Stiffness Of Members Research Articles

Effect of retrofit type on the blast performance and failure mode of HSC beams retrofitted with UHPFRC

This paper presents a strategy to prevent shear failure and improve the structural performance of existing high-strength concrete (HSC) beams under blast loading. The strategy involves retrofitting with ultra-high performance fiber reinforced concrete (UHPFRC), a novel material which is well-adapted for the blast hardening of concrete structures. Shock-tube air-blast tests are conducted on seven HSC beams which are retrofitted with UHPFRC. The objective was to characterize the effectiveness of various retrofit types on the blast behaviour of both shear-deficient and flexural-dominant HSC members. Three retrofit types were considered: U-jacketing (UJ), full-jacketing (FJ) and a tension-sided (T) overlay. Other parameters included the effects of the concrete substrate roughening method, as well as the tension steel ratio (1.6% or 2.4%) and presence of stirrups in the beams. Both the UJ and FJ retrofits were found to be effective in preventing shear failure in shear-deficient HSC beams having varying shear demands. In addition, both retrofits increased member strength and stiffness, thereby reducing blast-induced displacements and increasing overall blast resistance. Comparing the two retrofits, optimal performance was obtained with full-jacketing due its ability to delay concrete crushing. In HSC beams with sufficient stirrups, both the T-sided and FJ retrofits reduced blast-induced displacements; however, the use of full-jacketing was better able to control damage and increase blast capacity. The roughening method had no substantial effect on the FJ retrofit performance or failure mode, with no debonding observed in the tests.

Experimental and numerical study on tensile performance of GFRP bar reinforced UHPC members

Glass fiber reinforced polymer (GFRP) bar reinforced ultra-high performance concrete (UHPC) (GFRP-UHPC) members’ tensile performance should be significantly different from that of steel-UHPC members due to differences between GFRP and steel bars in mechanical and bond properties. In this paper, six dog-bone shaped specimens with different types of reinforcement materials, rebar diameters, and quantities of rebars were fabricated and tested under axial tension, and their failure modes, load-displacement curves, and cracking behavior were recorded and investigated. Furthermore, an extensive nonlinear finite element analysis considering the bond behavior between rebars and UHPC was conducted. Finally, formulas were proposed to predict the tensile stiffness and ultimate tensile capacity of GFRP-UHPC members. Results confirmed that bond shear strength (τcs) and stiffness (K) of the GFRP and UHPC interface were the key factors that affected GFRP-UHPC members’ tensile performance: τcs mainly determined the failure mode; increasing K and the reinforcement ratio can improve the post-cracking stiffness and obtain tension hardening behavior; the wedging effect caused the post-cracking curve of the tension member in bond failure mode re-ascend periodically. The proposed formulas could produce accurate and safe predictions after comparing predicted results with experimental and simulation results. This study provides the underlying insights needed to guide the design of GFRP-UHPC members.

Flexural behavior and design of rectangular ultra-high performance concrete-filled high-strength steel tube members

This study investigated the flexural behavior of rectangular ultra-high performance concrete-filled high-strength steel tube (CuFTh) members. A total of 11 tests were conducted. The influence of yield stress of steel (Fy), steel fiber volume content of UHPC (ρ), height (H) of steel tube, and thickness of steel tube wall (t) was investigated. 3D finite-element models were developed and benchmarked to conduct parametric studies. Results from the experimental tests and FEM analyses indicated that: (i) Fy, t, and H have a significant influence on the flexural strength, while the compressive strength of concrete has a negligible impact; and (ii) increasing ρ slightly improves the flexural strength, but obviously reduces the ductility. Additionally, results from the experimental tests and FEM analyses were compared with the strength estimated using AISC 360-16, GB 50936-2014, Eurocode 4, and AIJ. The comparisons showed that Eurocode 4 and AISC 360-16 can reasonably estimate the flexural strength of rectangular CuFTh members. AIJ is recommended for predicting the service-level flexural stiffness of rectangular CuFTh members.

