Stiffness Mode Research Articles

Varying the stiffness of Lamina Emergent Joint through origami and mortise-tenon structure

The variable stiffness joints can balance accuracy and safety compared to the single stiffness joints. To further explore the variable stiffness mode of Lamina Emergent Joint (LEJ), we designed a passive variable stiffness LEJ (PVS-LEJ) based on origami and mortise-tenon structure. Compared to the active variable stiffness flexible joints, the stiffness of PVS-LEJ can be adjusted according to load. This paper describes the working principle and design process of the PVS-LEJ in detail and explains the calculation process of block sizes. Then some simulation tests are conducted on the PVS-LEJ. The simulation results show that the contact between two blocks gradually failed in the high stiffness mode of the PVS-LEJ, and the stiffness deviated significantly from the theoretical calculation value. To address this contact failure problem, the PVS-LEJ is improved. The improved PVS-LEJ is also simulated, and the results indicate that the position where stiffness varies is the same as the design. The stiffness obtained from the simulation and theoretical calculation is consistent with each other, with an error of about 2%. Besides, some experimental tests are performed to verify the feasibility of PVS-LEJ. Finally, some problems encountered during the fabrication of PVS-LEJ are discussed, and appropriate suggestions are given.

Static test and theoretical study on semirigid pin joint for modular steel reticulated shell

SummaryIn order to realize the modularity and rapid assembly of steel reticulated shells in the construction site, a new type of simple assembled joint named semirigid pin joint is proposed for modular steel reticulated shell in this paper. While on the premise of meeting the stiffness and strength requirement, complicated procedures such as tightening nuts and controlling pretightening force are avoided in this joint. In addition, the joints can adapt to the complex curvature changes of reticulated shells. When it is connected in the middle of the member, the new joint can realize the connection of arc members. First, experiments were carried out on different screw rod diameters, wing plate pin diameters, and the number of wing plate pins. Different failure modes and M–Φ curves of semirigid pin joints were obtained. The stiffness and strength of the joints were studied. Second, a three‐dimensional finite element model of the joint was established by ABAQUS, and the comparison between the simulated results and the experimental results proved the accuracy of the finite element numerical analysis. On this basis, the antirotation stiffness, strength, and failure mode of the new joint with different parameters were compared and discussed, and the influence law of each parameter on the mechanical properties of the new joint was obtained. Finally, based on the power function model, a theoretical analysis model for estimating the M–Φ curve of the joint was established. Compared with the results of the experiments, the results indicated that the prediction formula has high accuracy.

Calibration and Validation of a Linear-Elastic Numerical Model for Timber Step Joints Based on the Results of Experimental Investigations.

The paper is dedicated to the numerical analysis of a single-step joint, enabling the prediction of stiffness and failure modes of both single- and double-step joints. An experimental analysis of the geometrically simplest version, the single-step joint, serves as a reference for the calibration of the subsequent finite element model. The inhomogeneous and anisotropic properties of solid timber make detailed modelling computationally intensive and strongly dependent on the respective specimen. Therefore, the authors present a strategy for simplified but still appropriate modelling for the prediction of local failure at certain load levels. The used mathematical approach is based on the linear elasticity theory and orthotropic material properties. The finite element calculations are performed in the environment of the software Abaqus FEA. The calibrated numerical model shows a good conformity until first failures occur. It allows for a satisfactory quantification of the stiffness of the connection and estimation of the force when local failure begins and is, therefore, recommended for future, non-destructive research of timber connections of various shapes.

Influence of cyclical hygrothermal aging on mechanical response and structural durability of composite bolted interference-fit joints

The paper deals with the long-term performance and durability of composite bolted interference-fit joints subjected to harsh environmental loads in flight-cycles. An accelerated cyclical hygrothermal aging spectrum with repeated temperature and moisture variation is specially designed to simulate real service condition. The single-lap composite joints with various stacking sequences, interference-fit sizes and tightening torques are aged in designed hygrothermal environments with different time duration, in which the material deterioration, stress relaxation and intrinsic frequency of joints are monitored to characterize structural evolution. Tensile tests are conducted to aged composite joints to obtain joint stiffness, bearing strength and failure modes to quantitatively evaluate their residual mechanical properties and structural degradation regulation. The results show that the moisture absorption rate presents a sharp rise and slow decent trend with a peek value of 0.213%. The aging process causes weathering phenomenon and reduces the structural benefits induced by such assembly technologies as interference fitting and bolt preloading. The reduction of joint stiffness and bearing strength exhibits a negative exponential decline trend with the growth of aging time. The matrix plasticization and interlaminar debonding are main hygrothermal damages. The safety factor of 0.7 to 0.8 is suggested on bearing strength value to reach hygrothermal aging bearing strength allowable in joint application.

