Elastic Limit Load Research Articles

Biomechanical characteristics of the meniscocapsular junction of the posterior segment of the medial meniscus.

Despite extensive literature available on the mechanical properties of knee ligaments and menisci, research on the mechanical properties of the meniscus-capsular junction (MCJ) is lacking. This study aims to investigate the biomechanical behavior of the MCJ of the medial meniscus using a tensile failure test. Seven dissected cadaveric knees were used for biomechanical analysis. Tensile failure tests were performed using an INSTRON ElectroPuls E1000 stress system to measure stress/strain curves, maximum load at failure, elastic limit load, elongation at break, elongation at the elastic limit, and linear stiffness, were collected and analyzed. All ruptures occurred at the MCJ. The MCJ displayed similar mechanical properties to knee ligaments. Average values were: maximum load at failure (63.9 ± 3.2N), yield load (52.9N ± 2.6N), elongation at break (2.5mm ± 0.3mm), elongation at the elastic limit (1.25mm ± 0.15mm), strain at break (47.0% ± 3.5%), strain at yield (23.2% ± 2.3%), and stiffness (56.6 ± 9.N/mm-1). The meniscus-capsular junction's mechanical properties are similar to other knee ligaments and may play a role in knee stability. The findings provide insights into the the behavior of the meniscus-capsular junction could have clinical implications for diagnosing and surgical treatment of meniscocapsular lesions.

Bending and Vibration Behaviour of CLT-Steel Composite Beams

A strengthening of cross-laminated timber (CLT) by a composite effect with steel girders can widen the application of CLT ceilings to spans over 8 m. Most possible shear connectors are not stiff enough to ensure a completely rigid composite. At present, it has not been sufficiently clarified how the elastic bending behaviour is affected by the influences of the flexibility of continuously and discontinuously shear connectors, the number of transverse layers of the CLT and the span width. Thus, 4-point bending tests and vibration tests were performed with different cross-section configurations and two different shear connectors in continuous and discontinuous spacing in spans of 8.10 and 10.80 m. To date, no comparable bending tests have been carried out in these spans, with more than five CLT-layers and discontinuously arranged shear connectors. The composite beams deformed linear-elastically until the yield strength of the steel was reached. The composite effect increased the elastic bending stiffness up to twofold compared to no composite. Increasing the span resulted in a higher bending stiffnesses. The elastic bending stiffness of the composite beams with shear studs was significantly lower than with fully threaded screws. For a worthwhile composite effect, both materials should contribute a balanced share of the stiffness. A larger share of the CLT in the bending stiffness compared to the steel girder created a higher elastic limit load capacity but an equivalent bending stiffness. It is necessary to discuss which cross-sectional configurations are appropriate in terms of load bearing capacity, economic efficiency and sustainability. To assess the practical application potential in spans between 8 and 12 m, the tests were additionally evaluated for the equivalent load level for the serviceability limit state of office or industrial buildings. For spans of 8.10 m, the limits according to EC5 for the initial deflection of L/300 and fundamental frequency of 8 Hz can be met. For spans of 10.80 m, only less strict deflection limits are achieved. However, by increasing the degree of composite through more shear connectors, compliance with the limit values mentioned could already be possible with the cross-sections tested. In case of fire, it may be sufficient to consider only the CLT with the reduced cross-section method (EN 1995-1-2) for load transfer, even for longer fire durations.

