Flexural Stiffness Reduction Research Articles

Flexural behavior of RC beams externally strengthened with CFRP composites exposed to severe environment conditions

This paper investigated the impact of room temperature, cyclic ponding salt water (15%), hot water of 65°C, and rapid freeze and thaw cycles for three years on the flexural behavior of reinforced concrete beams strengthened with different configuration of CFRP composites. Totally sixteen RC beams were casted and tested as simply supported load as four point loading with a shear span to a depth ratio of 2.25. The investigated parameters includes mode of failure, ultimate load and corresponding deflection, yielding load and corresponding deflection, stiffness, steel strain, concrete strain, and CFRP strain. Based on tested results, the environment conditions had no effect (No separation or debonding) on the bond strength between CFRP composites and tension side of concrete. After applying the load, the inelastic deformation was shown in concrete which leads to yielding of main steel reinforcement and then compression failure of tested beams. In addition, the strengthened beams indicated a reduction in flexural stiffness and enhancement in the ductility of the member through. Finally, the increasing of number of layers (CFRP bonded area) had a strong impact on concrete by shelter concrete from environmental consequences and undesirable effect on the CFRP-concrete bond performance.

An experimental study on the effects of matrix cracking to the stiffness of glass/epoxy cross plied laminates

Three independent measurement techniques are applied to characterize glass fiber laminates. The effects of distributed fatigue damage to the stiffness related behavior of cross plied laminates are quantified. Tensile and flexural stiffness reduction is obtained from quasi-static testing. Vibration testing shows the degradation of flexural and in-plane shear stiffnesses. The reduction of the phase velocity of symmetric S0 mode is observed from the experimental dispersion curves of Lamb waves. However, the mutual agreement of these results is less satisfactory than was earlier seen for virgin laminates. The phenomena causing the discrepancies are proposed and discussed.

Fatigue behavior of hybrid GFRP-concrete bridge decks under sagging moment

This paper presents a new cost-effective hybrid GFRP-Concrete deck system that the GFRP panel serves as both tensile reinforcement and stay-in-place form. In order to understand the fatigue behavior of such hybrid deck, fatigue test on a full-scale specimen under sagging moment was conducted, and a series of static tests were also carried out after certain repeated loading cycles. The fatigue test results indicated that such hybrid deck has a good fatigue performance even after 3.1 million repeated loading cycles. A three-dimensional finite element model of the hybrid deck was established based on experimental work. The results from finite element analyses are in good agreement with those from the tests. In addition, flexural fatigue analysis considering the reduction in flexural stiffness and modulus under cyclic loading was carried out. The predicted flexural strength agreed well with the analytical strength from finite element simulation, and the calculated fatigue failure cycle was consistent with the result based on related S-N curve and finite element analyses. However, the flexural fatigue analytical results tended to be conservative compared to the tested results in safety side. The presented overall investigation may provide reference for the design and construction of such hybrid deck system.

Ontogenetic changes in the olfactory antennules of the shore crab, Hemigrapsus oregonensis, maintain sniffing function during growth.

Malacostracan crustaceans capture odours using arrays of chemosensory hairs (aesthetascs) on antennules. Lobsters and stomatopods have sparse aesthetascs on long antennules that flick with a rapid downstroke when water flows between the aesthetascs and a slow return stroke when water is trapped within the array (sniffing). Changes in velocity only cause big differences in flow through an array in a critical range of hair size, spacing and speed. Crabs have short antennules bearing dense arrays of flexible aesthetascs that splay apart during downstroke and clump together during return. Can crabs sniff, and when during ontogeny are they big enough to sniff? Antennules of Hemigrapsus oregonensis representing an ontogenetic series from small juveniles to adults were used to design dynamically scaled physical models. Particle image velocimetry quantified fluid flow through each array and showed that even very small crabs capture a new water sample in their arrays during the downstroke and retain that sample during return stroke. Comparison with isometrically scaled antennules suggests that reduction in aesthetasc flexural stiffness during ontogeny, in addition to increase in aesthetasc number and decrease in relative size, maintain sniffing as crabs grow. Sniffing performance of intermediate-sized juveniles was worse than for smaller and larger crabs.

