Showing papers on "Bending moment published in 1975"

Lateral loading of deep foundations in stiff clay

Abstract: A full-sized drilled shaft, or drilled pier, was constructed in the field in a stratum of stiff clay. The foundation was instrumented so that bending moment could be measured at various depths. A series of lateral loads, both short-term static and cyclic, were applied to the foundation and families of bending moment curves, along with the boundary conditions at the groundline, were obtained. These data were analyzed and sets of curves were developed showing soil resistance p as a function of deflection y for various depths. Rational concepts concerning the behavior of soil around a laterally loaded deep foundation were employed, along with some empirical expressions, and equations are presented for the development of p-y curves for stiff clay, both for short-term static loading and for cyclic loading. The expressions were tested against available experiments and were found to yield satisfactory results.

The circular tunnel in elastic ground

Abstract: Neither the ground around a tunnel nor, usually, the tunnel lining, behaves in an elastic manner. Nevertheless, the linear characteristic of an elastic or visco-elastic analysis has great merit, particularly when, as frequently occurs, limitations of knowledge of the behaviour of the ground do not justify greater elaboration. This Paper sets out to establish the loading on a circular tunnel in the ‘elliptical’ mode of deformation, making certain simplifying assumptions. The effects of shear forces between ground and lining are first ignored and subsequently introduced in an explicit manner. Bending moments in a lining are related to a stiffness factor, Rs. While a higher mode of deformation of a tunnel lining is only applicable to problems of stability for thin linings, nevertheless, consideration of this condition allows the coefficient of ground reaction a to be evaluated for conditions of asymmetrical deformation. Direct radial loading of a tunnel lining is related to its compressibility factor Rc...

Collapse of Long Cylindrical Shells under Combined Bending and Pressure Loads

Abstract: The nonlinear collapse behavior of long cylindrical shell structures subject to a bending load only or combined bending and uniform normal pressure loads is studied using the STAGS computer code. Two modes of nonlinear collapse are investigated to determine maximum strength. One mode of collapse is described by circumferential flattening of the cylinder cross section, while the other mode is represented by axial wrinkling in the region of maximum compression. Results compare favorably with available published data for cylinders loaded by pure bending, and results are presented for combined loads which have not been previously reported. The collapse loads obtained in this study show that current design criteria are conservative except for a narrow range of length-to-radius ratios and pressures.

Side-Cracked Plates Subject to Combined Direct and Bending Forces

Abstract: The opening mode stress intensity factor and the associated crack mouth displacement are comprehensively treated using planar boundary collocation results supplemented by end point values from the literature. Data are expressed in terms of dimensionless coefficients of convenient form which are each functions of two dimensionless parameters, the relative crack length, and a load combination parameter which uniquely characterizes all possible combinations of tension or compression with bending or counterbending. Accurate interpolation expressions are provided which cover the entire ranges of both parameters. Application is limited to specimens with ratios of effective half-height to width not less than unity.

Dynamical Behaviours of Elastically Connected Double-Beam Systems Subjected to an Impulsive Load

Abstract: Dynamical behaviours of two beams connected with a set independent springs and subjected to an impulsive load are investigated taking the effect of the mass of springs into account. The solution is formulated by the method of the Laplace transformations with respect to both time and space variables, which allows one to analyze all the major performance characteristics in the system subjected to an arbitrarily distributed impulsive load. As a numerical example, the case of a concentrated half-sine impulsive force applied to the mid point of the upper beam is treated. It becomes evident that the amplitudes of deflection and bending moment in the beams decrease as the mass of the springs increases. The response curves are also compared with those for the mass-less springs of Wikler type. It is found that the similarities between the two responses diminish as the mass of the springs increases.