Key Design Parameters Analysis and Calculation Theory Research on Bending Performance of Steel–UHPC Lightweight Composite Deck Structure

This paper aims to study the influence of key design parameters (e.g., reinforcement ratio, cover thickness, stud spacing, and thickness of the ultra-high-performance concrete (UHPC) layer) on the longitudinal and transverse bending performance, as well as the cracking load and ultimate bearing capacity calculation theory of steel–UHPC lightweight composite deck (LWCD) structure. Four transverse bending tests and four longitudinal bending tests on steel–UHPC composite plates and steel–UHPC composite beams were conducted, respectively. The refined finite element models of components with different key design parameters based on ABAQUS were established. The influences of different key design parameters on the transverse and longitudinal flexural behaviors (e.g., load-mid-span displacement curve, cracking stress, stiffness, elastic limit load, critical slip load, ultimate bearing capacity and ductility) were compared and analyzed in detail. The ultimate bearing capacity can be improved by increasing the thickness of UHPC layer and the reinforcement ratio of longitudinal reinforcement, and reducing the cover thickness and the spacing of studs. According to the longitudinal bending characteristics of the steel–UHPC lightweight composite deck structure, the calculation formulas for the cracking load and the ultimate bearing capacity of the steel–UHPC composite beam are proposed, and the calculated values are in good agreement with test results (the errors are basically within 10%), which is convenient for practical engineering applications.

New insights into nonlinear stability of imperfect nanocomposite beams resting on a nonlinear medium

An analysis is performed in this research to study the nonlinear thermal stability of graphene platelet reinforced composite (GPLRC) beams based on the third-order shear deformation model of Reddy and von-Kármán kinematic assumptions. The influences of the three-parameter nonlinear hardening/softening elastic foundation and initial imperfection are also taken into account. GPLs are distributed in the layers of the composite media where the volume fraction of GPLs may be different in each layer, so a piecewise functionally graded media is achieved. The elasticity modulus of the composite media is estimated via the Halpin–Tsai rule which includes the dimensions of reinforcements while the thermal expansion coefficient and Poisson’s ratio are obtained via the simple Voigt’s rule. Three nonlinear and coupled governing equations are established using the concept of static version of the Hamilton principle. Due to the immovability of the edge supports, the equations are reformulated to reach two coupled equations in terms of lateral displacement and cross section rotation. For the case of a beam with both ends simply-supported, a two-step perturbation technique is implemented to extract the closed-form expression which provides the mid-span deflection as a function of temperature elevation. Results of this study are compared with the available data in the open literature with respect to simple cases. After that novel results are given to explore the effects of foundation parameters, beam geometry, GPL weight fraction and GPL patterns. It is shown that for sufficiently soft elastic foundation limit load type of instability occurs and the structure becomes imperfection sensitive.

Semi-mechanism-based hysteretic model for traditional heavy timber frames with forked column foot joints and various wood panel infill

Frames are essential lateral load-resisting elements in traditional Chinese timber structures. This paper presents a semi-mechanism-based hysteretic model for the lateral load-displacement relationship of traditional heavy timber frames with forked column foot joints and various wood panel infill. The backbone curve of the proposed model was determined based on the rocking and the racking mechanisms of the frames. Key points of the backbone curve, including the elastic limit point and the peak load point, and the corresponding tangent stiffness were expressed by the geometrical and physical parameters of the frames. Reloading and unloading paths were defined based on the elastic limit load and the elastic stiffness. Experimental results of typical frames were utilized to verify the proposed model regarding the backbone curve, hysteretic behavior and energy dissipation. Good agreement was achieved. Model-based parametric study was further conducted. The influence of infilled wood panels and vertical compression load was investigated. It is found that the lateral resistance contribution of the wood panels with a door opening is slightly greater than that of wood panels with a window opening, and the performance of frames under higher vertical compression load levels (without causing compression failure of the columns, which is rare) are superior to those under lower levels, e.g., a reduction of 50% in the vertical load can lead to a drop in the peak load and the cumulative dissipated energy of the frame of 13% and 30%, respectively.

