Search Results (44)

Channels with three standard symmetrical sections and one asymmetric section are mounted as cantilever beams with the web oriented vertically. A classical solution to the analysis of stress in each thin-walled cantilever channel is provided using the principle of wall shear flow superposition. The latter is coupled with a further superposition between axial stress arising from bending and from the constraint placed on free warping imposed at the fixed end. Closed solutions for design are tabulated for the net shear stress and the net axial stress at points around any section within the length. Stress distributions thus derived serve as a benchmark structure for alternative numerical solutions and for experimental investigations. The conversion of the transverse free end-loading applied to a thin-walled cantilever channel into the shear and axial stress that it must bear is outlined. It is shown that the point at which this loading is applied within the cross-section is crucial to this stress conversion. When a single force is applied to an arbitrary point at the free-end section, three loading effects arise generally: bending, flexural shear and torsion. The analysis of each effect requires that this force’s components are resolved to align with the section’s principal axes. These forces are then considered in reference to its centroid and to its shear centre. This shows that axial stress arises directly from bending and from the constraint imposed on free warping at the fixed end. Shear stress arises from flexural shear and also from torsion with a load offset from the shear centre. When the three actions are combined, the net stresses of each action are considered within the ability of the structure to resist collapse from plasticity and buckling. The novelty herein refers to the presentation of the shear flow calculations within a thin wall as they arise from an end load offset from the shear centre. It is shown how the principle of superposition can be applied to individual shear flow and axial stress distributions arising from flexural bending, shear and torsion. Therein, the new concept of a ‘trans-moment’ appears from the transfer in moments from their axes through centroid G to parallel axes through shear centre E. The trans-moment complements the static equilibrium condition, in which a shift in transverse force components from G to E is accompanied by torsion and bending about the flexural axis through E. Full article

This research investigated and compared the structural behavior of reinforced concrete straight beams and beams made with out-of-plane parts. This study focused on the influence of the location and number of out-of-plane parts, as well as encasing the beams with a steel section, on the ultimate strength, deflection, and rotation in addition to the ductility, energy absorption, and failure mode. A total of nine beams were modelized numerically, divided into three series. The first one included one straight beam, while the remaining two series included four beams each made with out-of-plane parts with and without steel sections. The beams with out-of-plane parts connected the two, three, four, and five concrete segments. The outcomes revealed that the beams made with out-of-plane parts showed less strength than straight beams, which increased the connected segments and reduced the ultimate strength capacity. The regular beam’s linearity was dissimilar to the zigzag beams, which showed a linearity of 32% and was reduced to 22%, 20%, 19.67%, and 16% for beam out-of-plane parts made with two, three, four, and five segments, respectively. Forming a zigzag in the plane of the beams reduced the cracking load, but the decrement depended on the number of parts, which led to more reduction in the yielding load. Concerning the deflection and deformations, the concrete straight beams failed in flexure, with maximum deflection occurring at the midspan of the beam, which was different for beams without plane parts, which showed a combined shear-torsional failure for which the maximum deformation occurred at the midspan with inclination of connected parts on the interior perpendicular axis. Encasing the beams’ out-of-plane parts with steel sections enhanced the structural behavior. The ductility and energy absorption of the out-of-plane parts beams were less than the straight ones, but encasing the beams with a steel section improved the ductility and energy absorption twice. Full article

The composite primary structures of railway vehicles endure not only mechanical loads including tension, compression, bending, and torsion, but also external impacts, such as by the crushed stone in ballast. In the present study, the low-velocity impact response of preloaded hybrid composite laminates with different thicknesses is examined using a finite element method based on a progressive damage model. The hybrid plate consists of carbon fiber-reinforced unidirectional and woven prepregs. The progressive damage model, based on the 3D Hashin model, is validated by experiments on hybrid laminate, and further compared with the post-impact appearance obtained from CT scans. Preloading, considered to be tensile, compressive, or shear, corresponds to different positions in a bending beam with flanges and a web. Finally, the effects of impact energy, preloading, thickness, and impact angle on the dynamic response are analyzed, with an emphasis on new results and failure mechanism analysis comparing the influence of preloads under a given impact energy and different thicknesses. Full article

