Showing papers on "Bending moment published in 1992"

Shear correction factors for plates and shells

Abstract: Multilayered plate and shell finite elements usually have a constant shear distribution across the thickness. This causes a decrease of accuracy, especially for sandwich structures. The problem is overcome by using shear correction factors which are defined by energy considerations. In this paper a study on shear correction factors is presented as well as typical applications. These factors are defined by studying a crossply laminate without midplane symmetry in cylindrical bending. It is possible to define one factor for a given cross section or several ones, one factor per ply. The two ways are equivalent. Special cases are studied: a multilayered plate, a symmetrical sandwich and a structure formed by two plates glued to each other. The importance of shear correction factors is illustrated in the case of plate and shell applications; the results are obtained by using three-dimensional degenerated shell finite elements.

Strength of materials and structures

Abstract: Preface * Introduction * Tension and compression: direct stress * Pin-jointed frames or trusses * Shearing stress * Joints and connections * Analysis of stress and strain * Thin shells under internal pressure * Bending moments and shearing forces * Geometrical properties of cross-sections * Longitudinal stresses in beams * Shearing stresses in beams * Beams of two materials * Bending stresses and direct stresses combined * Deflections of beams * Built-in and continuous beams * Plastic bending of mild-steel beams * Torsion of circular shafts and thin-walled tubes * Energy methods * Buckling of columns and beams * Lateral deflections of circular plates * Torsion of non-circular sections * Thick circular cylinders, discs and spheres * Introduction to matrix algebra * Matrix methods of structural analysis * The finite element method * Structural vibrations.

Mechanical properties of 3C silicon carbide

Abstract: The residual stress and Young's modulus of 3C silicon carbide (SiC) epitaxial films deposited on silicon substrates were measured by load-deflection measurements using suspended SiC diaphragms fabricated with silicon micromachining techniques. The film's residual stress was tensile and averaged 274 MPa while the in-plane Young's modulus averaged 394 GPa. In addition, the bending moment due to the residual stress variation through the thickness of the film was determined by measuring the deflection of free-standing 3C-SiC cantilever beams. The bending moment was in the range of 2.6 x 10 exp -8 -4.2 x 10 exp-8 N m.

Second-order wave diffraction by a vertical cylinder

Abstract: The main difficulty in second-order diffraction analysis stems from the contribution of the second-order potential, which obeys an inhomogeneous free-surface boundary condition. In some applications it is sufficient to know the second-order hydrodynamic force, which can be calculated without explicitly evaluating this second-order potential. This technique cannot however be used for calculating other quantities such as the hydrodynamic pressure at any point, the sectional force and bending moment in the cylinder or the free-surface elevation due to the second-order effects. This paper provides a detailed analysis of the second-order diffraction problem of a uniform vertical circular cylinder in regular waves. This furnishes results not only on the cylinder surface, but also on the free surface, and in principle in the fluid domain surrounding the body. The analysis may help to throw some light on the physical interpretation of the second-order theory and its mathematical description. Moreover, this information is intended to complement the development of general numerical methods for arbitrary bodies.

Square and rectangular hollow sections subject to combined actions

Abstract: A large number of tests on a range of cold‐formed square and rectangular hollow sections subjected to pure bending, pure concentrated force and combined bending, and concentrated force are described. The concentrated force is applied by means of a bearing plate that acts across the full flange width of the section. The ratio (γ) of the bearing length to the width of the bearing plate used varies from 0.5 to 1.0 in order to show the effects of the bearing length on the failure loads. The current tests are compared with previous T‐joint tests performed at the University of Sydney on similar sections to demonstrate the significant reductions in failure loads and the more severe interaction between bending moment and concentrated force for the tests using bearing plates. The test results are compared with the existing Australian, European, and American design procedures. Improved design procedures are also proposed.