Comparison of the elastic limit and yield load of nailed joints connecting solid wood and wood-based board material

Evaluations of the lateral properties of timber joints are necessary to ensure the safety of timber buildings. The yield load is an important property that is usually obtained using authorized engineering techniques. Although yield loads have been easily obtained using authorized techniques, events that have occurred in the joint during yielding have not been clarified. This study experimentally obtains elastic limit data using nailed joints. Mechanical tests measuring the residual displacement after various lateral loads with six-joint specimen specifications were conducted. In this study, the load at which the residual displacement reached 5% of the nail diameter was defined as the elastic limit. The experimentally obtained elastic limits were compared with the yield loads obtained using authorized engineering techniques. The ratios of elastic limits to the yield loads obtained using the perfect elasto-plastic model, method described in EN, and 5% offset method were 0.554–0.743, 0.557–0.834, and 0.648–0.801, respectively. The results numerically revealed that residual displacements occurred at a much lower load than the yield loads.

Failure modes of bonded wrapped composite joints for steel circular hollow sections in ultimate load experiments

The concept of an innovative bonded joining technology where welding is not required is presented as an alternative to traditional welded connection for steel circular hollow section (CHS). Wrapped composite joints have potential to greatly improve fatigue endurance when applied in multi-membered truss structures, e.g. offshore jackets for wind turbines. This paper focuses on characterization of resistance and understanding of failure modes of wrapped composite joints in static experiments, as the prerequisite for harvesting its potential for high fatigue endurance. Wrapped composite joints at two scales and with two different angles of X-joint geometry are made with GFRP composite material wrapped around steel sections without welding, and tested in 3 monotonic loading cases, tensile, compression and in-plane bending, until failure. Counterpart welded joints are tested at the smaller scale for stiffness, elastic limit and ultimate load comparisons. Two general failure modes of wrapped composite joints, debonding and fracture of the composite material are identified and quantified by surface strain measurements through 3D digital image correlation (DIC) technique. Testing results indicate that wrapped composite joints have 30% to 56% larger stiffness and 3% to 68% larger ultimate load compared to welded counterparts. Debonding and final pull-out of steel brace member from the composite wrap is predominant failure mode in tensile experiments at both scales while cracking of the composite material is the governing failure mode in the bending experiment. In tensile, compressive and bending experiments failure load of wrapped composite joints exceeds the yield resistance of the steel CHS indicating opportunity to optimize the composite wrapping thickness and length.

A novel methodology for determining the elastic shakedown limit loads via computing the plastic work dissipation

A methodology that targets determining the shakedown (SD) limit loads via computing the plastic work dissipation (PWD) is presented. The methodology is termed: Shakedown Limit - Plastic Work Dissipation (SDLim−PWD) method. Precisely, the SDLim−PWD method performs a fully automated systematic iterative series of elastic-plastic finite element full cyclic loading simulations till the SD limit load is determined via tracking the PWD history of the applied load cycles. Since the SDLim−PWD method is an energy-based approach for determining the SD limit loads; hence, it permits the incorporation of large displacement formulation and/or cyclic plasticity constitutive material models. The SDLim−PWD method is successfully verified against the closed-form solutions of two classical SD benchmark problems. Additionally, it is validated against the test recordings of a full-scale experimental setup conducted at Berkeley Nuclear Laboratories in the UK concerning a large spherical vessel with a thin radial protruding nozzle subjected to pressurization/depressurization cycles.

A comparative study of shape imperfection and internal pressure effects on plastic, shakedown and elastic limit loads using large and small strain formulation of 90° pipe bends

The present work quantifies the effect of ovality and wall thinning on plastic, shakedown and elastic limit load of pipe bends under cyclic in-plane closing bending load and internal pressure. Three-dimensional finite element analyses with large strain (geometric nonlinear analysis) formulation was performed by considering the pipe bend material to be elastic-perfectly plastic. Plastic limit loads are determined from the plot of reaction moment versus angular rotation curve. Abdalla's simplified technique (ST) was used to calculate elastic and shakedown limit loads. The presence of ovality shows significant effect on plastic, shakedown and elastic limit loads and their boundaries for all the models. Thinning has minimal effect on plastic limit loads for large strain analysis while it has a remarkable effect on elastic and shakedown limit loads for ovality up to 5%. Experimental plastic limit moments in open literature was used to validate the present finite element (FE) plastic limit loads. Plastic, shakedown and elastic limit boundaries of large strain analysis or geometric non linear (GNL) analysis were compared with the respective boundaries of small strain analysis or Geometric linear (GL) analysis. Mathematical equations are formulated to express the generated limit moment boundaries for shape imperfect pipe bends.

