Despite the importance of plates in structural analysis the flexural analysis of plates under parabolic load has not been extensively studied. This paper presents single finite sine transform method for exact bending solutions of simply supported Kirchhoff plate under parabolic load. The governing equation of equilibrium is a fourth order non-homogeneous differential equation in terms of the deflection The considered thin plate problem has Dirichlet boundary conditions at all the edges. This recommends the use of the finite sine integral transform method whose sinusoidal kernel function satisfies the boundary conditions. The sinusoidal function of x used for the sine transform kernel in this paper satisfies the Dirichlet boundary conditions along edges. The transformation simplifies the problem from a partial differential equation (PDE) to an ordinary differential equation (ODE) in the transformed space. The general solution, obtained using methods for solving ODEs is found in terms of unknown constants of integration which are found by using the finite sine transform of Dirichlet boundary conditions along the and edges. The solution in the physical domain space variables is then found by inversion as a rapidly convergent single series with infinite terms. A one term truncation of the single infinite series yields center deflection solution that is only 2% greater than the exact solution. A three term truncation of the infinite series for gave exact center deflections. Bending moments are found using the bending moment deflection relations as convergent single series with infinite terms.
The principal objective of this paper is to investigation the experimental of the flexural behavior of strengthened and repaired reinforced concrete slabs with ferrocement tension zone. The result of tests on 10 simply supported one way slabs were presented, at which include 1control slab, 5strengthened slabs and 4repaired one way slabs. In the strengthened slabs, the cover of the control slab replacing with ferrocement cover, cold joint between ferrocement layer and the slab, connection type between the ferrocement layer and the slab, on the ultimate load, first crack load, the mid span-deflection, crack width and spacing were examined. In the repaired part the slabs were loaded to (55 %) of measured ultimate load of control slab, the effect of the thickness and number of wire mesh layers on crack pattern, mid span deflection and ultimate load was examined. In the repaired part the slabs were loaded to (55 %) of measured ultimate load of control slab, effect of the number of wire mesh layers of ferrocement on the mid span deflection, ultimate load and crack pattern was examined. The experimental results of strengthened and repaired slabs indicate that; the ultimate loads and mid span deflection were more effected by using ferrocement mortar at tension zone. The increase in ultimate load (8.2-18%) for strengthen slab and (9.1-17.3%) for repaired slab respect to the control slab.
Ferrocement is a type of concrete made of mortar with different wire meshes. It has wide and varied applications in addition to its strength and durability. This research aims to combine ferrocement and sustainability, as over time, the consumption of plastics, especially plastic bottles, has increased and has serious negative effects if buried, burned, or chemically analyzed. Therefore, this research aims to benefit from this plastic waste and introduce it into the construction field by using plastic waste fibers in the concrete mixture instead of cement at a rate of 0.5% and 1% by volume. This research studied the mechanical properties of nine samples of ferrocement beams with dimensions of 1200 × 200 × 150 mm3. A longitudinal hole with a diameter of 50 mm was drilled in different places of the beams and filled with lightweight concrete to facilitate the use of the hole in service passes when drilled, with a study of the initial cracking loads and the resulting deflection in addition to the failure modes and the deflection resulting from the maximum load. The results showed an improvement in load resistance with an improvement in deflection at the maximum load, In addition to an increase in the improvement of Toughness and Stiffness of ferrocement beams.
The structural behavior of composite steel concrete beams with long term deflection was investigated, taking in considerations several variables including degree of shear connectors 50%, 75%, 100%, and type of connectors including headed and hooked studs smooth or deformed. Five composite steel-concrete beams were tested each consist of steel section W12x35 and 300x100 concrete slabs. The composite beams were tested under uniformly distributed loads for different time interval up to 180 days. The results showed that the degree of interaction have significant influence on the long- term behavior of the composite steel concrete beam . When the degree of interaction decreased from 100% to 75% then to 50% the maximum long-term mid span deflection increased about 35.1% and 65.9% respectively at 180 days after loading. Also, the end slip increased about 67.5% and 112.4% respectively at 180 days after loading. The results showed that the type of the used shear connectors has slight influence on the long-term behavior of the composite steel concrete beams. For certain degree of interaction (75%)with using headed and hooked studs smooth or deformed the maximum long-term mid span deflection decreased about 7.1% and 11.7%at 180 days after loading, and the end slip decreased about 4.8% and 12.5% at 180 days after loading.
