Deflection Diagrams Research Articles

Mesoscopic simulations of a fracture process in reinforced concrete beam in bending using a 2D coupled DEM/micro-CT approach

In this study, a complex fracture process in a short rectangular concrete (RC) beam reinforced by one longitudinal bar (without vertical reinforcement) and subjected to quasi-static three-point bending was numerically explored in 2D conditions. A critical diagonal shear crack in the beam caused it to fail during the experiment. The numerical simulations were conducted with a classical particle discrete element method (DEM). A three-phase concrete description (aggregate, mortar, and interfacial transitional zones (ITZs) around aggregates) accounted for the concrete heterogeneity. In mesoscopic DEM calculations based on a 2D X-ray CT scan, the actual shape and placement of aggregate particles in concrete were taken for granted. In the study, the steel bar with ribs was replicated. ITZ was also assumed between the bar and mortar. Without imposing any bond-slip law, a geometrical bar/concrete interface condition was explicitly considered. The focus was on the force–deflection diagram, fracture process, contact forces, and stresses along the bar. A good level of agreement about the evolution of the vertical force versus the deflection and failure mechanism was attained between DEM analyses and in-house laboratory tests despite simplified 2D conditions. A strong effect of concrete mesostructure on the crack pattern was found.

Flexural strengthening of fire-damaged GFRP-reinforced concrete beams using CFRP sheet: Experimental and analytical study

Since the strengthening of fiber-reinforced polymer (FRP) bar-reinforced structures after a fire incident has rarely been considered in research works, in this work, the flexural response of plain and fiber-reinforced concrete beam specimens with embedded glass FRP (GFRP) bars strengthened with carbon FRP (CFRP) sheets was examined after a fire. Variables understudy in 10 GFRP bar-reinforced concrete beams included the exposure temperature (20, 400, and 600 °C), percentage of steel fiber in volume (0 and 1%), ratio of rebars (0.00314 and 0.00872), and CFRP sheet layers (0, 1, and 2), together with the presence or absence of the U-shaped anchorage. After conducting the four-point quasi-static bending experiment on the non-heated and heated beams, several parameters including the ductility, cracking pattern, and failure mode of the beams, together with their load–deflection diagrams, were assessed. The results showed that the flexural strengthening using CFRP sheets improved the flexural capacity of the specimens and this performance improvement became more notable with an increase in the exposure temperature. In the end, the sectional analysis method was utilized to propose an analytical model capable of estimating the load–deflection response of beams strengthened with CFRP sheets; this model properly estimated the test results.

Design of a beam of variable cross-section on the elastic base by the quasi-analytical method considering boundary conditions

Purpose. Improvement of the quasi-analytical method of nonlinear differential equation solution and its approbation with reference to beams of variable cross-section on the elastic base with two base factors.
 Research methods. Boundary conditions in the form of required number of correspondently transformed equations are added to the system of the linear algebraic equations which results from substitution of approximating function with constant factors (for example – power function) in the nonlinear differential equation and fixation of a set of variable values. The total number of the equations have to correspond to quantity of constant factors if the further solution will be carried out by an analytical method.
 Results. Deflection diagram of a trapezoid concrete beam with rectangular cross-section of variable height on the elastic base with two base factors has been calculated during approbation. Average solution error was equal to 0.06%. Distributions of the bending moments and normal stresses along the beam have been researched.
 Scientific novelty. The authors did not meet in literature such method of nonlinear differential equation solution.
 Practical value. The quasi-analytical method with realised consideration of boundary conditions that has been offered can be used for solution of differential equations of any order with various types of nonlinearity, including calculations of beams of variable cross-section on the elastic base.

Pilot Fracture Tests of Special Fine-Grained Composites

Mechanical fracture parameters were obtained for special fine-grained cement-based composites from three-point bending tests. A total of four sets of composite specimens were tested. All of the sets of composites were based on a general recipe and differ in the amount of high-strength aggregate and/or dispersed steel fibres present. Standardized prism specimens with a nominal size of 40 × 40 × 160 mm were used for the fracture tests after 131 days of curing. An initial notch was cut in the centre of the prisms with a depth approximately equal to one third of the specimen’s height. Three specimens from each set of composites were tested in the three-point bending fracture test configuration. Load versus midspan deflection diagrams were recorded. Experimentally obtained load vs displacement diagrams were corrected and analysed using the Effective Crack Model, the Work-of-Fracture method and an independent identification technique using numerical modelling. The most important mechanical fracture parameters, such as static modulus of elasticity, effective fracture toughness, specific fracture energy and effective tensile strength, were determined. Compressive and splitting tensile strength values were obtained from the halves of the specimens left over after the bending tests.