Experimental Investigation on the Structural Performance of Mass Timber Panel-Concrete Composite Floors with Notched Connections

Mass timber panel (MTP)-concrete composite floors are gaining increasing interest from builders and designers due to their optimized structural performance, light self-weight, and aesthetically exposed wood ceilings. Among various connecting techniques between timber and concrete, notched connections made by cutting grooves on timber and filling them with concrete are considered as one of the most structurally efficient and cost-saving connecting solutions. Numerous ways of making and reinforcing the notched connections, however, hinder the standardization and development of the design guidelines for this type of connection, which reduces the competitiveness of MTP-concrete composite floors. In this study, experiments were carried out to investigate the performance of MTP-concrete composite floors with different connection designs. Nine composite floor specimens with varying span, connection number, notch depth, concrete thickness, and loading direction were designed and tested under bending. The bending stiffness, load-carrying capacity, ductility, and failure mode of tested specimens were studied and discussed. Test results show that the connection number, notch depth, and concrete thickness affect the bending stiffness and strength of the floor positively, an increase in floor span impacts the floor performance negatively, whereas the effect of a limited number of self-tapping screws in the notch is negligible. The study also shows that MTP-concrete composite floors with high strength, high stiffness, and good ductility can be achieved through the optimized design of notched connections.

Cyclic behavior of interior RC beam-column joints strengthened with NSM-CFRP ropes

Beam-column joints in existing concrete structures could become unsafe for many reasons, such as design error and seismic loading. Thus, in this study, the effectiveness of near surface mounted carbon reinforced polymer (NSM-CFRP) ropes for enhancing interior reinforced concrete (RC) beam-column joints was investigated. Five interior one-third scale RC beam-column joints without transverse reinforcement (stirrups) at the beam-column joints were tested under cyclic loading. The first specimen was tested as a control beam-column joint, while the four remaining beam-column joints were strengthened using NSM-CFRP ropes with a variety of CFRP rope configurations. Results were drawn based on hysteretic curves, envelope curves (load vs. drift ratio), energy dissipation, stiffness, ductility index and failure modes. The results showed that the stiffness and yield load of strengthened beam-column joints was improved compared with the control beam-column joint. The use of NSM-CFRP ropes resulted in an increase in the yield load of the strengthened beam-column joints ranging from 118.7% to 164.1% than the control beam-column joint depending on the NSM-CFRP ropes’ number and its position. The use of X- shaped rope with two ropes on each side of beam and two on each side of column imparted the best effectiveness on stiffness and yield load, for instance, the stiffness increased by 236.7% compared to control beam-column joint. Finally, the bond slip occurred between the rope and concrete; therefore, the rope was only effective before the drift ratio reached 1%-1.5%, therefore, the maximum load is only affected by the RC.

Effect of using Waste Rubber as Partial Replacement of Coarse Aggregate on Torsional Strength of Square Reinforced Concrete Beam

The aim of this study is to test the rubberized concrete beams subjected to pure torsional moments. The study focused on the effect of the partial replacement of coarse aggregates with waste rubber chips of different proportions 10%, 20%, and 30% in volume on the beams ultimate torque, and rotation, as well as the ductility index, stiffness, cracking torque, and failure modes. Six specimens of concrete beams as the same size (225×225mm) have been tested. The same steel reinforcement has been applied to four specimens and two without reinforcement. According to experimental findings for reinforced specimens, the ultimate torque for the control beam (without replacement) is higher than beams with replacement rubber but the angle of twist of beams with replacement rubber rose more than the control beam. the ultimate torque decreases compared with the control beam by 4.49%, 10.08%, 13.98%, while the twist angle increases at ultimate torque by 11.16%, 26.79%, 39.69% when the percentage replacement of rubber is 10%, 20%, 30% respectively. When coarse aggregate was replaced with 30% rubber, the ductility index of specimens increased by 39.83%, and ultimate cracking stiffness was lowered by 38.42% as compared with the control beam.

