Precast Concrete Segmental Bridges Research Articles

Study on the performance of cast in situ concrete wet joints in PCSBs under cyclic loading

The wet joint is usually adopted in the closure section of precast concrete segmental bridges (PCSBs); the regular longitudinal reinforcement is discontinuous, which makes this section the most vulnerable part. To study the performance of the wet joint in the closure section under cyclic loading, six specimens are tested, considering loading mode, interface treatment method, setting of regular reinforcement and prestressing. Results show that the damage of the wet joint accumulates and plasticity develops under cyclic loading; the specimens undergo residual deformation, strength attenuation and stiffness degradation. Increase in prestressing level can delay cracking; the cracking load of specimens with a prestressing level of 8 MPa and 10 MPa is 21.9% and 32.8% higher, respectively, than that of the specimen with a stress level of 6 MPa; the results also confirm that an excessive prestressing level cannot significantly improve the shear strength of specimens. When the controlled displacement is small, the residual deformation of the specimen is small and the strength attenuates slowly; with the increase in controlled displacement, the residual deformation of the specimen increases and speeds up, the strength decreases continuously and the development of the crack tends to be stable, leading to a levelling off in the degradation of stiffness.

Effect of high-strength SCC with and without steel fibres on the shear behaviour of dry joints in PCSBs

The structural behaviour of precast concrete segmental bridges (PCSBs) heavily relies on the strength of the joints between segments. Multi-keyed dry joints are currently the most commonly used solution in these discontinuity zones. Employing high-strength concrete is becoming increasingly common in civil engineering given its higher strength and improved durability. It specifically allows higher prestressing levels in PCSBs. Using self-compacting concrete enhances workability and adding steel fibres improves mechanical properties. The existing scientific literature includes experimental tests to analyse the shear behaviour of castellated dry joints in different concrete types. However, no experimental tests appear specifically for the castellated dry joints made with high-strength self-compacting concrete (HS-SCC) with and without steel fibres. Therefore, this experimental study conducted 31 push-off-type tests to analyse the behaviour and shear capacity of dry joints made of HS-SCC by investigating the influence of adding steel fibres to the concrete mix. The study examined crack patterns, load-displacement behaviour, failure modes and different (cracking, ultimate and residual) loads. The addition of steel fibres improved joints’ shear capacity. However, brittle behaviour was observed after reaching ultimate load when using HS-SCC, even when steel fibres were added to the concrete mix. Finally, the adequacy of existing formulations was analysed. Standard AASHTO proved to be on the unsafe side for the castellated dry joints specimens made of HS-SCC without steel fibres, and provided a good approximation for the specimens with steel fibres.

Seismic performance of novel high-strength steel external assembled 3U energy dissipator

The development of easily implemented, cost-efficient, and replaceable energy dissipation devices is increasingly emphasized to improve bridge resilience. This study introduces a novel external assembled 3U energy dissipator (EA3UED) made of high-strength steel, designed to enhance the performance of precast segmental concrete bridge piers. The EA3UED, featuring three distinct U-shaped components to provide multi-directional resistance, was evaluated through comprehensive cyclic loading tests on five different specimens to assess their failure modes and practical feasibility. Finite element analysis conducted in Abaqus further assessed parameters such as ultimate bearing capacity, energy dissipation, stiffness, and ductility to identify the optimal geometric configuration. The results indicate that the EA3UED exhibits high energy dissipation, strength, stiffness, and ductility alongside cost-effective benefits. Two primary failure modes were observed: U-shape failure and bolt fractures. The validated finite element models successfully simulated the hysteretic behavior of the EA3UED. And a parametric study based on these models examined the effects of the width of U-shape and the steel grade on the device performance. These improvements demonstrate the EA3UED’s potential for integration in future bridge pier designs, improving their resilience and performance under seismic loads.

