Load Moment Research Articles

The effect of fracture growth rate on the fracture process zone of salt rock after heat treatment

The importance of rate on the mechanical properties of rocks has been widely acknowledged by numerous scholars. Currently, most researchers mainly focus on investigating the influence of loading rate, while there is limited research on the effects of fracture growth rate on mechanical properties such as fracture process zone (FPZ) and fracture toughness of rocks. In order to explore the impact of fracture growth rate on the mechanical properties of rocks, this study conducted three-point bending pure I-mode fracture experiments on salt rocks at temperatures ranging from ambient to 700 °C using different quasi-static loading rates (0.02–2 mm/min). Meanwhile, digital image correlation (DIC) technology was employed to monitor displacement and strain variations, identify and calculate the fracture growth rate and FPZ size, and subsequently compute the corrected fracture toughness. The study discussed the effects of temperature and fracture growth rate on the FPZ and fracture toughness of rocks. The following main conclusions are drawn based on the analyzed results: (1) Temperature and loading rate have a great influence on the onset of FPZ in salt rocks. The higher the temperature and loading rate, the earlier the onset of FPZ. (2) With the increase of the average fracture growth rate, the FPZ length at the peak load of rock salt and the modified fracture toughness increased continuously, and was divided into two stages, in the stage of the crack extension rate generated by the loading rate of 0.02 mm/min-1 mm/min grew faster, and the growth of the crack extension rate generated by the loading rate of more than 1 mm/min became slower. (3) The effect of temperature on the fracture parameters of rock salt is significant, the peak load moment FPZ length and fracture toughness first increase and then slowly decrease with increasing temperature from room temperature to 700℃. The inflection point is at 500℃, where the fracture toughness and FPZ length reach the maximum value. (4) As the loading rate increases the proportion of transgranular fracture in the rock salt fracture surface gradually rises, and the crack extension path becomes smoother and smoother.

Coordinated, Centralized, and Simultaneous Control of Fast Charging Stations and Distributed Energy Resources

The growing penetration of fast charging stations (FCSs) to electric vehicles (EVs) and distributed energy resources (DERs) in the electrical power system brings technical issue changes in the voltage profile throughout grid nodes and feeder current overload. The provision of ancillary services by DERs and FCSs arises as an appealing solution to reduce these adverse effects, enhancing the grid hosting capacity. The control of microgrids is essential for the coordinated implementation of these services. Although microgrid control is widely applied to DERs, few studies address the coordinated control of DERs and FCSs to obtain benefits for the electrical power system. This paper proposes a coordinated and simultaneous control of DERs and FCSs based on the power-based control (PBC) strategy, efficiently exploiting FCSs in a microgrid model previously unaddressed in the literature. The results show that, with the coordinated control of DERs and FCSs, the control of the power flow in a minigrid (MG) is achieved both in moments of high generation and in moments of high load, even with the maximum operation of DERs. This method allows for the maintenance of voltage levels within values considered acceptable by technical standards (above 0.93 pu). The maintenance of voltage levels is derived from reducing the overload on the point of common coupling (PCC) of the minigrid by 28%, performing the peak shaving ancillary service. Furthermore, the method allows for the control of zero power flow in the PCC of the minigrid with the upstream electric grid in periods of high generation, performing the ancillary service of valley filling. The method performs this control without compromising vehicle recharging and power dispatch by DERs.

Investigation of local soil resistance on suction caissons at capacity in undrained clay under combined loading

Winkler modelling offers a flexible and computationally efficient framework for estimating suction caisson capacity. However, there is a limited understanding of the local soil resistance acting on caissons at capacity under combined six degrees-of-freedom (6DoF) loading, which is essential for accurately estimating caisson failure envelopes. Furthermore, existing simplified design models for caissons cannot assess capacity under non-planar lateral and moment loading, which is common in offshore wind applications. To address these limitations, this paper presents a comprehensive three-dimensional (3D) finite element analysis (FEA) study, which investigates the local soil resistance acting on the caisson at capacity in undrained clay under combined 6DoF loading. The paper introduces the concept of ‘soil reaction failure envelopes’ to characterise the interactions between soil reactions at capacity. Closed-form formulations are derived to approximate these soil reaction failure envelopes. An elastoplastic Winkler model is then developed, incorporating linear elastic perfectly plastic soil reactions based on these formulations. The results demonstrate that the Winkler model can provide efficient and reasonably accurate estimations of caisson capacity under combined 6DoF loading, even for irregular soil profiles that pose much uncertainty and challenges to existing macro-element models.

