Bending Stiffness Of Beam Research Articles

Shear performance of glued and screwed timber-steel composite connections for composite timber-steel beams

Mid- to high-rise mass timber buildings gained popularity in the last decade. Yet, engineered wood products (EWPs) used to erect these buildings have structural limitations. EWPs present brittle failure modes, particularly in bending, shear and tension, and have a low modulus of elasticity resulting in shorted spans and deeper beams relative to those in the steel and reinforced concrete counterparts. Timber-steel hybrid beams represent a potential sustainable solution to overcome these limitations by taking advantages of the high strength, stiffness and ductility of steel, and the high capacity to weight ratio of timber. However, for this solution to be structurally performant, it is essential to create effective composite action between the two materials. This study therefore compares the structural efficiency of various bonding techniques between the steel and the timber materials. Two sets of assembly solutions, representing four connection types, were proposed and experimentally investigated: (1) connecting an embedded steel plate into the timber elements by using either polyurethane (PUR) structural adhesive with two manufacturing variations or 14 G×75 mm heavy duty screws, and (2) connecting a steel plate on the surface of the timber element using either PUR structural adhesive with self-tapping M4×40 mm screws or only self-tapping screws. Softwood Laminated Veneer Lumbers (LVL) and Grade 350 steel plates were used in the experimental tests. All bonding techniques were tested in shear. The shear capacity, the slip stiffness and the failure mode were evaluated. Additionally, the efficiency of the proposed manufacturing solutions was quantified by analytically evaluate the effective bending stiffness of a timber-steel composite beam manufactured with different bonding techniques being investigated. Results indicated that the glued connections allowed a significantly more efficient composite action, with failure occurring in the timber instead of at the composite interface and near-full composite action was reached, than the screwed connections. To achieve high composite action with the screwed solutions, a large number of screws was needed which may incur high manufacturing costs.

Numerical Study on the Mechanical Performance of a Flexible Arch Composite Bridge with Steel Truss Beams over Its Entire Lifespan

Steel truss–arch composite bridge systems are widely used in bridge engineering to provide sufficient space for double lanes. However, a lack of research exists on their mechanical performance throughout their lifespan, resulting in uncertainties regarding bearing capacity and the risk of bridge failure. This paper conducts a numerical study of the structural mechanical performance of a flexible arch composite bridge with steel truss beams throughout its lifespan to determine the critical components and their mechanical behavior. Critical vehicle loads are used to assess the bridge’s mechanical performance. The results show that the mechanical performance of the bridge changes significantly when the temporary piers and the bridge deck pavement are removed, substantially influencing the effects of the vehicle loads on the service life. The compressive axial force of the diagonal bar significantly increases to 33,101 kN near the supports during the two construction stages, and the axial force in the upper chord of the midspan increases by 4.1 times under a critical load. Moreover, the suspender tensions and maximum vertical displacement are probably larger than the limit of this bridge system in the service stage, and this is caused by the insufficient longitudinal bending stiffness of truss beams. Therefore, monitoring and inspection of critical members are necessary during the removal of temporary piers and bridge deck paving, and an appropriate design in steel truss beams is required to improve the life cycle assessment of this bridge system.

Damage detection for continuous beams by using the tap-scan method

Damage detection for bridges using a passing vehicle has drawn much interest. Recent studies demonstrate that the tap-scan method is an efficient way to detect the change of beam bending stiffness. A quantitative relationship between the change of beam bending stiffness and the acceleration of a vehicle can be evaluated. However, the reported relationship is calibrated for a simply-supported beam, which may be unsuitable for continuous beams due to inherent structural differences. Addressing this, an analytical solution for damage detection for continuous beams using the tap-scan method is presented in this paper. Case studies reveal that damage relationships across different spans of continuous beams show negligible dependence on modal parameters and beam lengths. Consequently, the damage identification within any span of a continuous beam can be accomplished using the same damage relationship calibrated on a simply-supported beam. But it should be noticed that the damage relationship might differ by beam structural forms. The above result holds substantial implications for practical engineering scenarios, notably by diminishing the labor and complexity associated with the calibration of damage relationships for continuous beams.

