Accordion Effect Research Articles

Investigating the mechanical properties related to the vertical bending of composite I‐beams with corrugated steel webs

AbstractThe maximum angular rotation attributable to the in‐plane shear deformation of flange slabs is used as generalised displacement in the conventional analysis method for I‐beams. However, the mechanical concepts are poorly understood due to the complex nature of this analysis method. Consequently, a novel strategy for analysing vertical bending in composite I‐beams is proposed in this study. This approach uses the additional deflection of composite I‐beams induced by the shear lag effect as the generalised displacement. Furthermore, this research comprehensively considers the accordion effect, shear lag and self‐equilibrium conditions for the shear lag warping stress and bending moment. Moreover, two longitudinal warping displacement difference functions are employed to accurately describe the variation of shear lag in composite I‐beams with varying flange slab widths. The differential equations of the I‐beams with corrugated steel webs in the elastic range are established based on the energy‐variation method. A complete mechanical system of a composite I‐beam is decomposed into two parts, namely, the shear lag mechanical system and the elementary beam mechanical system, which are independent of each other. The theory presented in this paper reflects the internal mechanical mechanism of composite I‐beams. The calculation accuracy is considerably improved in this study. Therefore, this method is more unambiguous and well‐defined. It enriches and advances the current analysis theory of composite structures, which can guide the design of composite I‐beams.

Analysis of influential factors on additional shear force induced by shear deformation in girder bridges with corrugated steel webs

Girder bridges with corrugated steel webs (CSWs) exhibit critical shear regions proximate to supports, where the CSWs are subjected to peak shear forces and bending moments potentially inducing shear buckling. This study explores the shear behavior within critical regions experiencing hogging bending moments, where the accordion effect of CSWs dramatically exacerbates shear deformation. However, due to the substantially reduced shear stiffness of CSWs relative to concrete slabs and crossbeams, the shear deformation of CSWs is constrained, causing additional shear forces to form within them. The traditional basic shear method proves inadequate in predicting shear stress within CSWs for it omits these additional shear forces. The study introduces an enhanced formula to precisely assess shear stresses within CSWs, particularly in hogging moment regions of girders, considering the additional shear force induced by CSWs' shear deformation. A strong correlation between the additional shear forces and the geometric characteristics of CSWs has been identified through theoretical analysis. Accordingly, the study systematically investigates the impact of various parameters on the additional shear force through finite element parametric analysis. Comparative analysis demonstrates that the CSWs’ thickness, the height-to-span ratio, and the boundary constraint conditions of girders significantly impact additional shear forces, thereby affecting the shear transfer efficiency within the cross-section of the girder.

Modified calculation on shear stress of girder bridges with corrugated steel webs

The study examines the shear behaviors in girder bridges with corrugated steel webs (CSWs) considering different boundary constraints through theoretical analysis, experimental investigation, and numerical simulation. The accordion effect significantly amplifies shear deformation in CSWs at support locations. The substantial difference in shear stiffness between the CSWs and the concrete slabs constrains the shear deformation of CSWs, resulting in the generation of additional shear force within the CSWs. Therefore, the existing basic shear method is inaccurate for calculating shear stress in CSWs because it neglects this influencing factor. The study proposes an advanced formula for accurately predicting shear stresses near the supports of a cantilever prismatic girder bridge with CSWs by incorporating the additional shear forces induced by the shear deformation of CSWs. Theoretical analysis has revealed that the expression and magnitude of the additional shear force are correlated with the boundary conditions of the girder bridge. The study formulates expressions for the additional shear force induced by shear deformation in girder bridges with CSWs, considering various boundary conditions such as cantilever, simply supported, fixed-end, and continuous spans. It contributes to further enhancing the analytical method for calculating shear stress in prismatic girder bridges with CSWs, accommodating diverse support constraint conditions. The findings have practical implications for guiding the shear design of girder bridges with CSWs under various support systems.

