This work describes the development and validation of an innovative shear deformable beam theory and conducts an experimental study designed for the elastic analysis of steel beams suffering from area losses, such as those caused by corrosion. This new theory introduces a kinematic model postulating two distinct rotation angles for cross-sections to accurately account for the complex shear deformations and stiffness reductions observed in damaged sections, which classical theories often fail to predict. The authors validate their proposed finite element formulation against extensive experimental data and three-dimensional finite element analyses (3D FEA), demonstrating that their approach provides structural response predictions—including deflections, and longitudinal normal and transversal shear stresses—with high accuracy and significantly reduced computational effort compared to 3D FEA. The research concludes that area losses, particularly their length, substantially increase beam deflections and stresses, underscoring the need for this improved analytical method.

Mất ổn định xoắn ngang là một dạng mất ổn định quan trọng của dầm thép chữ I chịu uốn, trong đó các khiếm khuyết hình học ban đầu có thể ảnh hưởng đáng kể đến độ cứng và sức kháng của cấu kiện. Tuy nhiên, các dữ liệu thực nghiệm về ảnh hưởng của các sai lệch hình học này đến ứng xử mất ổn định của dầm thép vẫn còn hạn chế. Nghiên cứu này trình bày kết quả thí nghiệm nhằm làm rõ ảnh hưởng của khiếm khuyết hình học ban đầu đến ứng xử mất ổn định xoắn ngang của dầm thép chữ I cán nóng chịu uốn bốn điểm. Ba dầm có tiết diện đối xứng kép được thí nghiệm; độ cong vênh ban đầu của dầm được đo trước khi thí nghiệm và được xét trong quá trình phân tích kết quả. Quan hệ tải trọng – chuyển vị, sự phát triển chuyển vị ngang kết hợp xoắn tại giữa nhịp và tải trọng mất ổn định của dầm có khiếm khuyết hình học ban đầu được xác định và đánh giá. Kết quả thực nghiệm cho thấy sự khác biệt về dạng phân bố và biên độ của khiếm khuyết hình học ban đầu làm thay đổi đáng kể quá trình phát triển chuyển vị ngang kết hợp với xoắn, từ đó ảnh hưởng trực tiếp đến khả năng chống mất ổn định xoắn ngang của các mẫu dầm được khảo sát. Cơ sở dữ liệu thực nghiệm thu được từ nghiên cứu có thể được sử dụng để hiệu chỉnh và kiểm chứng các mô hình phân tích phần tử hữu hạn, đồng thời hỗ trợ nâng cao độ tin cậy trong dự báo khả năng chịu mất ổn định xoắn ngang của dầm thép có xét đến ảnh hưởng của các khiếm khuyết hình học ban đầu

Việc nghiên cứu mất ổn định đàn hồi của kết cấu dàn thép gia cường tấm FRP có ý nghĩa quan trọng trong việc nâng cao khả năng chịu lực và độ bền công trình, đặc biệt khi nhu cầu sử dụng các vật liệu nhẹ, bền và hiệu quả ngày càng gia tăng. Nghiên cứu này xây dựng một công thức nghiệm kín đơn giản, dựa trên lý thuyết biến phân của thế năng biến dạng kết cấu, nhằm tính toán tải trọng tới hạn và dạng mất ổn định của thanh dàn thép có gia cường FRP. Kết quả tính toán từ công thức được kiểm chứng và cho thấy sự phù hợp với lời giải số bằng phần mềm phân tích kết cấu, chứng minh tính chính xác và khả năng ứng dụng của mô hình. Thông qua phân tích tham số, nghiên cứu chỉ ra rằng (i) tấm FRP với hướng sợi 0° tạo ra tải trọng mất ổn định lớn nhất, trong khi các tấm có góc bằng hoặc lớn hơn ± 45° gần như không ảnh hưởng đến tải trọng, (ii) tải trọng mất ổn định tăng tuyến tính theo chiều dày tấm dán, và (iii) việc sử dụng FRP mang lại hiệu quả rõ rệt trong gia cường dàn thép. Những kết quả này khẳng định tính khả thi của công thức đề xuất, đồng thời cung cấp cơ sở khoa học hữu ích cho thiết kế và gia cường kết cấu thép bằng vật liệu FRP trong thực tiễn

Bài báo nghiên cứu khả năng chịu lực của dầm thép bị ăn mòn liên kết và ăn mòn bản bụng bằng phần mềm phần tử hữu hạn Abaqus. Ba trường hợp được nghiên cứu: (i) bu lông bị ăn mòn, (ii)bản bụng bị ăn mòn, (iii) kết hợp bu lông và bản bụng bị ăn mòn. Kết quả cho thấy rằng dầm thép bị ăn mòn bị suy giảm đáng kể khả năng chịu lực.