Experimental Study on the Bending Behavior of Precast Concrete Segmental Bridges with Continuous Rebars at Joints

Longitudinal ordinary rebars are discontinuous at the joints of precast concrete segmental bridges (PCSBs), which can open under tensile stresses induced by bending moments. This will lead to durability issues with the joints. To improve the bending properties of PCSBs, a novel joint type featuring continuous rebars was proposed in the present study. Three specimens were subjected to testing to examine the bending behavior of PCSBs using this new joint design compared to traditional joints. The crack propagation, structural deformation, joint opening width, strain in rebars, failure mode, stiffness, and flexural capacity were comprehensively investigated. The test results reveal that the continuous rebars effectively transferred bending normal stress between joints, ensuring full development of cracks in each beam segment. Effective control of joint opening width was also observed. Compared to traditional joints, the new joints exhibited a 29% to 33% increase in cracking load and a 32% increase in ultimate load. Failure in the continuous rebar joints was characterized by partial anchorage failure of the rebars along with localized concrete crushing in the top compression zone. Based on the test results, a computational method was proposed for calculating the cracking strength and flexural capacity of the new joints.

Investigation of Failures of Three Precast Post-Tensioned Segmental Concrete (PSC) Box Girder Bridges During Construction

Considering the fast pace of construction development, with a consistent increase in the volume of traffic, both road and rail traffic in developing countries like India, which are constrained by the limitation of land availability, especially in built-up or urban areas, lateral expansion in transport facilities has become increasingly challenging. Under such circumstances, vertical expansion through the construction of long flyovers or elevated structures is the most viable solution to meet traffic demand. Road and railway bridges are complex structures by nature with respect to their design and construction requirements based on a high level of knowledge, expertise and experience. Hence, some structural failures are taking place even during the construction stage of bridges owing to material quality issues as well as human error, to name but a few of the causes. This paper presents three case studies related to the investigation process and the primary cause(s) of the collapse of three different precast concrete post-tensioned segmental concrete (PSC) box girder bridges in India, with the corresponding lessons learnt and proposed recommendations. This paper covers issues relating to the investigation of the reasons leading to the failures of three precast concrete PSC box girders and a few suggestions for remedial measures.

Investigation into Discrepancies in Alignment and Levelling of Precast Segmental Box Girders (SBGs) During Launching for LRT 3, from Bandar Utama to Johan Setia (Package GS10)

In recent decades, there has been a notable global increase in the utilization of precast concrete segmental bridges within construction projects. However, discrepancies have been observed in the height of precast Segmental Box Girders (SBGs) installed alongside PS1 (monolithic), deviating from project specifications. This discrepancy impacts the deck level and consequently influences the Top of Rail (TOR). Consequently, a study was undertaken at AlKauthar Kinematics Sdn Bhd, a company involved in the LRT3 project's construction, with a specific focus on the casting and installation of Segmental Box Girders. The study's objectives include identifying the factors contributing to precast SBG misalignment during the LRT3 project's launch at P25-08, analyzing data for realignment purposes, and proposing design methodologies for manufacturing SBGs. The methodology employed in this study entails the analysis of data sourced from the industry, utilizing As-Built Surveys conducted by surveyors. Findings indicate that precast SBG misalignment during launching at P25-08 is primarily attributed to on-site errors, particularly casting errors during the construction of the cast-in-situ monolithic segment P25-08. This insight is invaluable for both governmental bodies and private construction organizations in mitigating project setbacks.

Shear behaviour and theoretical model of large shear key dry joints in precast concrete segmental bridges using advanced monitoring

Keyed dry joints are commonly utilised in segmental bridges for shear stress transmission. The aim of this study is to explore the shear behaviour and capacity of large shear key dry joints. The considered parameters included key base height, key number and concrete strength. The key base heights were found to have a significant impact on the failure mode and shear carrying capacity. When the key base height is increased by 100%, the shear carrying capacity of the joint is increased by 156%. Digital image correlation (DIC) and distributed fibre optic sensing (DFOS) technologies revealed the characteristics of load transfer in the large shear key, validated the principle of inclined strut column and observed the changing angle of inclined column with the increase in shear key size. Moreover, due to the shear transfer at the large key teeth, there is a trend of separation in the lower contact surfaces of the joint. Based on these findings, an improved calculation method for the shear strength of large key dry joints was established. The calculation results show more accurate predictions for large key dry joints than available calculation methods developed for smaller keyed dry joints.