This paper investigates the results of finite element analysis for three proposed full-scale two-way slabs. The aim of this study is to use finite element method (FEM) by using ANSYS-v15 program to analyze the proposed slabs and study the flexural behavior , especially load-deflection relationship and ultimate strength. Some parametric studies on these works are also done to cover the effect of some important parameters on the ultimate load capacity and deflection. Proposed slabs are divided into three groups with different dimensions to study the effect of using continuous large spans on the structural behavior of two-way ribbed (waffle) slabs as compared to solid slabs. In all three groups, each slab consists of three by three panels supported by concrete columns at corners. For the first group, when the void ratio (the ratio of volume of voids between ribs to total volume of ribbed slab) increases, the stiffness of waffle slab also increases. Increasing stiffness for waffle slab is continued up to some limit, and then will decrease with increasing void ratio. The best case in this example occurs when the void ratio equal to (0.667) which gives increase in stiffness of (0.347) as compared to solid slab with the same thickness. The results of ANSYS analysis shows that the best percentage of increase in deflection is (51%) with decreasing in concrete volume of (59%) for long to short span ratio of (1.5) and (300)mm thickness. For the third group of proposed models, the stiffness of two-way ribbed (waffle) slab is higher than the solid slab which has the same volume of concrete. The displacement of two-way ribbed (waffle) slab in the elastic range (at first crack ) is lower than the solid slab. In this manner, it will give the maximum reduction in concrete weight with higher thickness.
In this study, the structural behaviour of RC-deep beams of glass fibre-reinforced polymer (GFRP) rubberized concrete is investigated. Rubberized concrete is manufactured by replacing fine sand aggregate with rubber crumbs in volumetric replacement ratios. The main variables were the crumb rubber content (0%, 10%, and 20%) and the main reinforcement ratio. Tested Six samples of deep beams with different dimensions (b = 150, h = 300 mm, L= 1400 mm) were under a four-point load until failure. The parameters under investigation were the mechanical properties of mixtures, load-midspan deflection curves, toughness, and the load-strain relationship. The results indicate that the increased crumb rubber content led to a decrease in the mechanical properties of rubberized concrete mixtures. It was found that the behaviour of all samples of rubberized concrete affected the deflection load curve, the ultimate load, and the increase in deflection. The sample R2-10% Rub showed the highest toughness among the tested samples, with an increase of 301.6% compared to the reference.
This research include the study of flexural behavior of polymer modified concrete beams containing waste plastic fiber (WPF). Fifteen reinforced concrete beams are moulded of (100*150*1300) mm dimension with different steel reinforcement ratio (ρ). These steel reinforcement ratio were (0.0038, 0.0207 & 0.0262). Styrene Butadine Rubber (SBR) was added as cement replacement by weight equal to (5%). Reinforced concrete beams classified in to five groups, each contains three beams with different (ρ) value. The first group conducted of reference concrete mix , the second group made with SBR modified concrete, while the three remaining groups were make by PMC containing (WPF) with volumetric ratio equal to (0.75, 1.25 & 1.75)%. This study includes compressive and flexural tests for concrete which was used in this research, load deflection relationships, the moment at mid-span with deflection and ductility were established. The results prove that, polymer modified concrete wich content waste plastic fiber has compressive and flexural strengths more than reference mixes as well as the PMC beams wich content waste plastic fiber have a stiffer response in terms of structural behaviour, more ductility and lower cracking deflection than those made by reference concretes and that refer to good role of styrene Butadiene Rubber (SBR) polymer and plastic fiber on the properties and behaviour of reinforced concrete beams.
A study examined the ductility and toughness properties of beams made of reinforced concrete, including foamed, normal, and hybrid beams. Nine reinforced concrete beams were produced: three foamed concrete beams, three normal concrete beams, and three hybrid concrete beams. Each beam possessed identical rectangular cross-sectional dimensions of 1500 mm × 250 mm × 150 mm. The flexural parameters (ultimate load, ductility, deflection, and durability) were assessed for each type of concrete utilized. The study's results showed that the load-bearing capacity of hybrid concrete beams was comparable to that of normal concrete beams, whereas foamed concrete beams exhibited slight improvement in their ability to carry loads. The ductility of reinforced foamed concrete beams was lesser than that of normal concrete. For over-reinforced beams, the ductility of hybrid concrete beams showed a significant improvement of 61% compared to foamed beams and an even more significant increase of 91.7% compared to normal beams. Furthermore, the hybrid concrete beam with over-reinforcement had a flexural toughness of 18.7% greater than the normal concrete beam. Suggested that a hybrid section comprising conventional and foamed concrete be utilized to decrease ductility and improve stiffness.