Numerical procedures based on geometric and material nonlinearities are proposed in the present study to evaluate the inelastic responses of welded steel beams with the initial shape imperfections of welds, braces and out-of-straightness. The convergent deformations/moments of the present solutions are excellently validated against experimental results. Thirty-seven steel beams with different sectional classes are then proposed to quantify the effects of initial shape imperfections of welds, braces, and out-of-straightness on the system deformations and moment resistances. It is observed from the present study that the moment resistances strongly depend on the residual stresses, bracing heights, and out-of-straightness shapes for the beams with compact and non-compact sections, but they are insensitive for the beams with slender sections. The effects of weld shapes on the moment resistances are found to be small. Through an evaluation of the moment resistances of typical design specifications, design considerations are proposed for the steel beams subjected to the initial imperfection shapes.

The local and global imperfections of I-shaped steel beams are known to significantly impact the load-carrying capacity of the structure. This is particularly critical for structures subjected to heavy loads, where these factors must be meticulously controlled to prevent potential failures. Therefore, the objective of this project is to describe a numerical analysis that was conducted to evaluate the influence that initial global and local flaws have on the inelastic buckling resistances of steel truss members that are used in steel bridges. These numerical studies are based on Abaqus, and they have been validated quite well against the data that are now available. After that, the numerical models are utilized in order to assess the inelastic buckling resistances of the system, taking into consideration four distinct sorts of initial global and local imperfections which are feasible. The numerical results are compared to the standard evaluations, which are also examined and evaluated. In addition, parametric investigations of the impact of the thicknesses of the web and flange on the inelastic buckling resistances are carried out as part of the current research. The strengthening techniques assessed in this research can serve as a foundation for engineers to implement in actual steel beam structures.

Sự phân bố của ứng suất dư là một yếu tố rất quan trọng tác động tới sự làm việc của kết cấu thép hàn tổ hợp. Bài báo tập trung nghiên cứu ảnh hưởng của sự phân bố nhiệt độ trong dầm thép tổ hợp hàn nhiệt mặt cắt hình chữ I tới ứng suất dư. Một mô hình phần tử hữu hạn dựa trên phần mềm ABAQUS được thiết lập nhằm mô phỏng quá trình phát sinh ứng suất và biến dạng của các mối hàn nhiệt. Mô hình này dựa trên các phần tử ba chiều để có thể xem xét sự phân bố ứng suất theo chiều dày cấu kiện. Các phần tử này có tính đến sự thay đổi nhiệt độ của các quá trình hàn. Kết quả của mô hình sau đó được so sánh với một số tiêu chuẩn thiết kế và nghiên cứu khác cho thấy độ tin cậy và chính xác cao của mô hình đã xây dựng. Dựa trên mô hình này, ảnh hưởng của nhiệt độ tới sự hình thành, phát triển và tồn tại của ứng suất dư trong toàn bộ quá trình hàn được khảo sát và phân tích chi tiết

The present study develops a new finite element (FE) formulation for the lateral torsional buckling (LTB) analyses of steel beams exteriorly bonded with orthotropic fiber-reinforced polymer (FRP) layers. The formulation considers shear deformations, partial material interaction, local and global warping deformations, and orthotropic FRP properties. The buckling responses of multispan FRP-bonded steel beams predicted by the present solutions are excellently validated against experiment and numerical solutions. As observed, the FRP strengthening is highly effective for the LTB resistance of steel beams. However, the LTB responses are strongly dependent on the orthotropic properties and strengthening lengths of FRP layers. The effects of shear deformations, span ratios, and loading conditions on the LTB responses are also quantified in the present study.