Experimental investigation on shear behavior of PVA-ECC keyed joints

Keyed joints play a critical role in ensuring the overall behavior of a precast concrete segmental bridges. However, these joints can exhibit poor shear capacity and durability as well as brittle failure. Polyvinyl alcohol fiber-reinforced engineered cementitious composites (PVA-ECCs) exhibit high shear strength and ductility as well as excellent fracture performance, making them attractive for use in the joints of segmental bridges. This study fabricated 16 Z-shaped specimens with number of keys (one, two, or three), concrete materials (normal concrete or PVA-ECC), and types (monolithic, epoxy, or dry) to investigate their failure modes, cracking loads, shear capacities, residual capacities, and shear stress–vertical displacement curves. The results indicated that the keyed joints exhibited shear failure at the root of a shear key, and an increase in the number of keys increased the residual strengths and ductility of both the dry and epoxy joints, but it had a negative effect on the shear strengths. When PVA-ECC was applied instead of normal concrete, the cracking resistance index for all joints improved significantly and the shear strengths and ductility of the monolithic and keyed epoxy joints increased. Generally, the shear strengths of the epoxy joints were 6.3–29.1% higher than those of the corresponding dry joints; however, the ultimate displacements of the epoxy joints were 46.6–72.4% lower. Finally, a method for calculating method of the shear capacities of keyed PVA-ECC joints was proposed and verified to accurately predict the behaviors of previously tested joint specimens.

Experimental and numerical research on the performance of cast‐in‐situ concrete wet joints in closure section in precast concrete segmental bridges under cyclic loading

AbstractThe closure section of precast concrete segmental bridges (PCSBs) usually adopts the wet joint of cast‐in‐situ concrete, the width is generally 10–20 cm, and the regular longitudinal reinforcement is discontinuous, which makes the section the vulnerable part of the bridge. To explore the mechanical property of the wet joint in the closure section of PCSB under cyclic load, six wet joint specimens are tested to investigate the influence of loading mode, interface treatment mode, setting of regular reinforcement, and prestress level. The results show that the failure modes of wet joint specimens have similar characteristics, careful roughening of joint surfaces can improve the bonding effect of the new and old concrete and delay the cracking of the specimen, the cracking load of the specimen increases by 10.3% after careful roughening. When the prestress level increases from 6 to 8 MPa and 10 MPa, the stiffness of the specimens increases obviously, and the fracture development of the specimen in the loading process is improved. The cracking load increases by 21.9% and 32.8%, the shear strength increases by 9.9% and 6.6%, respectively, but the ultimate displacement decreases by 5.6% and 11.4%, respectively. Then, the finite element model of the wet joint was established and verified, the influence of shear key, concrete strength, and wet joint width are selected for parameter analysis. It is found that stress concentration is easy to occur after shear key is set, which has adverse effects on structural flexural resistance. The shear capacity of the model decreases by 22.4% and 21.5%, respectively after the setting of single and double‐shear keys, but the stiffness of the wet joint model before cracking is improved. Compared with C50 concrete model, the ultimate bearing capacity of C60 and C70 concrete models is increased by 11.5% and 24.8%, respectively. Wet joint width has little influence on the mechanical properties of wet joints in the closure section. The research results provide references for design and construction of PCSB wet joints in practical engineering.

A machine learning based method for predicting the shear strength of Fiber-Reinforced Concrete joints in precast segmental bridges

The utilization of Fiber-reinforced concrete (FRC) in the construction of Precast segmental concrete bridges (PSCBs) is progressively increasing. The design of joints among precast members can considerably impact the overall integrity and safety of the structure. Consequently, accurately estimating the shear capacities of FRC joints has become critical for evaluating the safety of PSCBs structures. However, the effectiveness and efficiency of formulas or models intended for prediction of the shear capacities of joints with normal concrete are unknown in predicting the shear capacities of FRC joints. In this study, the machine learning (ML) algorithms are employed to predict the ultimate load of FRC joints, utilizing a database of 192 push-off test results. Three individual models (Lasso, SVM, and KNN) and three ensemble models (RF, GBDT, and XGBoost) were developed for estimating the ultimate load. The GridSearchCV technique was utilized for parameter optimization based on the training set, in conjunction with a five-fold cross-validation method. A comparative study revealed that the XGBoost ensemble model surpassed other models, with a predictive performance ranking as follows: XGBoost > GBDT > RF > KNN > SVM > Lasso. The best-performing XGBoost model achieved performance metrics of R2 = 0.964, MAE = 41.318 kN, RMSE = 56.760 kN, and MAPE = 14.228%. The superior reliability of the XGBoost ensemble model was further validated through comparisons with current design codes and existing models. As ML-based models are typically black-box models, the SHapley Additive exPlanations (SHAP) method was employed to explicitly link the predicted output to the inputs. Based on SHAP results, confining stress (CS), depth of shear key (D), compressive strength of concrete (fcu), total height of joints (H), and height of flat part (Hsm) recognized as the crucial parameters affecting ultimate load.