Effect of punching shear on load–deformation behavior of flat slabs

Punching shear resistance usually constitutes the decisive design criterion for reinforced concrete flat slabs supported by columns. Modeling approaches based on Kinnunen and Nylander’s rotation-symmetric sector model, such as the Quadrilinear Sector Model (QSM), allow the prediction of the slab’s load–rotation behavior. To take into account an orthogonal reinforcement layout, the steel Young’s Modulus is usually reduced. A mechanically better justified flexural stiffness reduction factor is derived here which depends on the longitudinal reinforcement and modular ratio. The QSM also neglects shear deformations, which may reduce the flexural capacity. A Modified Sector Model (MSM) is derived which considers the influence of shear on the flexural behavior. A strength reduction factor for the shear crack-crossing longitudinal reinforcement is introduced which depends on the mechanical longitudinal reinforcement ratio. The factor takes into account that the longitudinal reinforcement also has to transmit forces resulting from shear. The MSM can also be applied to predict the load–rotation responses and punching shear resistances of flat slabs strengthened with prestressed carbon fiber-reinforced polymer (CFRP) straps.

Seismic performance of lateral load resisting systems

In buildings structures, the flexural stiffness reduction of beams and columns due to concrete cracking plays an important role in the nonlinear load-deformation response of reinforced concrete structures under service loads. Most Seismic Design Codes do not precise effective stiffness to be used in seismic analysis for structures of reinforced concrete elements, therefore uncracked section properties are usually considered in computing structural stiffness. But, uncracked stiffness will never be fully recovered during or after seismic response. In the present study, the effect of concrete cracking on the lateral response of structure has been taken into account. Totally 120 cases of 3 Dimensional Dynamic Analysis which considers the real and accidental torsional effects are performed using ETABS to determine the effective structural system across the height, which ensures the performance and the economic dimensions that achieve the saving in concrete and steel amounts thus achieve lower cost. The result findings exhibits that the dual system was the most efficient lateral load resisting system based on deflection criterion, as they yielded the least values of lateral displacements and inter-storey drifts. The shear wall system was the most economical lateral load resisting compared to moment resisting frame and dual system but they yielded the large values of lateral displacements in top storeys. Wall systems executes tremendous stiffness at the lower levels of the building, while moment frames typically restrain considerable deformations and provide significant energy dissipation under inelastic deformations at the upper levels. Cracking found to be more impact over moment resisting frames compared to the Shear wall systems. The behavior of various lateral load resisting systems with respect to time period, mode shapes, storey drift etc. are discussed in detail.

Characterizing vibration damping response of composite laminates containing silica nanoparticles and rubber particles

This research aims to characterize the damping properties of fiber/epoxy composites containing different degrees of silica nanoparticles and rubber particles. Conventionally, adding rubber particles into fiber/epoxy composites would lead to dramatic reduction of stiffness although the vibration damping could be improved accordingly. In order to enhance the damping properties of the fiber composites without sacrificing the stiffness, silica nanoparticles together with rubber particles were introduced into the epoxy resin through the sonication process. The epoxy resin was then treated as matrix and impregnated into the fiber layer by means of the vacuum hand lay-up process to form the composite laminates. The vibration damping as well as the flexural stiffness of the fiber composite was measured using the forced vibration technique together with the half-power method. In addition, the vibration damping of the composite laminates, consisting of silica nanoparticles and rubber particles, was characterized using the micromechanical analysis. The repeated unit cell with the fibers displaying randomly in the matrix was employed to represent the microstructures of the unidirectional composites. The loss factor as well as the moduli obtained from the micromechanical analysis were regarded as the effective properties homogenizing within the fiber composites. In conjunction with the modal shapes, the vibration damping of the composite laminates with stacking sequence of [0]10, [90]10, [±45]2s, and [90/0]2s was calculated using the finite element analysis. Experimental results indicated that with the incorporation of the silica nanoparticles together with the rubber particles, the reduction of flexural stiffness of fiber composites, especially for the [90]10 laminates, was diminished while the damping properties of laminates were improved. Moreover, it was found that the effect of the particles in the [0]10 laminates is relatively minimal. The vibration damping responses of composites laminates obtained using the micromechanical analysis together with the modal analysis exhibit an agreement with the experimental data.

