Bending Moment Research Articles

Experimental Study on Mechanical Behavior of Skirt–Pile Foundations in Saturated Clay under Horizontal Load

Skirt–pile foundations have gained widespread attention in the field of offshore engineering due to their ease of installation and high bearing capacity. In this study, the ultimate bearing capacity, pile bending moment distribution and development, cumulative deformation characteristics, and cyclic stiffness development of skirt–pile foundations were investigated using physical model tests. The experimental results indicate that the ultimate bearing capacity and deformation resistance of the foundation can effectively be improved by increasing the skirt diameter. The cumulative deformation of the skirt–piles exhibited rapid development during the initial stages of cyclic loading, eventually stabilizing. Under long-term cyclic loading, the existence of the skirt can share the bending moment, which then affects the internal force distribution of the pile foundation along the axis. The pile foundation’s cyclic stiffness reduces as the loading cycles increase and increases as the skirt diameter and length grow. Meanwhile, the horizontal cyclic stiffness decreases as the number of cycles increases, stabilizing after 3000 cycles. This study can not only deepen the understanding of the deformation laws of skirt–pile foundations in clay soil but also offers some references for the design of offshore pile foundations.

The Mechanics of Elastomeric Sheet Reinforced With Bidirectional Fiber Mesh Subjected to Flexure on Boundaries

Abstract We investigate the concurrent three-dimensional deformations of fiber-reinforced composite sheets subjected to out-of-plane bending moments via a continuum model, where we invoke the neo-Hookean strain energy model for the matrix material of fiber-reinforced composite, and assimilate the strain energy of fiber reinforcements into the matrix material model by accounting for stretching, bending, and twisting kinematics of the fibers through the computations of the first-order and second-order gradient of deformation. Emphasis is placed on deriving the Euler equation and boundary conditions of bending moment within the framework of the variational principle and configuring composite surfaces using differential geometry. Significant attention has been given to illustrating the concurrent three-dimensional deformation of fiber composite, meshwork deformation, and fiber kinematics. The simulation results reveal that for a square fiber composite subjected to the out-of-plane bending moment, the maximum in-plane deformation of matrix material occurs along the diagonal direction of the domain while the center of the domain experiences weak in-plane deformation. Notably, the matrix material performs isotropic/anisotropic properties depending on the domain size/shape. In addition, the simulated unit fiber deformations reasonably validate the overall deformation of the network, underscoring that the deformations of the embedded fiber units govern the overall mechanical performance of the fiber meshwork. More importantly, the continuum model qualitatively provides reasonable predictions on the damage patterns of construction materials by demonstrating the kinematics of matrix material and meshwork deformation.

Practical Considerations in the Design of Passive Free Piles in Sliding Soil

The stabilisation of shallow translational landslides can be carried out by using large diameter concrete piles, with the aim of increasing the available strength along the slip surface. In the following article, 3D numerical models of a free-head flexible pile embedded into a translational type of landslide are studied. The landslide model has a given inclination angle, β, and a thickness, D, while the reinforced concrete pile has a fixed diameter, d, and a length, D + L, in the perspective of studying the failure modes B1, BY and B2 of free-head flexible piles. In this category of piles, collapse is reached with the formation of plastic hinges. Both the soil and the concrete are modelled with simple constitutive models, such as Mohr–Coulomb for soil and the elastic-perfectly plastic for the concrete pile, in order to carry out the design approaches provided by Eurocode, as well as to highlight some practical aspects of soil–structure interaction during the landslide displacements. The results highlight how the achievement of the shear strength in a flexible free-head concrete pile generally precedes the achievement of the ultimate bending moment associated with the development of plastic hinges. Furthermore, the axial load supported by the pile may itself contribute to the overall strength available along the slip surface.

Consequences of the Improved Wave Statistics on a Hull Girder Reliability of Double Hull Oil Tankers

This paper investigates the change in hull girder failure probabilities and partial safety factors caused by the implementation of the new procedure for direct computation of wave loads recommended by the International Association of Classification Societies (IACS). Differences between new and previous procedures are primarily related to the different associated scatter diagrams, and secondarily due to the assumptions on wave spectrum, wave energy spreading, and ship speed. This study performs a comparative structural reliability analysis of the global longitudinal bending of five oil tankers of different sizes between two procedures for wave load computation. Firstly, failure probabilities are compared, and secondly, modified partial safety factors are proposed, resulting in similar failure probabilities according to two separate procedures. It is found that implementation of the new revision of the IACS procedure for direct computation of wave loads results in a reduction of the minimum required ultimate vertical bending capacity of a ship hull by 10%. In addition to the novel investigation of the safety of oil tankers using a revised wave scatter diagram, this study offers a new rapid method for calculation of extreme vertical wave bending moments based on the regression of the parameters of the Weibull function, used for the long-term probability distribution of wave-induced loads.

