Connection Stiffness Research Articles

A Review of the Degradation Research on the Single-Lap Bolted Joint

Bolted joints, with their advantages of simple structure and convenient disassembly and assembly, are widely used in complex equipment fields such as aerospace systems and weaponry. Subject to complex mechanical loads, the contact surfaces may undergo nonlinear behaviors such as contact–separation and viscous slip, leading to the nonlinear degradation of the connection stiffness, which severely threatens the safety and reliability. These have driven research on bolted joints to span multiple disciplines, from interfacial micro-friction to macro-structural dynamics. Therefore, from the field of micro-friction to macro-dynamics, this review summarizes and analyzes three major degradation models, outlines the experimental development in connected structures, and provides an overview of the numerical analysis methods for degradation simulation. This paper also looks forward to the development directions for future research on the degradation of connected structures.

An efficient framework for design optimization using parametric reduced order modeling in a virtual prototyping phase

Virtual Prototype Assembly is a tool enabling the virtual assembly of components, the prediction of noise and vibration performance, and the evaluation of component modification scenarios. FRF-based substructuring is the technique used to assemble the components, either obtained from experimental measurements or numerical simulation models. However, numerical simulations of components can be time-consuming, especially when exploring several component design modifications of large models. The paper proposes a framework combining Virtual Prototype Assembly with a parametric Model Order Reduction technique for vehicle design optimization. The proposed parametric Model Order Reduction technique generates a Reduced Order Model of a component maintaining an explicit dependency on material parameters and properties, such as: Young's Modulus, density, Poisson coefficient, connection stiffness, etc.. This enables fast and efficient simulation of components designs without the need of recomputing numerical models, thus streamlining the component design optimization process. The effect of component design modifications will be assessed at the predicted target vibration levels on an academic application case.

Group resistances of tensile-loaded anchored-bolted connections with CFST columns: Tests, simulations, and theoretical models

The performance of the connections in concrete-filled steel tubular (CFST) columns fabricated with a group of two anchored blind-bolts under tensile forces is evaluated. Based on the bolt group arrangement, two sets of experiments, comprising eight full-scale specimens, were tested. Test parameters include the presence of concrete, bolt anchorage length, pitch distance, and gauge distance. Further, numerical models were developed, which, after validation, were used for parametric studies. Key findings indicate that bolt gauge distance, anchorage length, concrete grade, and column cross-section slenderness significantly influence the connection behaviour, but pitch distance has the least influence. Tube and concrete failure modes, as well as critical gauge and pitch distances, are identified, which govern tube deformation and concrete crushing zones. Finally, a bi-linear theoretical model is developed that can provide a fair prediction of the connection strength and stiffness.

Sensibility Analysis of Traditional Span Frame

ABSTRACT Traditional timber frames may have a complex mechanical behavior regarding to today engineer skills and design standards. For an identical rebuilding as required for the Notre-Dame de Paris Cathedral, accurate modeling must be performed to assess modern reliability. Identical rebuilt means same green oak material, same geometry and timber connections. In the context of the rebuilt of the Notre-Dame carpentry, a part of the timber frame based on the original schemes of the nave extracted from historical graphic document was reproduced. A full-scale replica was erected in order to perform mechanical tests. Through an in-situ monitoring, this structure represents a case study in order to provide data relative to the kinetics of displacements. This investigation allows to evaluate the global behavior of the structure. Based on the finite element method (F.E.M), a dedicated model is used to analyze the sensitivity of the material properties, the beam geometry and the wood-to-wood connections in order to design the testing carried out on the wooden structure. From these full-scale tests, we determine the real stiffness of the carpentry. Then, a retro-analysis was proposed to evaluate the axial stiffness of connections according to the corresponding finite element model, by fitting data to reproduce the real displacements. The study reveals that this property is substantial to describe the global behavior. Furthermore, we carried out in the laboratory an experimental campaign consisting in characterizing traditional joints. The goal was to estimate their stiffness and their specific failure modes by using image correlation. Concomitantly, numerical simulations were developed in order to investigate the dependence of the stiffness according to moisture content variation of oak species. The global research supplies useful tools and results, which may be able to improve the understanding of the mechanical performance of traditional structures and provide valuable information for design purposes.