Dynamic response of girder bridges with corrugated steel webs subjected to moving loads

Girders with corrugated steel webs (CSWs), replacing traditional concrete webs in prestressed concrete box girders, exhibit a unique dynamic behavior due to the accordion effect and the thinner dimension of CSWs. The study aims to investigate the dynamic response of girder bridges with CSWs under moving loads. Utilizing the Timoshenko beam theory and modal analysis method, the analytical formula for the dynamic response, considering shear deformation and rotational inertia, was developed. The proposed analytical formula was validated through finite element simulation. Employing dimensionless parameters, a parametric analysis was conducted to examine the effects of multi-modes, loading position and shear deformation on the dynamic response of girders with CSWs. The results highlight the significant influence of the shear parameter αS and the speed parameter SE1 on the magnitude of the impact factor. Precise calculations for deflection and bending moment only require consideration of low-order modes, whereas accurate estimation of shear force requires attention to higher-order modes. In particular, a high-frequency resonance phenomenon is identified when the speed parameter SE1 and the shear parameter αS conform to the formula “πSE1αS = 1”. The suggested impact factor formulas for midpoint deflection, midpoint bending moment and end shear force have been developed and categorized into three groups based on the magnitude of the shear parameter αS.

Local buckling of the bottom flange in steel-concrete composite beams with trapezoidal corrugated webs subjected to end restraint at high temperatures

Steel-concrete composite beams with trapezoidal corrugated webs (SCBCW) are prone to rapid failure at high temperatures due to local instability of the bottom flange. The failure mechanism of SCBCW, which is an integral part of the holistic structure and subject to axial and rotational restraints from adjacent members at elevated temperatures, differs from conventionally simply supported steel-concrete composite beams with straight webs. To investigate the evolution of local buckling in the compressed flange of SCBCW under high temperature conditions, a composite beam model with frame restraints was developed using ABAQUS finite element software. In this model, the composite beam is connected to restraint frame columns through high-strength bolts. The changes in axial stress, bending moment, and deflection of the compressed flange of SCBCW were analyzed as temperature increased. Results indicate that at elevated temperatures, additional bending moments occur in the flange plane due to axial restraints, section temperature gradients, section negative bending moments and accordion effect caused by corrugated web on compressed bottom flange of SCBCW. This leads to a gradual increase in axial compressive stress before local buckling occurs followed by a decrease due to internal force redistribution upon onset of buckling. Studies show that initial buckling of bottom flange occurs on one side of flat section of web where axial compressive stress is relatively high while restraint effect on web is low; Subsequent local buckling of the beam then appears on opposite side adjacent flat section of web after initial buckle occure on one side. After local buckling appears on both sides of web tension bands appear on both sides where bottom flange experiences localized bucking. The setting of longitudinal stiffeners (LS) can effectively improve the local stability of the bottom flange of the composite beam, while the setting of transverse stiffeners (TS) has no significant impact.

A novel surgical correction using a combination of wave-like incision and Z-axis Z-plasty for congenital constriction band syndrome

BackgroundA congenital constriction band (CCB) is a relatively common anomaly among limb malformations. However, the number of cases treated at a given center is limited and differences in techniques used by surgeons at each facility have a significant impact on the treatment outcomes. Several surgical methods have been reported, but a standard technique that yields consistent satisfactory results is still needed. Here, we introduce a novel technique for the treatment of CCB syndrome that uses a combination of wave-like skin incision and Z-axis Z-plasty. Patients and methodsA wave-like incision was used for skin incision with the goals of achieving an accordion effect and a less noticeable post-operative scar. After the fibrous constriction band was completely excised, a Z-plasty of sufficient size in the Z-axis direction was performed on the dermis-inclusive adipose tissue. For over 10 years, this technique was applied to 11 sites in 6 patients. A retrospective study of the characteristics of these cases was performed, including age at surgery, gender, type of deformity, degree of constriction, types of examination, number of surgeries, and post-operative outcomes. ResultsIn all patients, a normal contour of the limbs was achieved and the hourglass-like deformity caused by the constriction band was satisfactorily improved. No additional corrective surgeries were needed, there was no abnormal growth of the treated limbs, and scarring was aesthetically acceptable in all cases. ConclusionThe novel technique described here uses deep subcutaneous fat to correct the hourglass-like deformity and restores a normal limb contour, while the wave-like skin incision minimizes post-operative scarring.

