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.
The structural behavior of steel plate girders with web opening is investigated in this study. An experimental and theoretical investigation of plate girders with different types of openings in the web was conducted. Two types of web opening is investigated (square & circular) opening. The experimental work included testing of seven plate girder specimens under two point loads. Three specimens were tested to observe the influence of the circular web opening. The influence of the presence of square web openings was studied by testing other three specimens. While the last one was tested without opening as a reference (control) specimen. These specimens had the same dimensions. From experimental results the ultimate load of girders decreases with increasing opening size, and the position of plastic hinge depends on the size of hole A nonlinear 3D finite element model was deveioped using FE program ANSYS to validate the experimental results Four- nodes shell element (SHELL 181) was used to represent the steel plate. The proposed finite element model was used to study the effect of web slenderness on shear resistance of plate girder with web opening. Equation was suggested to predict the shear resistance. The analysis study give good agreement with experimental work.
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.
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.
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.
In this study, eight rectangular reinforced concrete beams strengthened by bottom steel plates firmly interconnected to them by headed-stud shear connectors are manufactured using self compacting concrete and tested up to failure under two point loads to demonstrate the effect of steel-plate thicknesses, lengths, and the shear-connector distributions on the behavior, ductility and strength of this type of beams. A trial mix conforming to the EFNARC Constraints had been successfully carried out to satisfy the three fresh tests of SCC, these tests are flowability, passing ability and segregation resistance. The results show that there is a substantial improvement in the flexural resistance, increasing the flexural stiffness and decreasing the ductility ratio due to thickening steel plate, On contrary, increasing the spacing between shear connectors to 50% had slight effect on the flexural resistance, but subsequent increase of their spacing to 100% had seriously lowered that resistance, The spacing between shear connectors has a primary effect on the average flexural stiffness and ductility ratio. In regard to the steel plate length, its shortening has reduced the flexural resistance significantly, decreased the average flexural stiffness and had increased the ductility ratio. The experimentally determined ultimate flexural strength had been compared with its corresponding one computed by the "Strength Method" using ACI requirements where high agreement gained between them due to the nearly perfect interaction provided by SCC. The eight composite beams had also been analyzed by the non-linear three dimensional Finite Element Analysis employing ANSYS program (release 12.1),where high agreement is achieved compared with experimental results.
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.
AbstractIn this paper a nonlinear finite element analysis is presented to simulate the fire resistance of reinforced concrete slabs at elevated temperatures. An eight node layered degenerated shell element utilizing Mindlin/Reissner thick plate theory with initial stiffness technique is employed. The proposed model considered cracking, crushing, and yielding of concrete and steel at high temperatures. More complicated phenomena like concrete transient thermal strain and concrete spalling are excluded in the present analysis. The validation of the proposed model is examined against experimental data of previous researches and shows good agreement.Keywords: Fire resistance, Material nonlinearity, Reinforced Concrete Slabs
The Light Falling Weight Deflectometer (LFWD) was developed to estimate the in-situ elastic modulus directly to the layers near the base as subgrade and subbase layers. The field tests were carried out on selected sections from landfill project within Anbar Province. Furthermore, Forty test sections have been constructed and tested at the Civil Engineering Department- University of Anbar. All sections were tested using the ZFG 3000 model - LFWD in companion with the Plate Load Test (PLT) which were used as reference measures. Regression analyzes were performed to determine the best correlation between the elastic modulus obtained from LFWD and PLT tests. ANN model was used to calculate Evd and compare the regression statistical model. It was found that the ANN model showed a higher performance than regression analysis in predicting Evd. Satisfactory correlations were obtained, which showed that LFWD could be a promising device for in-situ characterizing of subsurface and subgrade layers.