Prismatic Beams Research Articles

Experimental and Numerical Characterization of Non-Proprietary UHPFRC Beam—Parametric Analyses of Mechanical Properties

Fabrication of ultra-high-performance concrete (UHPC) is costly, especially when commercial materials are used. Additionally, in contrast to conventional concrete, numerical procedures to simulate the behaviour of ultra-high-performance fibre-reinforced concrete (UHPFRC) are very limited. To contribute to the foregoing issues in this field, local materials were used in the fabrication process, while accounting for environmental issues and costs. Micro steel fibres (L: 13 mm, d: 0.16 mm, and ft: 2600 MPa; L: length, d: diameter, ft: tensile strength) were used in 2% volumetric ratios. Compression and indirect tests were carried out on cylindrical and prismatic beams according to international standards. To further enrich the research and contribute to the limited simulation data on UHPFRC, and better comprehension of the parameters, numerical analyses were performed using the ATENA software. Finally, nonlinear regression analyses were employed to capture the deflection-flexural response of the beams. The results were promising, indicating cost-effective fabrication using local materials that met the minimum requirements of UHFRC in terms of compressive strength. Furthermore, inverse analysis proved to be an easy and efficient method for capturing the flexural response of UHPFRC beams.

Semi-analytical solution for elastoplastic deflection of prismatic fixed-end beams with circular cross-section

Prismatic fixed-end beams with circular cross-section are often used in engineering. Therefore, there is a need for a solution of an elastoplastic deflection of prismatic fixed-end beams with circular cross-section loaded by lateral displacement at one end of the beam, which is suitable for practical use. The elastoplastic deflection beam theory does not provide a solution in a closed form for such a problem. Hence, a semi-analytical solution is proposed in this paper. Homogenous and isotropic beams with the bilinear elastoplastic strain hardening behaviour are covered in the proposed solution. The elastic deflection of a beam is determined by the Bernoulli–Euler formula. However, differential equation of beam bending in the plastic domain of material behaviour does not have a solution in a closed form. Therefore, an incremental procedure for determining the curvature of the plasticised region of the beam is suggested. The proposed semi-analytical solution is validated by comparing to the finite element analysis results of 16 different fixed-end beam models with varying geometric and material characteristics. Also, validation is done with experimental results of the bar damper device, available in the literature, which has been selected as a sample of a real engineering system where the proposed solution can be applied. A satisfying agreement between the proposed semi-analytical results and the subsequent numerical and experimental results is herein achieved, confirming the solution’s reliability. Finally, a parametric study is conducted using the proposed semi-analytical solution in order to determine the influence of geometrical parameters and material characteristics on the mechanical properties of prismatic fixed-end beams with circular cross-section loaded by lateral displacement at one end of the beam.

Верификация программных комплексов на примере статически определимой призматической балки

The paper considers issues of verifying software systems on the example of a prismatic beam. Verification refers to checking the software system results compliance with requirements and constraints. Verification was carried out on a test example, which was selected as calculation of displacements of a statically determined beam with one rigid attachment under the action of a transverse load. Analytical calculation of the statically determined prismatic beam displacement was performed, and its bending curve was obtained. The bending curve shape was found by integrating the beam elastic line differential equation. Maximum displacement at the beam edge was calculated. Results of the analytical method verification calculations were compared with data obtained using different software systems, where the problem was solved by the finite element method. Advantages and disadvantages of the ANSYS and SolidWorks software systems were indicated. The obtained results testify to accuracy of the performed engineering calculations.