Feasibility of producing ultra-high performance concrete with high elastic modulus by steel chips: An experimental study

Elastic modulus is one of the key parameters to weigh the stiffness of concrete members and structural design in civil engineering. Despite its excellent performance in durability and mechanical properties, ultra-high performance concrete (UHPC) is featured with relatively low elastic modulus, which prevents UHPC from being applied in a much larger scope. This study was conducted to explore the feasibility of preparing UHPC with high elastic modulus (HMUHPC) by using steel chips. The modified Andreasen and Andersen (MAA) particle packing model was used to design the initial mixture of HMUHPC. Based on this, some steps were followed to investigate the impacts of varying contents of steel chips on HMUHPC with regard to its mechanical properties, workability, and apparent density. In addition, attention was also paid to how steel chips affected the microstructure of HMUHPC and the ultrasonic pulse velocity (UPV) propagated in HMUHPC. It was found that: 1) Due to the addition of steel chips, there was an increase from 9.65% to 21.73%, 6.38% to 15.85%, 1.28% to 10.49%, and 3.11% to 16.44%, respectively, in the elastic modulus, compressive strength, flexural strength, and apparent density of HMUHPC; 2) The addition of steel chips could reduce the porosity of HMUHPC and optimize its pore size distribution; 3) Considering the effects of steel chips on HMUHPC regarding its microstructure, mechanical properties, and workability, the optimal content of steel chips in HMUHPC was 50 wt%.

Investigation of the Global Structural Behavior of the Prefabricated Shoring System Considering Structural Details

This study aims to investigate the structural behavior and load-carrying capacity of prefabricated shoring systems. The structural behavior and performance of shoring systems are influenced by the buckling of vertical members, where the compressive force acts as the main load. The buckling strength of a vertical member is sensitive to not only the material and geometrical properties of members but also the connection details between members, presence or absence of braces, and stiffness ratio between members. Therefore, in this study, the structural behavioral characteristics of the individual post member and the entire system are investigated by considering the structural details through eigenvalue and nonlinear finite element analyses. On the basis of the analytical studies, it was confirmed that the boundary condition of the vertical member, rotational and horizontal stiffnesses, and eccentricity condition of the end, which are directly affected by the compressive force acting on the prefabricated shoring system, have a direct effect on the elastic buckling strength. In addition, it was determined that factors such as whether the braces were installed, rotational stiffness of the vertical–horizontal member connection, and the number of installation stages affected the overall strength of the structure. According to the structural analysis results, the assembled structure was reduced by 92.9% and 82.2% compared to the elastic buckling strength of a single member as the height increased to two and three stories. In addition, when the bracing member was not installed, 12.1% and 23.6% strength reduction was confirmed as the elastic buckling strength increased by two and three stories compared to the case where the bracing member was installed. Consequently, the necessity of a whole structural performance evaluation technique was confirmed for a more practical structural performance evaluation.

3D printed negative stiffness meta-structures with superior energy absorption and super-elastic shape-recovery features

The aim of this paper is to create novel 3D cubic negative stiffness (NS) structures (NSSs) with superior mechanical performances such as high energy absorption, shape recovery, super-elasticity, and reversibility. The conceptual design is based on an understanding of geometrical influences, non-linear buckling-type instability, snap-through mechanism, elasto-plastic deformation growth and plastic hinges. A finite element (FE) based computational model with an elasto-plastic material behavior is developed to design and analyze NSSs, saving time, material, and energy consumption. Material samples and meta-structures are 3D printed by selective laser sintering printing method. Material properties are determined via mechanical testing revealing that the printing process does not introduce much anisotropy into the fabricated parts. Experimental tests are then conducted to study the behavior of novel designs under loading–unloading cycles verifying the accuracy of the computational model. A good correlation is observed between experimental and numerical data revealing the high accuracy of the FE modeling. The structural model is then implemented to digitally design and test NSSs. Effects of the geometrical parameters of the negative stiffness members under three cyclic loading are investigated, and their implications on the non-linear mechanical behavior of NSSs under cyclic loading are put into evidence, and pertinent conclusions are outlined. In addition, the dissipated energy and loss factor values of the designed structures are studied and the proposed unit cell is presented for the energy absorbing systems. The results show that the structural and geometry of energy absorbers are key parameters to improve the energy absorption capability of the designed structures. This paper is likely to fill a gap in the state-of-the-art NS meta-structures and provide guidelines that would be instrumental in the design of NSS with superior energy absorption, super-elasticity and reversibility features.

