Steel Shapes Research Articles

Punching Shear Capacity of RC Flat Slabs with Steel and Superelastic Ni-Ti Shape Memory Shear Reinforcement under Repeated Loads

Flat slab systems are a popular choice among engineers because of their numerous advantages, such as reduced building height, flexibility in spatial layout by eliminating the need for beams, and cost savings. However, Brittle slab failure under punching shear presents a considerable challenge. The primary objective of this study was to examine how flat slabs respond to PS and conduct an experiment using steel and superelastic Ni-Ti shape memory alloy (SMA) bars as shear reinforcement to assess their effectiveness in improving the PS capacity of flat slab-column connections under vertical Repeated load. Nine half-scale samples were tested, consisting of 1100 × 1100 × 120 mm slabs with a protruding column from one side of 150 × 150 mm and 400 mm height. The factors considered in this research were the type of materials, spacing between stirrups, stabilization method, and inner RFT. After that, finite element analysis by using ABAQUS 6.14 was developed to simulate all the tested specimens. The finite element analysis showed identical results compared to the experimental ones concerning energy absorption, load capacity, absorbed energy, and model stiffness. According to the experimental and finite element analysis findings, the flat slab reinforced with inclined stirrups exhibited a significant increase in punching strength, ranging from 28.8% to 51.3% compared with the control specimen. The stiffness increases by 8.5% when the distance between stirrups is reduced to 0.5d, and inclined-shaped memory alloy stirrups are employed.

Experiments and FE Modeling on the Seismic Behavior of Partially Precast Steel-Reinforced Concrete Squat Walls

This paper proposed an innovative precast steel-reinforced concrete (PPSRC) squat wall to simplify on-site construction. In PPSRC squat shear walls, the hollowly precast RC wall panel can be assembled on-site through the pre-erected steel shapes, and the boundary cores will be filled using fresh concrete together with the slab system. The seismic performance of PPSRC squat walls, influenced by different construction techniques (cast-in-place vs. precast) and steel ratios, was examined through pseudo-static experiments on three specimens. Some key performance indicators, including hysteretic behavior, skeleton curves, stiffness degradation, energy dissipation, and load-carrying capacity, were analyzed in detail. The test results indicated that all the PPSRC squat walls failed in typical shear failure, and no significant slippage between the precast and fresh concrete sections was observed during the loading process, indicating that the composite action could be fully achieved via the novel throat connectors. In addition, the PPSRC squat walls could achieve comparable seismic performance compared with that of cast-in-place SRC shear walls (the peak load of the PPSRC squat wall only increased by 0.26% compared with the control specimen), and the load-carrying capacity and deformability could be enhanced by increasing the steel ratio in the boundary elements. Finally, an elaborate finite element model was developed and validated using ABAQUS software. The parametric analysis of the concrete strengths of precast and cast-in-place parts and the axial load was conducted further to investigate the seismic performance of PPSRC squat walls.

Study on fatigue performance and topology optimization of cast steel bifurcation joint under alternating load

Abstract The numerical simulation analysis of a typical cast steel bifurcation joint under the alternating load was performed to comprehend its mechanical properties. The MSC Fatigue is used to explore and analyze the fatigue behavior of joints, and the control variable approach is used to examine the impact of various geometric parameters on fatigue life. Then, the load spectrum and fatigue life were invertedly calculated and transformed into maximum stress constraints by converting fatigue limitations into stress constraints. Finally, the optimal shape of cast steel bifurcation joint under fatigue limitations was studied using topology optimization methods, intending to solve the lightweight problem while still fulfilling fatigue design requirements. The research results show that the intersection of the main and branch pipes is the fatigue weakest part of the whole joint, and the geometric parameters significantly affect the joint's fatigue performance. The topology optimization shapes of cast steel bifurcated joints are different under vertical and horizontal loads, indicating that different load conditions significantly impact topology optimization shapes. The topology optimization method can reduce the self-weight while maintaining fatigue performance.

