Study on distortional buckling performance of cold-formed thin-walled steel flexural Members with stiffeners in the flange

This paper presents a finite strip program CUFSM used to calculate and analyze the elastic distortional buckling of cold-formed thin-walled steel flexural members with stiffeners in the flange, which has different sectional geometric parameters. According to the classical buckling stress formula, the distortional buckling coefficient of the flange can be calculated so as to analyze the influence of changed sectional geometric parameters on it. On this basis, this study provides a simplified formula of distortional buckling stress to calculate 40 members with different sections which are selected from the Technical Code of Cold-Formed Thin-Wall Steel Structures of China but not contained in this paper. Compared with the analysis results of CUFSM, it shows that the two simplified formulas have quite high accuracy and wide applicability for general members provided by the specification. So it is suggested that they can be used for engineering design and standard revision.     

Lateral bracing of I-girder with corrugated webs under uniform bending

Lateral-torsional buckling may occur in an unrestrained beam where its compression flange is free to displace laterally and rotate. This paper presents the results of the theoretical and finite element analyses of the lateral-torsional buckling of I-girders with corrugated webs and lateral bracing, under uniform bending. 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 lateral-torsional buckling has not been made especially for I-girder with corrugated webs. This paper develops a three-dimensional finite element model using ANSYS [User’s manual, version 10.0] for the lateral-torsional buckling analysis of I-girder with corrugated webs and uses it to investigate the effects of elastic lateral bracing stiffness on the critical moment of simply supported I-girders with corrugated webs under pure bending. It was found that for plastic and inelastic I-girder with corrugated webs, 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 I-girder. Also, the results show that Winter’s simplified method to determine full brace requirements cannot be applied to I-girders with corrugated webs. Therefore, a general equation is proposed to determine the value of optimum stiffness (K_opt) in terms of the I-girder’s slenderness.     

Damage evolution mechanisms of rock in deep tunnels induced by cut blasting

The method of cut blasting is widely used in tunnelling excavation, which concerns the success in subsequent stop blasting and smooth blasting. Rock masses in deep tunnels are subjected to high in-situ stress, and the mechanisms of damage evolution of rock mass in deep tunnels induced by cut blasting are not well studied. In this paper, a tension and compression-shear damage model is developed, and then is implemented into the commercial software LS-DYNA as a user-defined material model. To validate the newly developed model, the comparison between numerical results and an existing field test is conducted. The effects of free-surface boundary conditions, in-situ stress and the coefficient of lateral pressure on cut blasting are considered in depth. Numerical results indicate that the superstition of stress wave and the reflected tension waves from free surfaces contribute to the damage interconnection near cut holes. The high in-situ stress has the resistance on the radially oriented pressure and the damage extension around cut holes. The coefficients of lateral pressure influence the extending direction of the tensile damage zone.     

Cyclic performance of concrete-filled steel CHS columns under flexural loading

Concrete-filled steel CHS (circular hollow section) columns are currently being increasingly used in the construction of buildings. Limited information is available on the models for the moment (M) versus curvature (?) response, and the lateral load (P) versus lateral displacement (Δ) relationship of these columns subjected to axial load and cyclically increasing flexural loading.Eight concrete-filled steel CHS specimens were tested under constant axial load and cyclically increasing flexural loading. The parameters in the study included the concrete strength (f_cu) and the axial load level (n). A mechanics model is developed in this paper for concrete-filled steel CHS columns subjected to constant axial load and cyclically increasing flexural loading. The predicted cyclic responses for the composite columns are in good agreement with test results.Based on the theoretical model, parametric analysis was performed on the behaviours of the moment (M) versus curvature (?) response, and the lateral load (P) versus lateral displacement (Δ) relationship, as well as the ductility coefficient (μ) for the composite columns. Finally, simplified models for the moment (M) versus curvature (?) response, and the lateral load (P) versus lateral displacement (Δ) relationship are suggested. A formula for the calculation of the ductility coefficient (μ) of the composite columns under constant axial load and cyclically increasing flexural loading is developed.     