Analytical 3D failure envelopes for RC pile groups under combined loading: A generalised design approach

The paper presents a generalised design approach for pile groups subjected to combined (VHM) loading. The Limit Equilibrium method is extended to pile groups under general planar loading, considering the axial load dependency of bending stiffness and strength of reinforced concrete (RC) piles. 3D failure envelopes are analytically derived for different layouts. The key simplifying assumptions are critically discussed, and the failure envelopes are verified against finite element (FE) analysis results. Key features of pile group response, such as plunging vs. non-plunging axial pile response and the role of transverse reinforcement, are identified and quantified. A key novelty of the proposed method lies on the consideration of coupling between the lateral–bending resistance of the piles. The method further incorporates well-recognised features of pile group response regarding the axial load dependency of bending moment capacity and stiffness of the RC piles. The latter results in redistribution of bending moments and shear forces along the piles of the group. These features allow the reproduction of key aspects observed in demanding FE simulations and centrifuge tests, regarding the ultimate resistance under VHM and in addition the load path dependent failure modes. The proposed method offers a practical engineering tool for preliminary design and optimisation.

Full-Scale Model Tests of Two Box-Type Soil–Steel Structures with Different Crown and Haunch Radii

Compared with circular, arched, and pipe-arched soil–steel structures, box-type soil–steel structures (BTSSSs) have the advantages of high cross-section utilization and low cover depth. However, the degree of influence of the crown and haunch radii on the mechanical performance of BTSSSs is still unclear. Therefore, two full-scale BTSSS models with a span of 6.6 m and a rise of 3.7 m but with different crown and haunch radii were established, and the mechanical properties during backfilling and under live load were tested. Afterward, 2D finite element models (FEMs) were established using the ABAQUS 2020 software and verified using the test data. The influence of cross-section geometric parameters on mechanical performance was analyzed by using the FEM, and a more accurate formula for calculating the bending moment during backfilling was proposed. The results show that the BTSSS with a smaller crown radius has a stronger soil–steel interaction, which promotes more uniform stress on the structure and makes the structure have smaller relative deformations, bending moments, and earth pressure. The span and arch height greatly influence the bending moment and deformation of the structure. Based on the CHBDC, the crown and haunch radii were included in the revised calculation formula.

Experiment investigation and theoretical analysis of an improved aluminum alloy gusset joint

This study presents enhancements made to traditional aluminum alloy gusset (AAG) joints, including the integration of a central stiffening (CS) system, an inter-panel stiffening (IS) system, and a peripheral stiffening (PS) system. Three sets of tests on a full-scale specimen are conducted to investigate the improved AAG joint's axial stiffness, in-plane and out-of-plane bending stiffness, as well as ultimate load-bearing capacity. Nonlinear refined finite element models (FEMs) are established and validated through experimental results. Theoretical mechanical models are developed by integrating experiments and FEMs. These models elucidate the contribution of the stiffening systems to the joint's mechanical performance. The CS system is proven to significantly assist in load transfer, particularly in out-of-plane bending conditions. The IS system enhances overall inter-panel integrity, especially during the plastic deformation phase under out-of-plane bending moments. The PS system improves joint stiffness by participating in load transmission under both axial load and in-plane bending moments. Compared to traditional AAG joints, the combined effects of the three stiffening systems enhance overall structural integrity, stiffness, and load-bearing capacity. This enables the full utilization of component material properties and provides excellent ductility before failure occurs.

Shear characterization in soft polyurethane foams: A critical comparison among experimental approaches

The study addresses the lack of standardization for the evaluation of the shear properties of hyperelastic soft foams. The results of three different standards used for sandwich structures or rigid materials (ASTM C 273, BS 4370, ASTM D 5379) are compared using specimens with different geometries and aspect ratios. Displacements are captured using Digital Image Correlation applying texture correlation and an incremental approach on three flame-retardant foams with densities around 85, 63, and 46 kg/m³. The study examines secondary effects like bending moments and normal stresses, finding the Iosipescu method effective for hyperelastic foams, ensuring minimal material wastage and test repeatability.