IMPROVED ANALYSIS OF A PROPPED CANTILEVER UNDER LATERAL VIBRATION

Continuous systems are sometimes analysed as lumped masses connected by massless elements. This reduces the structure’s degree of freedom and therefore simplifies the analysis. However this over simplification introduces an error in the analysis and the results are therefore approximate. In this work sections of the vibrating beam were isolated and the equations of the forces causing vibration obtained using the Hamilton’s principle. These forces were applied to the nodes of an equivalent lumped mass beam and the stiffness modification needed for it to behave as a continuous beam obtained. The beam’s stiffness was modified using a set of stiffness modification factors to . It was observed that by applying these factors in the dynamic analysis of the beam using the Lagrange’s equation, we obtain the exact values of the fundamental frequency irrespective of the way the mass of the beam was lumped. From this work we observed that in order to obtain an accurate dynamic response from a lumped mass beam there is need to modify the stiffness composition of the system and no linear modification of the stiffness distribution of lumped mass beams can cause them to be dynamically equivalent to the continuous beams. This is so because the values of the modification factors obtained for each beam segment were not equal. The stiffness modification factors were obtained for elements at different sections of the beam

Experimental and numerical study on the lateral torsional buckling of full-scale steel-timber composite beams

The lateral torsional buckling (LTB) of steel-timber composite (STC) beam with partial interaction was investigated in this paper. The composite beam is constructed by connecting the timber to both flanges of the H-shaped steel with bolts or screws. Twelve push-out specimens were designed to evaluate the shear performance of bolt or screw connectors. It was shown that the slip stiffness and the shear bearing capacity of the connectors increased with the thickness of timber increasing. Then, eight full-scale composite beams with lengths of 6000 mm were studied through bending tests and compared to a bare steel beam. The experimental behaviors of the specimens were identified, including the failure mode, load-deflection relationship and load-strain response. The LTB phenomenon and composite action were discussed by analyzing the strain distribution, stiffness and strength. The results demonstrated that the STC beams fastened with bolts or screws displayed partial composite action. Although the stiffness of the composite beam showed little augmentation, the maximum strength of the composite beam substantially increased by suppressing the LTB phenomenon. A finite element analysis was conducted to reveal the failure mechanism of the specimens with different geometric and physical parameters, including the number of timber layers, the interface shear stiffness and the initial imperfection. It was found that increasing the number of timber layers in the upper flange suppressed the lateral torsional buckling, and the interface shear stiffness was the key factor to control the stiffness and failure modes of STC beams.

Experimental assessment of different strengthening techniques for opening in reinforced concrete beams

The present experimental study includes testing thirteen reinforced concrete beams with openings at different locations to investigate the efficiency of strengthening such openings. Different strengthening techniques around the opening after and before casting include diagonal bars, upper and lower steel, and carbon fiber reinforced polymers (CFRP), were examined. All beams were made from 30 MPa compressive strength and tested under four-point loading. The cross section of the beams is 400 mm depth x 160 mm width and beam length 2400 mm. The dimensions of the opening are 200 mm x 200 mm. The stiffness, deflection, failure load, and failure mode of the strengthened beams were discussed. Experimental results showed that the beams strengthened with upper and lower steel around opening at mid-span increase the load-carrying capacity by 16.59%. However, beams strengthened by CFRP sheets around the opening in the shear zone increase the load carrying capacity by 47.7% compared to opened beam.