Study on the Shear Behavior of Prismatic and Tapered Continuous Beams with Corrugated Steel Webs under External Prestressing Force

This paper analyzes the shear behavior of prismatic and tapered continuous beams with corrugated steel webs (CSWs) under different external prestressing tendon layouts. For girder bridges with CSWs, the existing design specifications consider only the shear force caused by the external prestressing force when calculating the shear stress of CSWs under the external prestressing tendons. However, in a tapered continuous beam with CSWs, in addition to the shear force caused by the prestressing force, the prestressing bending moment and the horizontal component of prestressing can also induce additional shear stress, which results in a redistribution of the shear stress on the section. This finding has not been reported previously. Then, the reasons for the shear behavior differences of tapered and prismatic continuous beams with CSWs under external prestressing tendons are explored. The study reveals the factors affecting the distribution of shear stress on indeterminate static beams with CSWs under external prestressing and proves that the traditional method used for predicting the shear stress on CSWs is not applicable to tapered cases. In addition, it is found that the direction of the internal forces and moments also affects the shear-bearing ratios of CSWs and concrete slabs. Consequently, a unified analytical formula is proposed for calculating the shear stresses of the CSWs induced by external prestressing, and it can be applied to both tapered and prismatic continuous beams with CSWs under external prestressing tendons.

Studying the compressive, tensile and flexural properties of binary and ternary fiber-reinforced UHPC using experimental, numerical and multi-target digital image correlation methods

Compressive, tensile, and flexural properties of ultra-high-performance concrete (UHPFRC) specimens were studied in this research. Binary and ternary combinations of micro steel (MS), round crimped (RC), crimped (C), hooked-end (H), and polypropylene (PP) fibers were used in overall ratios of 2 % by volume of concrete. For this purpose, 100×200 mm cylindrical specimens, dog-bone specimens (length: 330 mm, width: 80 mm, thickness: 40 mm), and prismatic beams with a dimension of 100×100×500 mm (clear span: 450 mm) were cast and tested under compressive, tensile, and four-point bending tests (4PBT). A digital image correlation (DIC)-based method namely, multi-target digital image correlation (MT-DIC) was used to record the displacement and deflection values in tension and flexure tests. Furthermore, experimental findings were used in numerical simulations and additional analyses were carried out as complementary studies to provide a better understanding of the governing parameters; length, width, depth, and overall size of the beams. Results revealed that a hybrid combination of micro and macro steel fibers performs better than other specimens in all the investigated parameters and the MT-DIC method proved to be a very useful tool in capturing the displacement and deflection values. Furthermore, the inverse analysis approach for the numerical simulation of beams and nonlinear regression-based models captured the direct tension and flexural results with coefficient of determination (R2) values above 0.90.

Design of compliant mechanisms based on compliant building elements. Part II: Practice

In Part II, we present the use and application of the Compliant Building Elements (CBE) method to generate practical designs for different multiple degree-of-freedom (DOF) compliant mechanisms. We first create a compliant mechanism library based on the combination of prismatic beams, which includes commonly used basic elements (BEs), serial elements (SEs), and parallel elements (PEs). Examples are given during the construction of the library. Based on the library and CBE method, we demonstrate the design of a six-axis nanopositioner, a compliant steering mechanism, and a one-dimensional mechanical metamaterial structure. The outcome of each design process yields a flexure topology that meets the design requirements as well as the corresponding parametric stiffness and compliance matrices, from which we can efficiently obtain the kinematic characteristics of the flexure system and optimize the stiffnesses in selected axes.

A Study of the Structural Behavior of Recycled-Concrete Haunched Beams with Web Opening

The structural behavior of Reinforced Concrete Haunched Beams (RCHBs) was investigated in this study. One prismatic control beam and fourteen Haunched Beams (HBs) were used in the experimental test and numerical analysis. The variables considered are Recycled Concrete Aggregate (RCA) ratio which is taken as 0, 30 %, and 60 %, opening shape (square and circular with the same area of 4560 mm2), and haunch angle (α) of 6.34° and 9.46°. The samples of dimensions (1750x200x300) mm were tested under a two-point load. The samples were simulated numerically using the Abaqus/CAE tool. The experimental outcomes show that using 30% RCA decreased the resistance by 8.24% - 26.45% compared with the control sample. While at 60% RCA, the resistance decreased by 16.35% - 34.71%. HBs with α=6.34° give a strength quite close to the control beam (PN) by 1.93%, while α=9.46° decreases the strength by 12.94% compared with PN. Compared with the solid beam, square holes in HBs provide a strength reduction range of 5.83% - 18.79% for α=6.34° and α=9.46°, respectively. The beams with circular apertures have a resistance decrease of about 3.43% - 14.70%, which corresponds to α=6.34° and α=9.46°. The numerical findings were 8.41% of the experimental data.