Seismic performance of joints of prefabricated corrugated steel utility tunnels Part(I)–Experimental analysis

This paper presents the seismic performance of a corrugated steel plate utility tunnel, based on an engineering prototype. The research combines quasi-static testing and numerical simulation to investigate the behavior of the structure under cyclic loads in different directions. Specifically, six loading scenarios were considered: the quasi-static test was conducted for transverse tension and compression, transverse bending and shear, vertical shear test (Conditions (1–3)), while numerical simulations were performed for longitudinal tension and compression, transverse shear, and vertical bending shear test (Condition (4–6)) in Part(II). The results reveal comprehensive hysteresis curves for the plate under diverse loading directions, with an extended yield platform section that underscores its significant plastic deformation capacity. However, the “pinch” phenomenon of the hysteresis curve is obvious. The existence of rounded corners not only makes the hysteresis curve of the plate asymmetrical but also makes a great difference to the bearing capacity of the structure in the direction of positive and negative loading. The component exhibits superior bearing capacity and stiffness along the longitudinal direction compared to other orientations. Additionally, the structure demonstrates remarkable energy dissipation capabilities because of the inherent “accordion effect” of the corrugated steel plate. Moreover, the maximum energy dissipation coefficient in three directions is more than 1.0, illustrating its excellent energy dissipation capacity. The results provided valuable insight into the seismic performance of joints and contributed to the safe design of prefabricated corrugated steel utility tunnels.

Radial force analysis of long span bridge with trapezoidally corrugated steel webs

The study numerically and theoretically investigates the radial force effect of long span prestressed concrete (PC) box girders with trapezoidally corrugated steel webs (TCSWs). It reveals that under the influence of radial forces, the curved prestressing tendons in the bottom slab in long span box girder bridges with TCSWs exhibited higher levels of stress and deflection compared to conventional concrete box girder bridges due to the accordion effect of the TCSWs. Furthermore, this study simplifies the radial forces as concentrated forces of PC box girder with TCSWs. Based on this simplification, a formula is derived to accurately calculate the magnitude of these radial forces. Through parameter analysis of the power exponent in the equation defining the curve profile of the bottom slab, it was observed that lower power exponents result in more significant radial force effects. Finally, to eliminate the radial force effect, the study innovatively proposed an optimized structural scheme by adopting horizontal bottom slab at midspan and arranging horizontal diaphragms uniformly across the entire longitudinal span of the bridge. A contrastive study suggested that the horizontal arrangement of internal prestressing tendons in the bottom slab at midspan could effectively eliminate the negative impact of the radial force effects and greatly improve the overall bearing capacity of the box girders with TCSWs.

Mechanical performance of concrete-encased prismatic girders with corrugated steel webs

To enhance the shear buckling resistance of girder bridges with corrugated steel webs (CSWs), especially near the intermediate support where maximum shear force and negative bending moment are experienced, it is common practice to encase the CSWs with concrete. This paper analyses the mechanical performance of concrete-encased prismatic girders with CSWs based on finite element (FE) simulations, theoretical analysis and existing experiments. The concrete encasement restricts the axial free deformation of the concrete-encased CSWs (CCSWs), thereby diminishing the accordion effect of the CSWs. As a result, the normal strains in both the CCSWs and the concrete encasement become nearly identical, demonstrating a linear distribution that aligns with the plane section assumption. The study reveals that the concrete encasement assists the CCSWs in shouldering a portion of the shear force, and shear stress in the CCSWs is no longer uniformly distributed. In addition, a stiffness-based shear carrying calculation method for CCSWs and concrete encasement is theoretically derived. It is observed that due to the constraint of concrete encasement, the actual shear modulus of CCSWs surpasses that of CSWs without encased concrete, rendering it more similar to that of a flat steel plate. Lastly, this study firstly proposes a shear stress calculation formula for CCSWs, which theoretically explains the parabolic shear stress distribution in CCSWs. Error analysis reveals that traditional basic shear method, which assumes uniform shear stress distribution in CSWs, significantly underestimates the actual shear stress in CCSWs. Remarkably, the modified shear method proposed in this study accurately predicts shear stresses in CCSWs.

