Showing papers on "Bending moment published in 1968"

An application of the extended Kantorovich method to the stress analysis of a clamped rectangular plate

Abstract: The extendedKantorovich method discussed recently, byA. D. Kerr, is used to analyze a clamped rectangular plate subjected to a uniform lateral load. It was found that the generated one term solution approximates very closely, throughout the plate region, not only the deflections but also the bending moments and shearing forces. It is shown that the final form of the solution is independent of the initial choice, and that the convergence of the iterative procedure is very rapid. Because of the lack of a closed form exact solution in the technical literature, the coefficients occurring in the obtained solution were evaluated for various plate side ratios and are presented in graphs in order to simplify the utilization of the obtained results in engineering practice.

Force measuring device

Abstract: 1,209,954. Force transducers. BOFORS A.B. Jan.30, 1968 [Feb.7, 1967], No.4822/68. Heading G1N. A transducer for measuring a force F (Fig. 1a) comprises a beam 1 fixed to a support 2 at one end and with a second, parallel, shorter beam 7 attached to the other, the force F being applied to the free end of beam 7, where in the resulting distortion of beam 1 is measured by strain gauge pairs 3, 4 and 5, 6 (latter pair not shown), located symmetrically on beam 1 under the point of application of force F, the pairs of gauges 3, 4 and 5, 6 being disposed at right angles to each other, as shown. The strain gauges are connected into a bridge circuit whose output is indicative of the force F. The arrangement is automatically insensitive to bending moment, transverse force, axial force and torque. The sensitivity is improved by making beam 1 a hollow tube Fig. 5 (not shown) or of I cross-section Fig. 4b (not shown), at least where the strain gauges are mounted. The second beam 7 may be tubular surrounding beam 1. The transducer assembly may form the stationary shaft of a pulley 12 Fig. 9 whereby the tension is a wire carried by the pulley may be measured. In another embodiment Fig. 6 two tubular further beams 7 1 , 7 11 are attached one to each end of tubular first beam 1. In a further embodiment Fig. 10 (not shown) a transducer at each end of a wheel axle may be used to measure the weight of the vehicle.

Slab bridges with arbitrary shape and support conditions: a general method of analysis based on finite elements.

Abstract: THE APPLICATION OF A GENERAL FINITE ELEMENT PROGRAM INCORPORATING TRIANGULAR PLATES, BEAM AND SUPPORT COLUMN 'ELEMENTS' IS DESCRIBED. THE OBJECTIVE IS THE ASSESSMENT OF ACCURACY ATTAINABLE IN EVALUATING BENDING MOMENTS AND SUPPORT REACTIONS FOR COMPLEX SITUATIONS ENCOUNTERED IN MODERN BRIDGES. PARTICULAR ATTENTION IS GIVEN TO THE PROBLEM OF COLUMN SUPPORTS. COMPARISON WITH EXACT SOLUTIONS AND MODEL INVESTIGATION SHOWS EXCELLENT AGREEMENT AND INDICATES THAT A GENERAL, INEXPENSIVE, METHOD OF SOLUTION IS NOW AVAILABLE. THE PAPER ALSO PRESENTS AN EXPLICIT FORM OF THE STIFFNESS MATRIX FOR TRIANGULAR PLATE ELEMENTS USED TO MAKE THIS WIDELY AVAILABLE. /AUTHOR/

Shear buckling of unstiffened hybrid beams

Abstract: An investigation of the web buckling strength of hybrid beams was conducted with the specific objective of determining the maximum web slenderness ratio for unstiffened webs to prevent web buckling before general yielding in beams subjected to combined bending moment and shearing force. Theoretical equations were derived to predict the shear-buckling strength. Because the web of a hybrid beam yields before the flanges, the equations are written for any amount of web yielding. Six test results are presented for beams with A514 steel flanges and both carbon steel and high-strength low-alloy steel webs. The test variables included the web slenderness ratio, the depth of web yielding, and the web distortions. The experimental and theoretical results are in good agreement and shear buckling curves based on the theoretical equations are presented.