Power flow analysis of the three-beam system on double parameter elastic foundations based on the wave propagation approach

This article investigates the power flow of the three-beam system on Winkler–Pasternak elastic foundations under elastic boundary conditions. The time-averaged power flow of the beam on elastic foundations with elastic boundary conditions is calculated based on the internal shear force and bending moment and the wave propagation approach. The reliability and accuracy of the calculation method are verified by comparing the vibration acceleration calculated by calculation examples and the finite element method. In addition, the effects of structural parameters and boundary conditions on the power flow of the three-beam system are investigated. This contributes to the analysis of the dynamic characteristics of the beam on double parameter elastic foundations under complex boundary conditions.

Forces required to dynamize sliding screws in gamma nail and selfdynamizable internal fixator.

Single limb support phase of the gait-cycle in patients who are treated for a pertrochanteric fracture is characterized by transversal loads acting on the lag screw, tending to block its dynamization. If the simultaneous axial force overcomes transversal loads of the sliding screw, the dynamization can still occur. Biomechanical investigation was performed for three types of dynamic implants: Gamma Nail, and two types of Selfdynamizable Internal Fixators (SIF) - SIF-7 (containing two 7mm non-cannulated sliding screws), and SIF-10 (containing one 10mm cannulated sliding screw). Contact surface between the stem and the sliding screws is larger in SIF implants than in Gamma Nail, as the stem of Gamma Nail is hollow. A special testing device was designed for this study to provide simultaneous application of a controlled sliding screws bending moment and a controlled transversal load on sliding screws (Qt) without using of weights. Using each of the implants, axial forces required to initiate sliding screws dynamization (Qa) were applied and measured using a tensile testing machine, for several values of sliding screws bending moment. Standard least-squares method was used to present the results through the linear regression model. Positive correlation between Qt and Qa was confirmed (p < 0.05). While performing higher bending moments in all the tested implants, Qa was higher than it could be provided by the body weight. It was the highest in Gamma Nail, and the lowest in SIF-10. A larger contact surface between a sliding screw and stem results in lower forces required to initiate dynamization of a sliding screw. Patients treated for a pertrochanteric fracture by a sliding screw internal fixation who have longer femoral neck or higher body weight could have different programme of early postoperative rehabilitation than lighter patients or patients with shorter femoral neck.

Analytical Model for Non-linear $$\user2{M - }\,\,{\varvec{\theta}}$$ Relationships of Dowel-Type Timber Connections Exposed to Fire

AbstractRecent experimental evidence has shown that wood–steel–wood dowel-type connections exhibit a semi-rigid behaviour even after 90 min of fire exposure. Because a semi-rigid behaviour influences the bending moment distribution among structural members, considering the moment–rotation relationships within frame analyses in which structural members are modelled as beam elements can enable a realistic fire response analysis that is significantly simpler than the three-dimensional finite element method. This study proposes an analytical methodology that accounts for the thermo-mechanical behaviour of timber and dowels, enabling the simulation of the non-linear moment–rotation relationships under fire conditions. The proposed analytical model divides dowels into a series of elements on an elastoplastic foundation and performs a direct stiffness method in a time-incremental procedure using an element stiffness matrix derived from beam-on-elastic-foundation theory. This study also presents the results of load-carrying tests on timber frames with dowel-type connections performed under ambient and fire conditions. The analytical results were consistent with the fire test results. Additionally, the analyses were also performed under three conditions in which the dowels were rigid, linear elastic, and elastoplastic bodies. These three results converged to the same value after 65 min of heating, which suggests that the ultimate states of beams with dowel-type connections exposed to fire can be modelled by assuming that dowels are rigid bodies.

Seismic analysis of RC building with plan irregularity in Baghdad/Iraq to obtain the optimal behavior

Abstract A study was conducted for four-story reinforced concrete (RC) structure existing in Baghdad-Iraq (residential building) to evaluate the accuracy and reliability of the equivalent lateral force procedure (ELFP) analysis and the response spectrum model (RSA) according to Iraqi seismic code (ISC 2016) for designing and analyzing irregular buildings. The building was classified as an irregular in plan according to American Society of Civil Engineers (ASCE 7-16). The seismic behavior of the building was investigated by verifying many parameters: the ratio of shear demand to shear strength on the columns ( V V / V n {V}_{n} ), internal force (bending moment, shear force, and axial force) for beams and columns, and the inter-story drift ratio (IDR) obtained from the (ELFP and RSA); then, the results were compared with the nonlinear static procedure (NSP) and the nonlinear dynamic procedure (NDP) according to ASCE 7-16. Also, this study investigated the effects of the higher modes in the plan (roof plan displacement). From the results, it can be concluded that ELFP and RSA are not a suitable analysis for asymmetric structures and should use appropriate methods such as the NSP and NDP.