The Impact of the Polymer Layer Thickness in the Foundation Shim on the Stiffness of the Multi-Bolted Foundation Connection

The Impact of the Polymer Layer Thickness in the Foundation Shim on the Stiffness of the Multi-Bolted Foundation Connection

Experimental investigation on shear behavior of double-row perforated GFRP rib connectors in FRP-concrete hybrid beams

Perforated GFRP rib (PFR) connectors have been used in FRP-concrete hybrid beams due to durability and ease of construction. PFR connectors are parallel FRP plates with predrilled holes positioned in the flange of FRP beams. The optimal plate spacing needs to be determined because it affects the shear performance of PFR connectors. 18 push-out tests were conducted to investigate the effect of plate spacing ( Sl), penetrating GFRP bar diameter ( d), and concrete strength ( fc) on the failure mode, capacity, and shear load-slip (P-S) curves of double-row PFR connectors. Results showed that PFR connectors suffered plate shear failure with the concrete dowel undamaged. Typical P-S curves consisted of micro-slipping and significant-slipping phases. The shear capacity and stiffness of PFR connectors were improved by 33.3% and 45.1%, respectively, by increasing the plate spacing from 1.2 h (where h denotes the plate height) to 3.2 h. The effect of plate spacing on shear capacity and stiffness could be neglected if the ratio ( Sl/ h) was more than 3.2. Specimens with a larger diameter of penetrating bar and higher concrete strength demonstrated higher capacity and stiffness. An empirical equation based on the maximum stress failure criterion was proposed to estimate the capacity of PFR connectors, considering the plate spacing effect, and verified by available data. Additionally, a description of the P-S curve was developed and calibrated by the experimental results.

Lateral stiffness of modular steel joint with semi-rigid bolted intra-module connection

In contrast to the beam-column joints found in traditional assembled steel structures, modular steel structures feature inter-module and intra-module connections within their joints. While existing research has largely focused on the mechanical properties of inter-module connections, the impact of intra-module connection stiffness on the performance of modular steel joints remains unclear. This study introduces a novel corner-fitting-reinforced fully bolted joint specifically designed for modular steel structures. A series of experiments were conducted, including a flexural test on bolted intra-module connection to determine its initial rotational stiffness, and four groups of lateral static tests on full-scale modular steel joints with varying intra-module connection stiffnesses. These tests aimed to characterize mechanical properties such as load-carrying capacity, lateral stiffness, strain development, and ductility. The study elucidates the influence of intra-module connection stiffness on the lateral stiffness of modular steel joints. Furthermore, a refined finite-element (FE) model of the corner-fitting-reinforced fully bolted joint was developed. Simulation results showed good agreement with experimental findings., with an average error of less than 10 % for ultimate load-carrying capacity prediction. The FE model also, analyzed the stress-strain development of the corner fitting throughout the process. The study establishes a theoretical analysis model for the corner-fitting-reinforced fully bolted joint and derives a theoretical formula for the initial lateral stiffness of the modular steel joint, considering semi-rigid intra-module connections. This formula aligns well with both experimental and FE results, with a maximum error of 15 %. Finally, the study delves into the force-transfer mechanism of the corner-fitting-reinforced fully bolted joint, providing valuable insights for its design.

Characterization of inter-panel connections in CLT floors using finite element model updating

Large cross-laminated timber (CLT) floors are inevitably composed of multiple CLT panels assembled on the construction site. Due to the sheer lack of adequate numerical characterization of the inter-panel connections, CLT floors are normally modelled as monolithic structures or independent “piano keyboards”, yielding errors between simulated and the actual vibration response. This paper presents a benchmark study for a deterministic finite element (FE) model updating of so called “an equivalent elastic strip” representation of the inter-panel connections. Fitting modelling parameters of the strip, i.e. its width and material properties, featured FE modelling and modal testing of two full-scale CLT floors composed of one and two panels connected with a half-lapped joint. The floors were made of (almost) identical panels and placed on elastic mats along their shorter edges. First, the single-panel floor was used to fit material properties of the timber and the boundary conditions. Then, the FE model updating (FEMU) of two-panel floor yielded the actual values of the strip modelling parameters. Finally, these were successfully verified by direct comparison between numerically calculated and experimentally measured modal properties of a full-scale model of a simply supported three-panel floor. The results implied that the rotational stiffness of the inter-panel connection depends strongly on its vertical vibration displacement. Consequently, values of the rotational stiffness derived from rare static tests published so far cannot be used reliably in a much subtler vibration response analysis. Future studies should feature other types of the inter-panel connections in various floor layouts and a probabilistic FEMU.