A Study on Enhancing Axial Flux Motor Efficiency Using Cladding Core Technology

With the rise of eco-friendly policies, advanced motor technologies are being developed to replace fossil fuel-based engines in the mobility industry. Axial flux motors, known for their ability to reduce size and increase output torque compared to radial flux motors, require different materials and manufacturing techniques. Specifically, the production of complex stator cores and segmented magnets presents significant challenges, often leading to higher costs. To address this issue, soft magnetic composite (SMC) materials, which offer greater design flexibility, are being explored for use in stator cores. However, soft magnetic composite materials exhibit lower permeability and saturation flux density compared to laminated silicon steel, resulting in reduced output torque and efficiency. This paper investigates the effects of stator geometry on axial flux motor performance and explores cladding core technology, which combines soft magnetic composite materials with silicon steel. By conducting finite element method (FEM) analysis to evaluate the output torque and efficiency based on the shape of the silicon steel within the cladding core, this study proposes an optimized cladding core design to enhance the efficiency and output torque of axial flux motors.

Shear Connectors Behavior Under Elevated Temperature: A review

A composite member is described as a structural steel shape that has been built up or rolled and filled with concrete, covered in reinforced concrete, or structurally attached to a slab of reinforced concrete. The shear connection between the steel beam and the concrete slab is the primary component of the composite beam. In risky situations, like building fires, the performance of a composite structures and steel structures are heavily dependent on the execution of connection. Numerous kinds of shear connectors exist and being utilized in the construction engineering rendering to their use. This paper reviews research conducted in the past years on the performance of shear connectors such as (ASTM A325 bolts, channel shear connector, T, T-mass and T-Proband shear connectors) exposed to raise heat degree. This research covers the experimental testing of push-out specimens, behavior of connectors in steel structures, various shapes of shear connectors under elevated temperatures, main failure modes, finite element modeling of shear connectors, design approaches offered by investigators, and various codes. Compared to the size of work available on shear connectors at room temperature, relatively slight research has been done on the conduct of shear connectors (studs) under high temperature. In addition, this report indicates several topics that need further investigations. Through this article, it was concluded that when temperatures raise, the strength of all shear connectors decreases proportionally regardless of its shape and type. A comparative study showed that the channel connectors are an economic and reliable option to standard shear connectors. Among the findings of some studies is that the effect of temperature on the shear resistance of head stud connector is significantly above 400℃, whether the test is done at temperature or post temperature conditions. Also, adding some materials to the concrete mix such as carbon nanotubes will be not effective on the ultimate shear at temperatures less than 400 ℃, but it reduces the spalling and cracking of the concrete. In general, the influence of elevated temperatures on the ultimate shear capacity of the headed stud connector is noticeably clearer when the test was conducted at exposed to certain temperature compared to post temperature conditions (the test is conducted after exposure the specimen to heat and cooling).

Effects of different corrugated rolls on the performance of BTW1/Q345R composite plate

Abstract BTW1/Q345R composite plate not only has the advantages of high strength and high wear resistance, but also helps to reduce energy consumption and production cost. This paper proposes a novel rolling process based on corrugated rolls for the preparation of wear-resistant steel BTW1/Q345R composite plates. In order to analyze and study the microstructure, and mechanical properties of BTW1/Q345R composite plates after rolling, techniques such as electron backscatter diffraction (EBSD) were used. The results indicate that the composite plate obtained through rolling with the corrugated roll of 72 cycles (3# corrugated roll) exhibits a yield strength of 550 MPa, tensile strength of 705 MPa, elongation at break of 17.57%, and shear strength of the composite interface at 242 MPa. Notably, the rolling process with a 3# corrugated roll yields the best combination of tensile mechanical performance and interface bonding performance for the composite plate.

Experimental-Numerical Assessment of Mechanical Behavior of Laboratory-Made Steel and NiTi Shape Memory Alloy Wire Ropes

The mechanical behaviors of laboratory-fabricated steel and superelastic shape memory alloy (SMA) wire ropes are assessed in this study through a comprehensive approach encompassing both experimental investigations and finite element (FE) numerical simulations. The assessment of steel wire ropes involves experimental scrutiny under sinusoidal cyclic loading and natural earthquake loading conditions. In parallel, SMA wire ropes’ behaviors are analyzed utilizing FE simulations employing the widely acknowledged ABAQUS software version 2020. The validation of all numerical simulations is undertaken against the experimentally observed behaviors. Moreover, full-scale steel wire ropes are subjected to shaking table tests to validate the simulations, facilitating a comparative analysis between the mechanical responses of SMA and steel wire ropes. The findings demonstrate that SMA wire ropes exhibit superelastic behavior akin to SMA wires, with marginal variations in overall response observed across distinct configurations, akin to steel wire ropes. Furthermore, augmenting the helix angle of SMA wire ropes results in reduced stress and increased strain when exposed to the El Centro earthquake scenario. Nevertheless, the mechanical response of SMA wire ropes closely mirrors that of a single wire.