Acoustic emission monitoring during elastic bending of cross laminated timber-steel composite beams

Reinforcement of cross laminated timber (CLT) floors by a composite design with steel girders can provide an innovative and sustainable alternative for highly stressable floor systems made of steel and concrete for spans exceeding 8 m. To make this construction method economical and resource efficient, a significant contribution of the CLT panel to the composite stiffness is necessary. One key aspect of the composite design is the formation of the shear-resistant connection between CLT panel and steel girder. The effect of both composites on the bending stiffness of CLT-steel composite beams was investigated in large-scale 4-point bending tests with spans of 8.1 m and 10.6 m. To monitor the damage of the specimen using acoustic emission (AE), a network with 16 AE sensors were attached to the surface of the specimen in area of largest deflection and highest load. For this purpose broadband AE sensors with a measurement frequency of up to 200 kHz were used. The ultimate failure of the specimen occurred at a maximum test load of approximately 197 kN. The highest deflection at this force was about 192 mm. During the tests, which lasted about 50 minutes, more than 8,500 AE events were detected. In this contribution, the relationship between the mechanical quantities and the AE activity is shown.

Experimental study of flexural behavior of glulam Douglas Fir beams spliced with engineered bamboo cover plates and inclined self-tapping screws

Due to the limitation of transportation and installation, long-span timber structural components need to be extended through multiple spliced joints. Among the common spliced joints, spliced beam joints with self-tapping screws have the advantages of low cross-section weakening, beautiful appearance, and convenient construction. However, the beam joints spliced by self-tapping screws have limitations in terms of bearing capacity and stiffness. To overcome these limitations, this paper proposes inclined self-tapping screw-engineered bamboo joints. In this novel joint, the high-strength engineered bamboo connection plates are used to improve the mechanical properties of spliced glulam beams. A total of thirteen glulam beams were designed. The effects of the layout and number of self-tapping screws, types of connection plates, and spliced gaps on the flexural performance of novel glulam beams were experimentally investigated through four-point bending tests. The results show that the mechanical properties of the spliced beam with parallel self-tapping screws are better than those with staggered self-tapping screws. The bending capacity of the glulam beams spliced with bamboo scrimber plates arranged in parallel increases with the increase of the number of self-tapping screws. The average bending capacity and stiffness can reach 97.3 % and 93.3 % of the intact beams, respectively. The bending capacity and stiffness of glulam beams with the same number of self-tapping screws arranged in parallel and spliced with plybamboo are lower than those of glulam beams spliced with bamboo scrimber. The gap between the spliced cross-sections of glulam beams significantly reduces the flexural mechanical properties of spliced beams, especially the stiffness.

Flexural performance and damage of reinforced fly ash and slag-based geopolymer concrete after coupling effect of freeze-thaw cycles and sustained loading

To better represent field conditions, the bending performance of reinforced geopolymer concrete (GPC) beams after the coupling effect of freeze-thaw cycling and sustained flexural load was investigated. Two types of GPC (G10 and G50) with different content of fly ash and slag were included and compared with ordinary Portland cement concrete (OPC). The mechanical strength of concrete and bond strength of rebars in concrete before and after freeze-thaw cycles were measured. It was found that the frost resistance of G10 was the weakest followed by OPC and G50. Three scenarios of bending tests on reinforced concrete beams were included: (1) control (without freeze-thaw damage); (2) individual freeze-thaw cycling; (3) coupling effect before bending. Rebound tests were conducted to evaluate frost damages at different areas of the beams as the base to analyze bending behaviors of the beams. The failure mode, load-displacement(strain) relationship, ultimate flexural strength, and bending stiffness of beams from bending tests are analyzed. All beams in scenario (1) were dominant in flexural failure. For scenario (2), G10 and G50 failed in debonding failure due to significant reduction in bond strength, while OPC failed in diagonal tension failure as OPC could sustain bond stiffness, thus preventing debonding failure. For scenario (3), damages in GPC were exacerbated, while damages in OPC were limited.