The contribution of higher order modes in the dynamic response of slender vertical structures with application to wind turbine towers

Understanding the contribution of the vibration modes to the response of a tower-like structure subjected to base excitations is crucial for a safe and optimized design. The modal contributions to the structural response are generally assessed through modal participation factors and effective masses; however, relatively recent studies pointed out the variability of the modal contributions depending on the response effect (e.g., top displacement, base shear force, base bending moment). The formulation proposed here derives the shear force and the bending moment at the base of a tower-like structure by combining the influence function technique with the quasi-static equivalent forces technique. The resulting formulation of the tower response relies on the concept of modal contribution factors, which provides a straightforward indication of the modal contributions associated with a given response effect. The proposed methodology is applied to the case of wind turbine towers erected on temporary foundations at the port quayside without rotor nacelle assembly to assess the forces on the foundations due to the seismic loading on the towers. This technique may be of great relevance for assessing the tower integrity during installation and for the design of the temporary foundations at the quayside of harbors in seismic area, also considering the quick expansion of the offshore wind energy in countries prone to earthquakes.

Dynamic ultimate capacity analysis of rectangular girder under hammer impact

The dynamic failure and ultimate capacity analysis of rectangular girder under bending moment has not been fully studied. In this paper, a rectangular girder scaled from actual ship deck structure is selected as the study objective to analyze the dynamic failure and ultimate flexure capacity. The dynamic response under hammer drop impact is studied, and then two criteria of dynamic ultimate flexure capacity of the girder are proposed based on the bending moment in section and permanent deformation. The novelty of this paper is the proposed evaluation criterion of dynamic ultimate capacity.

Refined VFIFE modeling on dynamic behaviours of deepwater S-lay pipeline in overbend section

The deepwater S-lay pipeline maintains high tension, bending moment, and stress in the overbend section, exhibiting substantially dynamic responses due to pipe-stinger roller interactions. This paper presents a refined S-lay pipeline model capable of accurately describing the forces and deformations on the pipeline section. In this model, the pipeline is discretized into beam particles and beam elements using the vector form intrinsic finite element (VFIFE) method. Meanwhile, the equivalent beam particle technique is developed to account for both the local forces and deformations of the pipeline as well as its overall static and dynamic responses. Through program coding, a dynamic time-domain simulation was accomplished for a 12-inch pipeline being laid to a water depth of 1000 m to provide a detailed illustration of the S-lay modeling process. Furthermore, dynamic behaviours of the pipeline in the overbend were systematically investigated under various groups of the pipe diameter and the stinger roller spacing. The results indicate that the stress and deformation on the upper section of the pipeline are more significant than those on the lower section. The equivalent beam particle method extends the capabilities of the VFIFE for the detailed analyses of local dynamic behaviours of deepwater S-lay pipelines.

Relationship between peak ground acceleration and damages indices for steel sheet pile quay wall in Bejaia-Algeria

Purpose The purpose of this paper is the dynamic analysis and seismic damage assessment of steel sheet pile quay wall with inelastic behavior underground motions using several accelerograms. Design/methodology/approach Finite element analysis is conducted using the Plaxis 2D software to generate the numerical model of quay wall. The extension of berth 25 at the port of Bejaia, located in northeastern Algeria, represents a case study. Incremental dynamic analyses are carried out to examine variation of the main response parameters under seismic excitations with increasing Peak ground acceleration (PGA) levels. Two global damage indices based on the safety factor and bending moment are introduced to assess the relationship between PGA and the damage levels. Findings The results obtained indicate that the sheet pile quay wall can safely withstand seismic loads up to PGAs of 0.35 g and that above 0.45 g, care should be taken with the risk of reaching the ultimate moment capacity of the steel sheet pile. However, for PGAs greater than 0.5 g, it was clearly demonstrated that the excessive deformations with material are likely to occur in the soil layers and in the structural elements. Originality/value The main contribution of the present work is a new double seismic damage index for a steel sheet pile supported quay wharf. The numerical modeling is first validated in the static case. Then, the results obtained by performing several incremental dynamic analyses are exploited to evaluate the degradation of the soil safety factor and the seismic capacity of the pile sheet wall. Computed values of the proposed damage indices of the considered quay wharf are a practical helping tool for decision-making regarding the seismic safety of the structure.