Research on Flexural Stiffness Reduction Factor of Reinforced Concrete Column with Equiaxial + Shaped Section

The reduced stiffness method had been adopted to evaluate the material nonlinearity characteristics of reinforced concrete structures in compliance with concrete structure standards of the United States, New Zealand and Canada. Concrete structure design code in China also accepts the reduced stiffness method as a supplement of the second-order effects. However, the concrete structure with specially shaped columns code of China still use amplified coefficients of eccentricity to consider nonlinearity characteristics of reinforced concrete structure with special shaped columns. Based on the numerical integral method, a flexural stiffness reduction factor is proposed to consider characteristics of material nonlinearity and geometrical nonlinearity of reinforced concrete columns with equiaxial + shaped section

High Performance Composites with Active Stiffness Control

High performance carbon fiber reinforced composites with controllable stiffness could revolutionize the use of composite materials in structural applications. Here we describe a structural material, which has a stiffness that can be actively controlled on demand. Such a material could have applications in morphing wings or deployable structures. A carbon fiber reinforced-epoxy composite is described that can undergo an 88% reduction in flexural stiffness at elevated temperatures and fully recover when cooled, with no discernible damage or loss in properties. Once the stiffness has been reduced, the required deformations can be achieved at much lower actuation forces. For this proof-of-concept study a thin polyacrylamide (PAAm) layer was electrocoated onto carbon fibers that were then embedded into an epoxy matrix via resin infusion. Heating the PAAm coating above its glass transition temperature caused it to soften and allowed the fibers to slide within the matrix. To produce the stiffness change the carbon fibers were used as resistance heating elements by passing a current through them. When the PAAm coating had softened, the ability of the interphase to transfer load to the fibers was significantly reduced, greatly lowering the flexural stiffness of the composite. By changing the moisture content in PAAm fiber coating, the temperature at which the PAAm softens and the composites undergo a reduction in stiffness can be tuned.

Study on Flexural Stiffness Reduction Factor of Reinforced Concrete Column with Equiaxial T Shaped Section

The reduced stiffness method had been adopted to evaluate the material nonlinearity characteristics of reinforced concrete structures to be in compliance with concrete structure standards of the United States, New Zealand and Canada. Concrete structure design code in China also accepts the reduced stiffness method as a supplementary method of considering the second-order effects problem. However, the concrete structure with specially shaped columns code of China still use amplified coefficients of eccentricity to consider nonlinearity characteristics of reinforced concrete structure with special shaped columns. Based on the numerical integral method, a flexural stiffness reduction factor is proposed to consider characteristics of material nonlinearity and geometrical nonlinearity of reinforced concrete columns with equiaxial T shaped section.

Validation of algorithms for delamination detection in composite structures using experimental data