Study on deformation-induced martensitic transformation behavior of 304 and 316 stainless steels

In this paper, the deformation-induced martensitic transformation behavior of 304 and 316 stainless steels is studied. The results show that martensitic transformation occurs in both 304 stainless steel and 316 stainless steel. With the increase of the strain, the martensitic transformation of the stainless steel samples increases, but the 304 stainless steel increases more significantly. The external shape of stainless steel has a certain influence on martensitic transformation behavior, and the martensite content of bar-shaped stainless steel is lower than that of plate-shaped samples under the same strain. The study results can provide technical guidance for the selection of stainless steel materials in the power grid.

Evaluation of recycled galvanised steel as a resource for Zn production

The high reduction potential of zinc has enabled its extensive use in the steel industry as a protective galvanising coating. Galvanising, which consumes approximately 50-60% of the global production of zinc, significantly increases the life span of steel products and contributes towards addressing the costly global problem of corrosion. While there does not appear to be a readily available and agreed-upon annual quantity of galvanised steel produced, it has been estimated by the authors to be 320-390 Mt/a (equating to 15-20% of the annual steel production). Due to the various methods employed to galvanise steel and different steel shapes which are coated, there is no clarity on the average percentage of zinc which galvanised steel is comprised of. However, a zinc content of between 1.5-2.5% appears to correlate with the estimated annual galvanised steel production.The reprocessing of secondary zinc streams is becoming increasingly important due to legislation changes and increased consumer demand for recycled and low carbon metals. Within the steel industry this will include the recycling of galvanised scrap steel, using primary process routes, as well as the re-processing of waste streams, such as steel dusts, using additional technologies such as the Waelz kiln. Zinc associated with galvanised scrap steel would exclusively report to these dusts, and thus represents a key resource for recycled zinc.Although there are two main steel process routes preceding the galvanising process, the focus here is on the Electric Arc Furnace (EAF) process route due to its ability to incorporate high levels of secondary (zinc containing) steel feeds, and the dust produced typically contains economically recoverable levels of zinc. EAF dust production is estimated between 5-10 Mt/a at a zinc content of 10-36%. Failure to recover this zinc would represent a loss of 0.5-3.6 Mt Zn/a to waste. The Waelz kiln is the most prominent technology utilised to recover Zn from EAF dust. However, this process requires additional energy, and thus the associated carbon footprint needs to be included in the evaluation of the potential of Waelz oxide as a secondary Zn resource. To this end, model analysis of a simplified Waelz kiln using the HSC simulation software shows that the carbon footprint associated with the processing of EAF dust ranges from 4-12 kg CO2/kg Zn dust at 10 wt.% Zn in the dust to 1-4 kg CO2/kg Zn at 35 wt.% Zn in the dust.

Innovative hybrid CFRP composite and Fe-SMA bonded systems for structural glass flexural strengthening

Contemporary architecture is increasingly embracing the use of structural glass for challenging applications. Glass industry has been adopting thermal toughening and lamination as advanced techniques to enhance tensile strength and avoid sudden failures. However, unexpected failure persists and hinders a more widespread application of glass, including as a structural material. Researchers have tested alternative glass composite systems, integrating reinforcements like steel, fiber-reinforced polymers (FRP), or iron-based shape memory alloy (Fe-SMA). This study explores an innovative concept that involves the simultaneous application of CFRP and Fe-SMA reinforcements via near-surface mounted (NSM) or externally bonded reinforced (EBR) techniques for glass strengthening. This system is shown to effectively prevent premature debonding, enhance post-cracking response, and ensure ductile failure modes, while being simple. Bending tests on large-scale laminated glass beams were performed to characterize the effectiveness of the system, while also the benefits of post-tensioning were investigated by inducing different prestressing levels in the glass strengthened elements. The paper first highlights the advantages of Fe-SMA reinforcements in glass composite systems through experimental evidence, followed by exploration of the proposed innovative hybrid CFRP composite and Fe-SMA bonded systems.

