Weak Axis Bending Research Articles

Effect of joint stiffness on the load-carrying capacity of single-layer cylindrical reticulated shell with improved bolt-column (IBC) joint

To enlarge the application of single-layer reticulated shells, this study proposes an innovative semi-rigid joint based on the original bolt-column (OBC) joint, referred to as the improved bolt-column (IBC) joint. The mechanical behavior of the IBC joint under the pure load and the coupling effect of bending and axial force is investigated using numerical tests. Then, the practical analytical model of IBC joint is developed based on a three-parameters power model and component method. Subsequently, a mechanical model considering joint stiffness is developed to establish semi-rigidly connected single-layer cylindrical reticulated shell. A total of 456 numerical models of shells are conducted to examine the impact of different kinds of joint stiffness on the load-carrying capacity of shells systematically. The results demonstrate that (i) weak axis bending stiffness and axial stiffness significantly affect the load-carrying capacity of shells by approximately 19 % and 14 % on average respectively; (ii) strong axis bending stiffness and torsional stiffness have relatively minor effects on the critical load of shells, with average decline ratios of only 5 % and 6 % respectively; (iii) out-of-plane shear stiffness and in-plane shear stiffness exhibit negligible impacts on the load-carrying capacity of shells, with an average effect not exceeding 1 %. Finally, the findings of numerical simulation considering all stiffness of IBC joint reveal insights into both varying laws of load-carrying capacity and failure modes for shells. It is observed that the mean critical load can reach up to 59 % of the one of rigidly-connected shells, which is significantly higher than those observed in shells with pinned joints.

Hysteretic performance of thin-walled Q690 high-strength steel H-section beam-columns bent about the weak-axis

High-strength steel has broad application prospects in steel structures as its weight to strength ratio is low, but the reduced ductility limits its application in seismic design. In order to evaluate the application potential of high-strength steel in light steel structures, four Q690 high-strength steel beam–columns with large width to thickness ratios were tested under cyclic loading about the weak axis. The failure mode, ultimate strength, hysteretic curve, stiffness degradation, ductility and energy dissipation capacity of the tested specimens are discussed. Subsequently, a finite element analysis model is established, and an extensive parametric study is carried out using the verified finite element model. The test results show that the failure mode is the local buckling of column base. The hysteretic behavior of the specimens is mainly affected by the axial load ratio and the flange width to thickness ratio. The results of the parametric study show that the extent of development of plasticity in the cross-section is related to the axial load ratio. The calculated ultimate strength of the beam–column shows that Eurocode 3 is conservative for the classification of the beam–column as having a Class 4 cross-section, members with Class 4 cross-sections should in fact be classified as having Class 3 cross-sections. Accordingly, a section classification for a high-strength steel beam–column subjected to weak axis bending is discussed.

Shear lag effects on global bending moments in a long-span pontoon bridge under self-weight, traffic and environmental loads

The present paper deals with a systematic study of the shear lag effect on the bending moment distribution in girders of representative pontoon-type floating bridges (PTFBs). Comparative and parametric studies for well-developed beam and linear shell models for representative structural components of a reference PTFB subject to representative static and dynamic loads, e.g. self-weight load condition, traffic loads, and wave-induced vertical dynamic loads on PTFB's pontoons are carried out. The study is partly based on a simplified, generic PTFB model, denoted GPTFB. The study shows that elementary beam element models, for which shear lag effects are not accounted for, might, to some extent, inaccurately predict the bending stiffness, eigenmode shapes and eigen frequencies of PTFBs with large width and relatively short span lengths (e.g. the ratio of span length to girder width of PTFBs is less than 7.24), while the inaccurate prediction of beam model in weak axis bending moment in girder of the PTFBs is related to the load pattern and dynamic load frequency range. A practical method is proposed to judge when caution is needed in using elementary beam model for estimating the weak axis global bending moments in girder of PTFBs. In addition, a case study presented in this paper, shows that the part of the girder near the bank abutment might be subjected to complex boundary conditions since the girder is supported by floating pontoons and bottom fixed columns. In this part of the bridge girder, a significant influence of shear lag on weak axis bending moments is observed. Further analysis by using shell elements is necessary to estimate the stresses, including the effect of shear lag, in this part of the girder.