Centrifuge model tests of h-type anti-slide pile reinforced slope under different rainfall duration

The h-type anti-slide pile (h-pile) plays a crucial role in mitigating soil-rock mixture slope (SRMS) instability. Despite its significance, the limited availability of research outcomes has constrained the practical application of h-piles for SRMS reinforcement. This study employs three centrifuge model tests to investigate the behavior and performance of h-pile-reinforced SRMS under rainfall conditions. We systematically describe the response of earth pressure on the pile side and behind the pile, bending moment along the pile, and pore water pressure at the slope toe and pile side. This elucidates the evolution of soil arching for h-piles under rainfall conditions. The results reveal that rainfall duration influences the distribution pattern of earth pressure on the pile side, while the distribution pattern of bending moment for the h-pile remains unaffected. Additionally, the soil arching pattern between piles demonstrates joint arching, involving the combined action of frictional arching and end-bearing arching. The evolution process of soil arching between piles under rainfall conditions gradually dissipates from bottom to top and from far to near.

Experimental study on the progressive collapse mechanism of excavations retained by tied-back retaining systems

Progressive collapses of tied-back excavations caused by the failure of some anchors often occur. However, the mechanism through which partial failure evolves to global failure and how the local failure rate influences progressive collapse has not been investigated. In this study, anchor failure experiments involving tied-back excavation were designed to explore the load transfer path and rule in the case of partial anchor failure. The results showed that, anchor failure leads to an increase in the axial force on adjacent anchors, an increase in the maximum bending moment of capping beams, and easy damage in capping beams due to structural reinforcement. The lower the anchor elevation is, the greater the excavation depth, and the greater the load transfer coefficient (axial force). The failure rate of anchors has an effect on the stress redistribution of the structure and the soil arching effect. In multi-row anchored pile retaining excavations, more rows of anchor failure could trigger the remaining anchors failure because the load transfer coefficient (axial force) is greater for these anchors, which leads to large-scale excavation collapse.

Experimental Study on Flexural Resistance of UHPC Wet Joint Precast Reinforced Concrete Bridge Deck Slabs with Variable Cross-Section

With the convenient and fast requirements for construction in bridge engineering, prefabricated assembly technology is widely applied in engineering construction. Typically, prefabricated bridge decks are connected through cast-in-place wet joints. Wet joints, as the primary load-bearing parts of bridge decks, undergo complex stress and are prone to cracking and damage. Particularly in the negative bending moment region of bridges, the influence of tensile stress on wet joints is more severe, thus enhancing the mechanical performance and crack resistance of joints becomes crucial. This paper investigates the mechanical behavior of prefabricated reinforced concrete bridge deck panels with variable cross-sections under negative bending moments, focusing on the performance of Ultra High-Performance Concrete (UHPC) wet joints. Full-scale experimental tests were conducted on a 176 m steel truss composite continuous rigid bridge, employing C50 concrete panels with UHPC wet joints. Results show three distinct stages: elastic, crack initiation and propagation, and failure. The maximum failure load reached 822 kN, with a maximum displacement of 21.64 mm. Concrete strains indicate compressive stress near the wet joint and tensile stress near the loading positions. Cracks primarily develop at the wet joint interface and propagate under increasing load, ultimately leading to flexural–shear failure near the variable cross-section of the wet joint. Numerical simulations using ABAQUS/CAE (2020) corroborate experimental findings, closely matching load-displacement curves and identifying damage locations. The study demonstrates that UHPC wet joints significantly enhance crack resistance, meeting design requirements for improved mechanical performance in bridge structures subjected to negative bending moments.

The Use of PVD Coatings for Anti-Wear Protection of the Press-In Connection Elements

Press-in connections are the commonly used methods for connecting machinery components. In relation to that wide use, those connections are liable to various types of damage and wear. Therefore, this article proposes one of the methods which may improve the life of the press-in connection. CrN+OX, TiN, and ZrN coatings made in the PVD technology were used. The coatings were applied on shafts mating with sleeves and subjected to a rotational bending moment. Tests and observations were conducted that enabled the assessment of the influence of those coatings on the development of wear, in particular fretting, in the tribological kinematic pair. The tests showed the development of wear on all the observed shaft surfaces, with a lower intensity of damage recorded on coated shafts compared to uncoated ones. The traces of fretting wear were noted each time at the edges of the connection, which is due to the mechanism of wear development under rotational bending conditions. In the case of uncoated shafts, wear occurs at the entire circumference of the axle seat in the form of a 3–4 mm wide ring; however, that width is different on either side. In the case of coated shafts, wear occurs on the circumference of the axle seat in the form of a thin ring 1–3 mm wide, depending on the coating. In the case of a ZrN coating, fretting wear appears locally. The largest surface area occupied by wear is 0.75 cm2. Fretting wear comprises mainly material build-ups, pits, and surface scratches. In addition to fretting wear, damage resulting from the process of forcing the sleeve onto the shaft was observed on the tested surfaces.