Wind turbine load optimization control and verification based on wind speed estimator with time series broad learning system method

AbstractWith the rapid development of wind power, the power performance and mechanical load characteristics of wind turbine are simultaneously considered and focused. Normally, wind turbine senses the incoming flow characteristics through the nacelle mounted anemometer, due to the inability to perceive the characteristics of wind speed in advance, the control strategy makes the wind turbine itself to be at a passive state during the operation process. In this paper, a wind turbine mechanical load optimization control strategy based on an accurate wind speed estimator with time series Broad Learning System Method (BLSM) is designed, simulated and also verified. Firstly, the basic control theory of the BLSM and also a mechanical load optimization controller is designed. Then the OpenFAST is used to conduct a full‐life cycle simulation comparison study on mechanical load characteristics of wind turbine before and after the implementation of the optimization control strategy. Finally, a field empirical mechanical load test is performed on the wind turbine, which is configured with BLSM mechanical load optimization control technology. The findings indicate that the implementation of this control strategy can significantly mitigate the ultimate and fatigue loads of wind turbines, particularly the fatigue loads of tower base tilt and roll bending moments, with a reduction rate of approximately 6.2% and 4.3%, respectively.

Influences of external moment on the contact characteristics of angular contact ball bearings under combined loads

Angular contact ball bearings are widely used in rotating machinery. The external moment about the bearing lateral direction (i.e. the lateral moment) applied to a bearing affects the service life and performance of the bearings by influencing its internal contact characteristics. This work established a quasi-dynamic model of the ball bearing by comprehensively considering the inclination angle of the inner ring due to external lateral moment, the viscous drag, the inertial force and moment of the ball, the spin and sliding of the ball in the contact ellipse. On this basis, the operation process of angular contact ball bearings was simulated under combined radial and moment loads. The effectiveness of the model was verified experimentally, and the influences of external moments about different directions on the contact angle, slip-roll ratio, and load distribution under combined loads were analyzed. The results show that the increase in moment intensifies the spin-sliding of the rolling element. When the lateral moment and the radial load are applied together, the lateral moment can reduce the maximum load of the rolling element and causes the maximum load of the rolling element to deviate from its original position. When the lateral moment is combined with the axial and radial loads, the bearing load zone is concentrated by the rolling elements near the lateral direction. The curve of the load distribution changes from an ideal oval to a distorted oval. The research results can be used to guide the design, service life calculation, and performance evaluation of rolling bearings.

Influence of Variation in Tie Reinforcement Diameter on the Ductility of Reinforced Concrete Columns

Reinforced concrete columns are crucial structural elements in ensuring the strength and stability of buildings. Column ductility, which is the ability to absorb energy and undergo deformation before failure, is a primary concern in structural engineering, especially in extreme external loading situations such as earthquakes. This study aims to evaluate the influence of variation in Tie reinforcement diameter on the ductility of reinforced concrete columns using Xtract software. The research method involves creating column structure models with specified dimensions and specifications, followed by the gradual application of axial loads to each model. Three models were created with varying Tie reinforcement diameters, namely 10 mm, 12 mm, and 14 mm. Structural analysis was conducted to examine the structure's response to the applied axial and moment loads, including evaluation of stresses, deformations, and column capacities. The analysis results show differences in ductility levels among the models. The model with a 10 mm Tie reinforcement diameter achieves higher ductility levels at low axial loads but fails to meet the requirements at higher axial loads according to the SNI 1726:2019 standard. However, models with Tie reinforcement diameters of 12 mm and 14 mm also exhibit a similar pattern, with good ductility at low axial loads but failing to meet the requirements at higher axial loads. In conclusion, variations in Tie reinforcement diameter affect the ductility of reinforced concrete columns. To ensure full ductility under various axial load conditions, adjustments to the design or specifications of the reinforced concrete column structure are necessary. This research contributes to understanding the factors influencing the ductility of reinforced concrete columns and can serve as a basis for the development of more effective design methods in the future.