Hydroelastic analysis of a floating bridge under spatially inhomogeneous waves, with emphasis on the effect of drift force modeling

The pontoon-supported floating bridge is an alternative concept for crossing a fjord with a width of up to 5 km. Due to the huge span, the first two natural periods of the bridge are more than 60 s, indicating that the corresponding modes can be excited by slowly-varying drift forces on the pontoons. A simplified approach for determining the drift forces is to assume that the pontoons are independent of the floating bridge, i.e., fixed or freely floating. However, the first-order motions of the pontoons, which are restricted by the deformation of the floating bridge, have a significant effect on the drift forces. To evaluate the uncertainties implied by the simplification of drift forces, in this study, a second-order beam-connected-discrete-modules (BCDM) hydroelastic method is adopted to assess the effect of different drift force models on the floating bridge. In this method, the first-order response amplitude operators (RAOs) of bridge-restricted pontoons are first solved in the frequency-domain. Based on the RAOs, the mean drift forces for each pontoon are then determined by using potential theory. Considering the spatial inhomogeneity of the wave field, the time series of the first- and second-order wave forces are generated by using the linear transfer functions and Newman’s approximation, respectively. Then, the method is applied to investigate the hydroelastic responses of a straight side-anchored floating bridge for the crossing site of Bjørnafjord. The results show that the horizontal displacement is very sensitive to the different force models implied by various pontoon boundary conditions, i.e., free, fixed, and bridge-restricted. The drift forces on the bridge-restricted pontoons are approximately 10%–20% larger than those for the fixed pontoons. Moreover, wave inhomogeneity results in increased vertical displacements and weak axis bending moments.

Effect of pile orientation on the fatigue performance of jointless bridge H-piles subjected to cyclic flexural strains

This paper explores the effect of pile orientation on the low cycle fatigue (LCF) performance of steel H–piles (SPs) at jointless bridge (JB) abutments via experimental testing and finite element simulation. The experimental testing program includes 42 full scale SP specimens subjected to strong axis (SA) and weak axis (WA) bending. The SPs are tested under cyclic displacement reversals mimicking the thermal induced displacement cycles associated with the seasonal elongation and contraction of the JB in the summer and winter times. The magnitude of the axial load is also kept as a variable in the experimental testing program to investigate its effect on the cyclic performance of JB SPs. The test results are then verified via finite element simulation and a parametric numerical study is performed to further understand the cyclic behavior of SPs as a function of numerous parameters. The tests and numerical analyses results revealed that for identical cyclic flexural strain amplitudes, SPs oriented for WA bending generally demonstrate a superior performance in terms of LCF life in the presence of axial loads compared to those oriented for SA bending. Moreover, the research results showed that at large flexural strains, local buckling becomes more critical than the pile orientation for the LCF life of SPs in JBs.

Soil-structure interaction of integral abutments

Integral abutment bridges (IABs) are pioneering structures that offer certain advantages over conventional bridges. The main difference is the ability of IABs to eliminate the necessity of utilizing bearings and expansion joints. This results in more economical construction and enhanced structural performance. However, the intricate soil-structure interactions of IABs under the influence of seasonal changes are not yet fully understood. This paper aims to improve the understanding of these innovative structures by utilizing comprehensive numerical models to investigate their geostructural performance under various conditions. The case study selected for this research was the Middlesex bridge in Vermont, USA. A full-scale monitoring program at this bridge measured and recorded the bridge acting pressures, deformations, and internal forces, making it possible to gain insight into the thermal response of such structures. For the numerical research, a comprehensive two-dimensional numerical model, developed by using the PLAXIS software, was verified against the available field measurements. Subsequently, parametric studies were conducted to investigate earth pressure and pile bending moment variations influenced by different model conditions. Key model parameters were varied, including the constitutive soil model, thermal loading, backfill stiffness, pile size and orientation, and span length. It was found that utilizing a linear constitutive soil model could lead to significant inaccuracies in the results. Increasing the backfill stiffness was seen to increase passive earth pressures and decrease pile bending moments. With smaller pile sections, oriented for weak-axis bending, pile bending moments decreased substantially and lateral earth pressures increased. Because dead load magnitudes were closely linked to span lengths, pile bending moments and backfill pressures increased when fewer and longer bridge spans were used.