Numerical investigations on flexural behavior of I-shaped CFRP-encased high-strength square concrete filled steel tubes

To enhance the mechanical properties of high-strength concrete-filled high-strength steel tubular (HSCFHST) members, a new type of composite structure is proposed in which an I-shaped CFRP is encased inside the HSCFHST member. The objective of this research is to improve the theoretical foundation for HSCFHST members by analyzing the flexural behavior of inner I-shaped CFRP on HSCFHST members. HSCFHST members' nonlinear finite element models is created using ABAQUS and confirmed by comparing simulation and test data. It is subjected to pure bending stresses. The flexural behavior of the HSCFHST members are examined with respect to failure mode, complete curve, moment sharing ratio, longitudinal and contact stresses in steel tubes and concrete. Additionally, material interaction mechanisms among three components are investigated to explore the range of restraint between the components. To assess a substance's effect and structural parameters on the flexural behavior of the members, including different combinations of the three types of materials, steel's yield strength, concrete's compressive strength, and the ratio of steel. The findings demonstrate that the steel tube's restraint of the concrete is mostly concentrated at its corners on the tensile side. The HSCFHST member's deformation capacity and stiffness were both increased by the usage of the CFRP encased in the member, which also decreased the height of the central axis' upward movement. The flexural load capacity is largely affected by the steel ratio, which also has an impact on steel strength.

A partially buckling-restrained brace with T-shaped double core for seismic retrofit: Experimental study, numerical analysis, and local stability design

A novel partially buckling-restrained brace with T-shaped double core (PTBRB) was proposed for the seismic retrofit of existing T-shaped steel members consisting of two separated steel angles. The retrofitting scheme primarily comprises two external steel angles and one cover plate which are bolted to serve as restrainer to prevent global buckling of existing T-shaped steel members. Cyclic tests were performed to verify the effectiveness of the retrofitting scheme and evaluate the PTBRB performance as seismic fuse. The results showed that adoption of the retrofitting scheme had negligible influence on the elastic stiffness of the T-shaped steel members, but their axial compression force capacity was increased by 60 %. The PTBRB specimens exhibited full hysteresis before failure, with the best ductility coefficient and cumulative plastic deformation capacity of 11.83 and 523, respectively. The controlled buckling mode of the PTBRB was identified by numerical analysis, and the results showed that the local buckling of a single steel angle member was responsible for the stiffness degradation of the PTBRB hysteresis. Theoretical local stability analysis of PTBRB was carried out according to Bleich’s theory and Lundquist’s theory and the test results confirm that the Bleich’s theory is more reliable for predicting the theoretical inelastic critical load. The maximum compression capacity of the PTBRB corresponding to the local stability requirement of a single steel angle member is proposed to achieve the seismic fuse function, which is further validated by numerical analysis.

Experimental cyclic response of rubberised concrete-filled steel tubes

This paper examines the behaviour of circular steel tubes infilled with concrete incorporating recycled rubber particles. The rubberised concrete-filled steel tubes are tested under lateral cyclic deformations with and without co-existing axial loading. A detailed account of the cyclic tests on twelve specimens is provided together with complementary material and section tests. The rubber replacement ratio is varied up to a relatively high value of 60%, under axial loads reaching up to 30% of the nominal capacity. Hollow steel members are also tested for comparison purposes. The experimental results are discussed in detail with respect to the member stiffness, capacity, ductility, energy dissipation and failure mechanisms. Although high rubber ratios lead to a considerable loss in concrete strength, the test results show that the corresponding reduction in member capacity is much less significant due to the contribution of the steel tube and the comparatively high confinement effects mobilised within the rubberised concrete. In comparison with the members incorporating normal concrete, the rubberised concrete members are found to exhibit up to about 10% and 17% increase in ductility and energy dissipation, respectively, depending on the rubber content. Analytical treatments are then used to suggest simplified relationships for predicting the stiffness, moment-axial strength interaction, plastic hinge length and local ductility criteria. Overall, the test results demonstrate the favourable inelastic cyclic performance of circular steel tubes infilled with rubberised concrete and provide valuable experimental data. The proposed expressions for key response parameters also offer the basis for developing practical assessment and design methods.