This research work deals with aspects concerned with delamination detection in composite structures as revealed by an approach based on vibration measurements. Variations in vibration characteristics generated in composite laminates indicate the existence of delaminations because degradation due to delamination causes reduction in flexural stiffness and strength of the material and as a result vibration parameters like natural frequency responses are changed. Hence, it is possible to monitor the variation in natural frequencies to identify the presence of delamination, and assess its size and location for online structural health monitoring (SHM). The approach to this paper, therefore, typically depends on undertaking the analysis of structural models implemented by finite element analysis (FEA). The numerical solutions using FE models known as the simulator computes the natural frequencies for the delaminated and undelaminated specimens of composite laminates. However, these FE models are computationally expensive, and surrogate (approximation) models are introduced to curtail the computational expense. The simulator is employed to solve the inverse problem using algorithms based on computational intelligence concepts. An artificial neural network (ANN) model is developed to also solve the inverse problem for delamination detection directly and to provide surrogate models integrated with optimization algorithms (the gradient-based local search and non-dominated sorting genetic algorithm-II) to contain the computationally expensive simulations by FEA. This approach is termed as surrogate assisted optimization and it is seen that the engagement of surrogate models in lieu of the FE models in the optimization loop greatly enhances the accuracy of delamination detection results within an affordable computational cost and provides control over handling different variables. Meanwhile, to aid with the building of effective surrogate models using substantial number of training datasets, K-means clustering algorithm is harnessed and this effectively reduces the large training datasets usually required for ANN training. This paper demonstrated that ANN and optimization algorithms with surrogates show immense potentialities for use in delamination damage detection scenarios. Prediction errors of the algorithms were quantified and they were shown to be satisfactory when applied to previously experimental data. The algorithms in their inverse formulations are capable of predicting accurately delamination parameters. Hence, these algorithms should be employed for application in the domain of SHM where their small computational requirements could be exploited for online damage detection.

Simple calculation model for evaluating the fire resistance of unreinforced concrete filled tubular columns

This paper presents a method for calculating the fire resistance of unreinforced axially loaded concrete filled circular hollow section columns, based on the guidelines of Eurocode 4 Part 1.2 for the fire design of composite columns. The different design approaches which are currently available worldwide are reviewed in this paper, focusing in particular on the European code, which is discussed and analysed in depth. Several of the aspects which are nowadays missing or thought to be arguable by researchers in the Eurocode 4 method are studied and on the basis of parametric studies a new proposal is developed, so that designers can easily apply the code in the future. The parametric studies investigate the main factors affecting the fire resistance of unreinforced concrete filled tubular (CFT) columns, such as the outer diameter, the thickness of the steel tube wall, the relative slenderness of the column at room temperature and the fire exposure time, widely covering the range of values which can be found in practice. From the results of these parametric studies, equations for obtaining the equivalent temperatures of steel and concrete are developed, and appropriate flexural stiffness reduction coefficients are integrated in the simple calculation model of Eurocode 4. The method presented here is valid for centrally loaded circular CFT columns filled with unreinforced normal strength concrete, and makes possible the calculation of slender columns, extending the current limitations in buckling length of the European code.

Mechanical Behavior of Composite Girder with Perfobond Shear Connector under Hogging Moment

The mechanical behavior of the support regions for continuous composite girders with tensile stresses in the concrete slab and compressive stresses in the lower steel profile becomes strongly nonlinear under negative bending moments. A static test on four half-scale model of a steel and concrete composite girders with different shear connectors including studs and PBL under hogging moments was conducted and observed to evaluate the influence of shear connector on inelastic behavior such as flexural stiffness reduction, crack initiation and development in concrete slab. From the test results, the flexural stiffness and loading capacity of the composite girders were improved by PBL shear connector. Higher initial cracking load and crack resistance stiffness of composite girders with PBL shear connector under serviceability limit state was obtained during crack development process. The test specimen could be assumed as full composite section until the ultimate state from load-slip relationship of shear connector. Analytical and experimental studies can serve as a basis for continuous composite bridges design.

Stiffness reduction factor for post-tensioned flat plate slabs

The effective beam width model (EBWM) has been used for estimating force and drift demands on flat plate frames under lateral loads. The accuracy of this model depends strongly on how to estimate the effective stiffness of flat plate slabs. With an increase in slab moments due to lateral loads, slab cracks occur and propagate on the slab, which leads to a reduction in slab flexural stiffness. For post-tensioned (PT) flat plate slabs, the initiation and propagation of slab cracks can be delayed due to slab in-plane compressive stress induced by PT tendon forces. This study investigates the contribution of slab in-plane compressive stress to the slab stiffness reduction factor, which is defined as the ratio of slab stiffness obtained from a cracked slab section to that from the corresponding uncracked slab section. For this purpose, this study collected the test results of PT flat plate slab–column connection specimens and estimated the slab stiffness reduction factors (β) for those specimens with respect to a level of applied slab moment. Non-linear regression analysis is used to propose an empirical equation computing β for PT flat plate slabs using β estimated from the test results. The accuracy of the empirical equation for β is verified by comparing the lateral stiffness of a two-storey PT flat plate frame, obtained using the EBWM with the empirical equations for β, with that estimated from shaking table test results on the frame.

