Combined Bending Research Articles

Research on the mechanics differences between single-row and double-row side piles of station using the PBA method

The side pile is a crucial mechanical component in station construction using the PBA (pile-beam-arch) method, and its stability during the construction process cannot be overstated. The mechanical differences between single-row and double-row side piles in this construction method have garnered significant attention, yet few studies have been conducted on this matter. Therefore, this paper employs numerical simulation to compare the deformation and mechanical properties of single-row and double-row side piles (the adopted pile type is micro steel pipe pile, abbreviated as MSPP) in a metro station using the PBA method. The findings are validated through the model experiment. It is found that the soil arch effect created by the front-row pile of the double-row piles serves as the primary lining, offering a certain shielding effect to the soil stress behind the back-row pile. Notably, the soil stress values in double-row pile conditions are slightly higher compared to single-row pile condition, leading to a noticeably smaller final deformation of the pile top. The combined bending moments and axial forces of the front-row and back-row piles in double-row piles exceed those of a single-row pile. Specifically, bending moments are highest in single-row piles, followed by front-row piles and then back-row piles, while axial forces are highest in single-row piles, followed by back-row piles and then front-row piles. This suggests that the bending moments and axial forces of double-row piles are smaller than those of a single-row pile. The internal force distribution within the double-row pile is more balanced, thereby enhancing the lining strength and improving the station’s safety through the PBA method. The findings in this paper can serve as valuable references for the design and construction of similar projects.

Cross-section behaviour of cold-formed high strength steel irregular hexagonal hollow section stub columns under combined compression and bending

Cross-section behaviour for cold-formed high strength steel (HSS) irregular hexagonal hollow section (IHexHS) stub columns under combined compression and bending is studied and presented in this paper. Finite element models were developed and validated using the existing experimental data collated from the previous research. Upon the validated finite element models, extensive parametric studies were subsequently carried out to generate more numerical data covering a wider range of cross-section dimensions, steel grades and load combinations from pure compression to pure bending. The obtained numerical results were utilised to assess the accuracy and the applicability of the current design codes, such as Eurocode of EN 1993-1-12 (EC3) and the North American code of ANSI/AISC 360-16 (AISC) for cold-formed HSS IHexHS stub columns under combined loading. It was demonstrated that the existing design codes can be safely applied and can be extended for cold-formed HSS IHexHS stub columns design under combined loading. In cross-sectional resistance predictions, conservative results were provided from the existing design codes. The over-predictions were primarily due to the neglect of the strain hardening and plate element interaction. The end points used in the interaction curves of EC3 and AISC adopt an idealised elastic-plastic material model to derive the corresponding resistance in cross-sectional level. The employment of Continuous Strength Method (CSM) leads to improved accuracy in cross-sectional resistance prediction with updated end points in the interaction curve. More consistent and reliable predictions were revealed by carrying out reliability analysis in accordance with EN 1990.

Behavior and Capacity of Moment-Frame Members and Connections during Fire

This paper focuses on investigating the structural behavior of members and connections that are part of moment frames under the combined effect of bending moment and thermally induced axial force during a compartment-fire event. The finite-element analysis method was employed to conduct this study using models benchmarked against experimental data from several past studies while utilizing temperature-dependent material models. A numerical parametric study on typical floor beams with slender elements for compression were conducted under combined bending and axial loading to develop interaction-capacity curves at temperatures representing fire events. The results were compared against the member-strength equations provided in the AISC Specification. The analysis results demonstrated that the AISC beam-column strength equations including the combined effects of axial-load and bending moment provided reasonable estimates for member-slenderness ratios greater than 60, but overestimated the strength of beams with slender elements for low member-slenderness ratios. Combined-load-strength studies were also conducted on a typical connection used in moment frames. The moment-connection behavior was governed by failure modes exhibited at the ends of floor beams. Therefore, the interaction equations available for beam columns resulted in conservative estimates and are recommended for calculating moment-connection capacity during compartment-fire scenarios.