A Variable Clutch Mechanism for Adjustable Stiffness Actuators Based on Bending and Torsion of Prismatic Beams

Today, a major obstacle to developing locomotion mechanisms that are as safe and energy efficient as living organisms has been overcome with the development of actuators with adjustable stiffness. This work presents an innovative clutch mechanism whose stiffness can be adjusted based on the combined bending and torsion of the prismatic beams. In this way, the stiffness of any rotary actuator can be adjusted with the help of this clutch mechanism. The adjustable clutch mechanism consists of elastic prismatic beams placed in any position in the power transmission unit. The stiffness of the clutch mechanism is controlled by varying the active clutch length of these prismatic elastic beams using an additional actuator. This work is a new version developed to solve the mechanical problems observed in our previous studies using elastic cylindrical beams. Cylindrical beams subjected to dynamic bending have a higher risk of cracking on the cylindrical surface over time. The cross-section of cylindrical beams subjected to bending is very narrow at the point furthest from the center, which bears the greatest load in bending. For this reason, it has been observed that the beams break due to micro-cracks on the surfaces of the cylindrical beams in long-term use. However, the rectangular beam proposed as a solution to this mechanical problem is subject to combined torsion and bending, complicating the analytical solution. In this study, the stiffness variation of an adjustable elastic coupling mechanism depending on the coupling length was obtained with a simplified discrete analytical approach. Torsional and bending stiffness of the prismatic beams were calculated separately, and their sum gave the angular stiffness of the actuator. The analytical results obtained using this simple approach are compared with the experimental and finite element analysis results. The results show that the current design can adjust the stiffness over a wide range and the simple analytical approach gives more accurate results as the clutch length increases.

Influence of moment modification factor in lateral torsional buckling of doubly and monosymmetric sections

Simply supported doubly symmetric prismatic beam subjected to uniform moment along the unsupported length is the simplest and basic case in the buckling analysis. The closed form solution for the elastic critical moment was derived based on the assumptions of perfect beam with standard restraint conditions at both ends of the beam. A perfect beam will be having linear-elastic behaviour without any type of geometrical or material imperfections. The standard conditions of restraint at each end of the beam in basic case are restrained against lateral movement, restrained against rotation about the longitudinal axis and free to rotate on plan. But in reality, loading conditions and conditions of restraint will vary widely from the basic case. An equivalent uniform moment factor is typically applied to elastic critical moment to account for the effects of variable moment and end restraints along an unbraced girder length. The values are derived numerically and varies with specifications. In this article equivalent uniform moment factor for IS 800-2007 and Eurocode 3 provisions are compared. The study is also extended to monosymmetric I sections.

Empirical Modeling of Transverse Displacements of Single-Sided Transversely Cracked Prismatic Tension Beams

While the effects of axial compression on beams have long been known, the effect of tensile axial loads on one-sided transversely cracked beams is less known. The crack namely shifts the position of the resultant of the axial normal stresses deeper into the uncracked part of the cross-section, and the crack tends to open, causing a transverse displacement. Therefore, this paper focuses on empirical modeling of the considered phenomenon for slender prismatic beams in order to establish a suitable 1D computational model based on detailed 3D FE mesh results. This goal can be achieved through the already established simplified model, where the crack is represented by an internal hinge endowed with a rotational spring. Several analyses of various beams differing in geometry, crack locations, and boundary conditions were executed by implementing 3D FE meshes to establish the appropriate model’s bending governing differential equation. After that, the corresponding parameter definitions were calibrated from the database of 3D FE models. By redefining the model’s input parameters, a suitable solution is achieved, offering a good balance between the results’ accuracy and the required computational effort. The functionality of the newly obtained solutions was verified through some comparative case studies that supplement the derivations.

