Bending of Floating Wedges with Initial Curvature Under Deformation Dependent Loading (original) (raw)
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Journal of Civil Engineering and Architecture
In early winter it is usual, in cold regions, that ice features approach offshore structures, like offshore platforms, impacting them, in a slow process of constant deformation build up. Interaction follows, in many cases, up to the point where ice-failure caused by bending fracture takes place. This supposes very large contact forces that the structure has to resist. Therefore, quantification of these efforts is of vital importance to the structural design of platforms. In several designs, these platforms are constructed with inclined walls so as to cause ice to fail in a flex-compression mode. In such a case the ice feature is analyzed as a beam constituted of a linear elastic material in brittle state with constant ice thickness. The simplification renders the problem solvable in a close form. However, this hypothesis goes against field observations. Marine currents action, wind and the sequence of contacts among features lead to thickness variations. Here this factor is addressed in the construction of a model, for harmonic forms of variation of thickness profile, and the accompanying curvature variations, whose solution determines field variables used to address the failure question. Due to the deformation dependency of the loading, a numerical scheme for the two-point boundary value problem in the semi-infinite space is developed. Failure pressures are computed based on a Rankine locus of failure. Variations of the order of 20% in the failure loads, as compared to the uniform beam model, are observed.
Effect of the Modeling Technique on the Bending Moments in Raft Foundation
CERM, Civil Engineering Research Magazine, Civil Engineering Department, Faculty of Engineering, Al-Azhar University, Nasr City, Cairo, Egypt., 2013
Several techniques for modeling the loads applied on the raft were studied in this research. The goal of this research is to study the effect of applying the load on the raft on the bending moments in the raft. Four models for the loads are used, the first model considers the loads concentrated of the center of gravity of the column and acting directly on the raft, the second model considers the loads distributed on the area of the column, the third model considers the column as solid elements in the model and apply the load at the top of it, the fourth model considers a three dimensional model of the entire 5-story structure. All these models are made by SAP2000v14 finite element program. The results of this research outlined the large variation in straining actions among these models. Based on the results, the use of second model is recommended.
Structural Concrete, 2018
A standard approach is presented to obtain analytical solutions for deflection field of determinate beams subjected to conventional loading patterns. The solutions are based on a trilinear moment–curvature response using a deflection hardening behavior characterized by flexural crack initiation, inelastic response due to crack extension, and full plastic hinge formation. Methodology for full span deflection and rotation distributions are presented for multiple cases that include three‐ and four‐point bending, uniform load, concentrated moment, and cantilever beams. The proposed approach provides analytical expressions for the curvature, rotation, and deflection at any point along the beam, and correlated to stress or strain distribution. The procedure can therefore be integrated into a serviceability‐based design approach. A parametric study of the effects of model parameters on the stages of the response is addressed. Several case studies involving steel fiber reinforced concrete (...
Plane elasticity problem for a multi-wedge system with a thin wedge
International Journal of Solids and Structures, 2010
The paper presents a method for studying a system of elastic wedges containing a thin wedge with the angle H 0 , which may be arbitrary small. An analysis shows that the considered problem, involving 2-D vectors of tractions and displacements, cannot be solved by straightforward extension of the method previously worked out by the authors for analogous scalar problems. The difficulty arises because of the disclosed feature of the dependences between the Mellin transformed displacements and tractions at the boundaries of a thin wedge: they are linearly dependent when their Taylor's expansions in H 0 are represented by the first terms only. The difficulty is removed by using the consequences of the linear dependence and by an appropriate rearrangement of variables. Then simple physical models, simulating the influence of a thin wedge on a multi-wedge system, become available. The models cover the cases of a very rigid and very compliant thin wedge and also intermediate cases. The ranges of the models applicability are studied analytically and illustrated by numerical results.
Bending Behavior on Beam with Supporting Part
Civil Engineering and Architecture, 2020
Equipment used to help road users during road maintenance activities is called a flexible bridge. It helps maintain the accessible area of the road when repairs occur. Collapse has occurred sometimes at frame when bending load exceeds the yield strength. In addition to increase the ability of the structure and avoid buckling added a link as damper. Parameters of the absorber are stiffness rate, and elongation of link. A simple square tube beam model supported by a link was created to investigate the bending behavior using finite element analysis. The analysis result showed that beam supported by a link able to reduce buckling moreover provides longer curvature than beam without a link.
