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 paper presents the experimental results of eight slabs made of Ferrocement. All specimens were )700mm (long, )300mm (wide and )50mm (thick. These specimens were divided into two groups (The first group has four specimens coursed of normal sand gradient and in the other four specimens, the sand that passing from sieve No. 8 was neglected), to investigate behavior of slabs under bending effect and studying the cracks that generated after bending then, comparing the results between these two groups. A thin square welded wire mesh was used as reinforcement. The number of wire mesh layers was varied between 0 to 3 layers. Ultrasonic Pulse Velocity (UPV) Test was used to detect the cracks. The results showed that there was a slight rise in bending for first group slabs compared with second group slabs. Maximum bending strength was achieved for both slab groups with 3 layers of wire mesh. it was shown that there was a significant convergence in the load values required to cause appearing of the first crack and final failure for the two groups. The percentage of ultimate load between slab reinforced with 3 layers and without reinforcement was (25.27%) for the first group, while the increase in ultimate load for a specimen that reinforced with 3 layers was (24.16%) compared to specimen without reinforcement for the same group. On the other hand, the results showed an improvement in the performance of the second group slabs due to its resistance to appearing of cracks resulted from bending. The percentage of increasing cracks after bending for the unreinforced specimen in group 1 was (9%) compared with the unreinforced slab in group 2. Whereas the numbers of cracks number in slab reinforced with 1 and 2 layers in the second group were less than slabs with 1 and 2 layers in the first group about (8.86 %) and (7.77%), respectively. While this percentage for a specimen with 3 layers in group 2 was about (8.62%) less compared to the specimen with 3 layers in group 1..
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.
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.
Slurry infiltrated fiber concrete (SIFCON) is a relatively new high performance material and can be considered a special type of fiber concrete (FRC) with high fiber content. The matrix consists of a flowing mortar or cement slurry that must penetrate well through the network of fibers placed in the mold. SIFCON has excellent mechanical properties combined with high ductility and toughness values. SIFCON a relatively new material, is composed of mud (cement or cement and sand), water, a plasticizer (water reducer), and fibers. All previous studies have used waste steel fibers, steel fibers and other fibers, but in this study, plastic fibers were made from polyethylene terephthalate (PET) by cutting carbonated beverage bottles. The main objectives of this study are: Determination the effect of the waste plastic fiber volume ratio on the strength and deformation of (SIFCON) samples under the influence of bending loads. Both flexural strength and toughness properties were determined by testing samples (100×100×400) mm at 28 and 56 days of age. The results obtained from these tests were compared with those performed on conventional tests. Aspect Ratio equal to (36.8) and three volume ratios (3%, 5% and 7%) of the total volume of the concrete mixture were used to add fibers with different volume ratios. A conventional concrete mix was created as a reference for comparison. Bending strength and fresh concrete tests were performed. And compared with the reference mixture and according to the analysis of the results. The results showed an improvement in bending strength .It was found through the flexural examination that the flexural strength of the mixture containing fiber percentage (7%) achieved the highest strength compared to the rest of the ratios used, compared with the reference mixture (Ref.) by (32.25, 27.5)% for ages (28, 56), respectively.
Most concrete structures are reinforced with steel bars to enhance their performance. However, engineers face two major challenges: the high cost of steel compared to concrete and congestion of reinforcement, especially in beams and beam-column joints. These issues can largely be mitigated by using high-strength (HS) steel instead of normal-strength (NS) steel. This study investigates twelve concrete beams (150 × 250 mm), divided into three groups of four specimens. The first group was reinforced with NS steel bars, the second with HS steel, and the third with a combination of both. All beams were tested under four-point bending over a clear span of 2000 mm. Grade 1860 steel (G-270) was used for the HS steel reinforcement. Results showed that achieving the same flexural strength required nearly three times more NS steel than HS steel, leading to reduced reinforcement congestion, lower material usage, and decreased labor costs. Beam specimens were reinforced with steel contents of 1.80 kg/m (NS steel), 1.76 kg/m (HS steel), and 1.66 kg/m (combined reinforcement). Beams with HS steel showed significantly higher ultimate load capacity and improved stiffness (load-deflection behavior) compared to beams with NS steel or combined reinforcement. The analysis confirmed that the applied design method offers conservative and reliable predictions.
