Flexural Response Research Articles

Material comparative analysis of crack-bridging degradation of SFRC structural beams under flexural fatigue loading

This study experimentally investigates the influence of several material parameters on steel fiber reinforced concrete (SFRC) structural beams and their crack-bridging degradation over constant and variable amplitudes of flexural cyclic loading. Crack-bridging stress is evaluated using inverse analysis and its degradation against maximum rebars strain is derived. Four series of SRFC beams are prepared and characterized with different concrete compressive strengths, hooked-end steel fiber shapes in two different volume fractions, and two longitudinal reinforcement ratios. The results reveal lower crack-bridging degradation rates, and associated longer fatigue life and higher residual capacity, for beams with higher concrete strength. Further, SFRC fracture energy is shown to have a significant effect on fatigue response, with higher fracture energy associated with lower rates of crack-bridging degradation. However, steel fibers with double hooks are shown to have a relatively insignificant effect on controlling crack-bridging degradation rates and the flexural cyclic responses of SFRC beams as compared to single hook fibers. Also demonstrated is that a lower longitudinal reinforcement ratio leads to higher rebar strain rates with no influence on crack-bridging stress. Crack-bridging degradation diagrams are proposed for SFRC beams that quantitatively capture several material parameters effects based on their mechanical properties over the fatigue life.

Two-dimensional elasticity model for composite beams with deformable shear connectors: Analytical and numerical solutions

A novel and efficient exact two-dimensional (2D) model is developed for predicting the flexural response of two-layered composite beams made of different materials based on the elasticity theory. The beam is considered as a specific case of plane stress problem laying in the longitudinal vertical plane passing through the centroid of the beam section. The proposed two-dimensional model considers the orthotropic properties of materials used in composite beams. The partial shear interaction between two material layers in the form of shear slip at their interface is also considered in this study. The deformable shear connectors between these layers are modeled using distributed shear springs along the beam length. The present 2D model's accuracy is validated by comparing its results with published results as well as numerical results generated by a thorough 2D finite element model using ABAQUS. Furthermore, the stretching effect over the direction of beam depth on the flexural response of two-layered composite beams is investigated by comparing the results produced by the one-dimensional (1D) HBT model and the proposed 2D elasticity model.

Numerical Simulations on the Flexural Responses of Rubberised Concrete

The increase in world population has led to a significant increase in the numbers of cars and used tyres. These tyres must be disposed of on an ongoing basis as a result of their consumption or deterioration. This can result in negative effects on the environment that must be preserved, especially from those materials, i.e., these waste materials are difficult to dispose of without special treatments. Hence, extensive experimental investigations and numerical simulations need to be conducted to use and recycle these wastes by exploring the possibility of using them as alternative ingredients in construction materials. For example, waste rubber pieces can be used as one of the main components of concrete. In this study, the main aim was to numerically simulate the flexural behaviours of rubberised concrete under the influence of an applied vertical loading with different contents of added rubbers by using the commercial finite element software ANSYS. The obtained numerical results were compared with the experimental results of a previous study and showed a good agreement with the deflections and moduli of rupture, with the variances from 2–7% in the deflections. However, the differences in the moduli of rupture varied between 5% and 9%. Finally, the statistical analyses indicated that these numerical mean values and standard deviations were acceptable and were very close to the experimental values.

Cover Picture: Steel Construction 2/2022

AbstractDouble‐skin sandwich panels with steel sheetings and low density aluminium foam have an excellent flexural response. Experimental results highligthed the key role of the type of adhesive and its strength on the ultimate performance. Simple equations are provided to predict the stiffness, yield and plastic strength (s. article Latour, M. et al, pp. 73–80)

Flexural response of sandwich composites integrated with 3D multi-layer stitched core

This experimental study investigates the flexural response of sandwich composites integrated with 3D multi-layer stitched core. Polypropylene 3D multi-layer woven fabric impregnated with an epoxy resin was selected as the core, while E-glass fiber reinforced epoxy was used for the sandwich composite face sheets. The sandwich composite exhibited a ductile behavior when loaded in three-point bending as the core layers increased. This is due to the drop in core shear strength with the increased number of core layers. The core layers that were not directly connected with the face sheets deformed most under shear, resulting in a more flexible plate behavior. The number of core layers, size of core unit-cell and stitching density were the critical design parameters determining the flexural strength and stiffness of the sandwich panel. The flexural modulus of sandwich composites with higher stitching density core stiffer than those of lower stitching density.