Derivation of an elastic shell model of order as tends to infinity

Starting from three-dimensional linear elasticity and performing the dimensional reduction by integration over the thickness, we derive a general form of the areal strain energy density for elastic shells. To obtain the new constitutive model, we do not approximate the deformation fields as polynomials in the thickness coordinate, but rather we keep all terms in the thickness-wise series expansions. As a result, we deduce the explicit form of the shell strain energy density in which the constitutive coefficients are expressed as integrals depending on the thickness h and on the initial curvature. Then, to obtain the shell model of order , we expand the integral coefficients in the strain energy function as power series of h and truncate them to the power . In the case , we recover the classical strain energy density for combined bending and stretching of linear shells, which leads to the Koiter model. Finally, we prove that the proposed shell strain energy function is coercive for any , as well as for the general case .

Mechanistic understanding of precast UHPC segmental beams with external tendons and epoxy joints subject to combined bending and shear

Precast ultra-high-performance concrete (UHPC) segmental bridges (PUSBs) have become a competitive bridge type in modern civil engineering. To establish a thorough mechanistic understanding of PUSBs, seven specimens were fabricated and experimentally investigated. These specimens were designed to have different longitudinal reinforcements, construction methods, joint types, shear span-to-depth ratios (λ), stirrup ratios, and numbers of shear keys. Two failure modes were observed in the tests: flexural failure with crushing of the UHPC at the joints, and shear failure with shear tension sliding and concrete spalling of the web. Additionally, it was found that although the ultimate capacity, stiffness, and cracking load of the segmental beams were slightly lower than those of the monolithic beams, the segmental beams tended to exhibit better ductility and deformation capacity. As λ increased, the ultimate capacity and stiffness of the segmental beams decreased, whereas the growth rates of the deflection and tendon stress increased. Moreover, the stirrups showed a positive effect on the cracking control ability and shear strength of the beams. The three-keyed specimen exhibited better structural behavior than the single-keyed specimen. Finally, calculation methods were proposed to predict the cracking strength and ultimate capacity of PUSBs.

Variable compression panel thickness for concrete members under bending and torsion: Experimental study

An experimental study was conducted on the behaviour of eight reinforced and prestressed concrete beams subjected to combined action of bending and torsion. The beams were heavily reinforced in the longitudinal direction so that the height of the concrete compression zone under pure bending would be much larger than the concrete diagonal strut thickness under pure torsion and measurements were done so that behaviour of this compressive zone could be observed. The amount of the reinforcement was designed close to the over-reinforcement limits, as would happen if the cross-section dimensions of an actual structure would be minimized in the design. The ultimate resistances and beam deformations were compared against the results of a plasticity-based space truss model where the panel on the compressive side of the cross-section had variable thickness in order to account for the resultant force demands of both the bending and torsion. Most heavily reinforced beams failed in a brittle manner due to the ineffectiveness of diagonally cracked concrete to resist the high normal stresses arising from the bending. The proposed model gave better predictions than the classical model where the panel thickness was constant, and the results showed the significance of concrete strength reduction factor contribution in ultimate resistance of concrete members under combined bending and torsion.

Mechanical properties of corrugated steel lap joint under combined compression and bending

The lap joint of a prefabricated corrugated steel structure is one of the most critical components to be considered during design. Full-scale mechanical tests under combined compression and bending (N–M) were conducted to investigate the effect of axial forces and bending moments on the mechanical behavior of lap joints. Numerical methods were used to examine the effects of different axial forces on the bending behavior of the joint. Analysis revealed that buckling of the corrugated steel plate lapped on the upper layer, located near the innermost row of bolt holes, was the failure mode of the lap joint. The yield of the bolt holes on the compression (crest) and tension (valley) sides was accelerated and postponed by the axial force, respectively. Additionally, three phases with linear, nonlinear, and linear characteristics were identified from the bending moment-rotational angle (M–θ) curves. The initial rotational stiffness of the joint was the highest and decreased gradually with increasing axial force. The residual rotational stiffness of the joint was minimal and was only minimally affected by the axial force. A greater axial force on the joint lowered the bending capacity. Compared with N = 0, when N = 1200 kN, the corresponding bending moment decreased by approximately 17.1% and 9.6% for θ = 0.02 and 0.1, respectively. An empirical formula for calculating the joint rotational stiffness (Kθ) was proposed based on the N–M–Kθ relationship. These findings provide a reference for the joint design of prefabricated corrugated steel structures.