An experimental investigation was conducted to study the strength, behaviour and deflection characteristics of two way slabs made with both self-consolidating concrete (SCC) and conventional concrete (CC). Six concrete slabs were tested to failure under simply supported uniform by distributed loading conditions. The variables were concrete type and macro synthetic fibres ratio (0%, 0.07% and 0.14%). The performance was evaluated based on crack pattern, ultimate load, load-deflection response and failure mode. The results showed that the ultimate strength of SCC slabs was larger than that of their CC counterparts. The results also showed an improvement of the behaviour and strength of slabs by adding the synthetic fibres.
This paper attempts to obtain bending solutions to plates under uniformly distributed and hydrostatic load distributions using Ritz variational methods and basis functions that are found by superposing trigonometric series and third degree polynomials. Two cases of boundary conditions were considered. In one case, three edges were simply supported and the fourth edge was clamped (SSCS thin plate). In the second case, the adjacent edges were clamped and the other edges were simply supported (SCCS thin plate). This work presents first principles, rigorous derivation of the governing Ritz variational functional and the displacement basis functions for the boundary conditions investigated. The solution is presented in analytical form. The obtained results are compared with previous results obtained using Levy series and Ritz methods and found to be in close agreement . The disadvantage of the method is the associated computational rigour, but the benefit is the accuracy of the results. Comparisons of the present results for center deflections and center bending moments with results in the literature show that there is negligible difference. Double series expressions were found for deflections and bending moments for the plate bending problems solved. Evaluation of the double series expressions at the plate center gave center deflection results that differed from the exact solutions by for to for for uniformly loaded thin plates with three simply supported edges and one clamped edge (SSSC). The differences in the center bending moments Mxx were found to vary from for to for In general, the present results yielded reasonably accurate solutions for the plate bending problems studied.
This study describes the results of tests carried out in order to investigate the structural behavior of reinforced concrete beams containing Expanded Polystyrene (EPS) stabilized Polystyrene beads. Three concrete mixtures were used with densities 350kg/m3, 500 kg/m3 and 600 kg/m3. A total of 12 beams, with control specimens were tested after 28 days of curing immersion in water. Four types of steel reinforcement were utilized: Two ratios of tensile steel reinforcement without compression steel and the same two ratios of tensile reinforcement with compression steel and stirrups. The beams were tested under 4- points loading up to failure. The main variables considered in this study were: different types of Izocrete densities and types of reinforcement steel bars. The results indicated that the amount of polystyrene beads significantly affects the strength of the concrete produced. In general, it can be observed that the compression, tensile and flexure strengths decreased as the EPS beads contents increased, and the moment capacity of the beams reduced with the increase of the beads ratio.The load deflection behavior of the Izocrete beams were similar to other lightweight concrete beams .The failure in most of the beams was initiated at the compression region undergoing large deformation due to the high compressibility of the material.
In this paper, AlMg3-plates are studied through experimental and numerical using finite element representation under concentrated load at the center point. The plates of (300- × 200 mm) are clamped at the shorter ends and strengthened longitudinally by one rib at the centerline and two at different spans. the stiffened plates were modeled using a 3-D 10-node tetrahedral element with a non dimensional analysis. The models were validated using the results of tests on full-size stiffened plate specimens and were subsequently used to perform the study of the parameters presented in this paper. The parameters investigated are: the maximum stress, deflection of the plate and the position of ribs. Effect of the investigated parameters on the concentrated load strength were studied within elastic range. FEA give closer results with those of experimental and these results show that the use of two parallel ribs with a 40-mm span improves the strength of the plate. Due to these results, further investigation is presented to show the optimum thickness of the ribs at the best span.