In order to investigate the mechanical behavior of a novel pre-tensioned polygonal prestressed T-beam subject to combined bending, shear, and torsion, this study meticulously designed and fabricated a full-scale specimen with a calculated span of 28.28 m, a beam height of 1.8 m, and a top flange width of 1.75 m. A systematic static loading test was conducted. A multi-source data acquisition methodology was employed throughout the experiment. A variety of embedded and external sensors were strategically arranged, in conjunction with non-contact digital image correlation (VIC-3D) technology, to thoroughly monitor and analyze key mechanical performance indicators, including deformation capacity, strain distribution characteristics, cracking resistance, and crack propagation behavior. This study provides valuable insights into the damage evolution process of novel polygonal pre-tensioned T-beams under complex loading conditions. The experimental results indicate that the loading process of the specimen when subjected to combined bending, shear, and torsion, can be divided into two distinct stages: the elastic stage and the crack development stage. Cracks initially manifested at the junction of the upper flange and web at the extremities of the beam and at the bottom flange of the loaded segment. Subsequently, numerous diagonal and flexural–shear cracks developed within the web, while diagonal cracks also commenced to form on the top surface, exhibiting a propensity to propagate toward the support section. Following the appearance of diagonal cracks in the web concrete, both stirrup strain and concrete strain demonstrated abrupt changes. The peak strain observed within the upper stirrups was markedly greater than that measured in the middle and lower regions. On the front elevation of the web, the principal strain peak was concentrated near the connection line between the loading bottom and the upper support. In contrast, on the back elevation of the web, the principal tensile strain was more pronounced near the connection line between the loading top and the lower support. Full article

This paper proposes a beam model integrating the Timoshenko beam theory with Vlasov beam theory to capture the coupled behavior of bidirectional bending, torsion, and axial vibration in thin-walled beams subjected to axial loads. Our model incorporates the effects of shear deformation, rotational inertia, and axial loads, offering a comprehensive approach to complex dynamic behaviors. By utilizing Hamilton’s principle, we derived a complete set of coupled dynamic equations and boundary conditions. The highlight of this model is its capacity to accurately predict the dynamic response of thin-walled beams under multifaceted loading conditions, surpassing traditional models by integrating coupled axial vibrations. This research significantly advances the understanding of the dynamic behavior of thin-walled beams, providing a precise analytical tool for structural design and safety assessment. The robustness and accuracy of the proposed model were validated through extensive theoretical analysis and empirical validation, equipping engineers with critical insights to optimize the design of engineering structures subjected to complex dynamic loads. Full article

Thin-walled channel beams such as cold-formed steel purlins are primarily used to withstand wind forces in the roofing and walling systems of buildings. Traditionally, these types of members are usually designed for bending moments, with the effects of torsion ignored. However, the loading on thin-walled channels can be much more complicated than simple bending actions. Because of the position of the shear centre outside the section, channels can undergo bending and torsion when subjected to vertical load on the top flange. The applied torsion may cause significant stresses in the channel, which may need to be accounted for in design. There appears to be no research on quantifying the effects of torsion on thin-walled channels subjected to a uniformly distributed load acting on the top flange. In this paper, a theoretical solution is derived for calculating the longitudinal stresses in thin-walled channels subjected to torsion caused by a uniformly distributed load acting on the top flange. The theory is validated by modelling the channels in a finite-element analysis. The theoretical results include calculations of the twist rotation, bimoment, sectorial coordinate and longitudinal stresses, while the results from the finite-element analysis include the twist rotation and longitudinal stresses. The results show that the longitudinal stresses caused by torsion can significantly exceed those caused by the bending moment. Practical advice is also given for engineers on how to minimize torsion in cold-formed steel purlins. Full article

A torsional strength model for prestressed concrete beams was proposed considering the initial crack angle, principal stress angle, and longitudinal strain, which are affected by the axial stress induced by the effective prestress. The use of the torsional effective thickness was also proposed to calculate the torsional strength of prestressed concrete beams by considering the effect of prestress. The shear element in the torsional member was simplified under the assumption that the principal tensile stress and principal compressive strain were negligible in the ultimate state. The torsional strength was determined when the principal compressive stress or shear stress at the crack surface in the shear element reached the failure criterion according to the multipotential capacity model, which considers concrete crushing and aggregate interlocking as the main resistances to the applied load. The proposed strength model was verified using test specimens collected from existing experimental studies. The proposed model accurately evaluated the torsional strength of prestressed concrete beam specimens, regardless of the key variables of the prestressed concrete specimens, where the mean value of the tested results to the calculated torsional strengths was 1.123, and the corresponding coefficient of variation was 17.7% for 104 prestressed concrete beam specimens, while the ACI 318-19 torsional design method gave the mean and coefficient of variation of 0.880 and 24.3%, respectively. Full article

Functionally graded materials (FGMs) are revolutionizing various industries with their customizable properties, a key advantage over traditional composites. The rise of voxel-based 3D printing has furthered the development of FGMs with complex microstructures. Despite these advances, current design methods for FGMs often use abstract mathematical functions with limited relevance to actual performance. Furthermore, conventional micromechanics models for the analysis of FGMs tend to oversimplify, leading to inaccuracies in effective property predictions. To address these fundamental deficiencies, this paper introduces new gradation functions for functionally graded beams (FGBs) based on bending strain energy density, coupled with a voxel-based design and analysis approach. For the first time, these new gradation functions directly relate to structural performance and have proven to be more effective than conventional ones in improving beam performance, particularly under complex bending moments influenced by various loading and boundary conditions. This study reveals the significant role of primary and secondary gradation indices in material composition and distribution, both along the beam axis and across sections. It identifies optimal combinations of these indices for enhanced FGB performance. This research not only fills gaps in FGB design and analysis but also opens possibilities for applying these concepts to other strain energy density types, like shearing and torsion, and to different structural components such as plates and shells. Full article