Elastic analysis of I-girders with tubular flange and corrugated web

This study aims to investigate the mechanism of I-girders with corrugated web and tubular flange, including the deformation and the stress distribution. Based on the accordion effect of the corrugated web, theoretical analysis was carried out to present analytical equations for predicting the defection and the stress by considering the large shear deformation of the corrugated web. The accuracy of the presented equations was verified through comparison with experimental results of three full scaled specimens and numerical results of specimens with different loads and different boundary conditions obtained from finite element analysis. Both experimental and numerical results indicate that plane section assumption is not satisfied for such I-girder under transverse load. Simplifying such I-girder to a conventional Euler Bernoulli beam overestimates the flexural stiffness and produces much lower prediction on the deflection and inaccurate prediction on the normal stress and the shear stress. The tubular flange with a relatively large height compared to a flat-plate flange can sustain about 20% of the shear force on the cross section. Sensitivity analysis shows that the presented analytical equations can produce more accurate predictions on both deflection and stress distribution of such I-girder compared to classical theory of Euler Bernoulli beam.

Analytical theory of composite beams with CSWs using the state space method

Based on the zig-zag theoretical model of corrugated steel web beam (CSW), the governing equations in the form of state equations are derived and their analytical solutions are obtained for different loads, variable cross-sections and boundary conditions. Through numerical examples, it is verified that the bending moment, deflection and stresses predicted by the present analytical method have a good agreement with the results of the three-dimensional finite element model. The applicability of the present method for non-prismatic continuous beams with CSWs under different loads is also demonstrated. Meanwhile, it is found that the quasi-plane assumption is still valid in non-prismatic continuous beams with CSWs. Through quantitative analysis of the flexural stresses in the top and bottom slabs, it is confirmed that the zig-zag theory in this study can well reflect the accordion effect of CSWs. Because of the inclined bottom slabs in the non-prismatic beams with CSWs, the Resal effect on the shear stresses in the CSWs and bottom slabs, which is caused by the vertical component of the axial force in the bottom slab, is discussed. A refined shear formulation is developed for more accurate shear stresses in the CSWs and bottom slabs, which provides fundamental theoretical support for the strength prediction of the non-prismatic beam with CSWs.

Experimental study on axial resistant behavior of multi-celled corrugated-plate CFST walls

Multi-celled corrugated-plate concrete-filled steel tubular (MC-CFST) wall is an innovative type of steel–concrete composite wall for achieving lower steel consumption and higher load-resistance efficiency. Experiments on 14 specimens were conducted to investigate the performance of MC-CFST walls under axial compression. The key parameters included wall depth, corrugated cell width and corrugated plate form. The specimens exhibited good ductility and showed similar failure patterns with local buckling on steel tubes and corrugated plates. By analyzing the test results, failure modes and ultimate and residual resistances of the specimens were discussed in detail. In addition, the performance of corrugated plates during the whole loading process was analyzed based on the measured strain results. It can be found that the vertical performance of corrugated plates is the combination of the accordion effect and vertical compression effect, and the horizontal performance is the combination of the overall expansion effect and beam effect. A method for calculating the critical width of corrugated cells was presented. Moreover, the test results were compared with the typical equations specified in several existing design codes. It was found that AISC 360-16, EC4-2004 and GB50936-2014 could safely predict the ultimate resistance of MC-CFST walls, among which the results of GB50936-2014 were the closest to the experimental results.

Stability behaviour of sinusoidal corrugated web girders under fire conditions

AbstractSinusoidal corrugated web girders, which are in the focus of the current paper, have been increasingly used in the past years in civil engineering applications due to economical design. Recently, a number of experiments dealing with the particular behaviour of this girder type have been carried out at room temperature, while the structural behaviour at elevated temperature has not been widely analysed and requires further investigation and clarification. The current paper deals with the improved geometrically and materially nonlinear analysis with imperfections (GMNIA) of sinusoidal corrugated web girders under fire conditions. The developed finite element model, which is validated based on previous measurements during fire tests found in the international literature, is capable of modelling the specialties, e.g., the so‐called ‘accordion effect’, of corrugated web girders. The applicability of design formulae is also illustrated in the paper while an extensive numerical parametric study is also carried out to demonstrate the impact of different parameters on the stability behaviour and failure mode of corrugated web girders at elevated temperature.