Mathematical modelling of forced oscillations of continuous members of resonance vibratory system

The article considers the possibilities of developing the combined discrete-continuous vibratory systems, in which the disturbing member is designed in the form of the uniform elastic rod with distributed inertia and stiffness parameters. The forced oscillations of the continuous member of the three-mass vibratory system are analyzed. Based on the Krylov-Duncan functions (circular and hyperbolic functions), the system of equations describing the motion of the continuous rod is derived. The novelty of the present paper consists in deriving the mathematical model of the discrete-continuous vibratory system, in which the model of the discrete subsystem is combined with the model of the continuous subsystem by applying the reactions in the supports holding the uniform elastic rods. The inertia-stiffness parameters of the vibratory system are determined and the analytical dependencies for calculating the reactions in supports are derived. The frequency-response curves of the considered discrete-continuous vibratory system are constructed. The deflection (bending) diagram of the continuous members is plotted for the case of forced oscillations of the combined discrete-continuous vibratory system.

An experimental and analytical study on the out-of-plane behavior of URM prisms strengthened with SFRC overlays

The observed failures in recent earthquakes have demonstrated the out-of-plane vulnerability of unreinforced masonry walls. An extensive experimental investigation was conducted on the application of hooked steel fibers as reinforcement in concrete overlays for the out-of-plane strengthening of solid clay brick masonry prisms. The variables included the thickness of the overlay (20, 30, and 40 mm), the thickness of the masonry prisms (single-leaf and double-leaf), the strengthening sides (one side and both sides), the overlay loading condition, and the steel fiber content. The test results were compared qualitatively (observations and failure modes) and quantitatively (load–deflection diagrams, ultimate loads, and flexural strengths). Moreover, an analytical model was utilized to evaluate the load-bearing capacity of the experimental results. The SFRC overlays considerably improved the behavior of the specimens in terms of load-bearing capacity and flexural stiffness although the thickness of the SFRC overlays was more effective than the volume fraction of the steel fibers in the overlays.

Shock polar investigation in supersonic rarefied gas flows over a circular cylinder

Well-known polars in classical shock wave theory, that is, flow deflection angle-shock angle (θ-β), hodograph (u*,v*), and pressure deflection (θ-P*) diagrams, are investigated for the rarefied gas flows using a recently proposed shock wave detection technique by Akhlaghi and coworkers. The agreement between the obtained polars with the analytical relations in classical shock wave theory has been shown in the continuum limit for the cases of supersonic flow over the wedge and cylinder geometries. Investigations are performed using the RGS2D direct simulation Monte Carlo solver for supersonic gas flows over a circular cylinder at continuum limit and Kn = 10−4, 10−3, 0.01, 0.03, 0.07, and 0.10. Two species of nitrogen and argon at various Mach numbers of 1.5, 3.0, and 10.0 are considered. The shock polars are investigated along bow shock waves in front of the cylinder. The results indicate that rarefaction significantly affects the shock polars. As Knudsen number increases, shock angle, maximum flow deflection angle, and aft shock pressure increase. However, velocity components after the shock wave decrease as the flow becomes more rarefied. These effects are stronger for θ-β polar under the weak shock condition. Meanwhile, they are stronger for θ-P* and hodograph polars in strong shock situations.

Experimental investigation of buckling of dented cylindrical shells under axial compression

The results of unique experimental studies of buckling of dented axially compressed unstiffened cylindrical shells are provided in the suggested paper. The dimple-like geometrical imperfections of different shape, size, deflection amplitude, and number of dents were created on cylindrical shells before axial loading. The initial deflection amplitude varied in the wide range, up to several shell thicknesses. In all cases the plateaus were discovered on the buckling load initial deflection diagrams. Corresponding axial loads were close to local lower buckling loads of perfect shells. These loads are defined as minimum values of axial force when the post-buckling equilibrium states of the perfect structure with one or several dimples exist. It was shown that the lower local buckling loads slightly depend on geometrical imperfections and therefore can be used for estimation of design buckling load of the structure. Over 50 specimens were tested. Pre-buckling and post-buckling behavior of imperfect shells was studied.