Active flexible rods with embedded SMA fibers

Abstract: Embedding of shape memory alloy (SMA) fibers in slender flexible bodies results in shape changes of the host medium, whenever shape recovery of the SMA fibers takes place. The shape change of a cylindrical rod with a single off-axis embedded SMA fiber is modeled. The distributed axial compressive force and bending moment due to phase transformation in the SMA fiber is evaluated using an approximate analytical model and the deformed shape of the flexible rod is found by solving the equations of equilibrium of the rod. The stability analysis for the linearized theory is carried out and the critical value of the phase transformation induced strain for buckling is evaluated.

Ultimate Load Test of Slab‐on‐Girder Bridge

Abstract: An ultimate load test on a short-span simply supported bridge having six rolled-steel girders and a noncomposite deck slab is described. The main conclusions drawn from the test are as follows: (1) The bearing restraint forces reduced the bending moment at midspan by a minimum of 11%; (2) the transverse load distribution pattern of the bridge improves by a relatively small margin as the ultimate limit state is approached; (3) any composite action between the deck slab and a girder that may exist at service loads, and is due only to bond or friction between steel and concrete, completely breaks down as the load approaches the failure load for the girder; and (4) a girder continues to carry loads long after the formation of first yield.

Analysis for Soil Reinforcement with Bending Stiffness

Abstract: Soil nailing as a method of slope stabilization and repair finds widespread application despite the absence of a clear and unified design approach. The ability of soil nails to increase the shear strength of soil by acting under combined loading, namely, shear and tension, is one of the more controversial aspects of design. For any structural member there is a relationship between the maximum bending moment and axial force, where the bending moment is in turn a function of the shear force in the member. The magnitude of this shear force can be deduced by either an elastic or a plastic model of the soil-nail interaction. The analysis presented in the paper is for both grouted and ungrouted nails, and design equations are given. The finding is that for typical soil-nail diameters only a small proportion of the maximum shear strength of the nail can be mobilized. Expressed in terms of the improvement in soil shear resistance, the benefit from using shear force is found always to be modest when compared with that due to the axial force in the bar.

Progressive Collapse Analysis of a Ship's Hull under Longitudinal Bending (2nd Report)

Abstract: This paper describes the further improvement of the simplified method of progressive collapse analysis of a ship's hull under longitudinal bending proposed by the authors. Here, the method of analysis of flexural behaviour of stiffener elements was extended to deal with coupled flexural-torsional behaviour of angle bar stiffeners welded to continuous plating.A series of elastoplastic large deflection analysis was performed and the rationality of the proposed method was examined.With the improved computer code 'HULLST', two alternative analyses were performed on existing bulk carrier including and neglecting tripping of stiffener elements. It was found that the ultimate strength of stiffener elements decreases when stiffener tripping takes place, which results in reduction of ultimate bending moment of the cross-section. The load carrying capacity of stiffener elements in the post-ultimate strength range was more decreased and so that of the cross-section. The allowable bending moment according to the Lloyd's Register of Shipping was calculated and the reserve strength above it until the initial local collapse was 22.4% of the allowable bending moment. Interaction diagram for longitudinal hull strength under bi-axial bending is also presented.Progressive collapse analysis was performed also on a large scale frigate model tested by Dow, and the applicability of the present method was demonstrated.

Prestressed Composite Girders. I: Experimental Study for Negative Moment

Abstract: Limited experimental results were reported in the literature on the behavior of prestressed composite girders subjected to negative bending moment. This paper examines experimentally the behavior o...

Exact Vibration Solutions for Nonuniform Timoshenko Beams with Attachments

Abstract: The exact solution for the free vibration of a symmetric nonuniform Timoshenko beam with tip mass at one end and elastically restrained at the other end of the beam is derived. The two coupled governing characteristic differential equations are reduced into one complete fourth-order ordinary differential equation with variable coefficients in the angle of rotation due to bending. The frequency equation is derived in terms of the four normalized fundamental solutions of the differential equation. It can be shown that, if the coefficients of the reduced differential equation can be expressed in polynomial form, the exact fundamental solutions can be found by the method of Frobenius. Finally, several limiting cases are studied and the results are compared with those in the existing literature. A (x) E(x) G(x) I(x) J(x)

Three node triangular bending elements with one degree of freedom per node

Abstract: This investigation assesses the bending performance of triangular plate elements with only three translational degrees of freedom per node in which the out‐of‐plane degree of freedom is the only displacement considered. A review is presented of three element formulations followed by the results of a series of case studies which illustrate the element behaviour. Results obtained from elastic theory and finite element analysis using more complex element formulations are given for comparative purposes.