Analysis of the tension chord in the flexural response of concrete elements: Methodology and application to weft-knitted textile reinforcement

The use of high-strength fibrous materials offers great potential to serve as the main reinforcement in the flexural response of lightweight concrete structures. Specifically, weft-knitted textile reinforcement allows creating complex geometries (i.e. doubly curved or folded) and introducing straight inlays as well as spatial features such as ribs within the fabric to enhance the bond conditions between the reinforcement and the concrete. While the evaluation of uniaxial tension tests to characterise the mechanical behaviour is usually straightforward, the vast majority of bending tests of textile reinforced concrete elements in the literature are limited to load–displacement data, which does not give direct information on the mechanical behaviour and makes it difficult to compare specimens with different geometries or reinforcement contents. This study presents a methodology based on digital image correlation measurements to directly assess the response in the tension chord of reinforced concrete beams in four-point bending. This methodology was applied and validated in an experimental campaign consisting of 16 bending tests with weft-knitted textile reinforcement. Various fibre materials, coating types and specimen geometries were tested, and the results were compared to corresponding uniaxial tension tests with the same type of reinforcement, generally showing a good agreement in the load-deformation behaviour and the crack kinematics. However, the textile reinforcement could not be utilised to the tensile strength obtained in uniaxial tension since all bending beams failed prematurely either in a combined bending-shear type failure (for most of the cement paste-coated textiles) or due to the delamination of the textile within a shear crack (for all epoxy-coated textiles). The Tension Chord Model with an assumed constant bond-slip relationship and an equivalent reinforcement ratio in bending yielded a good prediction of the stress–strain relationship, the tension stiffening effect, the crack widths and spacing.

Mechanical behavior and fracture characteristics of polymeric pipes under curved three point bending tests: Experimental and numerical approaches

This study describes an investigation of the load–deflection response of the material used for production of polymeric pipes. Three point bending tests were performed on curved pipe samples to evaluate their flexural properties, namely the flexural strength, the modulus, the strain to failure and the mode of failure. Effects of various configurations and parameters are investigated: effect of internal or external loading, effect of notch, impact of aging, combined effect of notch and aging. In addition, FE models are established to predict pipe material response under flexural loading. From the main results, the average flexural stress–strain response of pipe material is characterized by a linear portion curve, followed by a non-linear deformation up to the ultimate failure stress. A ductile behavior was observed, but with a brutal rupture at the peak flexural stress. The flexure behavior of the pipe material depends also on the configuration, and it behaves differently under internal and external loading. The presence of notch in pipe material reduces its mechanical performance. A significant decrease of flexural properties was observed for hydrothermal aged pipe samples. The combined effect of both hydrothermal aging and notch affects dramatically the flexural performance of pipe material. Consequently, the service life of pipe structures risks to be reduced. Finally, a coupledexperimental–numericalapproach for the characterization of pipe material behavior under flexure loading has shown a good correlation, and therefore, the efficiency of the established FE model to predict the flexural response of pipe structures.

Nonlinear Analysis of Reinforced Geopolymer Concrete Beams

To decarbonise the current construction sector and meet the global net-zero target, there is a pressing need to develop an environmentally friendly alternative to Portland cement concrete. Alkali activated and geopolymer concrete have much to offer in this regard. At present, however, there is limited study on the behaviours of alkali activated structural members, particularly on flexural members, which encompass most practical design situations. This paper presents a database of 37 tests on slender alkali activated and geopolymer concrete beams available in the literature, with the aim to investigate the flexural strengths of this alternative concrete when used as a structural member. In addition, the results of nonlinear finite element analyses on fourteen reinforced geopolymer concrete beams are presented to highlight key influencing factors governing the behaviour and failure of flexural members. Of particular interest is to study the influence of reinforcement ratio, compressive strength, and material brittleness on the overall strength and ductility. Overall, it is shown that the flexural response of geopolymer concrete beams under short-term loading is comparable to that of ordinary reinforced concrete beams.

Wave propagation in carbon nanotube-reinforced nanocomposite doubly-curved shells resting on a viscoelastic foundation

This research aims at studying the propagation of waves in doubly-curved nanoshells made of carbon nanotube-reinforced composite (CNTRC) nanoshell panels while resting on a viscoelastic foundation. For the first time, a nonlocal strain gradient model of first-order shear deformation theory (FSDT) is developed in curvilinear coordinate for the wave propagation analysis of such properties, geometry, and foundation. The effective material properties of four types of CNTs’ distribution are estimated using a modified rule of mixture. The size-dependent governing equations are found using the Hamiltonian principle and after derivation, the equations are solved to find the damped flexural wave responses using a harmonic solving procedure. The results show the influence of viscoelastic foundation parameters, small-scale parameters, CNTs’ distribution schemes, and weight fraction of CNTs on the wave behavior of CNTRC doubly-curved shells with spherical, hyperbolic, cylindrical, and elliptical panels.