Six degree of freedom force transducer for a manipulator system

Abstract: A six degree of freedom force transducer is provided on a manipulator's hand and includes a plurality of I-beam modules having strain gauges on the flat surfaces of the thin legs of each I-beam for measuring the bending moments of each leg According to one embodiment, a pair of strain gauges are located on each side of the leg, providing a total of four gauges in each leg The end bells of each I-beam are adapted to be rigidly interconnected with either other I-beams, structural members of the manipulator fingers, the drive member for the manipulator, or to intermediate coupling blocks designed to rigidly interconnect I-beams A plurality of I-beams and interconnecting blocks can be connected in various configurations to provide a determination by the strain gauges of the six components of forces and moments which are applied by forces and moments on the fingers of the manipulator system The I-beams and interconnecting blocks are arranged in x-y-z orthogonal directions such that the structural stiffness is in the same order in different directions The moment at each basic module can be measured by the voltage output of a bridge associated with the strain gauges In this fashion, a determination of the position and orientation of an object in the manipulator's hand can be readily provided by a computer which solves the force and moment equilibrium equations associated with the I-beam strain gauges

Diaphragms for Curved Box Beam Bridges

Abstract: A finite difference procedure is used to determine the response of a single span curved single box beam bridge with any number of interior diaphragms. The bending and torsional distortions as well as cross-sectional distortions can then be determined throughout the curved box girder. The forces that are determined include bending moment and shear, pure torsion, warping torsion, and bimoment. These forces, in addition to distortional functions, yield resulting normal bending, normal warping, and normal distortional stresses. The technique is then used to determine the dead-load and live-load response of a series of typical curved box beams. A study of the data has resulted in a series of empirical design equations.

The Theory of the Rayleigh Distribution and Some of Its Applications

Abstract: The first part of the paper deals with the mathematical properties of the Rayleigh distribution, including but not limited to the density function, the moment generating function, the maximum likelihood estimator, confidence intervals, and the bivariate Rayleigh distribution. The second part deals with applications of the Rayleigh distribution to the analysis of the response of marine vehicles to wave excitation. These applications are illustrated with regard to ocean waves, short-and long- term bending moment responses of a ship, and the "target problem" applied to the relationship between wind speed, wave height, and stress.

Theoretical and experimental stress analyses of ORNL thin-shell cylinder-to- cylinder model 2

Abstract: Model 2 in a series of four thin-shell cylinder-to-cylinder models was tested, and the experimentally determined elastic stress distributions were compared with theoretical predictions obtained from a thin-shell finite-element analysis. Both the cylinder and the nozzle of model 2 had outside diameters of 10 in., giving a d$sub 0$/D$sub 0$ ratio of 1.0, and both had outside diameter/ thickness ratios of 100. Sixteen separate loading cases in which one end of the cylinder was rigidly held were analyzed. An internal pressure loading, three mutually perpendicular force components, and three mutually perpendicular moment components were individually applied at the free end of the cylinder and at the end of the nozzle. In addition to these 13 loadings, 3 additional loads were applied to the nozzle (in-plane bending moment, out-of-plane bending moment, and axial force) with the free end of the cylinder restrained. The experimental stress distributions for each of the 16 loadings were obtained using 152 three- gage strain rosettes located on the inner and outer surfaces. All the 16 loading cases were also analyzed theoretically using a finite-element shell analysis. The analysis used flat-plate elements and considered five degrees of freedom per node in the final assembled equations. The comparisons between theory and experiment show reasonably good general agreement, and it is felt that the analysis would be satisfactory for most engineering purposes. (auth)

Method of producing a pre-stressed beam of steel and concrete

Abstract: A method of producing a prestressed beam of steel or steel and concrete having at least one flange in which a plurality of spaced apart transmission elements arranged symmetrically with respect to the center of the span of the beam are secured to the flange, tensioning wires are attached to each two symmetrically disposed transmission elements with the wires extending at predetermined distances from the flange, tensioning the wires to apply to the beam, via the transmission elements, on the one hand solely compressive forces and, on the other hand, in positions corresponding to each transmission element, a bending moment which is opposite to that of the loads to be applied in use, and applying a stress to the beam during the tensioning of the wires substantially to counteract the bending moments. At least one guide element for the wires may be disposed between two symmetrically disposed transmission elements to prevent lateral buckling of the beam during tensioning of the wires. After tensioning the wires, the transmission elements and optionally the flange of the beam are encased in concrete.