Vibration response analysis of rotor system coupled with a novel 4-DOF SFD hydrodynamic model considering the influence of rotational displacement

As a damping structure, squeeze film dampers (SFDs) are commonly employed in turbomachinery. Aiming at the problem of hydrodynamic modeling and solution, this paper presents a four-degree-of-freedom (4-DOF) hydrodynamics model of SFD, which not only considers the influence of radial displacement on oil film clearance but also the influence of rotational displacement. The Reynolds equation of the SFD is solved utilizing the finite difference method (FDM). The oil film gap distribution and static properties of the SFD under different rotational displacements and journal eccentricity are analyzed. Then, the hydrodynamic model of the 4-DOF SFD is coupled with the rotor system, and the vibration characteristics of the SFD-rotor system are analyzed. Finally, the experimental verification is carried out. The analysis results reveal that the rotational displacement has little influence on the vibration response of the SFD-rotor system at the non-critical speed. However, near the critical speed, the occurrence of rotational displacement of the SFD is more beneficial to the vibration reduction effect. Moreover, the analysis results of the hydrodynamic characteristics of the SFD show that when the eccentricity is less than 0.4, the rotational displacement has little effect on the oil film gap distribution, load moment, and oil film reaction force. When the eccentricity exceeds 0.4, the rotational displacement has a great influence on the gap distribution, load moment, and oil film reaction force of SFD.

Mechanical Behavior Analysis of High Strength Concrete Beams in Architectural Design: Simplified Calculation Method of Flexural and Shear Bearing Capacity

This study advances the use of high-strength concrete beams in structural engineering by analyzing their flexural behavior. Utilizing a combination of theoretical and empirical methods, the research develops equations for calculating the cracking moment and ultimate load capacity of these beams. Key findings include a shear-bearing capacity calculation model, validated by experimental data, with discrepancies in cracking moment and ultimate load-bearing capacity formulas being only 6.16% and 1.53% respectively. These results offer significant insights for the design and analysis of high-strength concrete beams in architectural engineering, demonstrating high accuracy and stability.

An numerical investigation of the three dimensional multi-level force chain network of the sample with a single fissure under uniaxial compression

A novel three-dimensional grain-based model based on Particle Flow Code is proposed. Within this model, both quantitative calculations and multi-level classifications of force chain networks are achieved. A batch of numerical samples with a single pre-existing fissure with different inclination angle αs is constructed and then applied to the uniaxial compression. The result shows that the general force chains (GF) are approximately uniformly distributed in each orientation. The number of high-strength force chains (HF) reaches its maximum at the peak load moment, and the main orientation is consistent with the loading direction. The average value of the force chain in the tip regions of the fissure at any characteristic moment is the highest. In the whole region and the upper and lower regions of the fissure, the level of the force chain network rises as αs increases. Conversely, within the tip regions of the fissure, both the average value and sum value of GF decrease. The fracture resistance of intragranular structures is the highest, surpassing that of both all structures and intergranular structures. The fracture resistance within the tip regions of the fissure is the lowest compared to the entire region and the upper and lower regions of the fissure.