A finite element simulation approach for glued-laminated timber beams using continuum-damage model and sequentially linear analysis

Glued-laminated timber (GLT) is an efficient and renewable material with potential to enhance sustainability in construction, but its potential has been partly hindered by relatively large uncertainty related to its strength. Previous research indicate that by linking information from the grading process to the GLT fabrication more reliable GLT beams could be made. To this end, this paper represents a finite element based modelling approach combining a continuum damage model with sequentially linear analysis that is suitable for simulation of the bending stiffness and strength of GLT beams. The model has been implemented in Matlab and can be easily integrated into different parametric simulation workflows. Based on validation against 36 experimentally tested GLT beams, the model can predict bending stiffness with high accuracy and provides reasonably accurate predictions for bending strength. The model is also capable of producing qualitatively realistic fracture patterns of GLT beams. The mesh-size study suggests that the best agreement for bending strength with test data is obtained with a sparse mesh, which is discussed in detail. The model is considered suitable for follow-up studies involving the optimization of GLT beam layups.

Experimental Research on Fatigue Behavior of Reinforced UHPC-NC Composite Beams under Cyclic Loading.

Ultra-high-performance concrete (UHPC), a new cement-based material that offers high mechanical strength and good durability, has been widely applied in construction and rehabilitation projects in recent years. An optimum bending system is achieved by positioning the UHPC layer at the bottom tensile zone of the composite beam and placing the normal-strength concrete (NC) layer at the upper compression zone, which is described as the UHPC-NC composite beam. The fatigue behavior of reinforced UHPC-NC composite beams was described in this study, with an emphasis on the effects of UHPC layer thickness and fatigue load level on the fatigue life of the beam, deformation of the interface between UHPC and NC layers, as well as the bending stiffness of the beam. A total of 9 reinforced UHPC-NC composite beams were tested under cyclic loading. The test variables include UHPC layer thicknesses (zero, 200, and 360 mm), reinforcement ratios (1.184% and 1.786%), and the upper load levels (0.39~0.65). The results showed that good bonding had been achieved without delamination between UHPC and NC layers prior to the final fatigue failure of the beam, and the bending stiffness of the composite beam experienced a three-stage reduction under cyclic loading. Furthermore, an equation was proposed to predict the stiffness reduction coefficient of UHPC-NC composite beams under cyclic loading.

Experimental Analysis of Mechanical Behavior of Timber-Concrete Composite Beams with Different Connecting Systems

Timber-concrete composite structures are innovative structural systems which have become the subject of extensive research and practical usage, primarily due to their attractive mechanical properties. This article deals with the experimental procedure and the analysis of the mechanical behavior of two different series of timber-concrete composite beams with the same span and geometry of cross-sections. In the first BF-series, the screws were used as a connecting system between the timber and concrete parts, whereas in the BN-series the combination of notches and screws, as a more complex system, was used for the same purpose. Both series were exposed to loading up to a failure by means of the standard four-point bending test. The mechanical behavior of the BF and BN-series beams was analyzed by a comparative analysis referring to: the correlation of the failure loading and the deflection, mechanisms of failure, the strain development across the height of mid-span’s and support’s cross-sections, the horizontal displacement in the timber-concrete interlayer at the support zones, the value of shear stresses and the calculated values of the effective bending stiffness of the beams. The differences in bearing capacity between both series of beams were negligible (about 5%), the effective bending stiffness of BF beams is lower for 32.86% compared to the BN-series and the average value of deflections in BF-series beams is twice as high than in the BN-series. The BN-series beams showed better mechanical behavior in aspects of development of shear stresses in support zones, exhibiting lower shear stress values with an average of 40%.