A simple class of finite elements for plate and shell problems. I: Elements for beams and thin flat plates

Abstract: This is the first paper of a pair which together discuss the development of a class of overlapping hinged bending finite elements which are suitable for the analysis of thin-shell, plate and beam structures. These elements rely on a simple physical analogy, involving overlapping hinged facets. They are based on quadratic overlapping assumed displacement functions. Only translational nodal degrees of freedom are necessary, which is a significant simplification over most other currently available beam, plate and shell finite elements which employ translational, rotational and higher-order nodal variables. In this paper the hinged bending element concept is introduced, and the hinged beam bending (HBB) and hinged plate bending (HPB) elements are formulated. In paper II these concepts are extended to develop a hinged shell bending (HSB) element. The HSB element can be readily combined with the constant strain triangular (CST) plane stress finite element for the modelling of thin-shell structures.

Response of Plates of Arbitrary Shape Subject to Static Loading

Abstract: The paper presents the static analysis of arbitrarily shaped plates. The analysis is performed using the principle of minimum potential energy with the admissible pb‐2 Ritz functions. The pb‐2 Ritz functions consist of the product of a two‐dimensional polynomial (p‐2) and a basic function (b). The basic function is defined by the product of equations of the specified continuous piecewise boundary shape, each raised to the power of 0, 1, or 2 corresponding to free, simply supported, or clamped edge, respectively; thus satisfying the kinematic boundary conditions at the outset. Based on the proposed approach, deflections and bending moments for several plate problems having different combinations of free, simply supported, and clamped edges are obtained. The present solutions, where possible, are verified with those published values from the open literature.

Finite Element Method in Mechanical Design

Abstract: General: introduction to structural analysis Loads on structures Analysis of statically determinate structures: equilibrium and support reactions Plane and space trusses Beams and frames: shear and bending moment Deflections of beams: geometric methods Deflections of trusses, beams and frames work-energy methods Influence lines Application of influence lines Analysis of symmetric structures Analysis of statically indeterminate structures: approximate analysis of rectangular building frames Method of consistent defromations - force method Influence lines for statically indeterminate structures SlopE-deflection method Moment-distribution method Introduction to matrix structural analysis Appendices: areas and centroids of geometric shapes Review of matrix algebra Computer software

An assessment of four‐noded plate finite elements based on a generalized third‐order theory

Abstract: Plate finite elements based on the generalized third-order theory of Reddy and the first-order shear deformation theory are analyzed and compared on the basis of thick and thin plate modeling behavior, distortion sensitivity, overall accuracy, reliability, and efficiency. In particular, several four-noded Reddy-type elements and the nine-noded Lagrangian and heterosis (Mindlin-type) plate elements are analyzed to assess their behavior in bending, vibration, and stability of isotropic and laminated composite plates. A four-noded Reddy-type element is identified which is free of all spurious stiffness and zero energy modes, computationally efficient, and suitable for use in any general-purpose finite element program.

Model for Optimal Design of Reinforced Concrete Beam

Abstract: An infinite member of combinations of values of the effective depth, width, and area of reinforcement could yield the same nominal moment capacity of a reinforced concrete beam. In the conventional process, a designer often assumes a beam section not linked with cost, and the process is repeated if the assumed section is not adequate. This technical note presents a model for the optimal flexural design of singly reinforced concrete beam in which the process is reversed; i.e., applied bending moment and other parameters are inputs, and the beam section is the output of the model. Using this nonlinear programming model, the unique least-cost beam design could be achieved directly, exactly matching its ultimate moment of resistance with the ultimate applied bending moment, including that due to the self-weight. Application of this new design technique is illustrated with example problems showing considerable savings in cost and material consumption.