Seismic performance of the RBS connection with trapezoidal corrugated web (TCW-RBS)

This paper presents an evaluation of the performance of the trapezoidal corrugated web (TCW) reduced beam section (RBS) connection under cyclic loading. A series of experiments were conducted on three TCW-RBS specimens. The tests were carried out up to a 10% story drift ratio, and it was observed that the connection met the code-based limitations for a reduction in strength until reaching an 8% drift, surpassing the existing criterion for qualified connections in special moment frames. Additionally, nonlinear finite element analysis was utilized to investigate the influence of web angles on the behavior of TCW-RBS connections. The findings revealed that increasing the web angle resulted in a decrease in the maximum moment by up to 11%, while simultaneously enhancing the connection's ductility by up to 37%. Furthermore, the axial strain results in the web of the beam indicated that the corrugated web had a negligible impact on the flexural behavior of the connection due to the accordion effect. Notably, the maximum strain values in the flanges near the column face were three times lower than those in the reduced section zone, contributing to a reduced sensitivity of the welds to potential fractures.

Seismic performance of partially encased concrete composite columns with corrugated web

Partially encased concrete composite (PEC) components have gained popularity recently because they are suitable for prefabricated construction. Corrugated steel plates have higher buckling strength and out-of-plane stiffness than flat plates, in this paper, an innovative corrugated web PEC column (CPEC column) was proposed, and its seismic performance was studied by cyclic loading tests. The designs and fabrications of specimens and loading system were described in detail. The seismic behavior of CPEC columns was investigated comparatively by analysis of their failure modes, hysteretic curves, ductility, energy dissipation capacity, and stiffness degradation. The test results show that the ultimate lateral load of CPEC columns under minor-axis bending is more competitive than that of ordinary PEC columns, while the ductility, energy dissipation capacity and stiffness degradation rate are close to that of ordinary PEC columns. Under major-axis bending, the “accordion effect” of corrugated web has a negative influence on the seismic behavior of CPEC columns after the concrete is crushed severely. Finally, the modified equations can be used to predict the N-M interaction curves of the CPEC columns. More experimental or numerical research should be carried out to further evaluate the seismic performance of CPEC columns quantitatively in the future.

Sorption-Deformation Interplay in Hierarchical Porous Polymeric Structures Composed of a Slit Pore in an Amorphous Matrix.

Prevailing absorbents like wood-derived porous scaffolds or polymeric aerogels are normally featured with hierarchical porous structures. In former molecular simulation studies, sorption, deformation, and coupled sorption-deformation have been studied for single-scale materials, but scarcely for materials where micropores (<2 nm) and mesopores (2-50 nm) coexist. The present work, dealing with a mesoscopic slit pore between two slabs of microporous amorphous cellulose (AC), aims at modeling sorption-deformation interplay in hierarchical porous cellulosic structures inspired by polymeric modern adsorbents. Specifically, the atomic system is modeled by a hybrid workflow combining molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) simulations. The results clarify the multiple sorption/deformation mechanisms in porous materials with different slit-pore sizes, including water filling in micropores, surface covering at the solid-air interface, and subsequent capillary condensation in mesopores. In particular, before the onset of capillary condensation, the sorption behavior of the AC matrix in the hybrid system is almost the same as that of bulk AC, in which sorption and deformation enhance each other through sorption-induced swelling and additional sorption in the newly created voids. Upon capillary condensation, the interaction between the micropores and the mesopore emerges. Water molecules in the mesopore exert a negative hydrostatic pressure perpendicular to the slab surface on the matrices, resulting in an increase in porosity and water content, a decrease in distance between the centers of mass (COMs) of the slabs, and thus a thinning of the slit pore. As described by Bangham's Law, the surface area of the rough slit-pore slab increases proportionally to the surface energy variation during surface covering. For a system composed of a compliant polymer like AC, however, the surface area enlargement does not result in an in-plane swelling as expected but instead in an in-plane shrinkage along with an increase in local roughness or irregularity (an accordion effect).

Equivalent flat-web thicknesses and modified flange-based moment resistance for corrugated-web steel I-girders

This study proposed analytical formulations for equivalent flat-web thicknesses at horizontal and inclined fold sections and modified flange-based moment resistance for corrugated-web girders (CWGs), accounting for the accordion effect due to corrugations. The finite element (FE) analysis approach was used for examining the nonlinear flexural behavior of CWGs. Numerical models were first validated against flexural tests from two documented CWG studies. For additional verification, nonlinear theoretical analysis of flat-web girders was compared and verified against detailed FE-based analysis results. A detailed parametric study was performed to examine the effect of corrugated-web trapezoidal profiles and girder geometry on the moment resistance of CWGs using the validated nonlinear FE modeling. Then, the parametric study results were used in the theoretical nonlinear moment-curvature analysis on equivalent flat-web girders to derive the proposed formulations for flat-web thicknesses at horizontal and inclined fold sections of a CWG. Alternatively, a modified flange-based moment resistance formulation was proposed for CWGs by accounting for the accordion effect of their trapezoidal corrugated webs. Both the proposed formulations simplified the accordion effect analysis in CWGs and can result in potentially economical girder designs and further development of design specifications for CWGs.