A generic method for assessment of inhomogeneous wave load effects of very long floating bridges

Floating bridges are promising infrastructures used to cross wide and deep fjords. During the design of floating bridges, the wave field is usually assumed long-crested and homogeneous. However, the real wave field in fjords is short-crested and inhomogeneous due to the complicated topography. To evaluate the uncertainties implied by the homogeneous assumption, a generic method is proposed in this study for the assessment of inhomogeneous wave load effects of very long floating bridges. The inhomogeneous wave field is represented by the long-term variation and correlation of wave spectral parameters at the location of each pontoon and by coherence functions of wave elevations between pontoons. The correlated and inhomogeneous wave field is simulated by applying the Cholesky decomposition techniques based on auto- and cross-spectra of waves at pontoons. The wave spectral parameters can be determined with consideration of their long-term correlation while the coherence functions of wave elevations can be obtained by using phase-resolved methods. Based on the simulated wave elevations at each pontoon, the time series of first-order and second-order wave excitation forces are created by using the transfer functions and applied externally to each pontoon in the numerical model of the floating bridge. The proposed method is validated and applied to investigate the dynamic behavior of a floating bridge for the Bjørnafjord crossing as a case study. The inhomogeneous wave load effects are assessed by carrying out fully coupled time-domain simulations. It is found that the assumption of homogeneous wave conditions is conservative for the strong axis and weak axis bending moments, but significantly nonconservative for the axial force. The proposed method can also be applied for other very large floating structures subjected to the inhomogeneous wave field.

Fire testing and design of slender stainless steel I-sections in weak-axis flexure

The structural fire response of slender austenitic stainless steel I-sections in weak-axis flexure is studied experimentally for the first time. The presented experimental programme comprised local geometric imperfection measurements for all the test beams, room temperature material tests, a reference room temperature weak-axis bending test and a series of elevated temperature weak-axis bending tests. The experimental setup, procedure and measured responses of the test specimens are fully described. The results demonstrate that, despite the studied cross-section being slender, considerable inelastic strength reserves were displayed. Such behaviour has previously been observed in steel I-sections in weak-axis flexure at room temperature. The test results are used to assess the accuracy of existing fire design provisions in predicting the weak-axis bending moment resistances of slender stainless steel I-sections. Significantly improved capacity predictions were achieved through the application of a plastic effective width method in which the beneficial influence of the partial spread of plasticity is captured.

Experimental investigation of C-shaped glass-fiber-reinforced polymer connectors for sandwich insulation wall panels

A kind of C-shaped glass-fiber-reinforced polymer (GFRP) connector for panels was proposed and experimentally investigated in this study. The connector was extruded into C-shape with anchorage rebars at ends. The C-shaped GFRP connector has large stiffness and bearing capacity, allowing sufficient connection between panels with high thickness insulation layers. Shear, tensile, and compression tests were conducted to quantify the performance of connectors under different loading conditions. The length and loading direction of the connectors were main parameters investigated by shear testing. As the connector’s length increased, the failure mode of the connector with strong-axis bending tended to be anchorage failure instead of connector failure. The failure mode of the connector with weak-axis bending tended to be connector failure in the 60–300 mm length range. Equations were derived to predict the damage mode of the connector system. The results from tensile testing and compression testing revealed an anchor failure mode related to the anchorage rebars and concrete. Such C-shaped GFRP connector design was also capable of resisting the force and displacement of panels with a thick insulation layer up to 300 mm.