On the Dynamic Response of a Beam to a Randomly Moving Load

Abstract: The problem considered is that of an infinitely long elastic beam subject to a moving concentrated force whose position is a stochastic function of time, X(t). The expected deflection and expected bending moment are analyzed, with special attention being given to the case of a stationary process X(t) and to the case in which X(t) is a Wiener process.

Nonlinear bending of beams with concentrated loads

Abstract: A simple numerical method is proposed for analyzing nonlinear bending of beams. The success of the application of this method to the nonlinear problems is demonstrated by two examples: (1) a cantilever beam with a concentrated load at the free end, and (2) a simply supported beam subjected to a nonsymmetrical load. The results are checked by other known solutions.

Axial plunger pump

Abstract: An improved axial plunger pump construction where the thrust and bending moment produced during the piston operation of the plungers and imposed on the rotating shaft are effectively counteracted by flange means thereby to keep the shaft free of such undesirable forces.

Optimal Structure Design by Dynamic Programming

Abstract: The lower bound theorem of plastic theory offers a direct procedure for structural design: any equilibrium distribution of stress (or force, or bending moment) gives an admissible design if the structure is so proportioned that it is then everywhere at or below yield. A cost can be assigned to each element of the structure, and the total cost is the sum of these costs. The optimal structure is the cheapest of all admissible designs, and is associated with the optimal equilibrium stress distribution. Herein dynamic programming is applied to the problem of locating this optimal stress distribution, and thence the optimal design. An application to the optimal design of a continuous beam is described in detail. It turns out that realistic cost functions can be introduced without difficulty, taking account of nonlinearity, fabrication cost and limited section availability. Extensions of the technique to more complex structures are discussed, and illustrated by the design of a multistory single-bay frame.

Fabrication and full-scale structural evaluation of glass-fabric reinforced plastic shells.

Abstract: This paper reports the initial investigations on full-size sandwich shell structures consisting of cylindrically curved panels and full cylinders, although some previous work in fabrication and basic buckling tests on small flat panels is presented as background information. The large thin-walled sandwich shells were fabricated by bonding 2-ply epoxy-fiber glass laminate facings to aluminum honeycomb cores. The curved panels were tested in axial compression and in torsional shear. The complete cylinders were loaded in a special torsionbending testing frame capable of applying bending moments and torques of 3,000,000 in.Ib. each. In general, the buckling test results compared as well with calculated values as do those for buckling of homogeneous isotropic shells.

Review of Columns Behavior Under Biaxial Loading

Abstract: Columns in a multi-story building framework are usually designed to resist bending moments acting in the plane of the frame. An actual column, however, is frequently subjected to bending moments acting in two perpendicular directions in addition to an axial load. Except in Great Britain, no such considerations are now included in column design. It is the purpose of this paper to survey the present stand of the problem of columns under biaxial loading. The survey deals with two equally important aspects of progress—New solutions emerging from the analytical study and experimental results reported from laboratory tests, with emphasis placed on the fundamental concepts advanced by various investigators. Three typical solutions ranging from an almost exact to a rather crude approximation have been selected for a rather detailed discussion. Comparison of the analytical work with test results is reviewed. Directions of further study are indicated.

Design of beams with web openings

Abstract: Both elastic-design criteria (allowable bending and shear stresses) and plastic-design criteria (allowable bending moments and shear forces) are presented for wide-flange beams with unreinforced holes of varying shapes and sizes, with emphasis on circular and rectangular holes not exceeding 0.6 times the beam depth. The design criteria are related to the AISC specification. Beam deflections and the effects of hole reinforcement are not included. Some tentative rules governing design for buckling problems, particularly severe for beams with holes and for beams with eccentric holes and adjacent holes, are also presented, although it is emphasized that additional research is needed in these areas.

Integral Equation Method for a Corner Plate

Abstract: An integral equation method is developed for the analysis of thin elastic plates. The integral equations are based on a Green's formula and are adapted for the solution of the biharmonic problem of plate analysis. By means of this method, a numerical solution is obtained for a simply-supported, uniformly loaded corner plate. Deflections and bending moments along the diagonal and shear forces along the edges are found. Values of these quantities previously calculated by means of a finite difference technique for a right-angled plate are confirmed by this new method and the analysis is extended to corner plates with different angles at the corner. Furthermore, for a right-angled corner plate, detailed contour plots of bending and twisting moments inside the plate are presented. With a digital computer these results are obtained without undue difficulty, and it appears that the integral equation method is well suited to this type of problem.