Experimental and numerical study on behavior of demountable T-shaped bolt shear connectors in sustainable composite beams

This paper proposed a new type of demountable T-bolt shear connector to improve the disassembly efficiency of composite beams and realize the sustainable of the structure components. The shear behavior of nine groups of push-out specimens was experimentally investigated through monotonic loading push-out tests. The finite element analysis (FEA) models were validated against the test results, specifically in terms of the load-slip responses and failure modes of the T-bolt shear connectors in these push-out specimens. The obtained results show that all the specimens have no obvious deformation and cracks in the steel beam and RC slab. The separation between the slab and the steel beam is no more than 1 mm, indicating that the anti-lifting ability is excellent. Moreover, parametric analysis demonstrates that increasing the bolt pretension of the T-shaped shear connector and the friction coefficient between the bridge gasket and the steel beam significantly enhances the initial stiffness and ultimate strength of the shear connectors. However, the shear behavior is relatively insensitive to variations in the channel thickness and bolt grade. Based on regression analysis, a load-slip mechanical model has been proposed. This model accurately describes the mechanical properties of this type of shear connector, providing a theoretical foundation for the application of demountable composite beams.

Timber-timber composite (TTC) joints made of short-supply chain beech: Push-out tests of inclined screw connectors

This paper presents the results of experimental investigations on six-layered, homogeneous glulam beams made of Italian short supply chain beech (Fagus sylvatica L.). At first, the beams were produced and mechanically characterized for bending, then, they were employed to realize timber-timber composite joints and tested under quasi-static monotonic loading. The test configurations were adopted to reproduce connections used in timber-to-timber composite structures for applications in new constructions. Outcomes in terms of connection stiffness, strength, static ductility and failure modes are presented and discussed. Moreover, the experimental stiffness were used to carry out analytical verification at the serviceability and ultimate limit states to extend the validity of the proposed screw and specimen’s configurations.

Research on the distorted similitude of bolt-connected coupled cylindrical-conical shells

The model similitude technique, which employs scaled-down models to reflect the dynamic characteristics of full-scale models, has garnered significant attention in the engineering field. The inability to establish geometrically scaled models due to excessively thin shell structures has led to similitude distortion. For bolt-connected coupled cylindrical-conical shells, the dimensions of bolts (connection stiffness) vary with the radial dimension of the structure, and the coupling effects between parameters further complicate the establishment of scaling laws. To address these challenges, the distorted similitude method based on bolt equivalent stiffness modeling is proposed. For the first four bending mode natural frequencies, distorted scaling laws for the length, radius, and their coupling under double distorted reduction are established. The theoretical prediction errors of these scaling laws for the prototype are found to be within 5.43 %, 2.31 %, and 1.12 %, respectively. Experimental results demonstrate that the prediction error of the coupled distorted scaling law for length and radius is within 5.37 %. In cases of small radii, large thicknesses, and long axial lengths of bolted joint shell structures, the distortion of bolt dimensions due to radial distortion cannot be overlooked. Moreover, if the bolted joint is located at the vibration mode node, the corresponding scaling law can disregard the influence of connection stiffness. This study realizes the establishment of distorted models for complex bolted joint shell structures and enhances the prediction accuracy of coupled scaling laws, thus holding significant engineering application value.

A Compendium of Research, Tools, Structural Analysis, and Design for Bamboo Structures

Bamboo is known for its ability to grow at a high speed, with strong sustainability indicators and remarkable strength properties. However, despite these qualities, the practice of designing bamboo structures is still in its early stages in many regions. This paper aims to review the current approaches to structural analysis and design for bamboo structures as found in the existing literature. Through this comprehensive review, this study seeks to identify existing research gaps and areas that require further exploration. The limited design philosophy for bamboo structures can be attributed to the scarcity of studies on the characteristics and mechanics of bamboo material. These findings highlight the necessity for more comprehensive guidelines and standards to enhance the structural analysis and design of bamboo structures. This study identifies gaps in the following areas: lack of consideration for bamboo fiber distribution, lack of guidelines for load parameters specific to bamboo structures, inadequate coverage of bamboo culm connections, inadequate coverage on connection stiffness, limited scope on connection types, and species-specific limitations in standards.

Bolt looseness localization with connection-stiffness-varying flange

Electromechanical impedance analysis is a traditional method to identify the occurrence of bolt looseness, but accurate localization of blot looseness is hard to realize on the flange. In this study, a flange model with bolt connection stiffness varying with position is proposed. The location of bolt looseness can be then determined from the impedance spectrum of the model since the uniformity and symmetry of the flange are broken. The analytic model is established to reveal the distinguishability of the eigenfrequency shifting characteristics when the connection stiffness at different positions changes. The frequency shifting sequence is extracted from the coupling impedance spectrum as a feature, and the correlation between the sequences corresponding to bolt looseness at different positions is low. The relationship between the sequence and the degree of looseness is highly related so that the unknown degree of looseness can be matched with the calibrated sequence to realize the localization of the looseness. Based on the distinguishability of the frequency shifting sequence, the connection-stiffness-varying model shows great potential in the field of flanges or other connecting structures for structural health monitoring and damage localization.