Carbon reduction and strength enhancement in functionally graded reinforced concrete beams

The production of cement alone is responsible for 5–8% of global CO2 emissions. This high environmental footprint can be partly attributed to inefficiencies at the material and structural level in concrete structures. Although the performance requirements vary spatially within a structural element, a single concrete with the same properties is typically used ubiquitously, instead of being tailored to the requirements. This leads to inefficiencies in concrete utilisation and embodied carbon. This research addresses these inefficiencies and investigates a novel approach to the enhancement of the environmental and mechanical performance of reinforced concrete structures. Shear-critical elements with a shear span-to-depth ratio of 2.5, a longitudinal reinforcement ratio below 1.3% and no transverse reinforcement were tested to failure. Functionally graded concrete and voids were used to engage a preferential internal resisting mechanism reliant on the internal arch action. Volumes that were superfluous or detrimental were either cast with a lightweight concrete and with lower embodied carbon, or left unfilled. Novel geometries were developed through an innovative fabrication methodology with removable inserts, achieving wet-on-wet interfaces between concrete mixes. Net increases in performance were achieved in all specimens compared to conventional prismatic reference beams. In the specimen with the highest performance, the overall resistance almost doubled whilst the calculated embodied carbon was reduced by approximately a third. The strategic use of functional grading and voids altered the cracking pattern and the development of critical shear cracks in particular. The initiation, evolution and propagation of cracks was engineered to preserve the preferential resisting mechanism. Specimens were consequently allowed to deform and divert damage away from the internal arch. As a result, brittle shear failures were delayed or prevented. In the most beneficial cases, the full plastic flexural capacity of the specimens was developed through yielding of the steel reinforcement. These findings lead to a better fundamental understanding of damage, cracking and shear behaviour in reinforced concrete. They demonstrate the potential for a new generation of more sustainable reinforced concrete structures with higher mechanical resistance and lower environmental impact.

Analytical prediction of the cross-sectional shear flow in non-prismatic inhomogeneous beamlike solids

Non-prismatic beamlike elements are widespread in engineering applications. Unfortunately, analytical methods commonly used for stress analyses in prismatic beams provide mispredictions in non-prismatic cases. Referring for instance to components like towers and blades of large horizontal axis wind turbines, whose main length is much larger than the dimensions of the tapered transverse cross-sections, the cross-sectional taper produces shear stress distributions that are quite different from those obtainable by formulas valid in prismatic beams, notwithstanding the slender shape of such components, the limited magnitude of their tapering slopes, and the possible Navier-like distribution of their cross-sectional normal stresses. Here, we address the analytical determination of the cross-sectional stresses in elements of this kind, which are slender, non-prismatic, inhomogeneous, and susceptible to large deflections. Recalling the results of a recent work by the author, the field equations that govern the state of stress in the considered elements are exploited to obtain a new closed-form expression of the cross-sectional shear flow, which, in turn, can be used for stress predictions. Comparisons with results of non-linear 3D-FEM analyses for elements mimicking the shape of components used in applications confirm the effectiveness of the proposed analytical approach and formulas.

Shear behavior of prismatic and nonprismatic beams with trapezoidal steel web corrugations considering secondary internal force induced by external prestressing

This paper analyzes the shear behavior of statically determinate and statically indeterminate nonprismatic and prismatic beams with trapezoidal steel web corrugations (TSWCs) under external prestressing. The results indicate that for nonprismatic beams with TSWCs, the bending moments and axial forces can also induce additional shear stresses, which will lead to a redistribution of shear stresses on the sections. Moreover, for the nonprismatic statically indeterminate beams with TSWCs, the secondary bending moment and secondary axial force also affect the shear stresses distribution of the sections. This finding has not been reported previously. Therefore, it is not accurate to deem that all shear stresses on TSWCs are completely generated by shear force in the existing specifications. Then, the differences of the shear behaviors between prismatic and nonprismatic indeterminate beams with TSWCs under external prestressing are explored. Consequently, a new practical formula is derived for calculating the shear stresses on the TSWCs induced by external prestressing. The formula can be applied to not only statically determinate and statically indeterminate prismatic beam, but also statically determinate and statically indeterminate nonprismatic beams with TSWCs under external prestressing.