Housing represents a major world wide problem, especially for developing countries. It is essential to construct suitable housing units that are appropriate for the continuing population increase. Many countries have applied construction (policies) that depended on the available material and human resources. These schemes aim at producing the greatest number of dwelling units that are suitable for the people who do not own units. The aim of this research is the scope of low cost dwelling units in general, and through the reduction of roofing cost. The objective of the research, Economical feasibility study for production precast units (ferro cement units) for roofs of low cost dwelling and compare the cost of the proposed system With other conventional roofing systems: roofing by (jack arching) and reinforced concrete. Fifteen units of Ferrocement with square shape and three different dimensions were cast and tested for load test, tensile strength, compressive strength and bending. The optimized dimensions were (750*750*20)mm and the capacity ranges from (13 to 17.7)KNM2.The cost of (1m2 ) of these units was (38292.4)I.DM2 while the cost of (1m2 ) reinforced concrete (58534.94(I.D and (51062.7) I.DM2 for (jack arching)
Abstract In this study, a theoretical analysis is presented to estimate the in-plane large displacement elastic stability behavior of structures having non-prismatic members of linearly and nonlinearly varying sections resting on elastic foundation (Winkler type) and subjected to static loads applied at joints only. The analysis adopts the beam-column approach and models the structural members as beam-column elements resting on distributed springs. The formulation of beam-column element is based on Euler approach allowing for the influence of the axial force on bending stiffness. Changes in member chord length due to axial deformation and flexural bowing are taken into account. The stability and bowing functions are estimated using methods of finite differences and finite segments. Also, approximate results have been obtained by using approximate stability and bowing functions of linearly and nonlinearly tapered members resting on elastic foundation. A computer program has been coded in QB language to carry out the proposed analysis of structures with prismatic or non-prismatic members of linearly and nonlinearly varying sections resting on elastic foundation. As a result of this study; the only difference between the analysis of non-prismatic members resting on elastic foundation and those which are not, when adopting the beam-column approach, is represented in the stability and bowing functions, and this is reflected directly on the tangent stiffness matrix.
This study introduce a review on structural behavior of different structural elements such as beams, slabs, column….etc, under different type of loading. Through this review one can see the effectiveness of using ferrocement in casing slabs, beams subjecting to bending or impact load. Also the ferrocement make an essential role in strengthening of damage columns and beams.
The use of nanomaterials in asphalt binders has become a very promising approach to improve the performance of pavements under growing traffic and environmental load. This research focuses on the influence of zinc oxide (ZnO) nanoparticles on physical and rheological properties of asphalt binder. ZnO was added in dosages of 1%, 3%, 5% and 7% by binder weight in a high shear mixing process. The modified and control binders were tested for their physical properties (penetration, softening point, ductility, flash point and viscosity), Dynamic Shear Rheometer (DSR) tests for rutting and fatigue performance and Bending Beam Rheometer (BBR) testing for low temperature behaviour. The results showed that the addition of ZnO nanoparticles reduced penetration and increased softening point, flash point and viscosity, which indicated the improvement of stiffness and thermal stability. Ductility was not affected, which confirmed that flexibility was maintained. Rheological analysis revealed that rutting resistance was significantly improved and a 76.7% reduction in the fatigue factor was observed in intermediate temperatures, whereas BBR results revealed acceptable low-temperature performance. The Performance Grade (PG) of the binder was improved up to two grades in higher contents of ZnO without exceeding limits for workability or thermal cracking. These results show that ZnO nanoparticle is an efficient asphalt modifier that enhances thermal, mechanical and rheological properties and thus can be used in high performance pavements applications with a wide range of temperature.
To preserve the natural materials, applying the principles of sustainable engineering, to approach the principle of zero waste and to contribute the solution of the negative environmental impact of two decades, which is caused by excessive use of bottles of polyethylene terephthalate (PET) in packaging, has led to the approach of alternative, clean and innovative technologies aimed at recycling and reuse to address this environmental problem. Proposed re-use empty bottles as a way to get rid of them and benefit from them at the same time the way, this method through which the empty bottles cutting into fibres using these fibres made of PET to improve the properties of concrete. Percentage of fiber that has been used are 1%, 1.5%, 2%, 3%, 4%, and 5%. Suitable tests were performed to measure properties of concrete reinforcement by recycle PET fibre such as compressive strength, splitting tensile strength, four-point bending strength, modulus of elasticity and toughness index. Flexural toughness tests were performed to measure the ductility capacities of reinforced concrete members with recycled PET fibre reinforced concrete. The results obtained indicate Toughness index was enhanced by using PET fibre reinforced concrete specimens, compared to no ductility performance of concrete specimens without fibre reinforcement. A significant change in ductility was when observed PET used fibre with 3%.