Design and analysis of novel negative stiffness structures with significant energy absorption

Negative stiffness structures (NSS) are a type of mechanical metamaterials that absorb energy via buckling of negative stiffness members. However, these structures have limitations in energy absorption and reusability. Therefore, this study aimed to design, simulate, fabricate, and perform experimental tests on novel designed negative stiffness (NS) structures and improve the performances of negative stiffness structures in terms of energy absorption and keeping their original configuration under cyclic loading. First, the finite element method (FEM) and parametric study of the geometrical dimensions of NS members were considered to investigate the activation/non-activation snap-through mechanisms in the designed structures under quasi-static compression loading. Subsequently, two designed structures were manufactured via the Fused deposition modeling (FDM) printing method and one cyclic loading with a quasi-static state was carried out. The results of the FE simulation and experimental tests were compared, and good agreements were found between them. Afterward, the dissipated energy values and loss factor values of the designed structures under two cyclic loading (two loading/unloading processes) were investigated. Considering both the parameters of the energy absorption values and the remaining members in the elastic region, the proposed NSS was presented for energy absorber structures.

FINITE ELEMENT ANALYSIS FOR THIN-WALLED MEMBER SUBJECTED TO COMBINED LOADING

Thin-walled structures are widely used in various structural engineering applications due to their advantage of high bearing strength when compared to self-weight and used in a complex loading situation where subjected to combined loadings. When a thin-walled section is subjected to a combined load with restrained torsion, they are ineffective at resisting, resulting in a reduction in beam capacity due to torsion and additional warping stresses. A finite element calculation can be used to analyze a 3D bar of thin-walled structural sections. Different commercial software and studies commonly consider six degrees of freedom at each node of a member for a space frame without considering the effect of warping restraint at the member's ends. This paper presents a finite element calculation for thin-walled sections with restrained torsion using the 14x14 member stiffness matrix, which includes warping as an additional degree of freedom and is commonly used for open thin-walled sections. In this study, we considered two different methods for including the additional degree of freedom for the stiffness matrix, which are very close to each other for small values of characteristics number.

Uniaxial model for simulating the cyclic behavior of reinforced concrete members

AbstractA new computational model is proposed within the lumped‐plasticity framework to simulate the lateral load‐deformation response of reinforced concrete members up to complete loss of lateral strength. The proposed model implements new features that enhance simulation fidelity of reinforced concrete members. It employs a cubic spline function to simulate the gradual changes of stiffness observed in the unloading‐reloading behavior of concrete members under seismic loading. The proposed model takes a different approach to simulating cyclic behavior from existing models, by utilizing an energy dissipation term as the central parameter to adjust the level of pinching in a response. The model replicates the amount of cyclic energy dissipation specified by the user, regardless of other parameters. It also automatically adjusts cyclic energy dissipation with increasing lateral deformations, to match experimental observations from concrete members. The model is equipped with deformation and energy‐based damage functions that can realistically capture stiffness and strength damage in concrete members, even under non‐symmetric cyclic loading. Using these functionalities, the model can adjust the lateral load‐deformation backbone response based on load‐history to account for short‐ or long‐duration non‐symmetric ground motion inputs. The proposed model is applicable for simulating the lateral shear or moment behaviors of reinforced concrete members, such as columns, beams, walls, and joints. The model is implemented in the open‐source simulation platform OpenSees as the CyclicReinforcedConcrete model.