Nonlinear Free Vibration of Beams with Clamped Ends and with One End Clamped, Other End Simply Supported

Abstract: In this paper, an approximate solution is given by the use of Galerkin's procedure for the large amplitude free vibration of a beam with immovable clamped ends, subjected to an initial axial load. The results of the vibrations of a beam with one end clamped and other end simply supported are known from those of the vibrations of the antisymmetric modes of a clamped beam. Numerical calculations are carried out for cases of the fundamental vibration of both beams. Finally, a comparison of the increasing rate of the fundamental frequency with the amplitude is made among the beams having different end conditions : both ends clamped, one end clamped and other end simply supported, and both ends simply supported.

Strain concentration in beams under cyclic plastic straining

Abstract: Cyclic plastic-straining tests with controlled deflections have been conducted on beams subject to uniform bending, three-point bending, and a cosine distribution of bending moment; the second and third beams represent cases of strain concentration. Three different materials were used, namely mild steel, stainless steel, and aluminium.The strain-concentration tests show stainless steel and aluminium to be more resistant to deflection cycling than mild steel. A similar difference is not found in the uniform bending tests to anything like the same extent. Stainless steel shows a more pronounced strain-hardening characteristic in the cyclic stress-strain curve than does mild steel and it is concluded that this produces a more favourable strain distribution along the length of the beam, so that the maximum strain is less and the endurance is correspondingly greater.For materials which show settled cyclic stress-strain relations, reasonable predictions may be made of life in deflection cycling of beams...

Bending behavior of composite hybrid beams

Abstract: THEORETICAL MOMENT-CURVATURE AND MOMENT-STRESS RELATIONS ARE DEVELOPED TO DESCRIBE THE BENDING BEHAVIOR OF COMPOSITE HYBRID BEAMS, WHICH DIFFERS FROM THAT OF NONCOMPOSITE HYBRID BEAMS AND OF COMPOSITE HOMOGENEOUS BEAMS. FORMULAS ARE DEVELOPED FOR THE ULTIMATE STRENGTH OF COMPOSITE HYBRID BEAMS, AS LIMITED BY EITHER CRUSHING OF THE CONCRETE OR YIELDING OF THE FULL CROSS SECTION OF THE STEEL BEAM. CURVES OF MOMENT VS (1) CURVATURE, (2) LOCATION OF THE NEUTRAL AXIS, (3) BOTTOM-FLANGE STRESS, AND (4) TOP-FLANGE STRESS ARE PRESENTED TO ILLUSTRATE THE THEORETICAL BENDING BEHAVIOR OF COMPOSITE HYBRID BEAMS AND TO COMPARE THIS BEHAVIOR WITH THAT OF COMPOSITE HOMOGENEOUS BEAMS. THESE CURVES SHOW THAT THERE IS A SMALL DIFFERENCE BETWEEN THE BEHAVIOR OF THE TWO TYPES OF BEAMS AS A RESULT OF WEB YIELDING IN THE HYBRID BEAM. FOR DESIGN PURPOSES, THE SMALL REDUCTION IN THE FLANGE-YIELD MOMENT CAUSED BY WEB YIELDING CAN BE ACCOUNTED FOR BY AN APPROXIMATE DESIGN FORMULA THAT GIVES A REDUCED ALLOWABLE FLANGE STRESS. IF THIS REDUCED ALLOWABLE STRESS IS USED THE BENDING STRESS IN THE WEB NEED NOT BE CHECKED. /ASCE/

Transverse Shearing Stress in Rectangular Plates

Abstract: By means of the plate equations developed by Eric Reissner, the transverse shearing stresses in a thin, simply-supported, rectangular plate are determined. The load distribution may be defined by any function which can be represented by a double cosine series. The solution for uniform loading is discussed in detail. Experimental results obtained by the frozen-stress technique of photoelasticity are compared with the predictions of the Reissner theory and the classical theory. The boundary conditions used are the vanishing of deflection, bending moments, and twisting moments. The results show a marked difference between the two theories near the corner zones of the plate.