Design and Control of the Rehab-Exos, a Joint Torque-Controlled Upper Limb Exoskeleton

This work presents the design of the Rehab-Exos, a novel upper limb exoskeleton designed for rehabilitation purposes. It is equipped with high-reduction-ratio actuators and compact elastic joints to obtain torque sensors based on strain gauges. In this study, we address the torque sensor performances and the design aspects that could cause unwanted non-axial moment load crosstalk. Moreover, a new full-state feedback torque controller is designed by modeling the multi-DOF, non-linear system dynamics and providing compensation for non-linear effects such as friction and gravity. To assess the proposed upper limb exoskeleton in terms of both control system performances and mechanical structure validation, the full-state feedback controller was compared with two other benchmark-state feedback controllers in both a transparency test—ten subjects, two reference speeds—and a haptic rendering evaluation. Both of the experiments were representative of the intended purpose of the device, i.e., physical interaction with patients affected by limited motion skills. In all experimental conditions, our proposed joint torque controller achieved higher performances, providing transparency to the joints and asserting the feasibility of the exoskeleton for assistive applications.

A Numerical Investigation of the Hydrodynamic Performance of a Pitch-Type Wave Energy Converter Using Weakly and Fully Nonlinear Models

In this study, the performance of a wave energy converter (WEC) rotor under regular and irregular wave conditions was investigated using 3D nonlinear numerical models. Factors such as the power take-off (PTO) load torque, wave periods, spacing of multiple WEC rotors, and wave steepness were analyzed. Two models were employed: a weakly nonlinear model formulated by incorporating the nonlinear restoring moment and Coulomb-type PTO load torque based on the potential flow theory, and a fully nonlinear model based on computational fluid dynamics. The results show that the average power estimated by both numerical models is consistent, with a wave steepness of 0.03 for the range of one-way and two-way PTO load torques, except for the deviations observed in the long range of the one-way PTO load torque. Furthermore, the average power of the WEC rotor under the applied PTO load torque exhibits a quadratic dependency, regardless of the wave steepness. In addition, adopting a one-way PTO load torque was more efficient than adopting a two-way PTO load torque. Therefore, the fully nonlinear model demonstrated its ability to handle a high degree of nonlinearity, surpassing the limitations of the weakly nonlinear model, which was limited to moderate wave steepness.

Intact stability analysis of crane barge due to loading orientation effect during heavy lifting operation

Changes in the position of the lifting load on the crane barge during heavy lifting operation significantly affect the stability of the vessel. The changes in stability during this heavy lifting operation must be analysed to prevent operational failures. This study conducted an intact stability analysis of the crane barge during lifting of topside structures in the installation phase. The analysis was performed with variations in the position of the lifted load from starboard to bow for every 15° change in the crane angle. The stability results of the Crane Barge for all variations, using both analytical and numerical methods, have met the IMO requirements. The extreme condition occurred in load case 8, with a maximum GZ value of 2.904 m at a 22° angle and an area of 103,894 m.deg. The comparison of the stability results of the crane barge during the structural lifting operation using analytical calculation and numerical methods indicates that the overall validation error values have met the ±5% requirement according to the ABS Rules. However, when considering the corrections for changes in the lifting load moment in the analytical calculation, stability error values increase significantly as the heeling angle of the vessel increases.

Influence of cervical total disc replacement on motion in the target and adjacent segments