Research on local buckling capacity of lipped C-section stainless steel beams under weak axis bending

In order to obtain the local buckling capacity of lipped C-section stainless steel beams under weak axis bending, local buckling tests were carried out on 6 stainless steel beams under weak axis bending made of Austenitic stainless steel S30408 (AISI304), revealing the mechanical properties and failure mechanism when local buckling occurred, and the failure phenomenon, load–displacement curves, load–strain curves and local buckling capacity of the specimens were obtained. The test results showed that the failure mode of the specimen was local buckling located in the mid-span web, showing a convex or concave mode. The wave peak was near the mid-span section, and the local buckling of the web along the longitudinal direction occurred in multi-wave buckling mode. The refined finite element model of lipped C-section stainless steel beam specimens under weak axis bending was established. The mechanical properties and local buckling bearing capacity of each specimen were simulated and analysed. The accuracy of the refined model was verified by comparing the finite element results with the test results. In order to simplify the finite element simulation analysis, the refined finite element simulation was simplified. Then 4 kinds of imperfection simplification models were established considering different initial imperfections, and 8 kinds of length simplification models were built based on different lengths and support constraints. Detailed comparison and analysis were performed on results of simplified model refined finite element model and tests to verify the accuracy of the simplified model.

Extreme responses and associated uncertainties for a long end-anchored floating bridge

Very-long floating bridges represent an innovative marine structure for crossing wide and deep fjords. During the design of a floating bridge, extreme structural responses at a specified probability of exceedance are required to be properly evaluated for ultimate limit state (ULS) design check. This study addresses the estimation of extreme structural responses due to wind and wave loads and associated uncertainties. An end-anchored floating bridge, about 4600 m, is considered in a case study. The long-term extreme responses are estimated by using a simplified engineering approach, in which the long-term extreme response is approximated by the one-hour short-term extreme responses at a high fractile (90% in this study) for selected short-term sea states. The extreme responses are expressed as μ+κ·σ, where μ and σ are the ensemble mean and standard deviation, and κ is a multiplying factor. Statistical analyses indicate that the structural responses, including axial force, strong and weak axis bending moments of the bridge girder, are close to follow a Gaussian distribution. A simplified analytical method, the Gumbel method and the mean upcrossing rate (MUR) method are employed to estimate the multiplying factor κ and extremes. The κ estimated by these three methods are generally close, varying in the vicinity of 4. The κ and extremes estimated by the simplified method have a much smaller variation than the Gumbel and MUR methods. Statistical uncertainties and model uncertainties in the extreme value prediction are also addressed. Based on the results of 10 sets of 10 1-h ensembles, the mean and coefficient of variation (CoV) of μ,κ,σ and extremes of structural responses of 10 1-h simulations under two selected sea states are evaluated. The CoV of σ is less than 0.045, but the CoV of κ is relatively large, mainly between 3.5×10-2 and 6.5×10-2. The CoV of extremes estimated by the simplified analytical method is fairly small, less than 0.035. While the CoV of extremes estimated by the Gumbel and MUR methods are much larger and can reach 0.137 and 0.158, respectively. In practical design of floating bridge, only a limited number of simulations (e.g. 10 1-h) are conducted to predict the extreme structural responses. This will introduce statistical uncertainties and should be corrected by a factor for a conservative estimate. A simplified procedure to derive the correction factor is presented in this study. For the floating bridge considered with 10 1-h simulations, the correction factor is recommended to be 1.1 when the absolute value of mean μ is smaller than σ, and be 1.2 when the absolute value of mean μ is larger than σ, in order to achieve a 90% conservative estimation of extreme.

Validation of simple superelement model of warping transfer in moment connections of portal frames

ABSTRACTA simple beam element‐based modelling technique has been developed to allow the analytic definition of a stiffness matrix to describe the behavior of corner region between two doubly symmetric thin‐walled I beams connected through moment connection. The stiffness matrix describes the relation between „out‐of‐plane” type deformations of connected beam ends and related internal forces including shear force parallel to the flanges, torsion, weak axis bending and warping of flanges. The model allows to simulate the warping and distortion of the beams within the connection region. The resulting stiffness matrix is compatible with the thin walled beam theory with 7DOF beam elements. A parametric study has been performed to validate the model with shell element‐based simulation, using Abaqus and ConSteel software, concentrating on the direct out‐of‐plane behavior of portal frames. In the validation process first and second order analysis results and results of linear buckling analysis have been analyzed. The correctness of the shell element‐based simulation has been proved by full‐scale laboratory test. The test result has shown excellent agreement with the numerical simulation and with the proposed model.