Stress analysis of cracked reinforced and prestressed concrete thin-walled beams and shells

Abstract: Summary This paper proposes a method for the stress analysis of thin-walled reinforced and prestressed concrete beams under the combined effect of axial force bending moments and ‘bimoments’. The assumption that plane surfaces remain plane is not applicable to beams of this type. The distribution of strains and stresses in an uncracked thin-walled beam follows closely the theory developed by Vlasov. This theory is extended here to the problem of the stress distribution in a cracked section of a reinforced concrete beam. The analysis is limited to beams of an ‘open cross-section’ working in the elastic range of internal stresses. Results of model tests at Southampton have substantiated the validity of this theory.

Estimation of bending moments in box-beam bridges using cross-sectional deflections

Abstract: THIS REPORT DESCRIBES PART OF THE RESEARCH WORK CONDUCTED UNDER THE FRITZ LABORATORY PROJECT 322, ENTITLED A STRUCTURAL MODEL STUDY OF LOAD DISTRIBUTION IN HIGHWAY BRIDGES. THE PURPOSES OF THIS WORK WERE TO: (1) FIND AN ANALYTICAL CORRELATION BETWEEN THE TRANSVERSE DISTRIBUTIONS OF LONGITUDINAL BENDING MOMENTS AND THE CROSS-SECTIONAL DEFLECTIONS IN BOX-BEAMS BRIDGES, AND (2) DEVELOP A PRACTICAL METHOD FOR THE ESTIMATION OF BENDING MOMENTS IN BOX-BEAM BRIDGES BY THE USE OF CROSS-SECTIONAL DEFLECTIONS. TO EXPERIMENTALLY VERIFY THE PROPOSED METHOD, TEST RESULTS FROM SEVENTEEN SMALL SCALE (1/16) PLEXIGLAS BOX-BEAM BRIDGE MODELS ARE REPORTED. DETAILS OF THE FABRICATION, INSTRUMENTATION AND TESTING OF THE MODELS ARE REFERENCED. IN PARTICULAR, IT SHOULD BE NOTED THAT THESE SEVENTEEN PLEXIGLAS MODELS WERE TESTED UNDER STATIC VEHICULAR LOADS, USING THE CREEP COMPENSATING TECHNIQUE. AN ANALYSIS OF THE EXPERIMENTAL RESULTS AND A PROPOSED METHOD FOR ESTIMATING BENDING MOMENTS ARE PRESENTED. THE ESTIMATED VALUES EXHIBIT AGREEMENT WITH THE MODEL TEST RESULTS. THE CONTRIBUTION OF CURBS AND PARAPETS TO THE FLEXURAL STIFFNESS OF THE BRIDGE WAS TAKEN INTO ACCOUNT IN THE ANALYSIS. THE INFLUENCES ON THE CORRELATION BETWEEN BENDING MOMENTS AND CROSS-SECTIONAL DEFLECTIONS DUE TO CURBS, PARAPETS, DIAPHRAGMS, SIZE AND SPACING OF BEAMS, AND THICKNESS OF SLAB ARE DISCUSSED. THE PROPOSED METHOD WAS USED TO ESTABLISH BENDING MOMENTS IN ONE EXISTING BRIDGE. THE ESTIMATED VALUES WERE FOUND TO BE CLOSE TO THOSE OBTAINED IN THE FIELD TEST. AS A RESULT OF THIS INVESTIGATION, IT IS BELIEVED THAT THE USE OF MEASURED DEFLECTIONS, ALONG WITH THE GEOMETRIC PROPERTIES OF THE CROSS-SECTION, MAY ENABLE AN ECONOMICAL AND ACCURATE ESTIMATION OF THE LATERAL LOAD DISTRIBUTION IN PRESTRESSED CONCRETE BOX-BEAM BRIDGES. /AUTHOR/

Bending Strength of Aluminum Formed Sheet Members

Abstract: An experimental and analytical investigation produced a method of calculating the bending strength of aluminum formed sheet members such as are used for roofing and siding. These members fail by crippling of the flange or web elements at stresses that may be well in excess of the local buckling strength. Specimens (numbering 46) were tested under either uniform bending moment or air pressure loading. Formulas are presented for local buckling and crippling of flange and web elements. Crippling failures occur simultaneously with local buckling in sections with relatively thick plate elements. In other sections, weighted average crippling stresses for the compression elements are used to predict ultimate bending strengths. Agreement with test results is achieved.