The present study develops a shear deformable finite element (FE) formulation for the analysis of the elastic lateral torsional buckling (LTB) of steel beams. Four governing displacement fields are proposed to describe the LTB deformation. The buckling strains/stresses and the total buckling potential energy of the system are subsequently expressed in terms of the governing displacements. The theory considers the contributions of local and global warping deformations and shear deformations. A FE formulation is then developed by using linear and cubic shape functions. Based on the validations conducted in four examples, the buckling loads/modes of single and continuous span steel beams predicted by the present solutions are observed to excellently agree with those predicted by other analytical, experimental, numerical solutions. The buckling loads evaluated by using standard moment modification factors are also discussed to clarify the restrictions of the evaluation method. The effects of shear deformations, different loading conditions, and span ratios on the buckling responses of various steel beams are also investigated in the present study.

When a unbraced flexural steel beam is subjected to a ununiform moment distribution, a simplified moment modification factor (denoted as Cb) should be evaluated for the design of the buckling resistance of that member. However, typical standards for the buckling design of steel structures (e.g., American AISC A360, Australian AS-4100, Canadian CSA S16, Eurocode 3 and Japanese standards) currently recommend different design equations for the factor. Also, such equations are based on simplified expressions those are not exact solutions. Thus, the present study firstly revise the standard equations to discuss their advantages and disadvantages in application. Also, a numerical solution based on a finite element analysis package is then conducted in the present study to predict the Cb factor. The numerical solution is successfully validated against available research results. Based on the comparison of the modification factors between of the present numerical study and those based on the design standards, it is observed that the modification factors based on the current design standards maybe not safety enough to predict the buckling resistances in several loading cases. The present study finally recommends a new modification more on the safe side for the Cb factor to ensure a conservative design

The present study develops an innovated shear deformable theory and four finite element formulations based on a total potential energy variational principle for the analysis of steel beams strengthened with GFRP laminates. The present theory captures orthotropic properties of the GFRP laminae, GFRP lamina stacking sequences, partial interaction between the steel beam and the GFRP laminates, and shear deformations. Three examples are conducted for the validation of the present theory. Through comparisons, the system responses predicted by the present solutions are excellently validated against those of recent experimental studies and three-dimensional finite element analyses. Key results obtained in the present study include: (i) the responses of GFRP-strengthened beams are strongly influenced by GFRP fiber angle arrangements. (ii) The strengthening is the most effective for steel beams strengthened with a GFRP laminate stacked with fiber angles of 0 degree. Based on two parametric studies, the effects of the orthotropic GFRP lamina properties and GFRP laminate thicknesses on the system deflections are also investigated.

An experimental study is conducted and a theoretical solution is proposed in the present study to investigate the ductile/brittle failure mode of reinforced concrete (RC) beams strengthened with an external steel plate. In the present experimental study, 6 steel plate-strengthened RC beams and 1 non-strengthened RC beam are fabricated and tested under 4-point bending loads. Then, a new theoretical model is successfully developed to predict the rupture mechanism of the RC beams strengthened with external steel plates. The model is based on the observed experimental results regarding to crack formations, and it is can be used to determine the distance between vertical cracks and to quantitatively predict the ductile/brittle failure mode of platestrengthened RC beams. The experimental study shows that the failure mode is commonly based on the sliding of concrete along with the external plate at a random location. This slip is limited between two vertical cracks, from which the maximum stresses in the external steel is determined. Through result validations, the stresses/strains in the soffit plate, crack distances, and system failure modes as predicted by the present theoretical solution are found to excellently agree with those of the previous and present experimental results. This study may help to improve the design of such plate-strengthened RC beams to target on a better ductile performance, that has not been addressed before.

An innovated theory based on the principle of total stationary buckling energy is successfully developed for the elastic lateral torsional buckling analysis of steel beams/columns strengthened with symmetrically balanced GFRP laminates. Two closed form solutions and four eigenvalue solutions of the buckling resistances are then developed based on the theory and based on postulated buckling displacement functions. The present theory captures the partial interaction between the steel member and the GFRP laminates, stacking sequences and orthotropic properties of GFRP laminae, shear deformations in the GFRP laminates, and local and global warping deformations. The elastic buckling resistances predicted by the present solutions are well validated against those of three dimensional finite element analyses, as presented in three examples and two parametric studies of the present study. The present solutions are fast and convenient to predict the elastic buckling resistances of GFRP-strengthened beams/columns. Based on the parametric studies conducted, it is observed that the effects of GFRP lamina stacking sequences (with different fiber orientation angles), GFRP laminate thicknesses, GFRP moduli of elasticity, GFRP shear moduli, and adhesive shear moduli on the elastic buckling resistances are significant.