Horizontally curved steel I-beams exhibit a complicated mechanical response as they experience a combination of bending, shear, and torsion, which varies based on the geometry of the beam at hand. The behaviour of these beams is therefore quite difficult to predict, as they can fail due to either flexure, shear, torsion, lateral torsional buckling, or a combination of these types of failure. This therefore necessitates the usage of complicated nonlinear analyses in order to accurately model their behaviour. Currently, little guidance is provided by international design standards in consideration of the serviceability limit states of horizontally curved steel I-beams. In this research, an experimentally validated dataset was created and was used to train numerous machine learning (ML) algorithms for predicting the midspan deflection at failure as well as the failure load of numerous horizontally curved steel I-beams. According to the experimental and numerical investigation, the deep artificial neural network model was found to be the most accurate when used to predict the validation dataset, where a mean absolute error of 6.4 mm (16.20%) was observed. This accuracy far surpassed that of Castigliano’s second theorem, where the mean absolute error was found to be equal to 49.84 mm (126%). The deep artificial neural network was also capable of estimating the failure load with a mean absolute error of 30.43 kN (22.42%). This predictive model, which is the first of its kind in the international literature, can be used by professional engineers for the design of curved steel I-beams since it is currently the most accurate model ever developed. Full article

In a concrete beam, cracking is generated on the tension side under the effect of flexure, shear, and torsional loadings. Accordingly, these weak concrete members require repair and/or strengthening to increase or restore their internal load capacity. In the current experimental and numerical investigations on concrete beams, the impact of using notches with different width to depth ratios on the ultimate flexural load under a three-point test was considered. Further, the flexural behavior performance of a notched concrete beam repaired using the three repair materials—cement mortar, bacterial mortar, and adhesive—was also examined. Consequently, a comparative study was implemented between the experimental and numerical results. A concrete damage plasticity (CDP) model was used for the finite element numerical analysis of the beams. The differences in numerical and experimental measured results ranged from 0.65 to 22.20% for the ultimate load carrying capacity. As the notch size increased, the ultimate load carrying capacity of the beam reduced. Additionally, a linear regression model was used to predict the ultimate load values at a notch width interval of 5 mm up to a maximum notch width of 100 mm. It was observed that the ultimate load capacity for a repaired beam increased as compared to the notched beam for all three repair materials under consideration. And the maximum ultimate load increased in the case of notched beams repaired using adhesive. Furthermore, in comparison to the cement mortar, the performance of the bacterial mortar in terms of the ultimate load was more. The bacterial mortar was found to be more sustainable and more durable as a repair material for concrete structures. Full article

The effect of structure on the vibration response was explored for four piano soundboards with different but commonly adopted structures. The vibration response was obtained using the free-vibration method, and the values of the dynamic modulus of elasticity and dynamic shear modulus obtained using the free-vibration frequency method (E_F and G_F) were compared with the dynamic modulus of elasticity obtained using the Euler beam method (E_E) and dynamic shear modulus obtained using the free-plate torsional vibration method (G_T), respectively. It was found that the soundboards with different structures had different vibration modes and that excitation at different locations highlighted different vibration modes. For all the soundboards analyzed, the E_E and G_T were higher than E_F and G_F by 2.2% and 24.3%, respectively. However, the trends of the results of these methods were the same. The four piano soundboards with different structures possessed varying dynamic moduli of elasticity and dynamic shear moduli. These rules are consistent with the grain directions of the soundboards and the anisotropy of the wood (the direction of the units of the soundboards). The results show that the vibration mode of the piano soundboard is complex. The dynamic elastic modulus of the soundboard can be calculated using the Euler beam method. The results provide a reference for studies on the vibration response, material selection, production technology, and testing of piano soundboards. Full article