Local buckling behaviour of longitudinally stiffened stainless steel plate girders under combined bending and shear

This paper presents a comprehensive experimental and numerical investigation into the local buckling behaviour of longitudinally stiffened stainless steel plate girders under combined bending moment and shear force. Five plate girders configurated with longitudinal stiffeners with different geometrical proportions and vertical positions were fabricated from austenitic and duplex stainless steel plates. Initial geometric imperfections and material properties were measured, and all plate girders were tested to failure under a three-point loading configuration. The critical buckling strengths, ultimate capacities and failure modes were carefully analysed. Elaborate finite element (FE) models were developed and validated against the test results, and were then used to conduct parametric studies to generate further structural performance data over a wide range of cross-sectional properties, including various geometrical proportions and positions of longitudinal stiffeners, and loading combinations. The obtained test and FE results were utilised to assess the applicability of existing M–V interaction design methods in EN 1993-1-5 and that proposed by Jáger et al. for longitudinally stiffened plate girders. It was indicated that these two M–V interaction curves coupled with the design provisions in EN 1993-1-4 for determining the bending and shear endpoints, offer safe-sided predictions with a good level of consistency and accuracy, for longitudinally stiffened stainless steel plate girders under combined bending and shear. The reliability of these design approaches was further confirmed by statistical analysis.

Numerical and experimental study on structural behavior of restrained CHS T-joints in transient fire tests

Experimental and numerical studies have been conducted to investigate the structural behavior of restrained circular hollow section (CHS) T-joints subject to fire. Four CHS T-joints having two different brace-to-chord diameter ratios, 0.47 and 0.69, were tested subject to two kinds of loading: axial brace compression and in-plane bending in fire condition following the iSO-834 fire curve. The two chord ends were connected to reaction A-frames incorporating the thermal restraint effect. The joint behavior was discussed based on maximum deformation, fire resistance and critical temperature. When the joint was under in-plane bending, local plasticization was dominant; the observed failure mode combined global bending and local punching shear when the joint was under brace axial compression. Finite element (FE) models were constructed by incorporating thermal restraints and temperature distributions in the joint regions from the tests. The verified FE models were then adopted to predict the critical temperature of other CHS T-joints where brace-to-chord diameter ratio, load ratio and thermal restraints were taken as variable parameters. Unlike T-joint at ambient temperature, a larger brace-to-chord ratio resulted in a greater critical temperature. Moreover, greater load ratio and thermal restraint caused decrease in fire resistance and critical temperature of CHS T-joint subject to both axial compression and in plane bending.

Biomechanical properties of bicortical and monocortical plate fixation for rib fractures in the adolescent human rib fracture model

Purpose The technical advancement of surgical stabilization of ribs often prevents the surgeons from fixation, despite the procedure`s documented improved outcomes. The aim of this study was to evaluate a less invasive approach involving a simplified monocortical rib fixation technique. Methods Eighteen frozen human ribs obtained intraoperatively from young individuals aged 13-18 were employed for this study. First, the ribs were fractured under three-point bending, with their intrathoracic side put under tensile stress. Following this, the ChM 4.0 rib fixation system was utilized. The specimens were categorized into two groups: bicortical fixation (n=9), monocortical fixation (n=9). Subsequently, bicortical and monocortical fixation groups underwent dynamic testing over 400,000 cycles under combined sinusoidal tensile bending and torsional loading (2 N-5 N at 3Hz). In the final stage, all samples were subjected to a destructive load to failure. Results Our analysis revealed that the fixation method did not demonstrate statistically significant differences in terms of preliminary bending stiffness (p=0.379). Similarly, undergoing a course of 400,000 cycles involving combined tensile and torsional loading did not constitute a statistically significant factor affecting the monocortical and the bicortical fixation groups (p=0.894). In the monocortical fixation group, all specimens failed due to screws pulled out from the bone. In contrast, all specimens in the bicortical fixation group exhibited failure attributed to fractures occurring just behind the plate. Nonetheless, the fixation method was not a significant factor affecting bending strength (p=0.863). Conclusions The monocortial fixation could be a reasonable option among younger populations with comparable stability of fixation.