Shear mechanism and strength calculation of steel shear keyed dry joints in precast segmental bridges

Precast concrete segmental bridges (PCSBs) are prone to weakness at the joints. To ensure accurate positioning and effective force transmission between segments, steel shear keyed joints were designed in the present study. A comprehensive investigation was also conducted into the shear performance of such joints, drawing on existing experimental research and theoretical analysis, so as to facilitate more comprehensive understanding of the shear mechanism and calculation methods involved. The results reveal that the steel shear keyed joint effectively transmitted shear force through the contact pressure between the steel key and concrete, aided by confining pressure. The steel keyed joint was also found to possess high shear capacity and exhibit good ductility. A mechanical model of the steel shear keyed joint was constructed, and the shear mechanism and failure modes were revealed, including shear failure of the steel key, local compression failure of concrete, and tearing failure of concrete. Finally, the present authors suggest that the shear failure of the steel key should be used as the basis for the shear resistance design of steel shear keyed joints, which can be calculated according to the formula ( The strength of concrete around the steel key should also be checked.

Experimental study on the failure process of large shear key joints based on NDT methods

AbstractDry joints with keys are often used in precast concrete segmental bridges (PCSBs) to transfer shear stresses. Large dry joints with keys can often provide greater shear bearing capacity, which can meet the needs of rapid construction and simple assembly. This study focuses on the shear response of super‐sized dry joints with keys under direct shear. Various monitoring methods, including digital image correlation (DIC) and distributed optical fiber sensing (DFOS), were used to systematically study the stress process of large concrete keys. The results show that as the size of the key teeth increases, the shear bearing capacity and ultimate vertical displacement of the specimens also increase. DIC and DFOS techniques provide detailed information on key tooth failure, which is beneficial for subsequent stress analysis of shear keys.

Experimental study on oblique-shear performance of splicing joint for precast ultrahigh-performance concrete segmental bridges

This paper aims to study the effect of the normal stress on the shear performance of splicing joints for precast ultrahigh-performance concrete (UHPC) segmental bridges (PUSBs), an oblique-shear joint is designed to decompose the vertical force into a normal force and a shear force for the joint. The effect of the number, height and inclination angle of the keys on the bearing capacity of the joint is studied by 19 oblique-shear joints. Then, the bearing capacity and failure modes are analyzed significantly. The results show that the failure modes of the joints are shear failure, compression-shear failure and splitting failure, all showing primarily brittle failure. Moreover, the proportion of shear stress in the specimens increases with the increase of the inclination angle of the joint, and the shear capacity of the specimens decreases. Additionally, the shear capacity of the specimens increases with the increase of the height of the keys. After that, we derive a new formula for calculating the shear capacity utilizing Mohr’s stress circle theory and Mohr-Coulomb failure criterion, i.e., the interfacial frictional coefficient is 0.94 and the shear capacity of keys is 0.06. One may find the present formula shows a high guarantee by comparing with those from references. The formula established in this paper may be used to calculate the shear capacity of splicing joint of precast ultrahigh-performance concrete segmental bridges.

Cyclic loading test of self-centering precast segmental concrete high-speed railway bridge columns with UHPC-filled duct connections

Precast concrete high-speed railway (HSR) bridge columns are attractive for standardized HSR bridges, but their applications are rare partly due to a research gap in their lateral behavior. Traditional under-reinforced HSR bridge columns have huge lateral stiffness and poor drift capacity, which means that their prefabrication is not a simple separation-assembly process and requires special research. This study aims to develop a novel self-centering precast segmental concrete (SPSC) HSR bridge column, which is designed to have five major improvements including adopting large-diameter deformed bars as energy dissipation (ED) bars, inter-locking multi-hoops, unbonded post-tensioning (PT) tendons, a cast-in-situ ultra-high performance concrete (UHPC) layer at the bottom joint, and UHPC-filled duct connections. A 1/6 scaled cyclic loading test was conducted on three specimens to validate prefabrication feasibility and assess seismic behavior. The research results show that inter-locking multi-hoops can enable the developed bridge columns to have ductile flexural failure and a drift capacity of up to 5 %. The bridge columns have increased lateral stiffness and strength as well as decreased ductility. UHPC-filled duct connections can cause the strain amplification of ED bars at the bottom joint. The bottom joint opening dominates lateral deformation while the influence of joint sliding can be neglected. The bridge columns have good ED capacity and the equivalent hysteretic damping ratio of about 20 % at the drift ratio of 5 %. The bridge columns have the excellent self-centering capacity to control residual drift ratio in an allowable range before flexural failure. The acceptable drift ratios are suggested to be 3.5 % and 4.0 %, respectively, for the SPSC HSR bridge columns without and with PT force.