Flexural fatigue analysis of a CFRP form reinforced concrete bridge deck

Concrete bridge decks reinforced with fiber reinforced polymer (FRP) composite panels have recently been used where the FRP panels also serve as the permanent formwork for concrete. Comparing to their short-term behavior, their long-term performance especially under repeated traffic loads (fatigue) has not yet been widely known. This paper presents a fatigue analysis tool developed for a new steel-free concrete bridge deck reinforced with carbon FRP stay-in-place form. The developed model takes into account the cyclic creep of concrete in compression, the reduction in flexural stiffness due to fatigue tensile cracking and the reduction in modulus of rupture under cyclic loading. Comparisons with experimental data show reasonable agreement where a full-size 2-span deck specimen was subjected to millions of fatigue cycles. The parametric study recommends reducing the amount of FRP reinforcement and concrete strength of the current design, and lower loading rate may introduce more stiffness degradation in the system.

Mechanics of Composite Delamination under Flexural Loading

The mechanics of interface delamination in CFRP composite laminates is examined using finite element method. For this purpose a 12-ply CFRP composite, with a total thickness of 2.4 mm and anti-symmetric ply sequence of [45/-45/45/0/-45/0/0/45/0/-45/45/-45] is simulated under three-point bend test setup. Each unidirectional composite lamina is treated as an equivalent elastic and orthotropic panel. Interface behavior is defined using damage, linear elastic constitutive model and employed to describe the initiation and progression of delamination during flexural loading. Complementary three-point bend test on CFRP composite specimen is performed at crosshead speed of 2 mm/min. The measured load-deflection response at mid-span location compares well with predicted values. Interface delamination accounts for up to 46.7 % reduction in flexural stiffness from the undamaged state. Delamination initiated at the center mid-span region for interfaces in the compressive laminates while edge delamination started in interfaces with tensile flexural stress in the laminates. Anti-symmetric distribution of the delaminated region is derived from the corresponding anti-symmetric ply sequence in the CFRP composite. The dissipation energy for edge delamination is greater than that for internal center delamination. In addition, delamination failure process in CFRP composite can be described by an exponential rate of fracture energy dissipation under monotonic three-point bend loading.

Fire behaviour of concrete filled elliptical steel columns

In this work, a non-linear three-dimensional finite element model is presented in order to study the behaviour of axially loaded concrete filled elliptical hollow section (CFEHS) columns exposed to fire. This study builds on previous work carried out by the authors on concrete filled circular hollow section (CFCHS) columns both at room temperature and in fire. The numerical model is first validated at room temperature against a series of experiments on CFEHS stub columns available in the literature and subsequently extended to study the performance of slender columns at elevated temperatures. The aim of this work is to understand and represent the behaviour of axially loaded CFEHS columns in fire situations and to compare their effectiveness with that of the circular concrete filled tubular (CFT) columns. Parametric studies to explore the influence of variation in global member slenderness, load level, cross-section slenderness and section size are presented. Finally, guidance on the fire design of CFEHS columns is proposed: it is recommended to follow the guidelines of Clause 4.3.5.1 in EN 1994-1-2, but employing the flexural stiffness reduction coefficients established in the French National Annex with an equivalent EHS diameter equal to P/π, where P is the perimeter of the ellipse.