Thin plate bending analysis is an important research subject due to the extensive use of plates in the different fields of engineering and the need for accurate solutions. This article uses the Ritz variational method and a superposition of trigonometric and polynomial basis functions to solve the Kirchhoff-Love plate bending problems (KLPBPs). The unknown displacement function in the Ritz variational functional (RVF) to be minimized is sought as linear combinations of basis functions Fm(x) and Gn(y) that are found by superposing sine series and third degree polynomial functions with the polynomial parameters determined such that all boundary conditions of deformation and force are satisfied. The displacement is thus expressed in terms of unknown displacement parameters Amn which are found upon minimization of RVF with respect to Amn. The minimization process gave a matrix stiffness equation in Amn with the stiffness matrix and force matrix found from Fm(x) and Gn(y) and their derivatives. The algebraic equation is solved, and the deflection and bending moments obtained. The problems considered were clamped (CCCC) plates under uniform and hydrostatic distribution of loads and plates with opposite edges clamped, the rest simply supported (CSCS) under uniformly distributed loading. Comparison of the solutions by Generalized Integral transform method, Levy-Nadai series method, and symplectic eigenfunction superposition confirms that the present results are accurate.
The use of textile reinforcement made from non-corrosive materials, such as carbon and glass can reduce the required concrete material; this is known as Textile Reinforced Concrete (TRC). This study deals with plate specimens having dimension of 500×500×40mm tested under impact load at 28 and 90 days age under two conditions of ends, simply supported and fixed. Cement mortar with about 60 MPa, 7cm cube compressive strength at 28 days was designed for casting the plates. Plate specimens were divided into four groups, they consist of reference plates (no reinforcement) and plates reinforced with 3D glass fabric having three different thicknesses 6, 10 and 15mm. The results indicate that using 3D textile glass fabric cause an increase in number of blows, reduce in final stage deflection, an improvement in toughness and energy absorption under impact loads. Using 3D textile glass fiber with 10mm thickness gave higher number of blows for 28 and 90 days as compared with 6 and 15 mm. Plates with slice 6mm 3D textile glass fiber in two way reinforced has significantly enhancement in number of blows, the improvement was about (80 - 125%) and (128.5- 114. 3%) for 28 and 90 days respectively. The specimens showed increase in the energy absorption, besides the number and width of cracks was reduced and only few cracks are propagated up to the edge of the plates.
In this paper an experimental study of the effect of grooves on initial peak load and work done by plastic deformation of material is presented. A series of tests were conducted on polyvinylchloride PVC circular tubes with grooves and without grooves loaded statically and axially. The specimens with grooves were tested with constant depth of groove and constant axial length of groove. Load-deflection characteristics for the PVC circular tubes specimens and the influence of collapsing load were illustrated in this work. The experimental results were compared with proposed mathematical model giving a good agreement. Also in this work, it was showed that the value of plastic work decreases with increasing the number of grooves.
In this study an investigation of castellated beam are presented. The experimental and analytical results of seven simple castellated beams and other one has webbed section are summarized in this study. The target of the search was to study the structural behavior and mode of failure of castellated beams which have different geometric shape of hole and varies lengths span of beams, and attempt to find out the possibility of Biodgett equation and Halleux equation to determine ultimate and limit load respectively. Four angle off cutting were used to achieve the change in the geometry of hole (45, 50, 60 and 90 degree). The specimens were made from IB 203x133x25 and were expanded to 1.5 times the standard depth. Ultimate and limit load, load-deflection relation shapes and mode of failure were presented and discussed. The experimental results showed that the ultimate and limit load of castellated beams decreases with increasing the angle of cutting and Biodgett equation gives acceptable results for estimating ultimate load when the angle of cutting 50° or less. Also it is found that the limit load of castellated beam by Haleux equation is incorrect when the angle of cutting greater than 50°. As well as ANSYS-12 was used to analysis these beams by nonlinear finite element method. Four- nodes shell element (SHELL 181) was used to represent the castellated and webbed beams. This model was validated by comparison of the experimental and numerical results of ultimate load and their corresponding modes of failure.