Elastic limit load prediction and equivalent cylinder proposal for circular concave shells subjected to axial compression

The paper aims to propose an equivalent cylinder radius approach for circular cross-section concave shells under axial compression. Several buckling relations are introduced to predict critical stresses and to limit loads considering the extensive range of geometrical parameters. A detailed parametric study is conducted to reveal the influence of concavity on critical stress using geometrically nonlinear analysis (GNA). The amount of reduction in limit load of a concave shell, as a reference to an ideal case, is expressed as a function meridional curvature. An asymmetry factor is described to evaluate the change of critical stresses for longitudinally asymmetric concave shells. A similarity approach is given for the concave shells. A statistical procedure is utilized to examine the accuracy of the equations and relatively satisfactory results are achieved.

Behaviours of square UHPFRC-filled steel tubular stub columns under eccentric compression

Applications of ultra-high performance fiber-reinforced concrete (UHPFRC) in composite columns for high-rise buildings or bridges keep increasing to achieve improved structural performances. A testing program with 16 specimens was carried out to study the behaviour of UHPFRC-filled square steel tubular stub columns (UFST-SCs) under eccentric compression. Besides, influences of eccentric ratio (e/r) and thickness of steel tube (ts) on the behaviours of UFST-SCs were studied. The UFST-SCs under eccentric compression exhibited three working stages categorized as linear, nonlinear, and recession. Compression-flange yielding of steel tube and crushing of UHPFRC occurred at the elastic limit and peak load point of load-displacement curves, respectively. Despite the increasing e/r ratio decreased the stiffness and ultimate resistance of the UFST-SCs, its ductility was improved. Moreover, increasing thickness of steel tube enhanced the structural resistance of UFST-SCs under eccentric compression. The validations showed that EC4, AISC and GB50936 were conservative on estimating the Nu-Mu interaction relationships of UFST-SCs under eccentric compression. Considering the accuracy and reliability, EC4 was recommended to predict the Nu-Mu interaction curves of UFST-SCs.

Characteristics and strength of hybrid friction stir welding and adhesive bonding lap joints for AA2024-T3 aluminium alloy

ABSTRACT A hybrid process combining friction stir welding with adhesive bonding is used to connect AA2024-T3 aluminum alloy. The epoxy ester adhesive was evenly smeared on the sheet surface prior to welding. Regarding the function of the adhesive in different regions at the lap interface, the lap interface can be divided into a completely FSW zone (CWZ), transition zone (TZ) and completely sealed zone (CSZ). During the tensile-shear test, the load is initially shared by the CWZ and TZ. With the increase of the external load the cracks first initiate at the adhesive layer, leading to the fast decrease of load–displacement curves. When the CWZ bears the load alone, the joint recovers the load-carrying capacity and the load–displacement curves increase again until the CWZ cracks and fractures. The crack propagation process of the hybrid joint mainly includes adhesive layer cracking stage and FSW interface cracking stage. The cracking load of the adhesive layer is higher than the elastic limit load of the conventional joint, and thus the adhesive does not influence the design load. The adhesive layer on the TZ reduces the stress and makes the stress distribution uniform, and on the CSZ can block the corrosion media.

Research on non-pneumatic tire with gradient anti-tetrachiral structures

In this paper, a new type of non-pneumatic tire is designed. The pneumatic parts of standard pneumatic tire are replaced by gradient anti-tetrachiral structure. Firstly, the in-plane mechanical properties and elastic limit load of anti-tetrachiral structures with different gradient factors are studied by experiment, finite element method and theory. Based on this, the structural design of non-pneumatic tire is carried out, and its mechanical properties under compression load are studied by finite element method. Results show that the gradient anti-tetrachiral structure and the non-pneumatic tire based on this structure have certain similarities in the deformation mode. The basic research of gradient anti-tetrachiral structure is of guiding significance to the design of non-pneumatic tire. It also shows that the non-pneumatic tire with the gradient anti-tetrachiral structure has good load-carrying capacity, and has a wide engineering application potential.