Exploration of the behavior and evolution features of beam-column joints with T-stub using the structural strain energy method

Based on the structural strain energy method, the work behavior of four T-stub connection joints under cyclic loading is analyzed to visualize their working behavior and failure evolution. The experimental strain data are modeled as generalized strain energy density (GSED) to characterize the structural stress state and the corresponding characteristic parameters, and the Mann-Kendall (M-K) criterion is formulated to determine the performance characteristic points (P and Q) of the joint Mj-Ej curves and to derive the starting point of structural continuity damage. Then, by analyzing the parameters of the joint working state (strain, deformation, joint energy dissipation, connection stiffness, bolt force and pry force), the trends of the joint stressing state curves before and after the critical loading are reflected. Finally, the feature point data interpolation (EDI) method is introduced to effectively expand the joint test data, visualize the change process of the strain/stress field, and deeply reveal the mechanical response mechanism and evolutionary degradation law behind it. The contribution of the above work is to quantitatively identify the P and Q characteristic points in the changing trend of the joint working state, to reveal the mechanical mechanism and the failure degradation law from the perspective of energy evolution, and to visualize the mutation of the field data before and after the P/Q using the EDI method, which is a generalized method that can be applied to the other progressive failure structures.

Stability analysis of sandwich double nanobeam-system with varying cross-section interconnected by Kerr-type three-parameter elastic layer

In this study, the endurable buckling load of the elastically connected parallel sandwich nano-beams with varying cross-sections is assessed. In this regard, a layered beam system consisting of two parallel axially loaded tapered sandwich nanobeams that are interconnected via a Kerr-type three-parameter elastic foundation is considered. The geometric properties are assumed to be changed exponentially along the length of the beam element. The governing equilibrium equations of the system are described by a set of three coupled homogeneous differential equations, which originates in the context of Eringen's non-local elasticity theory and Euler beam model. Then, the numerical differential quadrature technique is used to estimate the endurable axial critical loads. Eventually, a comprehensive parameterization research is performed to investigate the sensitivity of linear buckling resistance to tapering ratio, nonlocal parameter, stiffness of elastic connections, volume fraction exponent, and thickness ratio. The research work of the present study is novel, and the attained numerical outcomes can be used as benchmarks for future researches in this field.

Finite Element Analysis and Optimization of the Rotational Stiffness of Semi-Rigid Base Connection under Simultaneous Moment and Tension

The base connection is flexible, not fully pinned/fixed, implying a nonlinear moment–rotation relationship. This deviates from a linear response, where rotation is not directly proportional to the applied moment. Numerical investigations using the commercial software ABAQUS were conducted to analyze the steel base plate connections. The finite element (FE) models were verified against previous experimental results. Moreover, numerical findings of a comprehensive parametric investigation were conducted. The studied connections were examined with different configurations, including variations in the diameter, spacing, and number of the anchor bolts; the thickness of the base plate; and the applied axial force. The current study aims to use numerical results combined with the whale optimization algorithm (WOA) and classical genetic algorithm (GA) to derive a formulation for the moment–rotation (M-θr) relationship. The distinctive aspect of this formulation is that it aims to simulate the nonlinear rotational behavior exhibited by flexible base connections under combined moment and tension loads, while also considering various parameters such as bolt number/diameter and plate thickness. The findings indicate that the WOA is capable of obtaining an optimal equation for accurately simulating the M-Ɵr relationship. This underscores the ability of the WOA to effectively address the complexity of the problem and provide a reliable equation for predicting the rotational behavior of such connections. Consequently, the WOA method can be utilized to calculate the rotational stiffness at H/150, offering valuable support for engineering design processes.

Nonlinear modeling and vibration response analysis of rod fastening rotor-bearing system with curvic coupling