Study on the Shear Characteristics of Perforated Lean Duplex Stainless Steel Rectangular Hollow Beams

Abstract: The paper deals with the shear behavior of the Lean duplex stainless steel perforated hollow beams. Lean duplex stainless steel offers significant advantages such as better economy, improved strength, high temperature properties, acceptable, weldability and fracture toughness properties. Hollow beams have wide range of applications in the construction industry, such as in buildings, bridges, oil refineries etc. The ultimate strength and elastic stiffness of a structural member can vary with perforation position, size, shape, and orientation. In this study the shear behaviour of perforated hollow beam is studied based on different shapes of perforation. . Different shapes of perforation mainly include circle, square and diamond. ANSYS Workbench is used to analyze the shear behavior of perforated lean duplex stainless steel rectangular hollow beams.

Resonance Suppression of a Controllable Mechanism Welding Robot End with Central Composite Design Methodology

Aiming to achieve resonance suppression of a controllable mechanism welding robot end using dynamic modeling and experimental verification, this paper applies a central composite design methodology to optimize suppression resonance using three variables: excitation source, rod stiffness and damping. Considering the coupling effects of the excitation source, member stiffness and damping, a combination optimization is carried out, and the optimal control result of the end is obtained, for which the optimized peak amplitudes are significantly reduced. The research provides an important technical basis for the dynamic design and resonance suppression control of controllable welding robot mechanisms.

Analysis of Interfacial Mechanical Properties of Steel Beams Strengthened with CFRP Sheets under Temperature and Creep.

Under the combined action of temperature and creep of CFRP (Carbon Fiber Reinforced Polymer) sheet, the interface between CFRP sheet and steel beams which are strengthened with CFRP sheet will produce relative slip. This slip will affect the interface interaction, reduce the bearing capacity and stiffness of members as well as increase the deformation. In this paper, the elastic method is used to introduce the creep effect of CFRP sheet and the temperature effect of steel beam. The calculation formulas of interface slip between CFRP sheet and steel beam, CFRP sheet tension and steel beam deformation under the combined action of temperature and CFRP creep are established. The accuracy of the analytical formula is verified by finite element analysis using the software ABAQUS. The results show that the CFRP sheet tension is smallest at the beam end while largest at the middle of the span. When the stiffness reaches about 3 ka, CFRP sheet tension basically does not change. When the temperature increases by 5 °C, the tensile force of CFRP sheet increases by about 3.7 kN, 1.8 kN and 2.3 kN, respectively. The increase of stiffness under creep has little effect on the change of CFRP sheet tension. The deformation is largest in the middle of the span while smallest at the beam end. Stiffness, temperature (5–25 °C), CFRP thickness and stiffness under creep have little effect on deformation. When the load increases by 5 kN under creep, the deformation increases by about 2.2 × 10−7 mm, 1.8 × 10−6 mm and 9.4 × 10−7 mm, respectively.

Ductility and failure mode of HSC and HSFRC tension stiffening members: a numerical investigation on singly reinforced beams

High-Strength Concrete (HSC) tension stiffening members with high tensile strength of concrete may have a low or even absent cross-section ductility, which affects the risk of occurrence of brittle flexural failures. This paper investigates numerically the cause of this problem by comparing and analyzing the moment-curvature relationship of diverse cross-section samples and evaluates the alternative of replacing HSC with High-Strength Fiber Reinforced Concrete (HSFRC) to address it. To perform this task, it has been proposed an original approach to interpret the moment-curvature relationships in terms of non-effective curvature, reduction of ductility index and effective ductility.