Behaviour of New Curved in Plan Composite Reinforced Concrete Beams

New composite reinforced concrete beams, in which reinforced concrete component is connected to steel T-section, are proposed. The stirrups of the beam were utilized as shear connectors by passing them through drilled holes in the web of the steel T-section. Experimental test and numerical analysis were conducted to determine the behaviour of such beams when subjected to combined shear, torsion, and bending stresses. Full scale one conventional reinforced concrete curved in plan beam C1, and four composite reinforced concrete ones, C2 to C5, were tested. The degree of shear connection between the two components of beams C2 to C5 was changed by varying the number of stirrups which are used as shear connectors. The increase in load carrying capacity of the composite reinforced concrete beams reached 55 % for beam C4 as compared to that of ordinary reinforced concrete beam. The experimental results demonstrated that the stirrups are very effective in providing the interaction between the two components of the beams. The degree of shear connection emerged not to have effect on the behaviour of tested beams. Three-dimensional finite element analysis was conducted using commercial software ABAQUS. To model the shear connection in composite reinforced concrete beam, the stirrups were connected to the web of the steel T-section by springs at the location of the stirrups. Good agreement is obtained between the results of the experimental tests and the finite element analysis.

A Variable Clutch Mechanism for Adjustable Stiffness Actuators Based on Bending and Torsion of Prismatic Beams

Today, a major obstacle to developing locomotion mechanisms that are as safe and energy efficient as living organisms has been overcome with the development of actuators with adjustable stiffness. This work presents an innovative clutch mechanism whose stiffness can be adjusted based on the combined bending and torsion of the prismatic beams. In this way, the stiffness of any rotary actuator can be adjusted with the help of this clutch mechanism. The adjustable clutch mechanism consists of elastic prismatic beams placed in any position in the power transmission unit. The stiffness of the clutch mechanism is controlled by varying the active clutch length of these prismatic elastic beams using an additional actuator. This work is a new version developed to solve the mechanical problems observed in our previous studies using elastic cylindrical beams. Cylindrical beams subjected to dynamic bending have a higher risk of cracking on the cylindrical surface over time. The cross-section of cylindrical beams subjected to bending is very narrow at the point furthest from the center, which bears the greatest load in bending. For this reason, it has been observed that the beams break due to micro-cracks on the surfaces of the cylindrical beams in long-term use. However, the rectangular beam proposed as a solution to this mechanical problem is subject to combined torsion and bending, complicating the analytical solution. In this study, the stiffness variation of an adjustable elastic coupling mechanism depending on the coupling length was obtained with a simplified discrete analytical approach. Torsional and bending stiffness of the prismatic beams were calculated separately, and their sum gave the angular stiffness of the actuator. The analytical results obtained using this simple approach are compared with the experimental and finite element analysis results. The results show that the current design can adjust the stiffness over a wide range and the simple analytical approach gives more accurate results as the clutch length increases.

Bending-shear interaction buckling of stainless steel plate girders: Numerical investigation and design method

A comprehensive numerical investigation of transversely stiffened stainless steel plate girders under combined bending and shear was carried out in this paper. By using the finite element (FE) software package ABAQUS, numerical models with incorporation of material nonlinearity, initial geometric imperfections and welding residual stresses were developed, and were used to replicate previously obtained test results. The validated numerical models were employed to perform parametric studies to generate structural data points for stainless steel plate girders over a broad range of cross-sectional properties, involving various combinations of bending moment and shear force. The summarised test and FE results were compared with the predicted strengths determined according to European code EN 1993-1-5 and proposals of Jáger et al., Chinese code GB 50017-2017, and American specification ANSI/AISC 370-21, highlighting that the applicability of existing design methods in predicting the ultimate resistances of stainless steel plate girders under combined bending moment and shear force was limited. By referring to the design methods in GB 50017-2017 and ANSI/AISC 370-21, two separate design recommendations were proposed, respectively. Further reliability analyses were performed to verify the applicability of the abovementioned design methods.