균열손상 후 동결융해를 경험한 철근콘크리트 보의 휨거동

이 연구에서는 동결융해 사이클을 경험한 2가지 종류의 휨부재의 거동특성을 평가하였다. 이 연구의 목적은 동결융해에 따른 철근콘크리트 보의 거동특성을 검토하는 것이다. 이를 위해 일부 실험체는 동결융해를 경험하기 전, 인장철근이 항복되기까지 손상을 입도록 계획되었다. 또한 반복하중 재하시 강성저하 특성을 평가하기 위하여 단조 및 반복재하 실험을 실시하였다. 재료 실험 결과, 동결융해 300사이클을 경험한 콘크리트의 상대동탄성계수는 86.8%까지 감소되었으나 내동해저항성은 충분히 가지고 있는 것으로 평가되었다. 단조재하 실험 결과, 동결융해 사이클에 따른 휨 강도, 연성 및 강성은 상대적으로 감소하는 것으로 나타났다. 특히, 인위적 균열손상을 경험한 BDF13 시리즈는 현행 콘크리트설계기준에서 요구하는 공칭모멘트를 만족하지 못하는 것으로 나타났다. 반복재하시 BF75 시리즈에서 동결융해를 경험함에 따라 10% 이상의 반복강성 저하를 나타내었다. 따라서 내진부재와 같이 반복하중을 받게 되는 부재를 설계할 경우, 동결융해로 인한 압축측 콘크리트의 변형 특성도 고려되어야 할 것으로 판단된다.

Durability study of neat/nanophased GFRP composites subjected to different environmental conditioning

Experimental investigations on the durability of E-glass/nanoclay–epoxy composites are reported. SC-15 epoxy system was modified using 1–2 wt.% of nanoclay. Extent of clay platelet exfoliation in epoxy was evaluated using X-ray diffraction (XRD). Glass fiber reinforced plastic (GFRP) composite panels were fabricated using modified epoxy and exposed to four different conditions, i.e. hot (elevated temperature-dry, wet: 60 and 80 °C) and cold (subzero-dry, wet) for 15, 45 and 90 days. Weight change due to conditioning, quasi-static flexure and micrographic characterization were studied on the conditioned samples. Room temperature samples were also tested for baseline consideration. XRD results showed exfoliation of clay platelets in nanoclay–epoxy samples with decrease in peak intensity and increase in interplanar spacing. Samples subjected to hot-wet conditions showed higher percentage weight gain with a maximum of 4.25% in neat and 3.1% in 2 wt.% samples. Flexural tests results showed degradation with increasing time. Maximum degradation were observed for hot-wet (80 °C) for 90 days neat samples, i.e. 22.6% and 29.8% reduction in flexural strength and stiffness, respectively. However, less degradation was noticed for nanophased composites under similar conditions. Scanning electron microscopy (SEM) results of failed samples showed better interfacial bonding in nanophased composites.

Effect of Nanoclay Incorporation on the Impact Properties of Adhesively Bonded Composite Structures

During manufacturing or service conditions, adhesively bonded composites are often subjected to impact. This impact may result in a reduction in strength and structural integrity of engineering components that are composed of adhesively bonded composite structures. The investigation of the degradation of strength of structural joints is, therefore, of paramount importance for their successful performance. Impact resistance of bondline in adhesively joined composites can be altered by the addition of nanoclay in the adhesive during fabrication of adhesive joints. In this study, impact test was carried out on graphite–epoxy composite panels bonded with nanoclay adhesive at different impact energies using drop-weight impact test equipment. Adhesive joints were fabricated by adding nanoclay in volume fractions of 1, 2 and 5% in the adhesive bondline. For comparison, plain adhesive joints were fabricated without nanoclay incorporation in the bondline. Impact testing was performed on these joints at 5, 10 and 20 J, to study the effect of inclusion of nanoclay in the epoxy adhesive. In order to determine the flexural load bearing capacity and stiffness reduction after impact, a three-point bending test was conducted on unimpacted and impacted specimens. The results showed that there was an improvement in impact capacity, however there was a reduction in flexural strength due to nanoclay incorporation.