Moment-Curvature-Thrust Relationships for Beam-Columns
Structures
Moment-curvature-thrust relationships (M-κ-N) are a useful resource for the solution of a variety of inelastic and geometrically non-linear structural problems involving elements under combined axial load and bending. A numerical discretised cross-section method is used in this research to generate such relationships for I-sections, rectangular box-sections and circular or elliptical hollow sections. The method is strain driven, with the maximum strain limited by an a priori defined local buckling strain, which can occur above or below the yield strain depending on the local slenderness of the cross-section. The relationship between the limiting strain and the local slenderness has been given for aluminium, mild steel and stainless steel cross-sections through the base curve of the Continuous Strength Method. Moment-curvature-thrust curves are derived from axial force and bending moment interaction curves by pairing the curvatures and moments for a given axial load level. These moment-curvature-thrust curves can be transformed into various formats to solve a variety of structural problems. The gradient of the curves is used to find the materially and geometrically non-linear solution of an example beam-column, by solving numerically the moment-curvature ordinary differential equations. The results capture the importance of the second order effects, particularly with regards to the plastic hinge formation at mid-height and the post-peak unloading response.
Influence lines for bending moments in beams on elastic foundations
Computers & Structures, 1996
finite difference method assuming parabolic variation of contact pressure distribution is presented to obtain the influence lines for bending moments in beams on an elastic foundation. These influence lines can conveniently be used to find moments in beams on elastic foundations due to any type of loads. The computational procedure presented is simple. Accurate results are obtained with only 10 elements.
NUMERICAL STUDY ON STRESS ANALYSIS OF CURVED BEAMS
The static analysis of naturally curved beams with closed thin walled cross section has many important applications in mechanical, civil and aeronautical engineering. Many of the curved beams subjected to bending moment find in real life applications .Due to bending moment, tensile stresses developed in one portion of the section and compressive stresses in other portion of cross section. The analytical computation to determine these stresses are more complex, therefore in this paper we attempted the determination of stresses and deflection of curved beams when it is subjected to bending moment with the help of ansys software. The result obtained from ansys software is validated with the simplified stress equations of curved beams developed by the other researchers. The material selected for curved beams for simulation studies is isotropic ductile material. The geometry of curved beams is described with central included angle in this paper. The work carried out exhaustively covers the estimation of stresses in quarter circle beam, semi circle beam, three quarter circle beam and full circle beam. The methodology adopted for simulation model briefed out step by step in this paper for further studies of other researchers
Stiffened plate bending analysis by the boundary element method
Computational Mechanics, 2002
In this work, the plate bending formulation of the boundary element method (BEM) based on the Kirchhoff's hypothesis, is extended to the analysis of stiffened elements usually present in building floor structures. Particular integral representations are derived to take directly into account the interactions between the beams forming grid and surface elements. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composite structure as a single body. Two possible procedures are shown for dealing with plate domain stiffened by beams. In the first, the beam element is considered as a stiffer region requiring therefore the discretization of two internal lines with two unknowns per node. In the second scheme, the number of degrees of freedom along the interface is reduced by two by assuming that the cross-section motion is defined by three independent components only.
NUMERICAL ANALYSIS OF CURVED THIN BEAMS ON WINKLER FOUNDATION
This research, deals with the linear elastic behavior of curved thin beams resting on Winkler foundation with both compressional and tangential resistances. Thin beam theory is extended to include the effect of curvature and externally distributed moments under static conditions. The computer program (CBFFD) coded in fortran_77 is developed to analyze curved thin beams on Winkler foundation by Fourier series and finite difference methods. The results from these methods are plotted with other solutions to compare and check the accuracy of the used methods. INTRODUCION The object of this research is to analyze curved thin beam using finite difference and Fourier series methods. The beam is resting on elastic foundation with Winkler frictional and compresional resistances, and loaded generally (both transverse distributed load and distributed moment). The linear elastic behavior of curved thin beams on elastic foundations is considered. The governing differential equation of curved thin beams (in terms of w only) is developed and converted into finite differences. A computer program in (Fortran language) is developed. This program assembles the finite difference equations to obtain a system of simultaneous algebraic equations and then the solution is obtained by using Gauss elimination method. The deflections and rotations for each node are obtained. The shear and moment are obtained by simple substitutions of the deflections into the finite difference equations of moment and shear. Also, this program used Fourier series method to solve the governing differential equation for simply supported beam and obtain the deflection, moment and shear. The obtained solutions compared with available results to check the accuracy of the used methods. Curved beams are one-dimensional structural elements that can sustain transverse loads by the development of bending, twisting and shearing resistances in the transverse sections of the beam. It's extensively used in engineering and other fields since such beams have many practical applications. The curved beam elements on elastic foundation would be helpful for the analysis of ring foundation of structures such as antennas, water towers structures, transmission towers and various other possible structures and superstructures. These are review of early studies on curved beam.