Stress Analysis of PCI-Girder Precast Concrete Segmental Bridge Based on SNI 1725:2016 (Case Study: Konaweha River Bridges, Southeast Sulawesi)

A prestressed bridge is an alternative way of structural design because of the ease of procurement and installation. For long-span bridges, prestressed beams only require minimum cross-sectional dimensions along with reliable performance. A prestressed concrete beam is always made in several segments to facilitate delivery. It is necessary to analyse and control the stress that occurs due to the external load and the loss of prestress. This study aims to provide a detailed stress analysis of PCI-girder precast concrete segmental bridges, considering the provisions and guidelines specified in SNI 1725:2016. Four stages of construction will be controlled. Namely at the transfer stage, the after-loss of the prestressed stage, the composite beam stage, and the service stage. The tensile and compressive stress analyses will be carried out on the upper side of the bridge surface, the upper side of the girder, and the bottom. If tensile stress occurs, it indicates that the girder is not capable of withstanding the applied load, and additional anchorages need to be installed at each joint between segments. The result obtained from the stress analysis conducted in this study is that no tensile stress is found in any critical sections of the girder. The stress that occurs has fulfilled the design capacity, without any tensile stress occurring in the bridge.

Shear behavior and construction method of steel shear keyed joints in precast segmental beams

The joints between segments represent weak points and introduce discontinuity into structures, therefore they are particularly significant in precast concrete segmental bridges. In this study, a new steel shear key was designed, and 6 full-scale tests were conducted. Various shear keys and joint types were taken as experimental parameters to study crack propagation, failure mode, shear slip, ultimate bearing capacity, and the residual bearing capacity of various joints under direct shear loading. The results show that the stiffness and shear capacity of steel shear keyed joints were higher than concrete key joints, and the structural system was more stable than concrete keyed joints at the moment of cracking. Both the concrete key and steel key epoxied joints suffered direct shear failure. However, different to the concrete epoxied joints which experienced brittle failure, steel key epoxied joints demonstrated a large residual capacity. Based on traditional segmental bridges construction, construction methods involving steel shear keyed joints included short-line match, long-line match, and modular methods are introduced. Finally, the feasibility of steel shear keyed joints construction was verified via engineering tests.

Flexural Behavior of Precast UHPC Segmental Beams with Unbonded Tendons and Epoxy Resin Joints

Precast concrete segmental bridges (PCSBs) with hybrid tendons may be the most competitive solution for achieving the advantages of rapid construction and favorable structural performance. Therefore, the flexural behavior of precast concrete segmental bridges (PCSBs) with unbonded tendons and epoxy joints was experimentally investigated in this study, and the effects of the joint types were recorded. Investigations were carried out on the ultimate loads, prestressed strand stresses, deflections, as well as failure modes, while an unbonded monolithic beam was tested for comparison. In addition, the strain measurement proved that the average strains agree with the assumption of plane section, regardless of whether the joints were set. The flexural strengths of prefabricated components were 9~15% lower than those of the monolithic beams with unbonded tendons. Meanwhile, the shape of the joints also influenced the flexural bearing capacity; the bearing capacity of the dual-tooth joint beam was 4.5% lower than that of the single-tooth one, and the bearing capacity of the flat butt joint member was 5.7% lower than that of the dual-tooth joint beam. Moreover, the experimental deflection curve and ultimate bearing capacity of the models with different shear keys showed a good correlation with the FE results. These research outcomes will aid in comprehending the roles of joints in the flexural behaviors of precast UHPC segmental bridges.