Assessment of K0 correlation to strength for granular materials

The coefficient of lateral stress at rest K₀ is a state soil variable, yet is well correlated to strength. As different types of friction angles can be defined, it is important to examine the applicability of K₀-strength correlation and further clarify the mechanism of K₀-stress state. In this study, the values of K₀ were experimentally investigated for different types of granular materials, focusing on its correlation to material strength and the effect of particle shape and surface roughness. For this purpose, laboratory tests were conducted to directly measure K₀ of natural sand, spherically shaped glass bead, and surface-etched glass bead packings under various stress and soil conditions. Triaxial and other basic property tests were also conducted to characterize the test granular materials. It was revealed that the effect of material density on K₀ differed depending on the stress history whereas the effect of particle surface roughness, within the range considered in this study, was relatively small. Test results highlight that the values of the friction angle employed into Jaky's K₀ equation to match measured K₀ values are not unique, showing a state-dependent aspect. Inter-particle stress analysis was introduced to assess the correlation of K₀ to the friction angle as postulated by Jaky's K₀ equation.     

Prediction of Lateral Effective Stresses in Sand using Artificial Neural Network

Predicting the lateral effective stress and the coefficient of lateral earth pressure at rest values is an important task in geotechnical engineering since it is used in the design and analysis of earth retaining structures, slope stability, piles and pier foundations. It needs sophisticated test procedures. The laboratory and in situ tests are also expensive and time consuming. In this study, an artificial neural network model is developed to predict the σ′_h, lateral effective stress in cohesionless soils. Back propagation neural networks are used for function approximation and model has been trained by Levenberg-Marqurdt (LM) learning algorithm. The data used in the running of network models have been obtained from extensive series of oedometer tests on Kilyos, Ayvalik and Yalikoy sands. Tests were carried out on loose, medium dense and dense state of compactness in normal loading, unloading and reloading conditions. The test results demonstrate that there is a linear relationship between vertical and lateral stresses for normally loaded cohesionless soils under K₀ conditions. K₀ values obtained for the loose state of compactness are higher than for the dense state of compactness. The results of the artificial neural network model indicate that the model serves as simple and reliable tool to predict σ′_h and also K₀ in cohesionless soils. The variation of K₀ values with internal friction angles is obtained and a simple expression is derived from this relationship.     

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.     

Calculating local geomembrane strains from gravel particle indentations with thin plate theory

A new general method is presented to calculate local strains in geomembranes from the deformed shape imposed by overlying coarse gravel particles under vertical pressure. Past methods assume that the geomembrane attains its deformed shape by only deforming vertically and hence neglect the effect of lateral displacements on strain. The new method treats the geomembrane as a thin plate with mid surface components of displacements in three directions (x, y and z). Lateral components of displacements (those in the x and y directions) are related to vertical displacements (z direction) by large-strain-displacement relationships and compatibility of strains. Normal and shear strains in the lateral directions are calculated using Airy's stress function and a linear elastic constitutive law. Bending and torsional strains calculated from curvature and are added to the mid surface strains to find strains on the top and bottom surfaces. The method was validated against data sets with known three-dimensional displacements and strain generated by finite element analysis. The application of the new method to calculate local strains in a geomembrane from the deformed shape obtained from a protection-layer-assessment physical test is illustrated.     

Simplified seismic axial collapse capacity prediction model for moderately compressed reinforced concrete shear walls adjacent to transfer structure in tall buildings

Nonseismically detailed reinforced concrete (RC) shear walls adjacent to transfer structure in tall buildings are found to have short shear spans and designed to hold considerable axial load. In a previous paper, a Modified Mohr's Axial Capacity Model was developed by the authors to estimate the axial collapse of these RC walls in seismic events, which is expressed as an axial load ratio devised based on classical Mohr's circle framework. It was noted that the previous model can be complicated and appears not suitable for direct adoption in engineering design check. Hence, in this paper, a new simplified seismic axial collapse capacity prediction model is formulated to improvise the previous model. This simplified model typifies the practical range of shear wall geometry, concrete strength, steel reinforcement stress and strain and reinforcement ratio. Simplified charts to estimate maximum shear stress are presented for quicker design check. The complex inelastic buckling stress calculation is simplified into graphs and design equations. A knife‐edge feasible solutions zone is defined, expressed as an inequality function of axial‐to‐shear capacity ratio and additional axial stress induced by lateral shear. Recommendations are made based on results obtained from Genetic Algorithm search and further justified by parametric studies.     