Elasto-plastic behaviour of cantilever beams containing varied stress concentration cut out features

In machine component design, it is necessary to introduce openings or cut outs to carry out specific service functions such as electrical wiring, piping, and inspection, among others. The introduction of these cut outs results in a high concentration of stress leading to degradation of the component strength, especially under cyclic loading. The geometrical features and orientation of these cut outs relative to the support and the applied loads will also influence the severity of the resulting stress concentration. Of particular interest to this study is the elastic and elasto-plastic behaviour of a cantilever beam containing rectangular, circular or diamond cut outs under plane strain conditions. Four aspects of the work were accordingly examined. The first is concerned with the elasto-plastic load–deflection diagram of the beam containing the cut out features. The second with the finite element predictions of the elastic behaviour and the associated stress concentration factor of the beam in the presence of the cut out features. The third with the elasto-plastic behaviour and etching results showing the remarkable agreement between the two. Finally, in the fourth, we focus our attention to unloading residual stresses. The results offer a complete coverage of the problem and should help in the elasto-plastic design of beams containing stress concentration features.

Investigations on fracture in reinforced concrete beams in 3-point bending using continuous micro-CT scanning

This study explores a fracture process in rectangular reinforced concrete (RC) beams subjected to quasi-static three-point bending. RC beams were short and long with included longitudinal reinforcement in the form of a steel or basalt bar. The ratio of the shear span to the effective depth was 1.5 and 0.75. The focus was on the load–deflection diagram and crack formation. Three-dimensional (3D) analyses of the size and distribution of pores and cracks were carried out with an X-ray micro-computed tomography system SkyScan 1173 of high resolution that is a very valuable non-destructive tool for studying a 3D material interior. The tomography system was connected with a quasi-static loading machine ISTRON 5569 to continuously follow fracture changes without loading breaks. The beams failed in shear due to a diagonal shear crack that was steeper with basalt reinforcement. The shear strength and flexural strength of RC beams with steel reinforcement were higher by about 10% than of RC beams with basalt reinforcement. The deflection corresponding to the maximum load of RC beams was higher by about 20–25% in RC beams with basalt reinforcement due to its lower basalt modulus of elasticity. The final volume of cracks in beams reinforced with basalt bars was higher by about 9–20% than in concrete beams reinforced with steel bars due to a higher beam deflection whereas the maximum crack width in concrete beams reinforced with basalt bars was higher by about 20–40% than in concrete beams reinforced with steel bars. The critical shear crack in RC beams with basalt reinforcement was wider by about 20–40% and steeper by about 10–45% as compared to concrete beams with steel reinforcement. The relationship between the crack volume and beam deflection was bi-linear. Both, aggregate breakage and crack branching occurred during beam bending.

Brace Forces in Horizontally Curved Steel Box Girder with Two Types of Lateral Bracing System by Using ANSYS Program

The U-shaped steel trapezoidal box girder is designed to work compositely with the concrete deck to form a closed-section for live loading. The critical stage of these girders are during construction since the fresh concrete and the whole construction load must be support by the non-composite steel section. At the top flange level, a lateral bracing system is typically mounted to form a quasi-closed section and thus increase the torsional stiffness at construction stage. In the current study, A horizontally curved steel box girder with two and three spans were used, lateral bracing includes two types of bracing system; Single Diagonal (SD) and a Crossed Diagonal (XD). Equations from prior studies estimate the lateral bracing forces for box girders with a good accuracy. The axial forces evaluated by 3-D Finite Element Analyses (ANSYS 19.2) are compared with the axial forces computed from the equations, there are excellent correlations between the finite element analysis and the equations, where the average of difference in the first case study with SD and XD was equal to 0.66% and 2%, respectively, while in the second case study it was 1.3%. Also it can be note that the deflection diagram for girder with XD bracing type is more uniform than the girder with SD bracing type. ANSYS software has been an efficient, inexpensive method and easy to use for designers of bridges.