Bridges often improve the visual appeal of urban landscapes by incorporating curve elements to create iconic forms. However, it is noteworthy that curved bridges have unique mechanical properties under loads compared to straight bridges. This study analyzes a spatial three-curved steel box girder bridge based on an actual engineering case with a complex configuration. Initially, the finite element software Midas/Civil 2021 is utilized to establish a beam element model and a plate element model to examine the structural responses under dead loads in detail. Then, two different temperature gradient distribution models are employed for the temperature effect analysis. The backpropagation neural network (BPNN) optimized by the WOA algorithm is trained as a surrogate model for finite element models based on the results of temperature stress simulation. The results reveal that the bending–torsion coupling effect in the second span of the spatial three-curved steel box girder bridge is pronounced, with the maximum torque reaching 40% of the bending moment. The uneven distribution of cross-section stress is particularly significant at the vertices, where the shear lag coefficient exceeds 3. Under the action of temperature gradients, the bridge displays a warped stress state; the stress results obtained from the exponential model exhibit a 21% increase compared to BS-5400. Optimization of the weights by the WOA algorithm results in a significant improvement in prediction accuracy, and the convergence speed is improved by 30%. The coefficient of determination (R²) for predicting temperature stress can reach as high as 0.99. Full article

Mutual dislocation of seismogenic faults during strong earthquakes will result in a large relative displacement on both sides of the fault. It is of great significance to explore the influence of the collision effect between the main beam and the transverse shear key on the seismic response of the bridge under fault dislocation. In this paper, a series of cross-fault ground motions with different ground permanent displacements are artificially synthesized using a hybrid simulation method. Based on the contact element theory, the Kelvin–Voigt model is used to simulate the lateral collision effect. The effect of lateral collision on the seismic response of the continuous girder bridge is compared from the two aspects of fault dislocation position and fault dislocation degree. On this basis, the analysis of lateral collision parameters is carried out with the aim of reasonably regulating the seismic response of the structure. The results show that, compared with the near-fault bridge, the influence of lateral collision on the cross-fault bridge is stronger. The amplification of the bending moment of the central pier and the limitation of the bearing displacement are five times and two times, respectively, for the near-fault bridge. When the fault has a large dislocation, the weak point of the structural damage is the bending failure of the pier bottom and the residual torsion after the earthquake. The collision parameters of conventional bridges will aggravate the bending moment demand of the pier bottom of cross-fault bridges and limit their bearing displacement too much. Therefore, by appropriately reducing the collision stiffness and increasing the initial gap, the internal force and displacement response distribution of the cross-fault bridge structure can be more reasonable. The study in this paper has reference significance for seismic analysis of cross-fault bridges with transverse shear keys. Full article

Over the last century, the seismic behavior of reinforced concrete (RC) beam–column joints has drawn many researchers’ attention due to their complex stress state. Such joints should possess sufficient capacity and ductility to ensure integrity and safety when subjected to cyclic loading during seismic events. In the literature, while most studies have focused on the behavior of concentric beam–column joints, few studies investigated the response of eccentric beam–column joints, in which the beam’s centerline is offset from the centerline of the column. Recent earthquakes demonstrated severe damage in eccentric beam–column joints due to their brittle torsional behavior, which may threaten the ductility required for the overall structural performance. To investigate the effect of brittle failure on the strength, ductility, and stability of eccentric beam–column joints, nonlinear finite element (FE) models were developed and validated. The FE model was employed to study the effect of some geometric parameters on the global and local behaviors of beam–column joints, including the joint type (exterior and interior), the column aspect ratio, and the joint aspect ratio. The results show that the joint aspect ratio, which is the ratio of beam-to-column depth, has a predominant effect on the failure behavior of the joint. Additionally, the increase in column aspect ratio alters the failure mode from brittle joint shear failure to ductile beam-hinge, although there is an increase in the joint torsional moment. The current study also showed that interior joints exhibited a higher out-of-plane moment as well as more extensive column torsion cracks compared to exterior joints. Full article

Reinforced concrete (RC) core walls are commonly used to provide buildings with lateral and torsional resistance against the actions of wind and earthquakes. In low-to-moderate seismic regions, it is not unusual to find a single peripheral core wall that alone should resist these actions, where the torsional (rotational) twist cannot be neglected. It has previously been difficult to have confidence in simulating the axial-flexure-torsion behavior of these RC core walls, primarily due to: (i) some types of modelling approaches being unable to appropriately account for the shear-flexural action, as well as torsional response; and (ii) the scarcity of experimental data, particularly for walls under torsional loads, which would be required to validate such models. In this research, beam-truss models (BTMs), which correspond to an interesting compromise between detailed modelling and practical applications, were used to simulate the in-plane and diagonal flexural response of RC U-shaped walls. Furthermore, the global torque-rotation results from a recent experimental wall test provided the evidence to further validate this powerful modelling technique. A case study building, comprising an RC U-shaped core wall structure with varying eccentricity values, was evaluated for an earthquake event with a 2475-year return period in the city of Melbourne, Australia, using the capacity spectrum method. Nonlinear static pushover analyses showed that, depending on the magnitude of torsion, the in-plane flexural strength and displacement capacity can be significantly reduced. The results from this research emphasize the importance of including torsional actions in the design and assessment of reinforced concrete buildings. Full article