Background ContextThe motion limitation after cervical discectomy and fusion alters the spine´s kinematics. Unphysiological strains may be the result and possible explanation for adjacent segment degeneration. Alterations to cervical kinematics due to cervical total disc replacement (TDR), especially two-level, are still underinvestigated. PurposeTo investigate cervical motion including coupled motions after one-level and two-level TDR in the treated and also the adjacent segments. Study DesignAn in-vitro study using pure moment loading of human donor spines. MethodsSeven fresh frozen human cervical spine specimens (C4-T1, median age 46 with range 19-60 years, four female) were included in this study. Specimens were tested in the intact condition first, followed by one-level TDR at C5-6 which was subsequently extended one level further caudal (C5-7). Each specimen was quasistatically loaded with pure moments up to 1.5 Nm in flexion/extension (FE), lateral bending (LB) and axial rotation (AR) in a universal spine tester for 3.5 cycles at 1 °/s. During the tests three dimensional motion tracking was performed for each vertebral body individually. From that the primary and coupled ROM of each spinal level during the third full cycle of motion were evaluated. Non-parametric statistical analysis was performed using a Friedman-test and post-hoc correction with Dunn-Bonferroni-tests (p < 0.05). Ethics approval was obtained in advance. ResultsIn FE, one-level TDR (C5-6) moderately increased primary FE in all four segments, but only significantly at the cranial adjacent level C4-5. Additional TDR at C6-7 further increased the ROM at the target segment without much influence on the other levels. Increasing implant height at C6-7 partially counteracted the increased FE. Coupled motions were minimal in all test conditions at all levels.In LB, coupled AR was observed in all test conditions at all levels. One-level TDR decreased primary LB at the target segment C5-6 significantly, without much influence on the other levels. Extending TDR to C6-7 decreased ROM in the target segment but without gaining statistical significance. Increasing implant height at C6-7 further decreased primary LB at the target segment, still without significance. Notably, coupled AR was significantly decreased at the cranial adjacent segment C4-5 compared to the intact condition.In AR, coupled LB was observed in all test conditions at the levels C4-5, C5-6 and C6-7, while the transition level to the thoracic spine C7-T1 showed only little coupled LB. Both one-level and two-level TDR showed little influence on primary AR or coupled motions at any level. Only after increasing implant height at C6-7 was the motion of the caudally adjacent level C7-T1 significantly altered. ConclusionEvaluating primary FE, LB and AR together with the associated coupled motions revealed widespread influence of cervical TDR not only on the motion of the treated level but also at the adjacent segments. The influence of two-level TDR is more widespread and involves more levels than one-level TDR. Clinical SignificanceThe prevention of unphysiological strains due to altered kinematics after cervical fusion, which could possibly explain adjacent segment degeneration, were a driving factor in the development of TDR. These experimental findings suggest cervical TDR influences the whole cervical spine, not only the treated segment. The effect becomes more extensive, involving more levels and motion directions, after two-level than after one-level TDR.

Crack Propagation Phenomenon in Gangue Concrete Using the Digital Image Correlation (DIC) Method

In order to study the mode I crack propagation mechanism of coal gangue concrete with different contents, the digital image correlation (DIC) method was used to carry out the three-point bending fracture tests on coal gangue concrete with different contents. The results show that the process of the mode I crack propagation of coal gangue concrete with different contents can be divided into three stages as follows: the elastic stage before crack initiation, extended viscoelastic stage, and extended fracture stage. The amount of coal gangue has a significant impact on the crack propagation path. The more the amount of coal gangue, the more the crack penetrates through the coal gangue coarse aggregate, the smaller the bending degree of the failure path, and the faster the crack propagation to the penetration speed. The crack initiation load, ultimate load, external force work, gravity work, and fracture energy all decrease with the increase of the coal gangue content. The data obtained by the DIC method and displacement extensometer are in good agreement, which proves that the DIC method is feasible. Based on the DIC method, before reaching the horizontal displacement on both sides of the crack tip, the horizontal displacement of the horizontal pixel is very small and there is a jump increase after the ultimate load. There are obvious inflection points on the left and right, and the horizontal displacement remains unchanged after the inflection point. After the horizontal displacement field of crack propagation reaches the limit load, there is an obvious limit; the limit gradually extends upward, and the corresponding crack tip strain field is also gradually enhanced. The more the coal gangue is added, the smaller the corresponding horizontal displacement and strain field is at the same limit load moment. The shape of the crack generation area of coal gangue concrete takes the crack tip as the axis of symmetry and is “gourd shaped.” The more the content of the crack, the larger the crack generation area.

Residual strength of a casing with corrosion semi-ellipsoid defect in high-sulfur gas wells

There are few studies on the residual strength of semi-ellipsoid defect casing considering the bending moment load in high sulfur gas well. In this paper, a numerical model of a casing with corrosion defects exposed to bending moment is proposed. The effect of the defect positions along the circumference on the residual strength of the casing with bending moment is investigated. Parametric studies highlight that defect size have significant effect on the residual strength of the casing, and the circumferential defect and the axial defect can change the critical internal pressure and the critical axial load. This finding has a significant guidance for residual intensity evaluation of a casing with defect.