Elastic and inelastic major-axis flexural buckling of cellular steel columns

This study investigates the elastic and inelastic major-axis flexural buckling of cellular steel columns. Based on the stationary principle of potential energy, the existing elastic buckling load equation is refined to incorporate the local bending deformations at web posts. The column strength curve for determining the critical loads is then derived. For the elastic buckling, the refinement provides a significant improvement. For the inelastic buckling, the effects of residual stresses and initial geometric imperfections on the column strength are examined by the validated nonlinear finite element (FE) models. The initial geometric imperfection amplitudes of L/300 and L/500, where L is the column length, are recommended for global buckling of cellular steel columns fabricated from the parent steel shapes with h/b ≤ 1.2 and h/b > 1.2, respectively, where h/b is the depth-to-width ratio of the parent steel shapes. The developed column strength curve conservatively predicts the major-axis flexural buckling strength of practical cellular steel shapes, with an average prediction-to-FE buckling stress ratio of 0.97. A comparison also shows that the current EC3 and AISC360 equations are applicable for predicting the strength of practical cellular columns, provided that the refined elastic buckling load is adopted.

Study on the protection mechanism and damage grade prediction of different corrugated steel‒concrete composite structures under underwater contact explosion

Considering that corrugated steel has a certain anti-explosion protective effect, the influences of corrugated steel shape parameters on the protective effect of corrugated steel–concrete composite structures have not been considered. In this paper, the FEM–SPH coupling method is used to establish a simulation model of an underwater contact explosion wall panel. The numerical results are compared with the experimental results to verify the effectiveness of the simulation method. Furthermore, the underwater energy absorption effect, protection effect and influences of the wall panel of different composite structure protective layers on the damage process and failure mode are explored, the underwater explosion-proof mechanism is revealed, and the prediction curve of the damage grade of the wall panel is constructed. The results show that simulation results of the concrete slab front and back explosion surfaces are basically consistent with the experimental results. Under different composite structure protection schemes, the peak pressures of the composite structure protection schemes with 12-mm-thick corrugated steel and with 75° corrugated steel are reduce by 63.2% and 60%, respectively, relative to the noncomposite protection scheme, while the total energies of the corresponding composite structure are increased by 50.6% and 61.4%, respectively; the damage ranges of the wall panel are reduced by 83% and 81.6%, respectively. This finding shows that changing the corrugated steel shape parameters in the composite structure can effectively improve the energy absorption effect and reduce damage to the wall panel. The blast wave first propagates to the corrugated steel in the form of an incident wave and then propagates in the form of transmitted and reflected waves. Part of the wave propagates to the wall panel when the transmitted wave arrives at the corrugated steel lower surface, while the rest of the wave forms a reflected longitudinal wave and reflected transverse wave through reflection. Then, the transmitted wave acting on the wall panel attenuates. Under the protection schemes of the corrugated steel composite structure with a 12-mm thickness and corrugated steel composite structure with a 75° angle, the maximum protection rates are 63.2% and 60.0%, respectively, the energy consumption sharing rates are 69.48% and 66.26%, respectively, and the damage levels are moderate. The multiangle comparative analyses of different protection schemes suggest that the corrugated steel composite structure with a 12-mm thickness should be selected. The prediction curve can intuitively evaluate the influences of the quantity of explosive loads and the thickness/angle of corrugated steel changes of the composite structure on the damage to the wall panel. The research results can serve as a reference for the adhibition of underwater explosion protective engineering projects.

Influence of the Shape and Content of Steel and Aluminum Fibers from Industrial Lathe Wastes on the Physico-Mechanical and Rheological Behavior of Concrete

Abstract The recycling of waste in civil engineering is important as long as it reduces costs and protects the environment. In several countries of the world, different wastes have been used to replace cement or aggregates, such as mineral admixtures, powders and fibers. The aim of this work is to study the influence of fibers from factories and lathing workshops on concrete slump, compressive strength and 3-point flexural strength. The tests have been carried out on concretes containing different types of fibers: stretched steel fibers, fine steel fibers, looped steel fibers and looped aluminium fibers, in proportions varying from 1% to 3% by weight of aggregate. The results show that the behaviour of the concrete in the fresh and hardened state is different depending on the fiber type and content. Fiber distribution analysis was carried out to support the discussion of the results using Gwyddion software.