Flexural response of fiber-metal laminate face-sheet/corrugated core sandwich beams

Flexural response of fiber-metal laminate face-sheet/corrugated core sandwich beams

Flexural toughness and compressive stress–strain behaviour of pseudoelastic shape memory alloy fibre reinforced concrete

The results of experimental analyses for the full-range compressive and flexural response of concrete reinforced with pseudoelastic shape memory alloy fibres (PSMAFs) are discussed in this paper. PSMAFs were manufactured with two types of end hooks and were used in four different fibre contents ranging between 0.5% and 1.25%, with an interval of 0.25% by volume. Cracking patterns and full-depth crack width profiles of PSMAFs reinforced concrete (PMSA-FRC) were also generated by the 2D digital image correlation (DIC) technique. The results obtained for PMSA-FRC are compared with those of steel fibre reinforced concrete (SFRC).The flexural responses of PSMA-FRC and SFRC were significantly different at fifferent stages of flexural behaviour. Compared to SFRC, PSMA-FRC showed lower flexural strength but considerably higher flexural toughness and deflection capacity. PSMA-FRC also exhibited slightly lower compressive strength (5-8%) and modulus of elasticity (4–10%) than SFRC. However, no significant difference was noticed between PSMA-FRC and SFRC regarding the overall shape of the compressive stress–strain curve, compressive toughness and failure mode. It is also shown that PSMAFs type 2, the fibre with 45° end hook, is more efficient in distributing stress over a larger cementitious matrix area. DIC analyses displayed better control over cracking, improved multiple-cracking performance, and tighter crack profiles for PSMAFs type 2 at all four fibre contents tested in this study.

A beam‐column element for modeling nonlinear flexural and shear behaviors of reinforced masonry walls

AbstractThis paper presents a computationally efficient beam‐column element to simulate the nonlinear flexural and shear behaviors of reinforced masonry shear walls subjected to bilateral seismic forces. A three‐field mixed formulation based on the Hu‐Washizu variational principle is adopted. This mixed element is free of shear locking, and allows a wall to be modeled with one element. The axial and flexural responses are evaluated with a fiber‐section model at each integration point along the element, while the shear response in each loading direction is represented by a phenomenological model. The element accounts for the influence of the axial load, wall aspect ratio, and wall flange, if any, on the shear response of a wall. To consider axial‐flexure‐shear interaction, the shear model takes into account the axial stress resultant from the fiber‐section model, and the compressive strength of masonry in the fiber‐section model decreases when severe shear damage developed. The model has been calibrated and validated with experiment data. It has been demonstrated that it is able to reproduce experimental results from quasi‐static cyclic loading tests of single walls as well as shake‐table tests of wall systems with good accuracy. Furthermore, the ability of the proposed model to simulate the response of reinforced masonry shear wall systems subjected to bilateral seismic forces has been examined by comparing with results from a detailed finite element model.

Timing and evolution of the Mississippian sedimentary system on southeastern Laurussia: Evidence from the Appalachian area, U.S.A.

This paper is a synthesis of Mississippian sedimentation on the southeastern, Appalachian margin of Laurussia. The Mississippian stratigraphic framework in the Appalachian area shows a large-scale, three-part, wedge-like, clastic‑carbonate-clastic sequence, which has been interpreted to be a likely flexural response to coeval Neoacadian Orogeny. Using an already established flexural framework and biostratigraphy, we have interpreted the approximate timing of flexural events based on biostratigraphy. These flexural events begin with active deformational loading that initiated rapid subsidence in the Appalachian foreland basin, during which the deeper-water, black Sunbury Shale and equivalents were deposited throughout the basin. Subsequent relaxational loading contributed to basin infilling through the deposition of a deeper-water, clastic succession, manifest as the extensive Cuyahoga-Logan-Borden-Grainger-Price-Rockwell-Pocono deltaic clastic wedge. By the time this clastic wedge had filled the foreland basin, clastic source areas in the orogen had apparently been lowered to the point that shallow seas migrated far eastward across former source areas. This brief period of equilibrium between the basin and source areas resulted in reduced clastic influx at a time when the basin entered subtropical latitudes, setting the stage for widespread carbonate deposition, represented by units like the Newman, Greenbrier, and Slade Limestones. Ensuing, rebound-related uplift, perhaps abetted by incipient, subsurface, Alleghanian thrusting, generated new sediment source areas and accompanying wedges of prograding marginal-marine and terrestrial sediment represented by the Pennington, Mauch Chunk and equivalent units. Marginal-marine sedimentation continued into Early Pennsylvanian time, when a combination of Alleghanian uplift and LPIA lowstand conditions generated a period of widespread, deep erosion that in many places across the Appalachian Basin destroyed substantial parts of the underlying Mississippian succession along the sub-Absaroka or “Mississippian-Pennsylvanian” unconformity. Although the basic Mississippian stratigraphic framework described above for the Appalachian Basin largely appears to be a consequence of Neoacadian flexural responses, major details regarding processes, timing and lithology were apparently controlled by concomitant interactions involving paleoclimate, eustasy, coeval Ouachita tectonism, and possibly early Alleghanian tectonism.