Elastic limit load estimation including similarity approach for different end conditioned conical shells with high semi-vertex angle under axial compression

Abstract This study investigates the stability loss of thin walled conical shell structures under axial loading. More specifically, conical shells with semi-vertex angle greater than 65 ∘ ( β c > 65 ∘ ) and with different bottom edge radial stiffness were studied in order to fill the gap in existing literature. The effects of geometrical parameters of the structure on the load bearing capacity were determined. Conical shell structures with high semi-vertex angle and different boundary conditions display highly non-linear character under axial loading, hence conventional analytical approaches are not adequate to predict the limit load. Therefore, a new method was proposed in this study which can accurately predict the limit load of these structures. The deviation between the proposed method and numerical results was found to be ± 13 % , while it was one order higher (+ ~ 300%) in classical shell theory, based on the configuration. Furthermore, similarity parameters were suggested to increase the range of application of the proposed method. Similarity parameters enable researchers to work with scaled-down models which are capable of simulating the behaviour of real-time-scale models. In addition, the effect of geometrical initial imperfections on the load bearing capacity was investigated and a new reduction coefficient was identified which is much more accurate compared to the overly conservative standard counterpart. A numerical model was developed with COSMOS/M software. This model was validated with experiments, and then was used for the parametric study.

Determination of plastic, shakedown and elastic limit loads of 90°pressurized pipe bends with shape imperfections

This study determines the plastic, shakedown and elastic limit loads and the corresponding regimes of 90° pressurized pipe bends with shape imperfections subjected to cyclic in-plane closing bending moment. Three dimensional FE analyses with small strain formulation was performed. The induced shape imperfections are ovality and thinning, which were varied from 0% to 20% with a 5% increment at every step. Plastic limit load was determined from the moment rotation curve while shakedown and elastic limit loads were determined by using Abdalla's simplified technique (ST). The analysis indicates that the presence of ovality produces considerable effect on plastic limit loads. Thinning alters plastic limit loads only for long bend radius models with no ovality when normalised internal pressure ratio is unity and in other cases its effect is minimal. Presence of ovality and thinning has a remarkable effect on shakedown and elastic limit loads and their regimes though the thinning effect is insignificant at higher ovality (10%–20%). Bree diagram was constructed for the reference pipe bend models. It was observed that the failure of pipe bends is due to either reversed plasticity or ratcheting. Mathematical equations are proposed to express the generated plastic, shakedown and elastic limit moment boundaries for the analyzed pipe bend models.

The Numerical Investigation of Thin-Walled Beams with Modified C-Sections

Abstract Demand for thin-walled structures has been increasing for many years. Cold- formed, thin-walled channel beams are the subject of presented research. The local elastic buckling and limit load of these beams subjected to pure bending are investigated. This study includes numerical investigation called the Finite Strip Method (FSM). The presented results give a deep insight into behaviour of such beams and may be used to validate analytical models. The number of works devoted to the theory of thin-walled structures has been steadily growing in recent years. It means that is an increasing interest in practical methods of manufacturing cold-formed thin-walled beams with complicated cross-sections, including also beams with web stiffeners. The ratio of transverse dimensions of beam to its wall-thickness is high, therefore, thin-walled beams are prone to local buckling that may interact with other buckling modes. The stability constraints should be always considered when using cold-formed thin-walled beams.