The strength design of deeply buried circular corrugated steel arches with considering only soil radial restraining

Buried circular corrugated steel arches (BCCSAs) are often adopted in underground engineering. However, the current design specifications cannot accurately estimate the BCCSA’s load-bearing capacity due to the complicated interaction between the soil and the arch. This paper presents the strength design recommendations for deeply buried circular corrugated steel arches with various rise–span ratios under axial compression and under combined axial compression and bending moment respectively, with meeting a proposed width–thickness ratio limit of the BCCSA for local buckling prevention. At first, a finite element model (FEM) of sinusoidally corrugated steel plate (S-CSP) for analyzing its local plate buckling under axial compression (FEM-l) is established, and this FEM can eliminate other possible buckling modes except the local buckling mode by constraining the out-of-plane displacement at the crest and valley lines in S-CSPs. Through FEM-l, the local buckling behaviors of S-CSPs are studied and the width–thickness ratio limit of S-CSPs under axial compression for local buckling prevention is determined in terms of a design principle that local buckling of plate elements does not occur before fully sectional yielding. Then, a global arch-spring model of BCCSA is established for analyzing its elastic global buckling, with considering the interaction between the soil and arches by simplifying the radial restraint of soil as radial unidirectional springs around the arch. The normalized slenderness of BCCSA in the arch-spring model is obtained from its elastic global buckling load calculated by theoretical derivation with bidirectional spring assumption. Finally, the ultimate load-bearing capacity of BCCSAs is calculated by employing elastoplastic finite element models under axial compression and under combined axial compression and bending moment respectively. Based on extensive numerical results obtained in this study, the conservative strength design methods for BCCSAs are proposed in practical engineering applications.

Machine learning (ML) based models for predicting the ultimate strength of rectangular concrete-filled steel tube (CFST) columns under eccentric loading

Concrete-filled steel tubes (CFSTs) are popularly used in structural applications. The accurate prediction of their ultimate strength is a key for the safety of the structure. Extensive studies have been conducted on the strength prediction of CFSTs under concentric loading. However, in real situation CFSTs are usually subjected to eccentric loading. The combined compression and bending will result in more complex failure mechanisms at the ultimate strength. The accuracy of methods in design codes is usually limited due to their simplicity. In this study, three machine learning (ML) methods, namely, Support Vector Regression (SVR), Random Forest Regression (RFR), and Neural Networks (NN), are adopted to develop models to predict the ultimate strength of CFSTs under eccentric loading. A database consisting of information of 403 experimental tests from literature is created and statistically analyzed. The database was then split to a training set which was used to optimize and train the ML models, and a test set which was used to evaluate performance of trained ML models. Compared with the methods in two typical design codes, the ML models achieved notable improvement in prediction accuracy. The parametric study revealed that the trained ML models could generally capture the effect of each primary input feature, which was verified by the relevant experimental test results.

Performance of concrete-filled double-skin shallow-corrugated steel plate composite walls under compression-bending load

This paper presents the study on the performance of concrete-filled double-skin shallow-corrugated steel plate composite walls (CDSCW) under combined compression and in-plane bending, where the CDSCW is composed of the concrete-filled double-skin shallow-corrugated steel plate wall (CDSW) and rectangular concrete-filled steel tubular (CFST) columns. The experiments on full-scale specimens show that the concrete and steel work together well under the combined loading, and the inner concrete is effectively confined by both steel tubes and shallow-corrugated steel plates. The numerical model is established for the CDSCW and the feasibility is verified by comparing with the test results. The equations for the resistance of composite wall under combined compression and bending are proposed through an extensive parametric study, and the validity and the reliability of the design methods are discussed. It is concluded that the proposed design methods can reasonably predict the resistance of CDSCW under combined compression and in-plane bending.

Local stability of laser-welded stainless steel slender I-sections under combined loading

This paper presents a comprehensive experimental and numerical investigation into the local buckling behaviour of laser-welded stainless steel slender I-sections under combined compression and bending moment. A testing programme was firstly carried out, including initial local geometric imperfection measurements and eccentric compression tests on ten laser-welded stainless steel slender I-section stub column specimens. Following the testing programme, a numerical modelling programme was conducted. Finite element models were developed and validated against the test results, and then adopted to perform parametric studies to generate additional numerical data. The obtained test and numerical data were used to evaluate the applicability of the interaction curves in the European and American codes and the continuous strength method to laser-welded stainless steel slender I-sections under combined loading. The evaluation results generally show that the three sets of considered interaction curves offer adequate design accuracy for laser-welded stainless steel slender I-sections under combined compression and major-axis bending moment, but they yield unduly conservative and scattered resistance predictions for laser-welded stainless steel slender I-sections under minor-axis combined loading, owing principally to the conservative minor-axis bending end points. Finally, an improved design interaction curve for the minor-axis combined loading case was developed and shown to yield substantially more accurate and consistent resistance predictions for laser-welded stainless steel slender I-sections under minor-axis combined loading than the three considered design methods. The reliability of the new design interaction curve was confirmed based on a reliability study.