Numerical and theoretical studies on shear behavior of steel-UHPC composite beams with waffle slab

UHPC waffle slab was proposed to utilize the excellent material properties of UHPC and improve the rigidity of bridge deck. The flexural behavior of steel-UHPC composite beams with waffle slabs (SUCBWS) has been studied recently while the shear behavior of SUCBWS is still limited. This paper aims to supply the gap in the research system of mechanical properties of the novel bridge deck system. Based on the experimental study of four SUCBWS, a three-dimensional finite element model (FEM) was developed to investigate the shear behavior of SUCBWS. Extensive validations of the numerical analyses against the reported tests proved that FEM is reasonable. Meanwhile, the shear working mechanism of SUCBWS was analyzed. A subsequent parametric study was conducted to investigate the effects of shear span ratio, yield strength of steel, degree of shear connection, the ratio of rib height to top flat plate thickness and adding haunch at the rib-to-plate interface on the shear behavior of SUCBWS. Results show that shear span ratio and degree of shear connection present an obvious influence on ultimate bearing capacity, stiffness, ultimate deflection and failure mode of the composite beam. The shear span-to-depth ratio increased 1.34 to 3.14 resulted in a decrease in stiffness and shear strength while an increase in ultimate deflection. The increase of the degree of shear connection (from 0.5 to 1) improved the stiffness and ultimate bearing capacity but reduced the ultimate deflection. Adding the haunch at the rib-to-plate interface can significantly improve the integrity and decrease the risk of longitudinal splitting failure of the UHPC waffle slab. The high-strength steel can match well with the UHPC waffle deck so as to improve the ultimate bearing capacity of SUCBWS. The increase of the ratio of rib height to top flat plate thickness showed a limited influence on shear behavior of composite beams and the value of 3 is recommended for the design of SUCBWS. Meanwhile, the shear composite action coefficient, shear contribution coefficient of top flat plate and ribs were proposed to develop the theoretical models for predicting the shear capacity of SUCBWS and providing a reference for the design of SUCBWS. Besides, the effect of the haunch size at the rib-to-plate interface on the mechanical performance of SUCBWS should be further quantitatively analyzed.

Finite Element Model Updating Method of Dynamic Systems

The finite element model updating method of dynamical systems based on results of modal tests is proposed. The purpose of updating is to change eigenspectrum. The method alters a stiffness matrix by adding an updating finite element model created on the nodes of the intial one with respect to the existing links between the linear degrees of freedom. The stiffnesses of the updating elements are utilized as the updating parameters to be defined. The objective function equals to the least square weighted sum of residuals between the target, which were determined experimentally, and current values of modal stiffnesses. The iterative solution process is carried out. At each iteration step the conjugate gradient method is applied to solve the unconstrained minimization problem. The modeshapes, which were calculated as the result of solving the generalized eigenvalue problem at the previous iteration step, are employed to calculate the current modal stiffnesses. The method does not have a limit to a size of matrices and keeps their sparsity and symmetry. It provides the model updating of selected regions of a structure and step-by-step model updating of predefined groups of eigenfrequencies. Moreover, geometrical features of a structure, such as the presence of the symmetry planes and structurally identical elements, may be taken into account. The method is implemented into a program and verified by the example of the free dynamically-scaled model of Tu-204. In order to perform the ground vibration testing, the model was suspended with a low-rigidity flexible support. The finite element model made of solid elements has been updated on the basis of the six experimentally determined sets of eigenfrequencies. The target frequencies from each set have been achieved with a high level of accuracy.

Seismic design of plane steel MRFS, EBFS and BRBFS by improved direct displacement-based design method

An improved direct displacement-based design (DDBD) method for the seismic design of three types of plane steel frames, i.e., moment-resisting frames (MRFs), steel eccentrically braced frames (EBFs), and buckling-restrained braced frames (BRBFs) is developed. The improvement lies in the fact that it uses a MDOF equivalent system instead of a SDOF one used by the original DDBD method. Thus, higher modes and P-Δ effects are considered more rationally and with higher accuracy than in the conventional method. The proposed method employs deformation-dependent equivalent modal damping ratios and design modal displacements for the first few modes significantly contributing to the response, as functions of target inter-storey drift ratios representing various performance levels. Employment of a displacement design spectrum for high amounts of damping in conjunction with the equivalent modal damping ratios and design modal displacements can provide the required modal periods, the modal stiffness values, and the modal base shear forces. The design base shear force is obtained by a modal combination rule, such as the SRSS rule, and is distributed to the stories of the frame for member dimensioning. Numerical examples illustrate the method and demonstrate its advantages over the original DDBD method.