Dynamic Properties of Timber–Concrete Composite Beams with Crossed Inclined Coach Screw Connections: Experimental and Theoretical Investigations

Due to the low density and stiffness of wood, traditional timber floor systems are prone to producing large vibration responses. By combining timber beams with concrete floors, timber–concrete composite (TCC) floor systems show stronger bearing capacity, higher bending stiffness, and better thermal and sound insulation behaviors when compared with traditional timber floor systems. In this study, the vibration performance of TCC beams with crossed inclined coach screw connectors was investigated using dynamic tests. The influence of the screw diameters and slab dimensions on the dynamic performance of the composite beams was evaluated. The test results demonstrated that TCC beams show good dynamic performance when used as a floor component and meet the preliminary requirements of floor vibration comfort for fundamental frequency. The fundamental frequency and damping ratio of TCC beams decreases with the increase in slab dimensions. The bending stiffness and natural frequency of TCC beams decrease smoothly when reducing the screw diameter from 16 to 12 mm. Additionally, two theoretical models were used to predict the natural frequencies of the TCC beams, and the predicted values show good consistency with the measured ones.

Experimental study on shear performance of CFRP-strengthened RC beams with geopolymer adhesive

PurposeThe effects of carbon fiber reinforced polymer (CFRP) reinforcement form, adhesive type and pre-crack width on failure mode, shear capacity, deflection response, CFRP strain response and crack patterns of strengthened specimens were investigated.Design/methodology/approachThis paper presents a geopolymer adhesive that matches the performance requirements of CFRP adhesive, which is applied to pre-cracked beams reinforced with CFRP strips. FindingsFor specimens with varying structural properties, two failure modes, the CFRP-concrete interface substrate failure and the fracture failure of CFRP, are observed. Moreover, the shear capacity, ultimate deflection and bending stiffness of the U-shaped CFRP-strengthened beams are enhanced in comparison to the complete-wrapping CFRP-strengthened beams. With an increase in pre-crack width, the increase in shear capacity of RC beams shear-strengthened with CFRP strips is less than that of non-cracked beams, resulting in a limited influence on the stiffness of CFRP-strengthened beams. The comparison of experimental results showed that the proposed finite element model (FEM) effectively evaluated the mechanical characteristics of CFRP-strengthened RC beams.Originality/valueTaking into consideration the reinforcement effect and the concept of environmental protection, the geopolymer adhesive reinforcement scheme is preferable to applying epoxy resin to the CFRP-strengthened RC beams.

Band Gap Design of Beam-Supported Phononic Crystal by Regulation and Control of Beam Bending Stiffness

Band Gap Design of Beam-Supported Phononic Crystal by Regulation and Control of Beam Bending Stiffness

Application of Transformed Cross-Section Method for Analytical Analysis of Laminated Veneer Lumber Beams Strengthened with Composite Materials

Due to the high cost of laboratory testing, many researchers are considering developing methods to predict the behavior of unreinforced and reinforced wood beams. This work aims to create either numerical or analytical models useful for extrapolating already conducted tests to other schemes/materials used as reinforcement. In the case of timber structures, due to the complexity of timber, this task is difficult. The first part of the article presents an analysis of the suitability of using a simplified mathematical model based on the equivalent cross-section method to describe the behavior of unreinforced and reinforced with carbon-fibre-reinforced polymer (CFRP) composite full-size laminated veneer lumber (LVL) beams. The theoretical results were compared with the results of conducted experimental tests. The scope of the analysis includes the estimation of modulus of rupture, bending stiffness, and determination of the neutral axis position. The equivalent cross-section method showed good agreement in determining the bending stiffness and neutral axis position of the strengthened sections. However, the suitability of using the equivalent cross-section method to estimate the load-carrying capacity of a cross-section reinforced with fiber composites still needs to be confirmed, which, according to the authors, is due to the differences between the assumed (linear) and actual (nonlinear) strain distribution in the compression zone. The second part uses the equivalent cross-section method to estimate the predicted bending stiffness of LVL beams strengthened with aramid-fibre-reinforced polymer (AFRP), glass-fibre-reinforced polymer (GFRP), and ultra-high modulus carbon-fibre-reinforced polymer (CFRP UHM) sheets. The proposed method can be used for preliminary evaluation of strengthening effectiveness of LVL beams.