The behavior of concrete beams strengthened with NSM CFRP strips: a numerical parametric study

A non-linear finite element (NLFE) model was developed to predict the flexural response of concrete beams, strengthened with near surface-mounted (NSM) carbon fiber-reinforced polymer (CFRP) strips. The model was employed for predicting the influence of a wider spectrum of key parameters, concrete compressive strength (25–55 MPa), NSM FRP strips number (2–4) or spacing (20–35 mm), bond length (100–450 mm), FRP type (carbon, glass, and basalt) and loading pattern (four-point, three-point, and distributed load), upon the performance of these beams. The results showed a clear improvement in the performance of the CFRP-strengthened concrete beams when made at a higher-strength class of concrete. Using a higher number of NSM FRP strips of the same cross-sectional area contributed to enhancing the mechanical performance noticeably. Moreover, the model developed was capable of capturing the negative impact of using a lower spacing for a constant number of NSM CFRP strips. The impact of the FRP strips' type varied upon the mechanical property predicted and the strength grade of concrete used in the casting of the beams. The load resistance of NSM FRP-strengthened specimens was the highest under three-point load configuration, followed, in sequence, by distributed and four-point loads, respectively.

Behaviour of Rectangular Hollow Thin Ply Carbon Thermoset and Thermoplastic Composite Tubes Subjected to Bending.

Tubular composites are widely used in many industrial applications, and there is need to use new material and reliable manufacturing processes to improve the performance and process aspects. The current research presents a detailed study to understand the flexure response of rectangular tubular composites based on thin ply carbon fibres and Elium® resin. Another aim was to understand the failure mechanisms of novel tubular thermoplastic composite systems and carry out a baseline comparison with Epoxy-based tubular systems. In the current research, a bladder-assisted resin transfer moulding process was used to manufacture hollow thermoplastic composite tubes, and the bending behaviour of thin ply carbon (TPC) composite parts with novel Elium® (EL) and Epoxy (EP) resin as the matrix material was studied using a detailed experimental study. A testing method with optimized support span and a saddle was used to carry out three-point bending tests on the tubular composite structures. The TPC/EL composite tubes have shown 10% higher bending strength, with a noticeable increase in deformation due the presence of extended plasticity attributes for acrylic Elium resin. Failure mechanisms studied with the detailed microscopic investigation have shown severe catastrophic failure for epoxy-based composite tubes; however, acrylic Elium®-based composite tubes have shown different damage modes such as fibre splitting, resin infragmentation, and fibre resin-interfacial cracking.

Geometrically nonlinear analysis for flexure response of FGM plate under patch load

Present work explores quadratic extrapolation (QE) technique for large deformation flexure study of FGM plate with five variables higher-order shear deformation theory (HSDT). Rule of mixtures is utilized in achieving effective material properties across the thickness. Governing differential equations (GDEs) and boundary conditions have been acquired using the principle of virtual work. Quadratic extrapolation (QE) and Newton-Raphson (NR) linearization techniques are considered and compared with respect to computational time. Von-Karman type nonlinearity is used in the present work. Multiquadric radial basis function (RBF) based meshfree technique discretizes GDEs in displacement form. FGM plates with different boundary conditions are investigated under different patch loadings. Present results are validated with some previously published results after a convergence study. Some new results are produced for the flexural response of the FGM plate under patch loads. Effect of types of loads, grading index, patch load location, and boundary conditions are presented.