AbstractA full three dimensional finite element computational model is constructed for nonlinear analysis of reinforced concrete curved beams. This model was presented utilizing computer program ANSYS (Version 11), which is capable of an efficient analysis of the response at different load levels including ultimate loads.This work deals with the structural analysis of concrete curved beams behaviour subjected to two concentrated loads. Concrete curved beams are widely used in building and bridge constructions. Some of the available experimental tests on reinforced concrete curved beams are theoretically analyzed. This covers load-deflection relationships, crack pattern and propagation of crack at different stages of load and ultimate load capacity. The reliability of the model is demonstrated by comparison with available experimental results and alternative numerical analyses which shows 4 – 8 % difference.
Research in Iraq has expanded in the field of material technology involving the properties of the light-weight concrete using natural aggregate. Research work on porcelinite concrete has been carried out in several Iraqi Universities. However , despite the great practical importance of such concrete in construction fields ,very limited amount of work has been carried out to investigate the (shear strength) of structural light-weight aggregate concrete , therefore it is important to study the properties and their structural behavior. In this work an attempt is made to study shear strength of porcelinite reinforced concrete beams without (stirrups). The results have been compared with the results predicted by the equations of International codes, such as ACI 318M-02, BS-8110 codes and with some authors' equations as for, Hanson. The experimental results also have been compared with results obtained from normal weight concrete specimens that had been prepared for this purpose. The study mainly deals with the structural behavior of porcelinite reinforced concrete beams without stirrups, especially the shear strength, besides, the short-term deflection, strain and cracks. The variables are, compressive strength ranging between (23.0-29.8) MPa and reinforcement percentages ranging between (0.0174-0.0307). A total of 12 beams are tested; (9) are light weight concrete beams without stirrups and (3) are normal weight concrete beams, also without stirrups. The dimensions of all those beams are 135 * 260 * 1800 mm. The structural results more often, give values 2.9 times more than that of (ACI-02)
Composite beams, made up of a concrete slab and steel in the IPE steel section, are commonly used in bridges and buildings. Their main function is to enhance structural efficiency by merging the compressive strength of concrete with the tensile resistance of steel, thereby improving overall stiffness, ductility, and load-bearing capacity. This study offers an extensive review of the flexural behavior of steel-concrete composite beams, focusing on the interplay of concrete strength, shear connector types, and interaction levels in determining structural performance. It integrates experimental and numerical research to analyze critical parameters, including load-deflection behavior, shear transfer efficiency, and crack propagation at the steel-concrete interface. The study emphasizes the effect of concrete compressive strength, particularly in ultra-high-performance concrete (UHPC) and lightweight concrete, on stiffness, ductility, and load-bearing capacity while reducing self-weight and enhancing sustainability. The study revealed that fully bonded shear connectors, using CFRP sheets and welded plates, enhance flexural capacity and stiffness. In contrast, partial bonding or pre-debonding reduces performance due to crack propagation. Indented and hot-rolled U-section connectors enhance interaction and minimize slip, while uniform distribution of shear connectors optimizes load capacity and stiffness. Lightweight concrete decreases slab weight without compromising performance, and high-performance materials such as ECC, SFRC, and UHPFRC improve strength and ductility. Numerical modeling, particularly finite element methods, and higher-order beam theories validate experimental results, providing accurate tools for predicting structural behavior under various loading and environmental conditions.
Nonlinear numerical analysis of nine reinforced concrete beams with dimensions (150 x 200 x 1200) width, height and length, respectively, was carried out through the finite element theory using the ANSYS software (version 15) to know the effect of different properties of layers in the one beam on the flexural behavior of reinforced concrete beams. The beams are consisting from two layers for the one cross-section. three beams are similar properties layers and the other six are with different properties layers. The beams differ among them depending on the percentage of Polyethylene terephthalate (PET) fibers added, the location of the fibrous concrete layer as well as the thickness of the layer. PET fibers were added in proportions (0%,0.5%, and 1%) from volume of the one layer, with dimension (50 x 4 x 0.3) mm length, width, and thickness respectively. All beams are reinforced with steel reinforcement (6 mm diameter at the top, 10 mm diameter for reinforcement against shear and 12 mm diameter in the tension area). The mechanical properties of each type of mixture have been studied. It was found that the different properties of the layers significantly affected the flexural behavior of reinforced concrete beams. Also the results of the numerical modeling were very close to the laboratory results obtained from the practical study, where the largest difference between the two studies was 8% and 11% for the load and deflection respectively at the ultimate point