Load-induced blood marker kinetics in patients with medial knee compartment osteoarthritis are associated with accumulated load and patient reported outcome measures.

This study aimed to quantify the mechanoresponse of 10 blood marker candidates for joint metabolism to a walking stress test in patients with knee osteoarthritis and to determine the association among marker kinetics and with accumulated load and patient reported outcomes. 24 patients with knee osteoarthritis completed questionnaires, and a 30-minute walking stress test with six blood serum samples and gait analysis. Concentrations of cartilage oligomeric matrix protein (COMP), matrix metalloproteinases (MMP)-1, -3, and -9, epitope resulting from cleavage of type II collagen by collagenases (C2C), type II procollagen (CPII), interleukin (IL)-6, proteoglycan (PRG)-4, A disintegrin and metalloproteinase with thrombospondin motifs (ADAMTS)-4, and resistin were determined by enzyme-linked immunosorbent assays, Joint load (moments and compartmental forces) was estimated using musculoskeletal modeling using gait analysis data. COMP and MMP-3 showed an immediate increase after the walking stress followed by a decrease. MMP-9 and resistin showed a delayed decrease below pre-stress levels. ∆COMP correlated with ∆MMP-3 for most time points. ∆MMP-9 correlated with ∆resistin for most time points. The load-induced increase in blood marker levels correlated among blood markers and time points. C2C and resistin correlated positively and C2C/CPII and MMP2 correlated negatively with load during gait. Immediate relative ∆CPII and ∆MMP1 and delayed relative ∆COMP, ∆IL6, ∆C2C, ∆CPII, ∆MMP1 and ∆MMP3 correlated with the load accumulated during the walking stress. Baseline C2C levels correlated with Knee Osteoarthritis Outcome Score (KOOS) subscales and load-induced changes in MMP-3 with KOOS and Short Form 36 quality of life subscores (P<0.05). The distinct and differentiated physiological response to the walking stress depends on accumulated load and appears relevant for patient reported osteoarthritis outcome and quality of life and warrants further investigation in the context of disease progression.ClinicalTrials.gov registration: NCT02622204.

Interaction domains for capacity- and performance-based design of pile groups

The aim of the paper is to propose design tools for pile groups when vertical and moment loads are applied simultaneously. This is done by presenting a method to derive the exact solution for the failure locus in the generalized force space, including a vertical load and a moment with components along two axes, to employ for capacity requirements which helps to get rid of overconservative assumptions usually adopted in design. Moreover, closed-form solutions for performance-based interaction domains are also provided allowing to detect all the combinations of external loads associated with a given value of settlement and/or rotation of the foundation that is extremely useful when the design is ruled by serviceability requirements. The application of these straightforward formulae provides results which are in very good agreement with the more rigorous solutions derived from a numerical procedure developed ad hoc for the problem at hand.

Buckling behavior of cold-formed steel sigma and lipped channel section beam-columns: Experimental and numerical investigation

In this study, the buckling behavior of cold-formed beam-column members with sigma and lipped channel sections under the combined effect of axial load and biaxial bending moment (P-Mx-My) was compared. A total of 30 specimens (15 with sigma sections and 15 with lipped channel sections), each measuring 1500 mm in length, were tested under monotonic loading. The performances of the specimens under eccentric loading such as strength and energy absorption capacity were investigated experimentally and numerically. The local, distortional and global buckling modes that determine the bearing capacity of the section and the length of the sigma and lipped channel member where all these buckling modes can be seen were determined. Finite element analysis (FEA) was performed with Abaqus software, and the numerical results were verified against experimental results. Using the validated finite element model, a comprehensive parametric study was carried out by performing 2894 FEA on sigma and lipped channel section members with various cross-sectional dimensions and lengths. Experimental results show that there are significant differences in load bearing capacity, energy absorption capacity and buckling modes of sigma and lipped channel section members. In the FEA/ AISI-S100 code comparison made at the end of the parametric study, it was determined that differences occurred according to the lengths, cross-sectional properties and loading points of the members. It was determined that the error rate was safer when the lips were subjected to tensile stresses than when they were subjected to compressive stresses. Finally, it was determined that the FEA/AISI-S100 error rate decreased as the length of the sigma-section members increased.