Load-sharing mechanism of piled-raft foundation: a numerical study

Responses of the piled-raft foundation are complex due to the combined working and the existence of load-sharing mechanism between piles and raft. A clear understanding of this mechanism leads to optimization of the design of the foundation. This paper presents numerical studies on the load-sharing mechanism characterized by the load-sharing ratio under using different numbers of piles and broad ranges of values of pile spacing, pile length, settlement of the piled-raft, and the depth of the raft base based on the finite element method constructed in PLAXIS 3D. The results show that the load-sharing ratio of the piled-raft increases significantly when increasing the value of pile spacing, the settlement of the foundation, and the depth of raft base, and decreasing the number of piles. This paper also introduces the stiffness modification ratios of piles and rafts. Interestingly, these stiffness modification ratios and the load-sharing ratio can be nicely collapsed on a master curve as a function of a dimensionless number which is defined as a ratio of pile stiffness and raft stiffness for each case of pile configuration. These scalings provide clear evidence for the unified description of the key parameters to control the load-sharing mechanism of the piled-raft foundation.

Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations

The Bayesian model updating approach (BMUA) benefits from identifying the most probable values of structural parameters and providing uncertainty quantification. However, the traditional BMUA is often used to update stiffness only with the assumption of well-known mass, which allows unidentifiable cases induced by the coupling effect of mass and stiffness to be circumvented and may not be optimal for structures experiencing damages in both mass and stiffness. In this paper, the new BMUA tailored to estimating both mass and stiffness is presented by using two measurement states (original and modified systems). A new eigenequation with a stiffness-modified system is formulated to address the coupling effect of mass and stiffness. The posterior function is treated using an asymptotic approximation method, giving the new objective functions with stiffness modification. Analytical formulations of modal parameters and structural parameters are then derived by a linear optimization method. In addition, the covariance matrix of uncertain parameters is determined by the inverse of the Hessian matrix of the objective function. The performance of the proposed BMUA is evaluated through two numerical examples in this study; a probabilistic damage estimation is also implemented. The results show the proposed BMUA is superior to the traditional one in mass and stiffness updating.

Optimality criteria-based minimum-weight design method for modular building systems subjected to generalised stiffness constraints: A comparative study

Recently, modular building construction has gained massive momentum as it continues to help many cities around the globe to tackle the ongoing housing crisis and the pressing demand for healthcare facilities during the pandemic. As a relatively new structural solution, there is a need to study modular buildings' optimal design. In this regard, previous studies focused only on employing optimisation techniques at the member level to enhance the structural capacity of steel beams in modular building systems (MBS). This paper explores the applicability and effectiveness of an optimality criteria (OC)-based minimum-weight design method in reducing self-weight of MBS while maintaining their overall lateral stiffness measured by natural frequency. This is achieved by pursuing an innovative optimisation investigation involving a three-storey, standalone MBS with hinged inter-module joints, together with a comparative moment-resisting frame (MRF) benchmark structure with two different beam-column connection rigidities. Continuous-valued sizing optimisation of two structural systems under a single frequency constraint is achieved through a novel, numerically stable, iterative OC algorithm. The latter is developed from frequency-related OC formulated rigorously through the Lagrange multiplier approach. The discrete minimum-weight design is supported by a mapping strategy designed to round the continuous optimum to the most economical standard steel sections. Pertinent numerical results show that the proposed method can achieve significant steel savings for the adopted MBS without compromising its modal stiffnesses. Further, it is found that the MRF structure with semi-rigid connections can meet the same target frequencies with slightly smaller steel tonnages. It is envisioned that this study will pave the way towards achieving more resilient and cost-effective modular units and tall modular buildings that further support the building industry in meeting its goals of construction efficiency and sustainability.

Geometrically Nonlinear Random Response of Stiffened Laminated Plates by Proper-Orthogonal-Decomposition-Based Reduced-Order Modeling

The geometrically nonlinear random vibration response of stiffened laminated plates under acoustic excitation is carried out by using the equivalent linearization (EL) technique combined with the reduced-order model and the finite element method. The nonlinear equations of motion of stiffened laminated plates are obtained based on large deflection finite element formulation. The proper orthogonal decomposition technique is used to select the modal basis, and a reduced-order model of the structures is established. Based on the force error minimization approach, the EL formulation for solving nonlinear random vibration response is derived. Then the EL technique is incorporated into finite element software NASTRAN by the direct matrix abstraction program, and the direct matrix abstraction program also realizes the iterative process of determining the modal equivalent linear stiffness matrix. Then, the statistical dynamic response results obtained by EL and linear method are compared and analyzed. It is verified that the proposed method has high accuracy and efficiency, and it can be applied to the geometric nonlinear random vibration response analysis of stiffened laminated plates. The results show that geometric nonlinearity plays an important role in the vibration response of stiffened laminated plates, especially under high sound pressure loads.