Inelastic second-order analysis of steel columns under minor-axis bending

Abstract The inelastic second-order behavior of steel structural columns under minor-axis bending is presented in this article. To study this behavior, a nonlinear frame element formulation is adopted in which the steel's plasticity process is accompanied at the nodal points of each finite element through the refined plastic-hinge method (RPHM). A tangent modulus approach is employed in order to consider the stiffness degradation in function of the internal forces' variation, and the second-order effects, residual stresses and geometric imperfections are considered in the modeling of column behavior. As a criterium for defining the ultimate limit state of the column cross-section, strength surfaces are adopted. These surfaces describe the interaction between the axial force and bending moment (N-M interaction diagrams). To solve the nonlinear equilibrium equation for the structural system, the Newton-Raphson method is used, coupled with continuation strategies. Columns with different slenderness, boundary and loading conditions are analyzed, and the results obtained are comparable to those found by other researchers. The results lead to the conclusion that the numerical approach adopted in this study can be used for a better behavioral understanding of the steel column under weak-axis bending.

Flexural rigidity of cold-formed steel built-up members

Cold-formed steel (CFS) built-up members are formed by connecting several single members by fasteners. This paper presents experimental, numerical and analytical studies on the effect of fastener configurations on the flexural rigidity of built-up sections. In this research, two zinc-coated steel C-sections are connected back-to-back to form a double-web built-up I-section, which is subject to weak-axis bending. A closed-formed expression for the flexural rigidity of built-up sections as a function of fastener stiffness, number and position of fasteners, and section geometry is then derived. This is validated against the tests and finite element modelling, and can be adapted more generally to determine the stiffness and global strength of CFS built-up members in bending.

Finite element modeling of rolled steel shapes subjected to weak axis bending

Finite element modeling of rolled steel shapes subjected to weak axis bending

Performance of segmental self-centering rubberized concrete columns under different loading directions

Segmental self-centering columns are an advantageous construction choice in earthquake prone areas due to their minimal or even zero residual deformation and their low repair/downtime costs. This research investigated the behavior of segmental rectangular column members with a high cross-sectional length to width ratio under different loading directions, with the aim of potentially extending the concept of segmental self-centering columns to wall members, such as shear walls and retaining walls. The main parameters of this study were the direction of loading: in-plane (strong-axis bending) and out-of-plane (weak-axis bending), provision (or absence) of reinforcement, and the type of concrete material (conventional concrete or rubberized concrete). Eight concrete columns with a cross-sectional length to width ratio of 2.5 and consisting of three concrete segments with dry joints in between, were tested under reversed-cyclic lateral loading. A pre-stressing force of 100 kN, corresponding to a stress of 2.8 MPa on the column, was applied using unbonded post-tensioning (PT) bars. The results indicated that although in-plane loaded columns had a higher load capacity, they exhibited a less ductile response, higher level of damage and higher loss in the PT force, compared with the out-of-plane loaded columns. The total equivalent viscous damping and its variation was very small in all tested specimens, and it increased slightly as the drift ratio increased. Empirical equations were developed to express the damping as a function of drift ratio. It was also concluded that in the out-of-plane loaded specimens, the effect of reinforcement on the load-displacement response was insignificant. In rectangular columns with high length-to-width ratio, under out-of-plane loading, if a minimum level of axial pre-stressing is applied (to prevent shear or sliding failure), no structural reinforcement is required. In addition, the strength reduction due to using rubber in concrete at the structural level was much lower than that at the material level. The results of this study can potentially be applied to segmental concrete walls due to the high length-to-width ratios of the tested columns.

Numerical Modeling and Dynamic Analysis of a Floating Bridge Subjected to Wind, Wave, and Current Loads

Designing reliable and cost-effective floating bridges for wide and deep fjords is very challenging. The floating bridge is subjected to various environmental loads, such as wind, wave, and current loads. All these loads and associated load effects should be properly evaluated for ultimate limit state design check. In this study, the wind-, wave-, and current-induced load effects are comprehensively investigated for an end-anchored curved floating bridge, which was an early concept for crossing the Bjørnafjorden. The considered floating bridge is about 4600 m long and consists of a cable-stayed high bridge part and a pontoon-supported low bridge part. It also has a large number of eigen-modes, which might be excited by the environmental loads. Modeling of wind loads on the bridge girder is first studied, indicating that apart from aerodynamic drag force, aerodynamic lift and moment on the bridge girder should also be considered due to their significant contribution to axial force. Turbulent wind spectrum and spatial coherence play an important role and should also be properly determined. The sway motion, axial force, and strong axis bending moment of the bridge girder are mainly induced by wind loads, while the heave motion, weak axis bending moment, and torsional moment are mainly induced by wave loads. Turbulent wind can cause significant larger low-frequency eigen-mode resonant responses than the second-order difference frequency wave loads. Current loads mainly contribute damping and reduce the variations of sway motion, axial force, and strong axis bending moment.