Analytical solutions and optimization design for bending behavior of cross-laminated timber beams considering orthotropy and interface slip

The aim of this work was to propose analytical solutions and an optimization design method for the bending behavior of cross-laminated timber (CLT) beam, in which the orthotropy of timber and interface slip between the neighboring layers were considered simultaneously. The lamina layers of orthotropic woods were modeled based on the two-dimensional (2D) elasticity theory without transverse shear deformation assumption. By means of series expansion and solving differential equations, the general solutions for stresses and deformations in the beam were obtained with undetermined coefficients. The unknown coefficients were further determined by the transfer matrix method. The comparison study indicated the proposed solutions had higher accuracy than the Euler-Bernoulli beam solution and isotropic solution, since the proposed solutions renounced the transverse shear deformation assumption and considered the orthotropy of wood. Moreover, it was found that the interfacial stiffness has an economical upper bound above which no significant gain on the bending stiffness of CLT beam can be obtained, and an optimal configuration of geometry and material can achieve an increase of bending stiffness. We release our program for the proposed analytical solutions, at https://github.com/Njtpw/CLT-Beam.git.

Experimental and Finite Element Study on Bending Performance of Glulam-Concrete Composite Beam Reinforced with Timber Board.

In this research, experimental research and finite element modelling of glulam-concrete composite (GCC) beams were undertaken to study the flexural properties of composite beams containing timber board interlayers. The experimental results demonstrated that the failure mechanism of the GCC beam was the combination of bend and tensile failure of the glulam beam. The three-dimensional non linear finite element model was confirmed by comparing the load-deflection curve and load-interface slip curve with the experimental results. Parametric analyses were completed to explore the impacts of the glulam beam height, shear connector spacing, timber board interlayer thickness and concrete slab thickness on the flexural properties of composite beams. The numerical outcomes revealed that with an increase of glulam beam height, the bending bearing capacity and flexural stiffness of the composite beams were significantly improved. The timber boards were placed on top of the glulam members and used as the formwork for concrete slab casting. In addition, the flexural properties of composite beams were improved with the increase of the timber board thickness. With the elevation of the shear connector spacing, the ultimate bearing capacity and bending stiffness of composite beams were decreased. The bending bearing capacity and flexural rigidity of the GCC beams were ameliorated with the increase of concrete slab thickness.

A comprehensive investigation on bending stiffness of composite grid-stiffened and functional foams sandwich beam

This paper investigates the bending stiffness of composite grid-reinforced sandwich beams with functional foam cores by a combination of analysis, simulation, and experiment. First, the sandwich layer composed of stiffeners and foam cores is homogenized, and the equivalent mechanical parameters of the sandwich layer are proposed. Then, based on the first-order shear deformation theory, the three-point bending deflection of the beam is derived and verified by tests and simulations. Finally, the factors affecting the bending stiffness are investigated, such as the elastic modulus of the foam cores, the thickness of the stiffeners, the longitudinal and transverse spacing of the stiffeners, and the fiber lay-up angle of the stiffeners. The results of this paper are of great significance to the stiffness design and parameter optimization of composite grid-stiffened sandwich structures with foams for underwater vibration and noise reduction.

Peeling of finite-length elastica on Winkler foundation until complete detachment

Quasi-static peeling of a finite-length, flexible, horizontal beam (strip, thin film) from a horizontal substrate is considered. The displaced end of the beam is subjected to an upward deflection or to a rotation. The action of the adhesive is modeled as a Winkler foundation, and debonding is based on the common fracture mechanics approach. The behavior is examined from the application of loading to the initiation of peeling and then to complete detachment of the beam from the substrate. During at least a portion of the debonding process, the model corresponds to what traditionally has been considered a short beam on an elastic foundation. In the analysis, the beam is modeled as an elastica, so that bending is paramount and large displacements are allowed. The effects of the relative foundation stiffness to the beam bending stiffness, the work of adhesion, and the length, self-weight, extensibility, and initial unbonded length of the beam are investigated. In addition, experiments are conducted to complement the analysis.