Finite Element Formulation of Timoshenko Non Prismatic Beam Column Element for Static and Dynamic Analysis of Wind Turbine Towers

Finite Element Formulation of Timoshenko Non Prismatic Beam Column Element for Static and Dynamic Analysis of Wind Turbine Towers

Arch action in reinforced concrete subjected to shear

Reinforced concrete elements without transverse reinforcement are vulnerable to shear failure. This premature failure mode prevents structures from developing their full flexural load bearing capacity. It is brittle in nature and occurs with the unstable propagation of cracks and limited preventive signs of distress. Moreover, the associated resistance is difficult to predict with accuracy. This uncertainty can lead to safety risks or inefficient structures. In this research, a novel approach was adopted to study the fundamental behaviour of reinforced concrete subjected to shear and to enhance the shear performance. Innovative specimen geometries and advanced monitoring techniques were used to investigate the interaction between internal resisting mechanisms on specimens with a span-to-depth ratio of 2.5 and a longitudinal reinforcement ratio below 1.3%. Novel configurations were developed through the targeted removal of material, with single or multiple voids denoted respectively Void and Truss. The behaviour of the specimens was enhanced by isolating the internal arch action and increasing the efficiency of the inclined struts. Contrary to common beliefs, it was shown that the targeted removal of material and reduction of internal redundancy can lead to a net increase in the overall resistance and ductility of reinforced concrete structures. Compared to the prismatic reference beams, the shear resistance of the Void and Truss specimens increased by +53% to +122% and the displacements at ultimate loads were 4 to 6 times greater. The isolation of a preferential load-path allowed for greater assurance and control of the resisting mechanism. Consequently, a brittle premature failure due to a critical shear crack was avoided, inducing a ductile failure mode through yielding of the longitudinal steel. Engaging the inherent plasticity of the system led to increased overall resistance and enhanced ductility. These conditions were associated with more reliable and consistent failure loads. The finding of this study can lead to enhanced design and assessment approaches, for the development of safer and more efficient structures.

A metastructure conceptual model of cantilever beam for transverse vibration attenuation

Minimum weight along with low vibration level of structures are main desires of engineers in various industries such as aerospace, automobile, and electronics. The metastructures are a kind of nontraditional structures with distributed vibration absorbers without any change in their general shape. In this article, transverse vibration suppression of a proposed metastructure cantilever beam (MSCB) was considered by a lumped mass-spring model. A prismatic cantilever beam with hollow square cross-section, carrying five uniformly distributed absorbers was investigated. Effects of combination of the absorbers’ first natural frequency on vibration suppression of the whole structure were examined. Results were validated by finite element method (FEM). Frequency response functions of the MSCB were compared by those of simple prismatic cantilever beams with the same mass. The results showed that the transverse vibration does not always decrease by increasing the number of absorbers. Also, linear combination of the first natural frequencies of absorbers leads to more vibration suppression for the MSCB.

Shear performance of prismatic and tapered beams with corrugated steel webs under external prestressing force