Vibration reliability of steel beams prestressed by drawing

Introduction. Vibrations of building structures and mechanism parts were analyzed. The need to investigate the oscillation processes and vibration reliability of steel beams prestressed by web drawing was formulated. The subject of study is structural steel. The object of study is bimetallic steel beam prestressed without rods.Materials and methods. The scientific inquiry is based on the basics of structural mechanics of buildings and structures: superposition principle, differential equation of deflection curve of a bar, energy method, and methods of determination of stress-strain state of prestressed steel bars.Results. A comparative analysis of vibration reliability of non-prestressed beams and prestressed structures of equal bearing capacity was performed. Rotations of the beam supporting nodes loaded by prestressing forces and external impacts were determined by integration of differential equation of deflection curve of a split bar. The support moments in rigid supporting nodes of structures were determined on the basis of superposition principle. The developed methods of stressed condition of prestressed bars are the basis for determination of normal stresses in the sections of beams under study. The resultant stresses were obtained by algebraic addition of prestresses and stresses from external loads. Dynamic parameters of bearing capacity of beams were determined on the basis of works by I.M. Rabinovich and V.A. Kiselev. The oscillation circular frequency of conventional and prestressed beams was established, analytical expressions for determination of angular velocity of prestressed bending elements were formulated, and the dynamic deflections and factors of structures were determined. It is found that the circular frequency of prestressed beams hinged in supporting nodes compared to the circular frequency of conventional beams decreases by a factor of 1.4 and by a factor of 5.6 in beams with rigid supports. Angular velocity decreases by a factor of 1.4 (hinge supports) and 6.8 (rigid supports), respectively. The deflections of prestressed beams are reduced by a factor of 1,87: 11,9. There is a significant reduction in the stressed condition of prestressed structures.Conclusions. A hinged traditional beam under external and vibration loads in limit state is in the material yield zone and does not meet the first and second limit state conditions. These structures have the lowest vibration reliability. Prestressed structures are more reliable. With rigid supporting nodes, the moments of prestressing forces coincide with the supporting moments and produce hogging with the vector opposite to the external load deflection vector. In the limit state, total deflections are less than the external load deflections. Stresses in the structure decrease. Since load moments and beam deflections are initial parameters for dealing with dynamic strength tasks, we may state that prestressed beams with rigid supporting nodes have an increased vibration reliability.

Study on Crack Resistance and Calculation Model of RAC Beams Strengthened with Prestressed CFRP

With the development of recycled aggregate concrete (RAC), the recovery rate of construction waste is improved, and the pollution problem is alleviated. In particular, RAC beams strengthened with prestressed carbon fiber reinforced plastics (CFRP) can exhibit improved mechanical properties, expanding RAC application. Four groups of reinforced RAC beam specimens contained 0%, 40%, 70%, and 100% recycled coarse aggregate, respectively. Each group of beams was first pre-cracked and then strengthened by prestressed CFRP with one layer and two layers respectively. Finally, the bearing capacity tests were performed for these beams. The test results show that as the recycled coarse aggregate content increases, the cracking moment and ultimate load capacity of the beam decrease, while its crack width increases. As the CFRP layer increases, the deformation and crack width of the beam decreases, while the number of cracks increases. The prestressed CFRP also exhibited tensile and peeling failure. A beam deflection calculation model was established by introducing a coefficient k representing the interaction between recycled aggregate and CFRP. The influence coefficient of concrete elongation on the crack width and average crack spacing of the beam was modified, and the crack width analysis model of the beam was established. The calculated results are in good agreement with the experimental observations. It can provide reference for the application and design of recycled concrete beams strengthened with prestressed CFRP.