Mechanical properties and microstructure of ultra-high-performance concrete with high elastic modulus

Elastic modulus is an important parameter in engineering structural design for evaluating the stiffness of concrete members. Ultra-high-performance concrete (UHPC) has excellent mechanical properties and durability, but the relatively low elastic modulus prohibits the widespread use of the UHPC. In this study, high elastic modulus UHPC (HEMUHPC) was designed according to Modified Andreasen and Andersen particle packing model proposed by Funk and Dinger. Effects of alumina micro-powder (the content of alumina is higher than 99%, and the particle size is lower than 100 μm) on the workability, microstructure, and mechanical properties of HEMUHPC were systematically investigated. The reason for the improvement of elastic modulus of HEMUHPC was revealed by nano indentation test. It was found that, 1) the porosity and threshold pore diameter of HEMUHPC were reduced because of the addition of alumina micro-powder; 2) the flexural strength, compressive strength, and elastic modulus of HEMUHPC were increased by 3.54–11.23%, 8.89–22.83%, and 6.19–16.37%, respectively, due to the addition of alumina micro-powder; 3) the optimal content of alumina micro-powder was 10%, considering its effects on the workability, mechanical properties, and microstructure of HEMUHPC; 4) Nano indentation experiments showed that the elastic modulus of the alumina micro-powder was 90–135 GPa, which is much higher than the elastic modulus of hydration products of HEMUHPC, and thus the elastic modulus of the HEMUHPC matrix could be improved, due to the addition of alumina micro-powder.

Nonlinear healing approach for reinforced concrete beams

ABSTRACT This paper has proposed a new formula relating the damage state and effective state of the flexural member, this formula enables studying different concrete healing variables. A new relation between the effective reinforced concrete healing/damage variable and the effective healing/ damage variables of concrete and steel has been introduced to relate concrete and steel healing/ damage and the reinforced concrete healing/ damage. The proposed formula has been verified with experimental results of full-healed flexural members, it has achieved good agreement. The flexural member stiffness has been studied considering different parameters like concrete healing variables, concrete cover and percentage of steel reinforcement. The flexural member stiffness has increased as the concrete healing variable has increased, it has increased as the concrete cover has increased and the steel reinforcement percentage of 1% has given the higher flexural member stiffness.

Exact Solutions for Torsion and Warping of Axial-Loaded Beam-Columns Based on Matrix Stiffness Method.

The typically-used element torsional stiffness GJ/L (where G is the shear modulus, J the St. Venant torsion constant, and L the element length) may severely underestimate the torsional stiffness of thin-walled nanostructural members, due to neglecting element warping deformations. In order to investigate the exact element torsional stiffness considering warping deformations, this paper presents a matrix stiffness method for the torsion and warping analysis of beam-columns. The equilibrium analysis of an axial-loaded torsion member is conducted, and the torsion-warping problem is solved based on a general solution of the established governing differential equation for the angle of twist. A dimensionless factor is defined to consider the effect of axial force and St. Venant torsion. The exact element stiffness matrix governing the relationship between the element-end torsion/warping deformations (angle and rate of twist) and the corresponding stress resultants (torque and bimoment) is derived based on a matrix formulation. Based on the matrix stiffness method, the exact element torsional stiffness considering the interaction of torsion and warping is derived for three typical element-end warping conditions. Then, the exact element second-order stiffness matrix of three-dimensional beam-columns is further assembled. Some classical torsion-warping problems are analyzed to demonstrate the established matrix stiffness method.

Estimation of nonstructural stiffness in instrumented steel frames

Lateral stiffness of nonstructural components may significantly influence the initial stiffness of the entire structure and consequently alter its dynamic characteristics. While methods for simulating structural members are well-established, approaches for modeling nonstructural components that also participate in seismic response are notably less developed. In this paper a simplified, physically-intuitive approach for estimating the stiffness of nonstructural members based on vibration recordings of buildings is presented. The method comprises two components: (1) identifying the instants during the time history wherein components of interstory velocity are negligible, such that damping forces are zero, and (2) at these instants, using static analysis to estimate story shears and story torsion in the structural members by applying the recorded displacements to the entire structure, and the accelerations to all masses above the story of interest. The method derives from first-principles of dynamics and structural analysis, and is assessed against experimental data from three datasets that include shake table data on steel frames with nonstructural walls as well as quasi-static tests on the similar walls. The results are critically discussed in the context of their prospective applications in practical settings, and limitations are summarized.