Flexural response of FRP-strengthened lightweight RC beams: hybrid bond efficiency of L‐shape ribbed bars and NSM technique

This paper presents the results of an experimental study on employing near surface mounted (NSM) fiber-reinforced polymer (FRP) reinforcement technique, and L‐shape ribbed bars, for flexural strengthening of lightweight reinforced concrete (RC) beams. 18 RC beams including 14 lightweight RC beams and four normal-weight concrete beams were designed. The beams were strengthened with glass fiber-reinforced polymer (GFRP) bars and carbon fiber-reinforced polymer (CFRP) laminate in bending tests. Test parameters included: (1) different FRP materials (glass bars and carbon sheets), (2) longitudinal steel reinforcement ratio, and (3) type of strengthening technique used (NSM reinforcement or hybrid). The ultimate tensile strength, deflection, compressive and tensile strain of concrete, and failure mode of the beams were examined under four-point flexural test. Results showed that the ultimate strength of all RC beams increased between 33 and 105% compared to the control beam. The ultimate strength of beams reinforced with CFRP in the mid-span region was 10% higher than that of beams strengthened at both ends, although the former exhibited 28% lower ultimate deflection. The ultimate strength and deflection of RC beams strengthened with combined steel reinforcing bars and GFRP bars were 10% and 108% higher, respectively, compared to those of RC beams strengthened with GFRP bars only. Hybrid L‐shape ribbed bars beams showed a considerably higher ductility (up to 170% increase in the ultimate deflection) compared to other beams. The comparison of the experimental results of the ultimate strength of the beams with ACI440-2R guidelines indicated a reasonable and conservative prediction of the code expression.

Improvement of flexural and cyclic performance of bridge deck slabs by utilizing steel fiber reinforced concrete (SFRC)

This paper aims at investigating how the utilization of steel fiber reinforced concrete (SFRC) improves the flexural and cyclic responses of reinforced concrete bridge deck slabs. Firstly, one plain concrete slab and two SFRC slabs reinforced by mill-cut steel fibers and corrugated steel fibers, respectively, were tested under cyclic loads. The load–deflection responses, cyclic deformation behaviors, strain and crack evolutions are discussed. Subsequently, a theoretical analysis method of SFRC slab is introduced and validated. Using this method, the effects of key strength parameters of SFRC, i.e. fL, fR1, fR4, on load–deflection responses and deck slab design indices (i.e. slab height, areas of steel rebars, slab span) are clarified through parametric analysis. Results demonstrate that using SFRC in deck slabs significantly enhances the cyclic deformation performance, decreases the residual strain in the slab section, and improves the crack behavior by reducing residual crack width and increasing cracking stiffness. An increase in fL and fR1 can enhance service capacity Ps and flexural stiffness ks, as well as improve design indices under the service requirement, whilst the influences of fR4 are minor. Increasing fR1 and fR4 can enhance ultimate capacity Pu and improve design indices under the ultimate requirement, whereas the effects of fL are rather limited. Since the use of mill-cut steel fibers produces higher fL and fR1 than corrugated steel fibers, the former has better advantages to enhance Ps and ks. These results may provide references for the application of SFRC in bridge deck slabs.

A Paper-Based Cantilever Beam Mini Actuator Using Hygro-Thermal Response

New technological and scientific advances in the development of sensors and actuators demand the development of new devices to deal with recent problems and challenges in these new and emerging processes. Moreover, paper-based devices have tremendous potential for developing actuators as paper exhibits capillary transport and hygroexpansion due to swelling of the fibers when absorbing water. Therefore, this paper proposes a mini actuator that is based on a hygro-thermal-paper-based cantilever beam that is activated by means of a droplet of an aqueous solution in combination with a circulating electrical current to analyze its response. The contribution of this proposal includes the analysis of the flexural response of the mini actuator when it is tested by using two different solutions: distilled water and a water/alcohol solution. Additionally, four cases related to the droplet volume are studied and a statistical analysis of the bending responses is presented. The results achieved show that that water-alcohol solutions have a lower deviation in comparison with water only. Moreover, it is demonstrated that a specific change in the maximum displacement is obtained according to the volume and the type of solution. Thus, it is suggested that the response of the mini actuator can be tuned using different aqueous solutions.

Flexural behavior RC beams strengthened and repaired with SRP composite

This paper presents the results of an experimental investigation conducted to study the flexural response of reinforced concrete (RC) beams strengthened and repaired using externally bonded steel reinforced polymer (SRP) composite. SRP composite strips were bonded to the tension face of four RC beams, which were tested in four-point bending. Parameters varied were the presence/absence of U-wrap anchorages and loading rate. The difference in the loading rates employed did not appear to have a significant effect on the yield load, maximum load, or failure mode. The strengthening system without anchorage increased the yield load by 16% relative to the control beam, whereas the strengthening system with U-wrap anchorages increased the yield load by 26–34% relative to the control beam. Values of the maximum strain in the composite at the maximum load of the strengthened beams with U-wrap anchorages ranged from 0.9% to 1.2% and were more than twice as large as that of the strengthened beam without anchorage. The peak fiber stress obtained from single-lap direct-shear tests of SRP-concrete joints was similar to the maximum fiber tensile stress obtained by sectional analysis for the strengthened beam without anchorage.