Elastic–Plastic Limit Load of Coiled Tubing Under Complex Stress State

Coiled tubing (CT) endures complex stresses during the operations. The loading imposed on the CT can push it close to its performance limits. This paper presents new analytical models to define the limit load of CT and solve the problem of CT failures. Elastic–plastic limit load models of CT are established based on the twin shear unified strength theory. Moreover, the effects of residual bending stress, buckling, axial force, and external pressure on the elastic–plastic limit load are discussed. The results indicate that the elastic–plastic limit load models determined using the twin shear unified strength theory can describe the mechanical behaviors of CT under complex stress state. The initial yield elastic limit load of CT decreases with increasing axial compressive force. The effect of buckling and residual bending stress on the initial yield elastic limit load cannot be ignored in the analysis of CT strength. With increasing internal pressure, the plastic region keeps extending to the outer surface of CT. Plastic limit load is the value of internal pressure for which the entire wall thickness of CT becomes plastic. The proposed approach can be used to set operation limits for other oil tubulars.

Validation of the Nonlinear Superposition Method (NSM) for elastic shakedown limit pressures via comparison with experimental test results of spherical vessels with radial and oblique nozzles

The present research revisits rare experiments which determined elastic shakedown (SD) limit pressures of full scale radial and oblique nozzles partially penetrating spherical vessels. The experiments were conducted at Berkeley Nuclear Laboratories in England [1]. The SD limit pressures were determined via conducting consecutive series of internal pressure cycles and observing cyclic strain variation recorded by strain gauges cemented at predetermined various critical locations within the junctions' vicinities. The Nonlinear Superposition Method (NSM), formulated for computing elastic SD limit loads based on Melan's lower bound SD theorem, is successfully validated against recorded experimental outcomes for both nozzle configurations. Furthermore, full elastic-plastic cyclic loading finite element simulations were executed and illustrated very good correlation to the NSM results.

Axial Uplift Behavior of Belled Piers in Sloping Ground

Belled piers are frequently utilized for self-supporting transmission line towers, and the uplift loading is normally the controlling design load. However, belled piers placed in sloping ground have less uplift resistance than the same foundations built on flat ground. This study elucidates the uplift behavior of axially uplift-loaded belled piers in sloping ground. Two full-scale belled piers were constructed in a loess slope having an inclination of 20° with the horizontal, and pullout load testing was conducted for each belled pier. Both the site conditions and the load tests were documented comprehensively. The uplift load versus vertical shaft-head displacement curve of the belled piers in sloping ground exhibited an initial linear region, a curvilinear transition, and a final linear region, which is similar to that of a typical uplift or compression load–displacement curve for level ground. However, the shaft-head displacement at the lower sloping side was larger than that at the upper sloping side. Therefore, the shaft head rotated in the uplift loading direction, and the instantaneous rotation angle increased with the applied load. Unlike the level ground case, the uplift failure of the belled piers in sloping ground initiated from the edge of the bell at the lower sloping side and propagated into the slope surface as the soils deformed and pushed laterally toward the lower sloping side. The failure cracks on the ground surface were not symmetric and developed mainly on the lower sloping side. A comparison of the elastic limit load and the interpreted failure load of the two belled piers revealed that additional embedment of the foundation in sloping ground can achieve an increase in uplift resistance to match the level ground uplift capacity.

Evaluation of static structural performance of a plate composite girder using CFT structures

In this research, a nonlinear finite element analysis using CEB-FIP 1990 code and Eurocode was performed to verify the confinement effect of a plate composite girder using CFT structures. In addition, a 50-m full scale specimen of the proposed composite girder was tested in a four-point bending experiment. The results of the experiment showed stable rigid behavior until the static actuator limit load (5,000 kN), which means that the stable rigid behavior is secured for the elastic limit load (3,200 kN) as well as for the service load (1,000 kN). The results of the nonlinear analysis and the experiment were similar until the static actuator limit load (5,000 kN). The comparison also indicated that the proposed analysis is a reasonable analysis method. The maximum displacement at mid-span of the composite girder was also compared to that of a common composite girder made only of steel. As a result, the ductility of the proposed composite girder was found to be higher than the common composite girder owing to the confinement effect.