Eccentric compressive behavior of steel fiber-reinforced RC columns strengthened with CFRP wraps: Experimental investigation and analytical modeling

Today, one of the most commonly used retrofitting techniques for reinforced concrete (RC) columns for enhancing their structural performance is to externally confine these columns with carbon fiber-reinforced polymers (CFRPs). From another aspect, the presence of steel fibers in the concrete mixture enhances the behavior of structural members. In this research, the eccentric compressive behavior of steel fiber-reinforced concrete columns strengthened with CFRP wraps, which has remained mainly under-researched, is explored experimentally and analytically. For that end, eighteen RC columns with plain concrete and fiber-reinforced concrete, confined and unconfined with CFRP sheets, length to width ratios (L/h) of 4.2 and 8.3, and load eccentricity ratios (e/h) of 0.29, 0.46, and 0.63 were manufactured and tested under eccentric compressive loading. The findings indicated that the CFRP sheets improved the loading capacity and ductility of the RC columns, while the presence of steel fibers in the concrete affected the loading capacity of the columns negligibly but made them more ductile. Further, the eccentricity of the applied load mitigated the effect of confinement with CFRP sheets on the reinforced concrete strength. Regarding the significance of the performance of these columns, an analytical model with the purpose of predicting the behavior of fibrous RC concrete columns strengthened with CFRP sheets under an eccentric compressive load was developed. In this model, by considering the simultaneous effects of the confinement with CFRP sheets and transverse reinforcement, the moment–curvature and the load–deflection diagrams were determined using the fiber section analysis method. Assessing the analytical findings against the experimental ones of the present work and those of others indicated that the proposed model is able to properly predict the behavior of fibrous concrete columns confined with transverse reinforcement and CFRP sheets under eccentric compressive loading.

Fracture response of cement-based composite with spherical glass aggregate exposed to high temperatures

This paper concerns an investigation into the effects of high temperatures acting on specimens made from specially designed fine-grained cement-based composite with spherical glass aggregate. The experimental programme was carried out on four sets of beam specimens with the dimensions 20 × 40 × 200 mm. The specimens were thermally loaded to pre-set temperatures of 100, 200 and 400 °C, after which these temperatures were maintained for 60 minutes (one of the sets contained three reference specimens which were placed in a laboratory at a temperature of 20 °C and were not exposed to heat). After the temperature loading had been performed, the specimens were left to cool down to ambient temperature. After that, fracture tests were used to determine the degree of damage caused to the specimens by temperature loading. Three-point bending tests were conducted on the previously loaded beam specimens, which were notched to provide them with an initial stress concentrator using a diamond blade saw before testing. The depth of the initial edge notch on the bottom side of the specimen was approximately 1/3 of the total specimen depth. The span length was 180 mm. Fracture response was evaluated via load versus deflection diagrams. The monitored parameters were modulus of elasticity, effective fracture toughness and specific fracture energy. Informative compressive strength values were also determined. Selected specimens were investigated using X-ray micro-tomography (micro-CT).

Mechanical Characteristics of Origami Mechanism Based on Thin Plate Bending Theory

Abstract This paper introduces a method for calculating the deformation displacement of the origami mechanism. The bearing capacity of each face can be analyzed by the relationship between the stress and displacement, which can provide a reference for the origami design. The Miura origami mechanism unit is considered. First, the folding angle of each crease is solved based on the geometric characteristics. The deforming form of the creases is then analyzed, and the bending moment acting on the paper surface is solved. Based on the geometric characteristics and stress forms, the paper surface is modeled as a sheet. Based on the bending theory of a thin plate with small deflection, the complex external load forms are decomposed by Levy's method and the superposition principle, and the expression of the deflection curve during the folding process is obtained. According to the stress and bending moment equations, the relationship between the bending moment and displacement is obtained. Finally, through an application example, the maximum deflection of the paper surface is calculated by matlab, and the deflection diagram of the deformed paper surface is drawn, which verifies the expression of the deflection curve.

Tangent modulus as a function of selected factors

This paper contributes to the understanding of a stress – strain diagram (SSD) in the region beyond the elastic limit (Viscoelastic and Plastic region). According to our results, the SSD in this region can be approximated by a second degree parabola. The advantage of such an approach is the possibility to simply calculate the value of stress if the strain is known and vice versa. Another advantage is in the possibility to simply calculate the tangent modulus.In the experimental part we determined the tangent and chord moduli for beech (Fagus sylvatica L.) and aspen (Populus tremula L.) “WS”. We also investigated the influence of the following factors on their value: material thickness “MT” (4, 6, 10, and 18 mm), degree of densification “DOD” (10% and 20% of the original thickness), and the number of loading cycles “NC” (0 versus 10,000).The paper describes the behavior of the tangent modulus in the whole force – deflection diagram.