A mixed finite element method for bending of plates

Abstract: A simple mixed finite element method is developed. The finite element is a rectangular triangle and rectangle. In the element the deflections are assumed to be simple four-element polynomials, bending moments, Mx and My with a partially linear distribution, and a constant, Mxy, expressed in terms of the node deflections. The element matrix is of the order of 8 × 8. It is derived in a common engineering way. The unknowns are the deflections at the nodes and mid-diagonal, the two moments at the end of the diagonal and the two moments on the cathetus. The results obtained by this method show good convergence and an improvement in the accuracy of the moments as well as in the deflections, compared with results obtained by similar methods, such as those of Herrmann.

Nonlinear Analysis of Orthotropic Plates

Abstract: The large deflection of a rectangular orthotropic plate subjected to the combined action of edge compression and transverse load is investigated on the basis of von Karman-type large-deflection equations. The edges of the plate are assumed to be either all clamped or all simply supported. A solution is obtained in the form of double Fourier series consisting of beam eigenfunctions for both transverse deflection and force function. The postbuckling of the plate is treated as a special case. Taking the first nine terms in each truncated series, numerical results in load-deflection relations and bending moments are graphically presented for three types of fibre-reinforced composite plates with various aspect ratios. The three types of transverse load considered in the combined loading are central patch load, eccentric patch load and hydrostatic pressure. The present results for postbuckling and large deflection of isotropic and orthotropic plates are in good agreement with available data.

Electromechanical moment-independent deflection sensor

Abstract: Apparatus for measuring the load applied in a selected plane to a cantilever-type beam, without regard to the exact point of load application. The apparatus, in one embodiment, features a pair of elongated bar-like devices mounted at points spaced along such beam, and projecting toward and overlapping each other--each device being constructed, under all conditions of beam bending, to remain tangent to a line parallel to the beam's neutral axis adjacent the point where the device is attached. The spacing which develops at a selected region between the overlapping portions of these devices with loaded beam bending is directly indicative of the amount of load on the beam. This indication does not depend upon how far from the beam's fixed end the load is applied, so long as the load is applied no further inwardly on the beam than the mounting point for the outermost bar-like device. Other embodiments feature interconnected or interengaged bar-like devices equipped with electromechanical deflection sensors. These devices tend to deflect with beam bending, and such deflection is directly indicative of beam loading.

Machine for continuous bending long bars or tubes - has bends with varying radius of curvature program controlled

Abstract: The bar or tube (1) which is to be bent is passed through a set of rollers (2) (3)(4)(2')(3')(4') which are driven by an electric motor. The bar or tube (1) then passes through an induction heater (9) controlled by a transformer (10). A cooling ring (H) which directs jets of water on air on the workpiece (1) is attached to the side of the heater (9). A sliding carriage (5) supports a cross-slide (6) which supports a rotatable chuck (7) which grips the end of the workpiece (1). By controlling the speed of the carriage (5) and of the cross-slide (6) the bending moment applied to the workpiece can be controlled. This bending moment produces plastic bending in the workpiece as it passes through the heater (9).

Random response of offshore structures to wave and current forces

Abstract: Dynamic responses of offshore structures to random waves and steady current are examined. The structural response quantities examined are the displacement, shear, and bending moment. The statistic sought is the peak response which is the quantity directly used in design considerations. Numerical results are obtained for four offshore towers, ranging in heights from 475 to 1075 feet, for various wave and current conditions. Results are presented graphically. It is shown that structural responses increase with increase in current speed but the effects of wave-current interactions are important only for tall slender structures. Also, the effects of current on structural response diminishes with increase in the strength of the waves.