This paper analyzes the shear performance of prismatic and tapered beams with corrugated steel webs (CSWs) under different layouts of external prestressing based on finite element (FE) simulations. The results show that when the external prestressing tendon distribution is straight, there is no shear stress in the prismatic beam with CSWs, but there is shear stress in the tapered beam with CSWs. Therefore, it is not generally accurate that only the vertical component of the external prestressing force can induce shear stress when calculating the shear stresses caused by external prestressing in the existing design specifications. In theory, it is proven, for the first time, that the axial force and prestressing bending moment generated by external prestressing will generate additional shear stresses, which will cause the shear stress redistribution in tapered beams with CSWs. However, these two factors were not taken into account in existing design specifications, which resulted in a significant error in predicting the shear stress for tapered beams with CSWs when ignoring the contribution of the axial force and prestressing bending moment. Consequently, a unified analytical formula is proposed for predicting the shear stresses caused by an external prestressing force on the CSW, and this formula can be appropriate for both tapered and prismatic beams with CSWs under both straight and bent external prestressing tendons. In addition, this study quantitatively investigates the ratios of shear stresses in the CSWs induced by the vertical and horizontal components of the external prestressing force, and their corresponding bending moments. Finally, the study reveals the factors affecting the distribution of shear stress on beams with CSWs under external prestressing and proves that using the traditional method to calculate the shear stress neglects the shear capacity of the inclined concrete bottom slab will produce a significant error when applied to tapered cases.

Detection of transversal cracks in prismatic cantilever beams with weak clamping using machine learning

Because our infrastructure is aging and approaching the end of its intended functioning time, the detection of damage or loosening of joints is a topic of high importance in structural health monitoring. The most desired way to assess the health of engineering structures during operation is to use non-destructive vibration-based methods that can offer a global evaluation of the structure’s integrity. A comparison of using different modal data for training feedforward backpropagation neural networks for detecting transverse damages in beam-like structures that can also be affected by imperfect boundary conditions is presented in the current paper. The different RFS, RFSmin, and DLC training datasets are generated by applying an analytical method, previously developed by our research team, that uses a known relation, based on the modal curvature, severity estimation of the transverse crack, and the estimated severity for the weak clamping. The obtained dataset values are employed for training three feedforward backpropagation neural networks that will be used to locate transverse cracks in cantilever beams and detect if the structure is affected by weak clamping. The output from the three ANN models is compared by plotting the calculated error for each case.

Mechanical and Durability Properties of Green Concrete

This research is designed to assess the durability characteristics of green concrete and its compressive and flexural behavior. It measures the possibility of using by product materials in the concrete mix as cement partial replacement. Thus, the experimental compressive stress-strain curves are measured for the cylinder specimens made with green concrete. Furthermore, the durability of green concrete is evaluated using the thaw-freeze test and ultrasonic pulse velocity test. The flexural behavior of green concrete is also investigated. Prismatic beams and cylinder specimens are cast from different types of green concrete made from different by product materials including fuel ash, silica fume, and iron filings using two different percentages 15% and 20% as cement partial replacement. The prismatic specimens are cured over 550 days and then exposed to 60 thaw-freeze cycles. Although concrete made with pulverized fuel ash has the highest compressive strength at 120 days, it has the worst durability characteristics when exposed to 60 iterative thaw/freeze cycles at 550 days. Concrete made with iron filings is more durable than other specimens are. It is recommended using iron filings, pulverized fuel ash and silica fume in the concrete mix. However, iron filings are highly recommended for durable concrete.

Determining the Severity of Open and Closed Cracks Using the Strain Energy Loss and the Hill-Climbing Method

Evaluating the integrity of structures is an important issue in engineering applications. The use of vibration-based techniques has become a common approach to assessing cracks, which are the most frequently occurring damage in structures. When involving an inverse method, it is necessary to know the influence of the position and the geometry of the crack on the modal parameter changes. The geometry of the crack, both in size and shape, defines the damage severity (DS). In this study, we present a method (DS-SHC) used for estimating the DS for closed and open transverse cracks in beam-like structures using the intact and damaged beam deflections under its weight and a Stochastic Hill Climbing (SHC) algorithm. After describing the procedure of applying DS-SHC, we calculate for a prismatic cantilever beam the severities for different crack types and depths. The results are tested by comparing the DS obtained with DS-SHC with those acquired from dynamic tests made using professional simulation software. We obtained a good fit between the severities determined in these two ways. Subsequently, we performed laboratory experiments and found that the severities obtained with the DS-SHC method can accurately predict the frequency changes due to the crack. Hence, these severities are a valuable tool for damage detection.