The inelastic buckling resistances of wide flange beams are strongly influenced by residual stresses and initial imperfections. However, the resistances as evaluated from simple solutions presented in several popular design specifications are found to be considerably different. The present study thus develop a numerical solution in ABAQUS software to investigate the inelastic buckling moment resistances of rolled steel beams with compact sections and subjected to the effects of residual stresses and initial imperfections. The residual stresses are taken as provided in AISC, CSA S16, EC 3 specifications, while the initial imperfections are taken as the first lateral-torsional buckling mode with a magnitude limited in AISC, CSA specifications. Through comparisons between the specifications and the numerical solutions, one observes a significant difference between the moment resistances predicted by the specifications, in which the AISC predicts the highest values, while the EC 3 predicts the lowest moments. The moment resistances based on the present numerical models lie between the EC 3 and CSA solutions and they are relatively close to EC 3 solutions. Effects of load height positions on the inelastic buckling moment resistances are significant, as investigated in the present study

The present paper successfully develops a closed form solution based on a shear deformation theory for elastic lateral-torsional buckling analyses of simply supported thin-walled steel beams. The theory captures the shear effects caused by transverse bending, lateral bending and warping deformations. The closed form solution is successfully validated against 3 dimensional finite element analyses conducted in commercial software. Through various comparisons between the buckling resistances based on a non-shear deformation theory and the buckling resistances based on the present shear deformation theory, the present study finds that (i) the effect of shear deformations on the buckling resistances decreases when the beam span increases, (ii) the effect of shear deformations on the buckling resistance is sensitive with the change of the flange width, and (iii) the effect of shear deformations in general is also influenced by the change of the section depth, and the flange and web thicknesses.

Tấm CFRP (Carbon Fiber Reinforced Polymer) là một loại vật liệu mới có nhiều nhiều ưu điểm nổi trội và nó đặc biệt thích hợp cho việc gia cường kết cấu bê tông cốt thép. Loại vật liệu này bắt đầu được ứng dụng ở các nước phát triển vào khoảng năm 1980, nhưng nó còn tương đối mới ở Việt Nam. Trong nghiên cứu này, một nghiên cứu thực nghiệm đã được thực hiện để đánh giá cường độ chịu nén của mẫu bê tông hình trụ tròn khi được kiềm chế nở ngang bằng tấm CFRP, của hãng Toray, Nhật Bản, ở các mức độ gia cường khác nhau. Kết quả cho thấy, hiệu quả gia cường của tấm CFRP trong nghiên cứu này là cơ bản phù hợp với các mô hình đã được đề xuất bởi những nghiên cứu trước đó trên thế giới. Hiệu quả gia cường của tấm CFRP phụ thuộc rất lớn vào chất lượng thi công tấm CFRP; nó đòi hỏi người thi công phải có kinh nghiệm và tuân thủ đúng hướng dẫn của nhà phân phối vật liệu CFRP. Từ những kết quả thí nghiệm, nghiên cứu này đề xuất sử dụng các mô hình phù hợp để đánh giá cường độ chịu nén của bê tông khi được kiềm chế nở ngang bằng tấm CFRP của hãng Toray, Nhật Bản, cũng như của các hãng khác.