The Multi-Functional Modelling Shear Lag Method for Accurate Calculation of Static Response and Accordion Effect of Improved Composite Box Girders

The composite box girder with corrugated web and steel bottom plate (CW-SBS) is a kind of improved steel-concrete structures. The design of CW-SBS box girders needs the accurate method to calculate the working response and accordion effect in consideration of the self-stress equilibrium condition of shear lag warping stress and shear deformation. This study proposes the multi-functional modelling shear lag (MFMSL) method which adopts the four longitudinal displacement difference functions to model the variation of shear lag in the CW-SBS box girders with different wing slab widths and thicknesses. Therefore, MFMSL is a method to calculate the static response and accordion effect of the CW-SBS composite box girders. Structural differential equations based on the energy-variation principle present that the MFMSL method effectively improves the calculating accuracy of the CW-SBS box girder static response, which can be verified by both experimental and simulative results. Also, the MFMSL method demonstrates that the accordion effect of the CW-SBS box girder is stronger than that of the traditional composite box girder and closely relates to the load distribution. Hence, the proposed method further lays the foundation for the analysis and design of CW-SBS box girders.

Race development and performance-determining factors in a mass-start cross-country skiing competition.

Although five of six Olympic events in cross-country skiing involve mass-starts, those events are sparsely examined scientifically. Therefore, in this study, we investigated speed profiles, pacing strategies, group dynamics and their performance-determining impact in a cross-country skiing mass-start competition. Continuous speed and position of 57 male skiers was measured in a six-lap, 21.8 km national mass-start competition in skating style and later followed up with an online questionnaire. Skiers ranked from 1 to 40 were split into four performance-groups: R1-10 for ranks 1 to 10, R11-20 for ranks 11 to 20, R21-30 for ranks 21 to 30, and R31-40 for ranks 31 to 40. All skiers moved together in one large pack for 2.3 km, after which lower-performing skiers gradually lost the leader pack and formed small, dynamic packs. A considerable accordion effect occurred during the first half of the competition that lead to additional decelerations and accelerations and a higher risk of incidents that disadvantaged skiers at the back of the pack. Overall, 31% of the skiers reported incidents, but none were in R1-10. The overall trend was that lap speed decreased after Lap 1 for all skiers and thereafter remained nearly unchanged for R1-10, while it gradually decreased for the lower-performing groups. Skiers in R31-40, R21-30, and R11-20 lost the leader pack during Lap 3, Lap 4, and Lap 5, respectively, and more than 60% of the time-loss relative to the leader pack occurred in the uphill terrain sections. Ultimately, skiers in R1-10 sprinted for the win during the last 1.2 km, in which 2.4 s separated the top five skiers, and a photo finish differentiated first from second place. Overall, a high correlation emerged between starting position and final rank. Our results suggest that (a) an adequate starting position, (b) the ability to avoid incidents and disadvantages from the accordion effect, (c) tolerate fluctuations in intensity, and (d) maintain speed throughout the competition, particularly in uphill terrain, as well as (e) having well-developed final sprint abilities, are key factors determining performance during skating-style mass-start cross-country skiing competitions.

Objections to Davidson’s Theory of Agency and Actions

Davidson’s theory of agency aims to solve the dilemma that the same action can be both intentional and not intentional. He explains primitive actions using primarily bodily movements and argues that event-causality can be described through the “accordion effect”, but not agent-causality. And Davidson uses reasons as causes to explain the actions and responds to five objections. In this paper, I critique Davidson’s argument, pointing out that he ignores certain factors in the belief-desire model, such as emotions. And his sentence holism has a problem because individual words that express complete thoughts can explain actions in language games. As a result, Davidson’s criticism of Wittgenstein is not reasonable.