Behaviour and design of high-strength octagonal CFST short columns subjected to combined compression and bending

A systematic experimental and numerical investigation on the behaviour of octagonal concrete-filled steel tube short columns fabricated with S690 high-strength steel and C90 high-strength concrete, and subjected to combined compression and bending is reported in this paper. Experiments were firstly performed on twelve short column specimens with different plate width-to-thickness ratios. The experimental results and observations including the ultimate loads, load versus displacement responses and failure modes of the specimens were discussed. In supplementary to the experimental investigation, numerical investigation using a validated finite element model was performed to examine the behaviour of the structures with a wide range of plate width-to-thickness ratios, yield strength of high-strength steel and compressive strength of high-strength concrete that subjected to various combinations of compression and bending. Based on the experimental and numerical results, the applicability of existing design approaches in standards was also evaluated. The assessment shows that the design approaches provide conservative strength predictions for the high-strength octagonal concrete-filled steel tube short columns under combined compression and bending and can be applied to provide safe designs for the structures.

The influence of bending loading on surface fatigue crack growth life

Engineering structures often serve under complex fatigue loading and the most common of which are tension and bending loading, or their combination. Fatigue cracks always initiate as surface and other three dimensional (3D) cracks and most of the fatigue life of structures spends on 3D crack growth, but fatigue crack propagation curves of materials are widely obtained using through-the-thickness specimens. In this work, a 3D fracture mechanics based method is developed to evaluate surface crack propagation life under combined tension and bending loadings by considering the plasticity induced fatigue crack closure. The method is validated firstly against available experimental data of surface fatigue cracked plates under the combined loadings, and then applied to predict fatigue crack propagation life of surface cracked railway axles under rotating bending. It is shown that the method can make prediction of life within 0.80 to 1.08 of the test life, and the predicted shape evolution of surface crack agrees well with experimental observation. With a modification of short crack closure being made and an equivalent initial crack being assumed, the proposed method can be extended to fatigue life prediction. It is found that the influence of bending loading on fatigue life increasing for larger initial cracks, especially in the submillimeter range. This fracture mechanics based method can serve as a unified way to calculate fatigue crack growth life as well as fatigue life of practical structures under both tension and bending loadings by use of the material crack growth curves obtained with straight-through cracked standard specimens.

Numerical modelling of LSF walls under combined compression and bending actions and fire conditions

Numerical modelling of cold-formed steel walls used in determining the ambient temperature ultimate capacities has evolved from the use of idealised stud-only models to advanced models by employing sheathing and connection characteristics. Due to the convergence issues associated with elevated temperature structural models, attempts to incorporate sheathing are scarcely seen in the literature. In this study, the behaviour of light gauge steel framed (LSF) walls under combined axial and lateral loads and fire exposure was investigated by using stud-only and advanced structural finite element (FE) models. The advanced model is an improved single stud model which included gypsum plasterboard sheathing while also making models computationally less demanding. It incorporated material and geometric non-linearities, contact interactions, idealised in-plane restraints and explicit modelling of gypsum plasterboard sheathing, and was validated using full-scale fire test results. The predicted fire resistance levels (FRLs), failure modes, axial shortening and lateral deflection plots showed good agreement with fire test results. Furthermore, thermal FE models were also developed and validated against fire test results. They will be extended to obtain the time–temperature profiles of cavity insulated and non-insulated single and double plasterboard sheathed LSF walls exposed to fire for use in structural parametric studies. This paper summarises the findings of this study and proposes suitable recommendations for FE modelling of LSF walls under combined compression and bending actions and fire conditions.