A series of solutions based on five different complementary strain energy assumptions (named as Assumptions A, B, C, D, E) are developed for the prediction of interfacial shear and normal stresses in plate flexural-strengthened beams. Basic differences between the Assumptions are that in the formulating of the energy, Assumption A includes the transverse normal and shear stress fields in the beam and in the plate, Assumption B includes the normal stresses but exclude the shear stresses, Assumption C includes the shear stresses but excludes the normal stresses, Assumptions D excludes the normal stresses and the shear stresses in the beam but include the shear stresses in the plate, and Assumption E excludes the normal and shear stresses in the beam and in the plate. The energy expressions of the five Assumptions are developed based on derived statically admissible stress fields and an a generalized 2D-Hooke's law constitutive model. Through an energy variation principle, compatibility equations and boundary conditions of the interfacial stresses are obtained. Closed form and numerical solutions are then developed for the compatibility equations. By comparing against the interfacial stresses of 2D- and 3D-finite element analyses (FEA), it is observed that Assumptions A and B significantly under predict the interfacial stresses, Assumption C excellently predicts the interfacial normal stresses, Assumptions D and E excellently predict both the interfacial shear and normal stresses, and Assumptions (C, D, E) excellently capture the FEA stress fields (those are strongly varied across the adhesive thickness). The present study is applicable to plate-strengthened beams with general force boundary conditions but it is limited to linearly elastic orthotropic/isotropic materials.

The present study performs a numerical investigation and then develops a simplified design-oriented model to determine the ultimate moment capacity for compact wide flange steel sections strengthened with a GFRP plate bonded to one of the flanges. The study aims at assessing failure modes and ultimate moments of the strengthened systems based on a series of 3D finite element analysis models that account for material and geometry nonlinear effects, initial out of straightness, residual stresses, GFRP plate length and thickness, and adhesive modulus of elasticity and rupture strength. The analytical model accounts for the elasto-plastic behaviour of steel, the shear capacity of the adhesive at the steel-GFRP interfaces, and the rupture strength of the GFRP. The ultimate moments and modes of failure predicted by the proposed analytical solutions are shown to agree well with the finite element predictions for beams strengthened with GFRP plates on the tension side. Additional comparisons with experimentally verified shell solutions by others also suggest the model to be equally applicable for beams strengthened by GFRP on the compression side.

A finite difference formulation is developed for the stress analyses in orthotropic three-layer composite beams with mono-symmetrical cross-sections under various force boundary and loading conditions. Four interfacial shear and peeling stress fields at material interfaces are assumed as unknown functions. Based on shear stress flow equilibrium conditions, three groups of stress fields including transverse shear, transverse normal and longitudinal normal stresses in the beam, the plate and the adhesive layer are expressed in terms of the unknown functions. A set of compatibility equations and corresponding boundary conditions are then derived from a variational principle of complementary strain energy and solved by a finite difference technique. The present theory eliminates kinematic assumptions of equal curvatures for the beam and the plate, it satisfies the infinitesimal stress equilibrium conditions of the interfacial shear and peeling stresses at material interfaces, and it captures the longitudinal normal stresses in the adhesive. By comparing to numerical and analytical solutions, the present theory is a solution for the prediction of concentrated transverse shear and transverse normal (peeling) in the adhesive occurring near the plate ends. Based on the present theory, a parametric study is conducted to quantify the effects of the strengthening length, thickness, and elasticity moduli of the FRP plate and adhesive layer on the peak values of the interfacial shear and peeling stresses.

A closed form solution and a finite difference formulation are developed for an accurate prediction of adhesive shear and normal stresses in soffit plate flexural-strengthened beams. First, three statically admissible stress fields (i.e., longitudinal normal, transverse shear and normal stresses) are derived and expressed in terms of four unknown interfacial shear and normal stresses. Then, a modified complementary strain energy is written in which the energy contributions of the transverse normal stress fields in the beam and in the plate, and the transverse shear stresses in the beam are omitted. Based on an energy variational principle, compatibility equations and corresponding boundary conditions are obtained. A closed form solution and a finite difference formulation are finally developed. Through validations, the adhesive shear and normal stresses near the plate ends predicted by the present study are in excellently agreements with those provided in several experimental and numerical studies. Also, the present study excellently captures stress fields strongly varied across the adhesive thickness, especially the transverse normal stresses. Based on the present theory, a parametric study is conducted to quantify the effects of the plate longitudinal modulus and the thickness on the interfacial shear and normal stresses. The parametric study indicates that the peak normal stresses are significantly higher than the peak shear stresses in the adhesive layer. The present study is applicable to predict the adhesive shear and normal stresses highly concentrated near the plate ends in plate-strengthened beams with general applied loads and force boundary conditions.