Rod fastening combined rotor system (RFCR) are particularly popular in gas turbine rotor systems. The bolted connection introduces a discontinuity in this RFCR, which has a substantial influence on system performance.Traditional models of RFCR tend to neglect the influence of the connection structure, especially failing to fully consider the contribution of the curvic coupling to the rotor dynamics. To address this problem, this study proposes a new nonlinear analytical model of the rotor system, which focuses on the impact of the curvic coupling. This study provides a detailed analysis of the structural parameters and load forces of the curvic coupling. Based on this analysis, a mechanical model is created to assess how bolt preload and torque impact the stiffness of the curvic connection. The stiffness matrix of the curvic coupling is derived by the gear stiffness analysis method, and the accuracy of the model is confirmed using the finite element method. Furthermore, the model also considers the viscous and sliding state between the curvic coupling, which effectively describes the damping effect of the curvic coupling. On this basis, the motion control equations for the RFCR are formed, and a dynamic model considering the curvic connection in the RFCR system is introduced. The results show that the curvic coupling results in a decrease in stiffness and the occurrence of nonlinear damping phenomena in the RFCR.The RFCR exhibits a significant stiffness loss compared to the continuous rotor system, resulting in a decrease in the critical rotor speed. The nonlinear damping is mainly excited at high friction coefficient conditions and may lead to a self-excited vibration component in the rotor response at supercritical speeds. The negative impact of structural discontinuities on rotor dynamic performance can be reduced by increasing the bolt preload, decreasing the friction coefficient, and adjusting the amount of imbalance. This study offers a theoretical foundation for predicting curvic coupling-induced instability and serves as a reference for enhancing rotor system stability.

Effect of solid blocking on lateral bracing requirements for cold-formed steel wall studs

The effectiveness of horizontal bracing in increasing the strength of cold-formed steel (CFS) load-bearing walls has been widely acknowledged. However, while significant research has been conducted regarding the bracing requirements for CFS bearing walls, the effect of solid blocking, which prevents columns (studs) within the wall from rotating, has not been fully explored. In this study, we propose an analytical method to quantitatively assess the effect of solid blocking on bracing requirements for CFS load-bearing walls. This method is comprehensive as it can be applied to systems with different bracing patterns, load patterns, or non-identical columns (studs), and it accounts for the columns’ initial curvature and semi-rigid end connections. It has been verified that considering the solid blocking always decrease the bracing requirements because the existence of solid blocking increases the system’s stiffness and subsequently decreases the additional displacement as well as the brace force, as expected. An example consisting of 23 CFS studs is presented to illustrate how the effect of solid blocking on bracing requirements is influenced by the location and interval of solid blocking, the stiffness of column end connections, and the characteristics of tie bracing. The results indicate that the effect of solid blocking on bracing requirements increases when the location of solid blocking is closer to the anchor and the solid blocking interval is smaller. Moreover, a modification to the equation in AISI S100 is proposed to account for the effect of solid blocking on the strength requirement of tie bracing. Overall, this research contributes to a better understanding of the role of solid blocking in CFS load-bearing walls and provides insights for optimizing bracing design in practice.

Testing novel hybrid inter-module joints for steel modular buildings under cyclic load

To bridge the gap between the unrealised disassembly and reuse potential of volumetric modular buildings and the lack for seismic resilience, a hybrid inter-module connection employing a high-damping rubber bearing was proposed to reduce the inelastic deformation in the members of the volumetric module. The cyclic behaviour of the proposed connection was previously investigated at connection level through validated proof-of-concept FEA, reflecting promising damping and re-centring capabilities. In this study, six in-plane cyclic loading tests on inter-module joints with the novel, hybrid inter-module connection were carried out to investigate the connection’s influence on the cyclic behaviour of steel modular buildings under lateral load at joint level. The tests focused on the contribution of the laminated elastomeric bearing to the joint’s lateral behaviour and the effect of different bolting assemblies on the working mechanism of the hybrid connection system. The standard FEMA/SAC loading sequence was employed on single-span, meso-scale joint prototypes with axial and in-plane lateral loading applied to the top post. The results showed that the hybrid IMJs exhibited nonlinear, multi-stage hysteretic responses, governed by the bending resistance of the bolting assembly and the stiffness of the intra-module connection. The aseismic performance of the joints was characterised by residual drifts below the permissible limit of 0.5 % up to 2 % drift ratio and high equivalent viscous damping during the low-amplitude cycles. Overall, the tests demonstrated the feasibility of the proposed connection with respect to the mitigation of damage in the structural elements of the volumetric modules after an earthquake, as proved by the low inelastic deformation recorded up to 4 % drift ratios.

Steel ribbed dome structural performance with different node connections and bracing system

The conventional design of steel structure objects relies on a first-order elastic analysis, where the entire object is treated as a set of individual structural elements requiring time-consuming, semi-empirical design calculations. Such an approach leads to inefficient design time and excessive material consumption and may additionally result in designing on the verge of structural safety. The AEC sector's technological and digitization advancement process forces designers to use advanced design methods. Hence, it is necessary to indicate the benefits of using effective optimization. The paper presents a comparative analysis of steel domes using two design approaches: traditional first-order analysis and an advanced second-order analysis. The latter method considers the influence of structural deformation on the magnitude of internal forces. Eight models were developed, varying in terms of the connection's stiffness. The work results identify the differences between the two selected design approaches and present opportunities for further structural performance of steel structures.