Nonlinear Analysis of External Post-Tensioning anchorage of Concrete Segment

Abstract: Precast concrete segmental bridges (PCSBs) have been the most common design technology used in the last decades. In these studies Non-linear structural performances of externally prestressed, precast concrete segmental bridges (PCSB). PCSBs with externally prestressed tendons have become very popular in construction because of economical and safety reasons, fast and practical construction, and outstanding serviceability. External tendons technique is widely used because it allows to inspect the cables and to replace them or to reinforce the tendons in case of damage while such kinds of actions are difficult to be taken in case of internal prestressing. It is widely recognized that segmental bridges have better durability, lower life-cycle costs and higher quality for maintenance than other types of bridges. However, there is lack of reliable computational model for analyzing behavior of post-tensioned PCSBs. Experimental analysis of bridge segment required more cost, time and effort for the analysis and also take cake of quality of material, cast process, curing, and testing. This research presents the results of stress and strain state of the local bearing area caused by a Prestressed cable anchor in reinforced concrete bridge segment. Nonlinear analysis of anchorage and rebar, concrete segment can be carried out by analytical solution calculated with the reference of ACI 318/19. ANSYS software is used for model and analyze the structure. The analysis process was carried out in 3 types : linear elastic analysis, nonlinear elastic analysis, and nonlinear analysis considering the destruction of concrete, and the value is compared with ANSYS software ( static structure).

Experimental study on direct shear performance of prefabricated splicing joints of ultrahigh-performance concrete

Splicing joints are the weak link of precast ultrahigh-performance concrete (UHPC) segmental bridges (PUSBs). Thus, this paper conducts direct shear tests on eight groups of UHPC keyed joints to investigate the shear performance of the interface of the key. The effects of lateral compressive stress (σn) and the number of keys on the shear performance are also examined. In addition, the load–displacement curves, failure modes, cracking loads, and ultimate loads of the specimens with different parameters are presented. After that, the direct shear capacity of the joints is theoretically analyzed based on the test results and relevant specifications, and a formula for calculating the direct shear capacity is derived. The results show that the failure mode of the UHPC keyed joints is primarily brittle failure. Moreover, the failure mode is the direct shear failure along the interface of the key when the lateral compressive stress is low; however, it is the local crushing of concrete in the key when the lateral compressive stress is high. Additionally, the direct shear capacity of the specimens increases linearly with raising the lateral compressive stress. The direct shear capacity of the double-keyed joints is 17.4–29.3 % higher than that of the single-keyed joints under the same conditions. The values calculated by specifications NF P-18 710 and Eurocode 2 2011 are lower than the experimental ones. The experimental data are evenly distributed on both sides of the curve calculated by specification JSCE 2008 when the lateral compressive stress is low, posing potential hazards in this case. The value predicted by specification AASHTO 2003 is also higher than the experimental value. Finally, we derive a formula for calculating the direct shear performance of the UHPC keyed joints utilizing Mohr’s stress circle theory, and it can be applied to engineering design with high accuracy.

Shear strength of steel fiber reinforced lightweight self-consolidating concrete joints under monotonic and cyclic loading

The shear behavior of precast concrete segmental bridges depends on the type of joints between the segments. However, there are few studies evaluating the shear strength of steel fiber reinforced lightweight self-consolidating concrete for application to precast concrete bridges. The purpose of this study is to compare the shear behavior of joints made of general concrete with developed concrete that includes lightweight aggregate and steel fiber under monotonic and cyclic loading. In this study, the push-off shear test was performed in accordance with experimental parameters of different concrete mixtures, key type, confining stress, and application of epoxy between the segments. The tests were carried out to assess the shear strength, shear behavior, crack propagation and failure mode of joints. The test results represented shear capacity of joints decreased 15.2% by replacing normal coarse aggregates with lightweight aggregates but could be enhanced through the incorporation of hooked-end steel fibers. The shear capacities of joints fabricated using developed mixture tended to be underestimated compared to analytically calculated strengths. Furthermore, the normalized stiffness of the joint was decreased with an increased number of load cycles under high-amplitude low-cycle load. The shear resistance through aggregate interlock may gradually decrease with increasing number of cycles resulting in failure at 85% of the failure load of the monotonically tested specimen. An appropriate level of confining stress and application of epoxy shall be considered to prevent sudden failure of joints at high amplitude cyclical loading conditions.