Buckling load prediction of an externally pressurized thin spherical shell with localized imperfections

A simple formula for buckling load was derived from the asymptotic analysis of nonlinear behavior of a thin spherical shell. Firstly, two asymptotic cases were studied: the initial post-buckling regime of a perfect structure with small (compared to shell thickness) deflections and equilibrium states with large deflections. Two asymptotic formulae were jointed to obtain the solution for the entire range of deflection amplitude. Then the solution was modified for an imperfect shell. Initial deflections were introduced by only one parameter: the slope of the load–deflection diagram at small pressure. This minimal information was enough to predict the buckling load of the structure with localized imperfections. The suggested asymptotic result was validated by the finite element method and by comparison with experimental data.

Time-Dependent Topology of Railway Prestressed Concrete Sleepers

The railway sleepers are very important component of railway track structure. The sleepers can be manufactured by using timber, concrete, steel or other engineered materials. Nowadays, prestressed concrete has become most commonly used type of sleepers. Prestressed concrete sleepers have longer life-cycle and lower maintenance cost than reinforced concrete sleepers. They are expected to withstand high dynamic loads and harsh environments. However, durability and long-term performance of prestressed concrete sleepers are largely dependent on creep and shrinkage responses. This study investigates the long-term behaviours of prestressed concrete sleepers and proposes the shortening and deflection diagrams. Comparison between design codes of Eurocode 2 and AS3600-2009 provides the insight into the time-dependent performance of prestressed concrete sleepers. The outcome of this paper will improve the rail maintenance and inspection criteria in order to establish appropriate sensible remote track condition monitor network in practice.

Fracture properties of concrete specimens made from alkali activated binders

The aim of this paper is to quantify crack initiation and other fracture properties – effective fracture toughness and specific fracture energy – of two types of concrete with an alkali activated binder. The beam specimens with a stress concentrator were tested in a three-point bending test after 28, 90, and 365 days of maturing. Records of fracture tests in the form of load versus deflection (P–d) diagrams were evaluated using effective crack model and work-of-fracture method and load versus mouth crack opening displacement (P–CMOD) diagrams were evaluated using the Double-K fracture model. The initiation of cracks during the fracture tests for all ages was also monitored by the acoustic emission method. The higher value of monitored mechanical fracture parameters of concrete with alkali activated blast furnace slag were achieved with substitution blast furnace slag by low calcium fly ash in comparison with substitution by cement kiln dust.

Structural analysis of a prestressed segmented girder using contact elements in ANSYS

Studying the structural behavior of prestressed segmented girders is quite important due to the large use this type of solution in viaducts and bridges. Thus, this work presents a nonlinear three-dimensional structural analysis of an externally prestressed segmented concrete girder through the Finite Element Method (FEM), using a customized ANSYS platform, version 14.5. Aiming the minimization of the computational effort by using the lowest number of finite elements, a new viscoelastoplastic material model has been implemented for the structural concrete with the UPF customization tool of ANSYS, adding new subroutines, written in FORTRAN programming language, to the main program. This model takes into consideration the cracking of concrete in its formulation, being based on fib Model Code 2010, which uses Ottosen rupture surface as the rupture criterion. By implementing this new material model, it was possible to use the three-dimensional 20-node quadratic element SOLID186 to model the concrete. Upon validation of the model, an externally prestressed segmented box concrete girder that was originally lab tested by Aparicio et al. (2002) has been computationally simulated. In the discretization of the structure, in addition to element SOLID186 for the concrete, unidimensional element LINK180 has been used to model the prestressing tendons, as well as contact elements CONTA174 and TARGE170 to simulate the dry joints along the segmented girder. Stresses in the concrete and in the prestressing tendons are assessed, as well as joint openings and load versus deflection diagrams. A comparison between numerical and experimental data is also presented, showing a good agreement.

Evaluation of Three-Point Bending Fracture Tests of Selected Concrete: Mechanical Fracture Parameters

In this paper, authors focus attention on mechanical fracture parameters obtained from records of three-point bending fracture tests on concrete specimens with initial notch. Total eight sets of specimens were tested. Three specimens at the age of 28 days were tested in each set. Concrete was different in dosage of Portland cement CEM I 42.5 R and amount of used superplasticizer. The Effective Crack Model (ECM) was used to evaluate the load vs deflection diagrams to obtain modulus of elasticity and effective fracture toughness; specific fracture energy was determined using work-of-fracture method. Modulus of elasticity, tensile strength and fracture energy were also subject of identification via inverse analysis based on artificial neural network, which aim is to transfer the input data obtained from the fracture test to the desired material parameters.