Analysis of Elastic-Plastic Grid Systems

Abstract: An incremental load method for analyzing the piecewise linear behavior of elastic-plastic grid systems with various support conditions is presented. The assumption is made that the torsional rigidity of the members is negligible. The equilibrium and compatibility equations are written in terms of bending moments, plastic hinge rotations, load parameters and an elastic-plastic transition function. The use of this transition function allows the formulation to be applicable to every regime as well as facilitates the treatment of the reversal of plastic hinge rotations. A technique of linear scaling is employed to determine the points of transition including the state of incipient plastic collapse. The collapse mechanism is verified by means of the solution of a system of hinge rotation equations. The analysis provides the complete load-deflection history of the grid systems from the elastic regime, through all the intermediate regimes, up to and including the collapse regime. Numerical examples are given to illustrate the method of analysis.

Similitude study of flexible buried arches subjected to blast loads

Abstract: : The objective of the study was to investigate and verify model-to-prototype scaling relations for blast loaded buried arches that respond both elastically and inelastically. Four geometrically similar, semicircular aluminum alloy arches with 4-, 8-, 12-, and 36-inch diameters were buried in dense dry sand and subjected to air-blast-induced loads on the surface. The tests were conducted at the Large Blast Load Generator located at the U. S. Army Engineer Waterways Experiment Station. The results of two series of tests, each consisting of 3 repeated shots, ranging from 70 to 300 psi, are presented. Within the range of parameters investigated, the scaling of the dependent variables were adequately verified. These variables included acceleration, velocity, displacement, thrust, and bending moment.

The solution for concentrated loads on shells by means of Thompson functions

Abstract: The paper deals with the displacements and stresses in arbitrary shells of positive Gauss curvature subjected to concentrated loads. The solutions for normal and tangential forces as well as for a bending moment applied to the shell are derived by means of Fourier integrals. Die Arbeit beschaftigt sich mit den Verschiebungen und Spannungen in beliebigen, konzentrierten Lasten unterworfenen Schalen positiver Gausscher Krummung. Fur die Falle, in denen Normal- und Tangentialkrafte und Biegemomente an der Schale angreifen, werden mit Hilfe von Fourier-Integralen Losungen ermittelt.

Bending moment distribution in a mariner cargo ship model in regular and irregular waves of extreme steepness

Abstract: : An experimental investigation was undertaken to determine (1) the lengthwise vertical wave-bending-moment distribution within the midship half-length and (2) the relationship between bending moment and extreme wave steepness, for a MARINER-type cargo ship. (Author)

Building method for multispans structures

Abstract: A METHOD OF BUILDING A CONTINUOUS GIRDER LYING ON INTERMEDIATE SUPPORTS AND TWO END SUPPORTS, WHICH CONSISTS IN BUILDING SYMMETRICALLY ON EACH SIDE OF EACH INTERMEDIATE SUPPORT GIRDER SECTIONS ACCORDING TO BALANCED CANTILEVER PRINCIPLE, AND REDUCING THE NEGATIVE BENDING MOMENT ON EACH INTERMEDIATE SUPPORT BY USING TEMPORARY SUPPORTS PROVIDING UPWARDLY DIRECTED FORCES ON CHOSEN GIRDER SECTION ENDS BEFORE CONNECTING THE ENDS OF SAID SECTIONS, AND LASTLY BUILDING THE END SECTIONS OF THE GIRDER.

Bending and torsion of reinforced concrete beams

Abstract: Summary Combined bending and torsion tests were carried out on 55 rectangular concrete beams to study the influence of concrete strength, reinforcement and the intensity of applied bending moment o...