Mindlin位移解推求锚固段侧阻力分布方法中的奇异性问题

基于弹性半无限空间的Mindlin位移解推求锚固段侧阻力分布,是一种力图以数理力学理论模型严格推导的研究思路,但不同解法间结论相异,与工程实际也相差较大。针对其原因,通过建立普适的求解侧阻力的积分方程进行理论分析。发现Mindlin位移解所具有的数学奇异性影响突出,在积分方程的数值求解中不能直接消除,虽以设置带取值任意性的最小微间距或以在锚固体横截圆面上积分的荷载转换方法可加以避免,却难以实现严格数理力学推导的初衷。而解析手段因引入了3个简化假设,虽数学求解上克服了奇异性困难,但使力学模型发生了失真,推导的结果仅属于特定定解条件下的数学表象。针对理论上以剪应力互等定律推断出锚固段始端侧阻力应为0,与工程实际间的矛盾,提出锚固段始端角点的应力可以是非对称的,以传统的剪应力互等定律来推断该局部区域的应力状况不尽合理。     

Nonlinear Analysis of Torsionally Loaded Pile Groups

An empirical approach is developed to analyze the nonlinear torsional behavior of free-standing pile groups with rigid pile caps. In this approach, the lateral and torsional responses of individual piles in a pile group are modeled by p-y and τ-θ curves; the interaction among lateral resistances of the individual piles is predicted through Mindlin's elastic solutions; the interactions between the torsional and lateral resistances of the individual piles are described through Randolph's solution; and the coupling effect of lateral resistance on torsional resistance of the individual piles is quantified using an empirical factor “β”. The proposed approach is capable of capturing the most significant aspects of pile-soil-pile interactions and coupling effect in pile groups subjected to torsion. The proposed approach is verified using results of centrifuge model tests. In general, the applied torque-twist angle response and the transfer of applied torque in pile groups can be reasonably well predicted and are sensitive to the pile group configuration.     

Linear and non-linear stability analyses of thin-walled beams with monosymmetric I sections

The paper investigates beam lateral buckling stability according to linear and non-linear models. First, the classical linear stability solutions are derived from the stability equation in the case of monosymmetric cross-sections. Bending distribution, load height parameter and Wagner's coefficient effects are taken into account. In the second step, they are extended to non-linear stability by considering pre-buckling deformation and improved solutions are then obtained. Based on a finite element model developed for large torsion of thin-walled beams with open sections, the stability of beams under gradient moments (M₀, ψM₀, ?1≤ψ≤1) is particularly investigated. It is then concluded that beam lateral buckling resistance depends not only on pre-buckling deformation but also on section shape and load distribution. For bisymmetric I beam, closed form solutions are possible and pre-buckling deformations have an incidence. In the case of beams with monosymmetric I and Tee sections, effects of pre-buckling deflections are important only when the largest flange is in compression under M₀ and positive gradient moment. Analytical solutions are possible. For negative gradient moments all available solutions fail and numerical solutions are more powerful. Effect of gradient moments on stability of redundant beams is investigated at the end. Under such boundary conditions, important axial forces are present due to non-linear beam deformation. These forces, omitted in literature, have an incidence on stability. The element is then concerned with beam-column behaviour rather than beam stability.     

不同侧压下再生混凝土与钢筋间黏结性能试验研究与理论分析

为研究不同侧压下再生混凝土与钢筋间的黏结 滑移性能,以再生粗骨料取代率、水灰比、侧向压力比为参数,完成了144个再生混凝土试件在单向、双向侧压作用下的钢筋中心拉拔试验,观察了再生混凝土试件的破坏形态,分析了上述参数变化对黏结强度、峰值滑移的影响;基于再生混凝土多轴破坏准则,推导了不同侧压作用下再生混凝土-钢筋的黏结强度理论模型及其简化公式。研究结果表明：再生混凝土中心拉拔试件的破坏形态与侧压力比明显相关,双向侧压力比较大时,试件破坏形态与单向侧压时破坏形态相似,当双向侧压力接近时,双向均有裂缝;黏结强度与峰值滑移随侧压力比的增大,整体呈现增加趋势;基于再生混凝土多轴强度理论的黏结强度计算值与实测值较为吻合,其简化计算公式能较好地预测不同侧压力下再生混凝土与钢筋间的黏结强度。     

Use of internal and external variables and extremum principle in limit equilibrium formulations with application to bearing capacity and slope stability problems

Limit equilibrium methods, satisfying both force and moment equilibrium can be formulated using assumptions on the internal variables or the external variables. Even though most stability methods are based on force and moment equilibrium, as well as the Mohr–Coulomb yield criterion, there are great differences between the results of the different formulations due to variations in the assumptions. The authors believe that the use of the interslice force function f(x), the thrust line or the base normal forces should provide an equivalent concept at the ultimate/failure state. In the present study, the authors have used the well-known bearing capacity solutions to determine f(x), the thrust line and the base normal forces for a “horizontal slope”. The equivalence between the different formulations under the ultimate condition is demonstrated. It is shown that it is not important which forces are used in the stability formulation, external boundary forces or internal forces, if only that the ultimate state is considered. It is also demonstrated in the present paper that the maximum extremum from the limit equilibrium analysis is equivalent to the slip line solution using a classical bearing capacity problem.     

