kurtoglu,Balázs Kövesdi,Euro Casanova 국제구조공학회 2023 Steel and Composite Structures, An International J Vol.49 No.4

This paper is aimed at investigating the effect of multiple longitudinal stiffeners on the patch loading resistance of slender steel plate girders. Firstly, a numerical study is conducted through geometrically and materially nonlinear analysis with imperfections included (GMNIA), the model is validated with experimental results taken from the literature. The structural responses of girders with multiple longitudinal stiffeners are compared to the one of girders with a single longitudinal stiffener. Thereafter, a patch loading resistance model is developed through machine learning (ML) using symbolic regression (SR). An extensive numerical dataset covering a wide range of bridge girder geometries is employed to fit the resistance model using SR. Finally, the performance of the SR prediction model is evaluated by comparison of the resistances predicted using available formulae from the literature.

Numerical investigation of buckling strength of longitudinally stiffened web of plate girders subjected to bending

김희순,박용명,김병준,김경식 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.2

In this study, the bend-buckling strength of the web in longitudinally stiffened plate girder was numerically investigated. The buckling strength of the reinforced web was evaluated through an eigenvalue analysis of the hypothetical model, in which the top and bottom junctions of the web to the flanges were assumed as simple support conditions. Major parameters in the analysis include asymmetrical cross-sectional property, aspect ratio of the web, stiffener locations, and bending rigidity of the stiffeners. The numerical results showed that current AASHTO LRFD specifications (2014) provides the buckling strength from considerably safe side to slightly unsafe side depending on the location of the stiffeners. A modified equation for buckling coefficients was proposed to solve the shortcomings. The bending rigidity requirements of longitudinal stiffeners stipulated in AASHTO were also investigated. It is desirable to increase the rigidity of the stiffeners when the aspect ratio is less than 1.0.

Numerical investigation of buckling strength of longitudinally stiffened web of plate girders subjected to bending

Kim, Hee Soon,Park, Yong Myung,Kim, Byung Jun,Kim, Kyungsik Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.2

In this study, the bend-buckling strength of the web in longitudinally stiffened plate girder was numerically investigated. The buckling strength of the reinforced web was evaluated through an eigenvalue analysis of the hypothetical model, in which the top and bottom junctions of the web to the flanges were assumed as simple support conditions. Major parameters in the analysis include asymmetrical cross-sectional property, aspect ratio of the web, stiffener locations, and bending rigidity of the stiffeners. The numerical results showed that current AASHTO LRFD specifications (2014) provides the buckling strength from considerably safe side to slightly unsafe side depending on the location of the stiffeners. A modified equation for buckling coefficients was proposed to solve the shortcomings. The bending rigidity requirements of longitudinal stiffeners stipulated in AASHTO were also investigated. It is desirable to increase the rigidity of the stiffeners when the aspect ratio is less than 1.0.

절곡강판을 적용한 강박스거더 압축플랜지의 탄성좌굴 및 극한 거동

김도형,이성철 한국강구조학회 2018 韓國鋼構造學會 論文集 Vol.30 No.4

강박스거더의 압축플랜지는 국부좌굴강도 증가를 위해 종방향 보강재가 설치된다. 종방향 보강재는 탄성좌굴이 발생할 때, 압축플랜지에 연속적인 지지조건을 제공하도록 설계된다. 보강재로 나누어진 서브 패널은 독립적으로 지지된 판으로 가정하며, 이때 서브패널의 경계조건은 보강재의 강성에 좌우된다. 본 연구에서는 압축플랜지에 종방향 보강재를 설치하는 대신 보강재 위치를 따라 종방향으로 판을 절곡하는 새로운 개념의 압축플랜지를 선형 좌굴해석 및 비선형 극한해석을 통해 검토하였다. 절곡을 통해 나누어진 서브패널은 적절한 각도 이상 절곡하는 경우 서로 단순지지조건을 제공한다. 본 연구에서 개발된 절곡 플랜지는 기존 보강 플랜지에 비해 경제적인 대안이 될 수 있을 것으로 판단된다. Wide compression flanges used in steel box girders are often stiffened with longitudinal stiffeners and sometimes in conjunction with transverse stiffeners, to increase local buckling strength. In a few design codes, longitudinal stiffeners are designed to provide continuous support during elastic buckling. The subpanels divided by the stiffeners are treated as independently supported plates, and the support condition depends on the rigidity of the stiffeners. This study introduces a new type of compression flange that is not stiffened with the longitudinal stiffeners and is instead folded longitudinally along the stiffener lines. The subpanels divided by folding provide simple support to each other if folded with a proper angle. The folded flange could be a cost-effective alternative to stiffened wide flanges.