LOAD-MOMENT INTERACTION DIAGRAMS OF SLENDER PARTIALLY ENCASED COMPOSITE COLUMNS

Partially Encased Composite (PEC) Columns consist of thin-walled built-up H-shaped steel sections with links welded near the flange tips and concrete cast between the flanges. To predict the strength and ductility of slender PEC columns, Newmark’s numerical iterative procedure is implemented. Overall column slenderness ratio, flange plate slenderness ratio and concrete strength are the selected parameters to observe the variation of strength and ductility of slender PEC column. Bending of column about both the strong and weak axis is considered to observe the significance of the selected parameters. In strong axis bending, a decrease in strength is found with the increase of overall slenderness ratio and flange plate slenderness ratio. Again, failure envelope of column strength curve becomes smaller with the increase of overall slenderness ratio. It implies the ductility of slender PEC column decreases with the increase of the overall slenderness ratio. Moreover, similar behaviour is observed with the increase of flange plate slenderness ratio. As the strength of concrete increases, strength of slender PEC column is observed to increase by significant amount. Similar behaviour is observed in weak axis bending along with some drop in strength

Stainless steel lipped C-section beams: Numerical modelling and development of design rules

Experimental results and finite element (FE) analysis results on stainless steel lipped C-section beams are scarce. Therefore, a series of tests were performed on S30408 stainless steel, including 6 major-axis bending and 6 weak-axis bending specimens. Two numerical modelling programmes, major-axis bending and weak-axis bending, have been carried out to investigate the behavior of stainless steel lipped C-section beams. The numerical models, which were developed using the FE package ABAQUS, were verified by experimental results. The models were used to conduct parametric studies of the impact of key parameters on the moment capacity of stainless steel lipped C-section beams subject to failure by local buckling. Finally, based on FE analysis of 238 specimens under major-axis bending and 229 members under weak-axis bending, direct strength equations for lipped C-section stainless steel beams under major-axis bending and weak-axis bending are proposed. A comparison of test results with equation predictions indicates that the formulas have high accuracy and reliability and can accurately calculate the moment capacity of stainless steel lipped C-section beams. • The key parameter influencing the moment capacity of beams is the cross-section aspect ratio. • Simplified model effectively simulates the failure mode and moment capacity of beams. • Direct strength equation for stainless steel lipped C-section beams is fitted. • The fitted equations can accurately calculate the moment capacity of beams.

Wave load effect analysis of a floating bridge in a fjord considering inhomogeneous wave conditions

When designing a floating bridge crossing a deep and wide fjord, a homogeneous wave field is usually assumed for simplicity. However, waves in fjords are commonly inhomogeneous, and hence the mentioned design practice introduces uncertainty, which should be assessed for the design. In this study, we proposed an approach to account for the inhomogeneous wave load effect on a floating bridge and applied it on a floating bridge that was initially proposed for crossing the Bjørnafjorden. The floating bridge considered is end-anchored, about 4600 m long and consists of a cable-stayed high bridge and a low bridge supported by 19 pontoons. Wave excitation loads on each pontoon were proposed to be modeled and applied separately to account for inhomogeneous waves. By considering 1-year and 100-year wave conditions, dynamic responses of the floating bridge subjected to homogeneous and inhomogeneous waves were analyzed and compared. It is found that inhomogeneous waves cause relatively larger sway motion, axial force, and strong axis bending moment, as well as significantly larger weak axis bending moment along the bridge girder than homogeneous waves. These responses depend on the inhomogeneity level of waves considered. Proper description of the wave field is therefore very important for evaluating the effect of inhomogeneous waves and associated uncertainties.