Experimental tests of slender reinforced concrete columns under combined axial load and lateral force

The use of high strength concrete (HSC) in columns has become more frequent since a substantial reduction of the cross-section is obtained, meaning that slenderness increases for the same axial load and length, producing higher second order effects. However, the experimental tests in the literature of reinforced concrete columns subjected to axial load and lateral force focus on shear span ratios, according to Eurocode 2 (2004), clause 5.6.3., (M/(V⋅h)) lower than 6.5. This gap in the literature limits technological development for the construction of these structural elements. This paper presents 44 experimental tests on reinforced concrete columns subjected to constant axial load and monotonic lateral force. The aim of this is to gain greater knowledge of the types of elements which will also be of use in calibrating the numerical models and validating the simplified methods. The test parameters are strength of concrete (normal- and high-strength concrete), shear span ratio, axial load level and longitudinal and transversal reinforcement ratios. The strength and deformation of the columns were studied, and an analysis of the simplified methods from Eurocode 2 (2004) and ACI-318 (2008) concluded that both are very conservative.     

Tension force analysis of geotextile tubes by half cross-section test

A simplified equation, which allows for the calculation of the tension force using the actual tube height and pumping pressure with the flexibility to use a coefficient of lateral pressure (K), is proposed and validated theoretically by comparing the proposed method with two well-known methods in the literature, and experimentally, by conducting several half cross-section tests. The half cross-section test proposed in this study is unique and configured in such a way that the top and bottom of the geotextile tube is supported by load cells to be able to quantitatively measure the maximum tension force, as well as the stress and strain of the geotextile tube. With the use of the simplified equation, the actual field conditions can be exceptionally represented, making it more advantageous over the previous methods.     

Analytical model for bond-slip behavior under monotonic loading

In this paper the distributions of bond stress, slip and strain are analyzed. The local bond-slip law is idealized by a piecewise linear relationship, for each part of which closed-form solutions are obtained for bond stress, slip and strain distributions. The steel bar length is divided into four zones in the general case. Conditions of continuity between zones and boundary conditions are used to solve the length of zones, and strain and slip distributions. Simultaneous transcendental equations are obtained and solved using Newton's tangent method. The analytical predicted results compare well with test results in tension and compression.     

Local buckling of structural steel shapes

The objectives of this paper are to (1) provide analytical expressions for the elastic cross-section local buckling stresses, including element interaction, of hot-rolled steel structural shapes, and (2) compare these local buckling results to the assumptions inherent in the local slenderness limits of the US AISC structural steel specification. The cross-section local buckling stress is determined by finite strip analysis (FSA). Local stability of each cross-section in the AISC shapes database (excluding pipes) is considered in axial compression, as well as positive and negative bending about the major and minor geometric axes. Local buckling stresses are converted into plate buckling coefficients (k’s) and simplified expressions are provided for all observed k’s. The new k’s explicitly include elastic web-flange interaction amongst the elements comprising the cross-section. The k values from the FSA are compared to those inherently assumed in the AISC Specification, significant differences are observed.     

Experimental and numerical crack analysis of mixed-mode failure in concrete by acoustic emission and boundary element method

Crack extension of mixed-mode in concrete is studied by applying the acoustic emission (AE) and the boundary element method (BEM). The theory of AE wave motions is briefly reviewed, including the historical development. AE waveforms are generated as elastic waves in concrete due to crack nucleation, and can be synthesized by the integral formulation, consisting of the spatial derivatives of Green's functions, the moment tensor, and the source-time function. Kinematics of cracks are represented by the moment tensors, which can be determined by a SiGMA (simplified Green's function for moment tensor analysis) code. In bending tests of notched beams, the crack extension of mixed-mode failure in concrete is studied. Crack traces are analyzed by the two-domain BEM, based on the maximum circumferential stress criterion by Erdogan-Sih, and are in remarkable agreement with those of tested beams. Then, locations, types, and orientations of AE sources are analyzed by the SiGMA to investigate crack kinematics in the fracture process zone. Furthermore, it is attempted to estimate the normalized stress intensity factors K_I*=K_I/K_IC and K_II*=K_II/K_IC.