Large-scale thermal bending fracture of sea ice plates

Abstract: A hypothesis that large-scale fracture of sea ice plates in the Arctic could be caused by the release of energy of thermal bending moments due to major temperature changes is advanced and examined. Bending propagation of a through-the-thiclrness crack along the floating plate, with negligible inertial forces, is analyzed, asswning the moment field in the plate near the traveling crack front and the fracture process zone to be in a steady state. The analysis uses the plate-bending theory, and the second-order geometric effects of the in-plane normal forces are taken into account. Quasi-elastic behavior is assumed, and creep is treated approximatdy according to the effective modulus method. The calculated temperature difference between the top and bottom of the plate required to produce this kind of fracture is fowid to be well within the range that actually occurs in the Arctic, but this cannot be regarded as a proof of the hypothesis becaU8e of the simplifying assumptions made as well as uncertainties about large-scale fracture properties of sea ice. Further, it is shown that this type of fracture must exhibit a size effect, such that the critical temperature difference decreases in proportion to (plate thickness) -3/8. This might explain why large fractures often form in an intact thick plate rather than only in a thin plate and along lines of weakness. For the case that the in-plane forces are significant, it is shown that beyond a certain critical crack length the thermally driven bending fracture (if it exists) must transit to a planar (nonfiexural) fracture driven by the release of the energy of the in-plane forces generated by wind and ocean currents. The effect of creep is to increase the required critical temperature difference, as well as the critical crack length for the aforementioned transition. For thermal bending fracture, the minimum possible spacing of parallel cracks increases with the plate thickness and is independent of the crack length, while after transition to planar fracture it increases in proportion to the crack length. The hypothesis of thermal bending fracture cannot be proven or disproven without new types of experiments and measurements in the Arctic, and their computer modeling.

Influence of crack closure on the stress intensity factor in bending plates - A classical plate solution

Abstract: Based on the classical plate theory in conjunction with the assumption of line contact at the compressive edge of a crack face, closed form solutions were presented for a through-the-thickness central crack in an infinite plate subjected to all around bending. The complete solutions were obtained by superposing the membrane components due to the contact forces at the crack face to the non-closure bending components. The distribution of the contact forces was found uniform by considering the contact condition which prevents mutual penetration of the crack faces at the compressive edges. The results showed that the closure of the crack faces tends to reduce the crack opening displacement at the tension side and, consequently, reduce the stress intensity factor. The finite element method was also used to investigate the present problem. The modified crack closure method in combination with the finite element method was used to find the stress intensity factors. Close agreement between the finite element and the analytical solutions was observed.

Buckling of symmetrically laminated plates with compression, shear, and in-plane bending

Abstract: A parametric study of the buckling behavior of infinitely long symmetrically laminated anisotropic plates subjected to combined loadings is presented. The loading conditions considered are pure in-plane bending, transverse tension and compression, and shear. Results obtained using a special purpose analysis that is well suited for parametric studies are presented for clamped and simply supported plates. Moreover, results are presented for some common laminate constructions, and generic buckling design charts are presented for a wide range of useful nondimensional parameters.

Three-axis acceleration sensor variable in capacitance under application of acceleration

Abstract: An acceleration sensor comprises an upper semiconductor substrate having a rigid frame, four deformable beams connected with the rigid frame, and a weight portion supported by the plurality of deformable beams, a lower semiconductor substrate bonded to the rigid frame, a plurality of movable electrodes attached to the weight portion, and electrically isolated from one another, and a plurality of stationary electrodes attached to the second semiconductor substrate, and opposite to the plurality of movable electrodes for forming a plurality of variable capacitors, and the center of gravity of the weight portion is spaced from a common neutral surface of the four beams for allowing acceleration to produce bending moment exerted on the four beams, thereby causing the variable capacitors to independently change the capacitance.