Shear behavior of short headed studs in Steel-ECC composite structure

Engineering cementitious composite (ECC) is a promising candidate as the overlay material of orthotropic steel bridge deck (OSBD), to improve the durability and extend the service life. The mechanical performance of short headed stud connectors in steel-ECC composite structure has been limited studied. This study investigated the shear behavior of short headed studs embedded in ECC through experimental push-out tests and validated finite element (FE) analysis. The experimental and analytical results were analyzed accordingly in terms of shear strength, shear stiffness and failure mode. The push-out testing results showed that the existence of natural interfacial bond was beneficial for improving the initial stiffness of the specimen. The FE simulation results agreed well with the experimental ones. Base on the validated FE model, a parametric analysis was then conducted to investigate the influence of the stud diameter, stud height, stud strength, corrosion of stud, and compressive strength of ECC on the shear capacity of short headed studs. The analysis indicated that the diameter and tensile strength of headed stud had a significant improvement on the shear strength of headed studs, while the stud height and compressive strength of ECC exhibited the opposite trend. The corrosion of stud drastically reduced the shear performance of headed studs in terms of shear strength and ductility. It was also observed that AASHTO LRFD specification overestimated the shear strength of short headed studs embedded in ECC, while the Eurocode 4 and Chinese code were relatively conservative.

Numerical analysis of in- and out-of-plane coupling effects on angle bracket connections in CLT structures

Angle bracket connections are commonly used to transfer shear loads in cross laminated timber (CLT) structures. In reality, these connections may experience multiple-direction loads simultaneously in the wind and seismic events. A two-phase numerical program was carried out to assess the coupling effect of biaxial loading on the performance of CLT wall-to-floor angle bracket connections. In phase I, a 3D finite element model of connections was developed using ABAQUS software and verified with the data from experimental tests previously carried out by the authors. In Phase II of the study, the verified model was used to simulate the performance of connections under three biaxial loads, i.e., in-plane shear and uplift, in-plane shear and out-of-plane outward shear, and in-plane shear and out-of-plane inward shear. The coupling effect on the performance of the connections was evaluated in terms of strength, stiffness, ductility, and failure modes under biaxial loads, and compared with the scenario where the connection was only loaded in in-plane shear. Results show that the application of biaxial loading may considerably decrease the in-plane shear performance of the angle bracket connections when the secondary load is more than 50% of its monoaxial resistance, while the effect of biaxial loading is limited when the secondary load is less than 25% of its monoaxial resistance.

Behaviour of castellated beam-to-column end-plate connection under monotonic load

The development of plastic hinges in a steel frame structure with steel beam-to-column end-plate connection joints by strengthening the end-plate area is a widely used design concept. This study explores the realization of this design concept with a beam web opening and without end-plate stiffening. The factors that impact the mechanical properties and failure modes of these joints are the end-plate thickness, opening diameter, opening position, and opening type. These parameters are tested for monotonic loading of six beam-column joints, and 220 finite element models are parametrically analysed. Additionally, the development of plastic hinge of the beam based on the development trend of maximum strain of each component section is studied. The initial rotational stiffness, ductility, bearing capacity, deformation capacity, and failure mode are used as the evaluation criteria to assess the behaviour of this joint. The research indicates that a castellated steel beam-to-column end-plate connection can realize the occurrence of plastic hinge and exhibit good ductility and load-bearing performance. This study highlights the premise that the beam web opening and end-plate thickness parameters must be within a specific range to achieve accurate results; additionally, the division method of the interval of parameters is described. The influence of end-plate thickness on the working mechanism of the connection is clarified, and the mechanical properties and failure modes of connections under different parameter intervals are studied. This study proposes a method for calculating the initial rotational stiffness of the connection to achieve good accuracy by considering the participation of the components on the beam in the rotation of the connection.