Effects of laser welding speed on the microstructure and microhardness of ultra-high strength steel S1100

Ultra-high strength steels strengthened via thermomechanical processing and low alloying constituents are currently quite popular for industrial applications. The popularity is primarily due to these steels being relatively economical compared with their high-alloy rivals, making them feasible to provide significant strength-to-weight ratios with reasonable costs in steel structures. However, welded joints in most steel structures cannot be avoided, and ultra-high strength steels, due to their thermomechanical strengthening mechanisms, are prone to loss of strength, toughness, or ductility after welding. Also, due to the ultra-high strength levels of the base metals, providing a suitable filler material with mechanical properties comparable to those of the base metals for filling the joint gap seems challenging. Accordingly, laser welding can be a relatively more suitable approach than arc welding to weld ultra-high strength steels, considering its easier control over the weld heat input, joint shape, and the possibility of welding without the requirement of filler metals. Therefore, this study investigates the influence of travel speed and its subsequent change in heat input of laser welding on the joint shape, microstructure, and hardness of the S1100 low-alloy carbon steel, one of the most commonly used ultra-high strength steels in modernized steel structures.

Linear and Nonlinear Dynamic Analysis of Reinforced Concrete Building with V Shape Steel Bracing

In this study, the RC-MRCBFs were used with V braced frame. The core objective of this examination is to understand the earthquake behavior of the RC-MRCBFs in steel V braced frames. Response spectrum analysis (RSA) is used to understand the seismic performance of the steel braced and un-braced RC frames. Total 12 steel braced RC frames and 12 un-braced frames for all 4 story, 8story, 12 stories and 16 stories are studied and observed the seismic parameter such as fundamental time period (FTP), top story displacements, inter-story drift, base shear and story stiffness of the structures. After studying the parametric study of the 4 to 16 story buildings with a linear and nonlinear analysis tool it was observed that to get the effective braced frame with expected failure mechanism, ductility, the columns should be designed such that, they resist at least 50% base shear contributions. It is observed that using the steel V bracing in the low rise to mid-rise buildings, improves the seismic behaviors of the structures. The steel bracing reduces the maximum top story displacements, drift and time period of the building and increases the seismic base shear demand, stiffness of the structures. The result shows that as increasing the base shear contribution in the columns, the drift and displacement of the story increases and base shear decreases. Key Words: Response Spectrum Analysis, displacement, Maximum storey drift, Storey shear, Storey stiffness, braced frame, RC buildings.

Hysteretic and rotational performance study of outwardly extending shape-steelprefabricated beam-column joints

This paper proposes fully-bolted extending shape steel prefabricated beam-column joints to achieve rapid construction and reliable connection of the precast reinforced concrete frame. The prefabricated component uses steel tube-concrete composite structures with outwardly extended shape steel, which achieves efficient installation and internal force transfer. Horizontal hysteresis tests were conducted on four components to determine the joint mode of failure and seismic performance index. The results show that the joint exhibits a “double plastic” failure mode, with plastic deformation occurring at the end of the reinforced concrete beam and buckling deformation at the shaped steel. Compared to cast-in-place joints, the new joints have a 30% increase in yield load, a 51% increase in peak load, an approximately 50% increase in initial stiffness, a 33% increase in equivalent viscous damping coefficient, and a ductility coefficient greater than 4.0. Analysis of strain showed that the stiffness of the connection area was too high, which will have a significant extrusion effect on the concrete at the end. Reducing the thickness of the steel plate in the joint space and weakening the shape stee by opening holes can significantly improve the rotational deformation capacity of the joint - further developing the plastic zone of reinforced concrete beams to improve the mechanical performance of the joint. Finally, the finite element model of the joint is established, and the numerical calculation is in good agreement with the experimental results. The research in this paper can provide technical support for the engineering application of the prefabricated joint.