Structural performance of steel–concrete composite beams with UHPC overlays under hogging moment

This paper investigates the usage of a thin layer of Ultra-high performance concrete (UHPC) reinforcing the concrete decks at the hogging moment region of steel–concrete composite beam bridges. An integrated experimental and numerical study was conducted to assess the influence of several parameters, such as the type of overlay concrete, arrangement of interfacial shear steel rebars, and presence of wire meshes, on the structural performance of the retrofitted composite beams. In the experimental program, five steel–concrete composite beams, including one normal concrete (NC)-strengthened composite beam and four UHPC-strengthened composite beams, were fabricated and tested. Experimental results indicate that the application of UHPC overlays significantly improved the structural performance of the retrofitted composite beams, and providing wire meshes in UHPC overlays restricted crack propagation of combined UHPC-NC decks. The bending stiffness and cracking resistance of the UHPC-strengthened composite beams were 25.2% and 368.7%, respectively higher than those of the NC-strengthened composite beams. As expected, the shear steel rebars can avoid sliding and uplifting at the substrate-to-overlay interface, and the utilization of shear steel rebars by a ratio of 0.28% magnified the bending stiffness and cracking resistance of the retrofitted beams by 9.7% and 5.1%, respectively, as compared to those without the rebars. In the numerical simulation, a three-dimensional finite element (FE) analysis of the composite beams was carried out, and the simulation results were validated with the experimental data. It is shown that the retrofitted beams under hogging moment finally failed due to fracture of the longitudinal steel reinforcements in the original decks, regardless of the presence of bonded overlays. Moreover, an analytical model for the combined UHPC-NC deck was developed to provide reliable predictions for the composite beams with UHPC overlays under hogging moment.

Stiffness Calculation for Negative Moment Region of Steel-Concrete Composite Beams considering the Influence of Cracking and Interface Slip

Concrete cracking and interface slip decrease the bending stiffness of steel-concrete composite beams (SCCBs) in the negative moment region. To evaluate this decrease in the stiffness of SCCBs, a static differential equation is used to derive analytical expressions of interface slip and deflection. Based on the static load test results for SCCBs, the influence of concrete cracking and interface slip on the stiffness is analyzed. A linear stiffness reduction method is proposed for calculating the stiffness of SCCBs in the negative moment region after the concrete undergoes cracking. The proposed method can be used in engineering applications as it enables the facile and accurate calculation of the deflection and slip and the changes in stiffness of SCCBs in the negative moment region. The method can also be used for predicting and evaluating performance in the field of structural design.

Bending stiffness of bamboo-concrete composite (BCC) beams under short-term loads

Bamboo-concrete composite (BCC) beams are newly-innovated products used for floor system which synergistically utilizes bamboo and concrete components. These composite beams at current technology belong to the beam characterized with partial composite action due to the existence of relative slip between bamboo segment and concrete slab. Existing investigations have demonstrated that the load bearing capacity of BCC beams depends on their bending stiffness; however, very limited prediction models are available to accurately estimate the bending stiffness of BCC beams. At present, the bending stiffness of BCC beams is predicted with the help of γ-method in Eurocode 5-Part 1-1, and available studies have demonstrated that this method overestimates the bending stiffness of BCC beams. To this end, this paper presents a novel explicit model characterized with mechanism and data mining to predict the bending stiffness of BCC beams under short-term loads. Three steps were performed to achieve the aforementioned research objective. The first step was to introduce the axial force transfer coefficient into the equilibrium equations of internal force for bamboo segment and concrete slab. Secondly, the bending stiffness of BCC beams was established by taking into account the effect of relative slip with the help of existing experimental results from the interfacial shear test and flexural test. Finally, the proposed model was validated by comparing with flexural performance results of BCC beams collected from available literature as well as those obtained from γ-method. The comparative results show that: i) the predicted bending stiffness of BCC beams is much closer to tested ones compared with γ-method; ii) the errors of proposed model predicting the bending stiffness for most BCC beams are within 10% of test results; however, nearly half of the predicted ones using γ-method have errors exceeding 10% of test results, both of which verify that the mechanism and data mining-dual driven model receives a better prediction for short-term bending stiffness of BCC beams.