Apparatus for determining the density of a fluid

Abstract: Apparatus for determining the density of a liquid comprises a resilient tube coupled at each end through resilient couplings to support flanges for connection in a pipeline or the like. Two cantilevers of the same material and cross section as the tube are secured to the tube so that they have a common axis parallel to that of the tube and their free ends are directed towards each other. The tube and cantilever are so excited that they vibrate in antiphase at the same transverse frequency of vibration, the frequency of the vibration being dependent upon the density of liquid in the tube. The cantilevers are provided with an annular collar at their free ends such that when the tube is filled with a liquid of a predetermined density the root shear force and bending moment of each cantilever cancels those of the tube.

Torque responsive device

Abstract: The invention is a device for controlling and adjusting the tension in the cable of mooring winches or cranes by measuring the torque exerted on a speed reducer having at least one intermediate gear-train, constituted of a pinion and a larger toothed-wheel integrally connected together. The device is characterized in that this intermediate gear-train rotates freely on two bearings supported by a stationary shaft concentric with the intermediate set, which stationary shaft is carried by two fixed supports located outside the bearings. The shaft also carries at least one pair of stress gauges secured between the bearings on two diametrically opposed generatrices of the shaft which are located in the same axial plane as the resultant compression force exerted on both bearings by the two tangential forces applied on the meshing teeth of the pinion and of the wheel of the intermediate gear-train. These stress gauges measure the bending moment on the stationary shaft by modulating an electric current, said bending moment being directly proportional to the resisting torque, and said current regulating said torque by way of responsive means acting on a motor driving said intermediate gear-train.

Analysis of bending stresses in soil beams

Abstract: Brief details are given of three methods used to analyse stress in soil beams composed of compacted clay. Two of the methods, direct method and differential method, apply to the calculation of stresses from the applied bending moment and the strains measured by the radiographic technique. In the third method, elastic bending theory method, the stresses and strains are calculated from the bending moment and the observed deflections of the beam using elastic bending theory. A comparison is made of the different methods and it is concluded that the differential and direct methods of stress analysis for bending tests give the same shape of stress-strain curves although not identical curves. Stress-strain curves obtained from the elastic bending theory differ in shape from those obtained by the other two methods. Tensile and compressive stresses obtained by the differential method are lower than those obtained by the other two methods because the differential method allows some plastic redistribution of stress. As failure is approached tensile stresses by direct and elastic bending theory are respectively 1.4 and 1.5 times average tensile stress by the differential method. /TRRL/

Limit Design of Frames for Movable Loads by Linear Programming

Abstract: This paper concerns perfectly plastic beams and frames in which the bending moment is the only generalized stress (that is the stress-type variable that enters the yield condition).

Hull bending moment due to ship bottom slamming in regular waves

Abstract: A review of the existing literature on the overall response of ships to bottom slamming is presented. A mathematical formulation of the vibratory bending moment due to bottom impact slamming in regular waves is then developed. The hydrodynamic problem concerning the definition of the loads is first discussed and a particular physical model is adopted for determining the hull vibratory behavior. Based on this formulation, a general computerized-procedure leading to the time-history representation of the midship bending moment is developed. Finally, an illustrative example of application to a Mariner ship is described and the results are related to some available data.

The significance of structure-foundation interaction

Abstract: An examination of the importance of structure-foundation-soil interaction with regard to the effect on differential displacement of the column bases, bending moments in the structure and column loads is presented. The structures considered are plane frames with pin-based columns, the foundations considered are strip footings of finite length, and the soil is regarded as being an isotropic homogeneous perfectly elastic continuum of infinite depth. The purpose of the paper is to show which factors are most important in controlling the magnitude of interaction effects and to provide graphs of change in differential displacement, bending moment and column load for a range of the most important of these variables. From these results it should be possible to decide when a full interaction analysis needs to be carried out for the structure under consideration, or to decide that interaction effects are of little significance and a complete analysis can be avoided.