Experimental and analytical investigation of WT‐shapes stiffened steel panel dampers

AbstractThe three‐segment steel panel damper (TSPD) is a type of shear panel damper (SPD) used for dissipating seismic energy. TSPDs consist of an inelastic core (IC) and two outer elastic joints (EJs), with the IC having a weaker shear strength than the EJs. Buckling restraining stiffeners delay shear buckling, and end stiffeners stabilize the IC to facilitate force transfer. However, the fabrication of TSPDs may be costly due to the use of built‐up shapes. This prompted the investigation of a more cost‐effective option, namely the WT‐shapes stiffened steel panel damper (WSPD). The WSPD can be built from a single hot rolled wide flange steel shape with four WT‐shapes cut from it. A practical procedure for seismic design using this method is developed in this study. The design procedure for IC web stiffeners is also considered. We propose elastic stiffness calculation methods for WSPDs, which match the analytical results of the proposed model using commercial software. Two full‐scale 2.6 m tall WSPD specimens were fabricated and tested. Different target IC buckling shear deformations of 0.08 and 0.12 radians resulted in two different stiffener designs for specimen WSPD‐0L2T and WSPD‐1L2T, respectively. The specimens had excellent energy dissipation performance. WSPD‐0L2T IC web buckled later than predicted, while WSPD‐1L2T IC web buckled slightly earlier than expected. The elastic lateral stiffness and maximum shear strength computed from the proposed procedures agree with the experimental results within 5%. The experimental responses of the two specimens can also be accurately simulated using Abaqus finite element model analysis.

Finite element modeling and design equations of partially steel-reinforced concrete beam-to-steel tube column joint

Steel reinforced concrete beams are increasingly used as novel transfer structures in high-rise buildings. In this paper, numerical and theoretical studies were carried out on a novel joint of steel-reinforced concrete beam and steel tube column, in which the beam was reinforced by a short steel beam with partial length. Based on the previous experimental studies, finite element modeling was performed to consider the evolution of the concrete damage and to investigate the effects of the main design parameters on the seismic performance of the new joint. It was found that the length of the steel shape, the thickness of the concrete cover, and the concrete compressive strength have significant effects on the initial stiffness and peak capacity of the new joint, while changing those parameters may not change the failure mode of the joint. A theoretical analysis was performed to establish an analytical model for the shear capacity of the new connection that takes into account the contributions of the steel web, stirrups, and concrete. The model was verified against the database of experimental and numerical analysis results. Design equations and recommendations for checking the flexural and shear strength of the embedded steel shape, the composite beam and the RC part of the beam were also provided.

Test and design of rectangular steel-reinforced concrete-filled stainless steel tubular short columns

In this study, the compressive behaviour of rectangular steel-reinforced concrete-filled stainless steel tubular (SRCFSST) short columns was investigated. Compressive tests on 10 rectangular SRCFSST stub columns and 2 rectangular concrete-filled stainless steel tubular (CFSST) counterparts were performed to study the effect of steel ratios and steel sectional shape on the compressive performance of SRCFSST short columns. Compression test results showed that the rectangular SRCFSST column has higher carrying capacity, deformability, and ductility than the rectangular CFSST column. A refined finite element (FE) model of the rectangular SRCFSST stub column was created. According to the FE study, adding carbon profiled steel to rectangular CFSST significantly improved confinement of concrete. Thus, ductility and bearing capacity of the composite column were greatly improved. The carrying capacity, peak strain, and compressive stiffness of the rectangular SRCFSST short column were evaluated using FE parametric analysis. Finally, design methods of the carrying capacity, peak strain, and compressive stiffness of the SRCFSST short column were recommended or refined.

Experimental and numerical study on seismic behavior of partially steel-reinforced concrete beam-to-steel tube column joint

Steel-reinforced concrete (SRC) beams are commonly used in the transfer structures of high- and super-high-rise buildings since concrete-encased steel elements have good resistance to buckling and seismic performance. However, the full-length steel shapes utilized in SRC beams are ineffective and pose many construction challenges. This study proposes a new steel-reinforced concrete beam-square steel tube (SST) column joint in which the SRC beam is embedded with a partial-length steel shape. Experimental tests are conducted on three joint specimens with varying cross-sectional dimensions of the SRC beam and lengths of the steel shape. The experimental results show that all the specimens exhibit good deformation, load-carrying capacity, and stable hysteresis responses. The three specimens demonstrate a considerable strength drop at drifts exceeding 5%. Besides, significant plastic deformation occurred at the column base region and in a limited region of the steel beam flange near the beam-column joint. Finite element models are developed to study the effects of single-side steel length, shear stud spacing, and thickness of beam concrete cover on the seismic performance of the proposed joint. The elastic deformations that caused the total column drift were theoretically analyzed. The predicted joint initial rotational stiffness using the proposed equation agrees well with the test and numerical results. The study’s limitations are also discussed.