Showing papers on "Bending moment published in 1969"

Cylindrical and spherical shells with cracks

Abstract: Meridional crack problem for cylindrical and spherical shells solved for uniform membrane load and bending moment, obtaining stress intensity components

Two nonlinear beams with definitions of ductility

Abstract: TWO MATHEMATICAL MODELS OF NONLINEAR BEAMS WHICH CAN BE USED TO REPRESENT THE GIRDERS AND COLUMNS OF A NONLINEAR MULTISTORY STRUCTURE ARE DESCRIBED AND COMPARED. ONE BEAM MODEL IS LIMITED TO BILINEAR BENDING MOMENT-END ROTATION HYSTERETIC CHARACTERISTICS. THE OTHER MODEL CAN HAVE DIFFERENT CURVILINEAR AND BILINEAR HYSTERETIC CHARACTERISTICS AT EACH END. THREE DIFINITIONS OF DUCTILITY FACTOR ARE MADE AND APPLIED TO YIELDING BEAMS. THESE TYPE OF BEAM MODELS CAN BE USED IN THE STUDIES OF THE DYNAMIC RESPONSE OF EARTHQUAKE EXCITED MULTI-DEGREE OF FREEDON YIELDING STRUCTURES. /ASCE/

Non-linear bending of beams with uniformly distributed loads

Abstract: The non-linear bending of both cantilever and simply supported beams subjected to a uniformly distributed load has been studied. The exact solutions for the slopes have been obtained and the solution for the maximum deflection and the horizontal projection of the beam length for the cantilever case are compared with a known approximate solution.

Free vibration of a centrally clamped spinning circular disk

Abstract: Centrally clamped spinning circular disk free transverse vibration analysis within accuracy of numerical computations

A comparison of approximate methods for the solution of plate bending problems.

Abstract: It is well known that classical, exact methods of analytical solution cannot be applied to the plate bending problem in cases of irregular boundary shape and arbitrary transverse loading and constraint. The paper summarizes and compares results obtained from using nine approximate analytical methods: point matching, boundary point least squares, TrefftzMorley, interior collocation, interior least squares, subdomain, Galerkin, Ritz, and Kantorovich. For purposes of concrete comparison, each of the methods is applied to two problems for which exact, although intricate, solutions are known: 1) a uniformly loaded, simply supported elliptical plate; 2) a square plate having free edges, supported at four asymmetrically located interior points, and loaded by its own weight. Comparative results are presented. Each technique is rated good, fair, or poor according to 11 important technical criteria and the underlying rationale is explained.

An analysis of the forces and bending moments generated during the notched beam impact test

Abstract: An analysis is presented which predicts the hammer force and specimen bending moment-time responses during impact from the dynamics of the system and the fracture characteristics of the material. The theoretical predictions are compared to available experimental observations and good agreement is obtained for brittle materials.

Numerical Analyses of Uniformly Loaded Circular Rafts on Elastic Layers of Finite Depth

Abstract: Synopsis A description is given of a method for determination of the reaction and bending moment distributions and the displacements of a uniformly loaded circular raft of any flexibility which rests on an isotropic elastic foundation layer of finite depth. The foundation layer is assumed to rest on a rough rigid base. The analysis is based on the solution presented by Burmister (1956) for the case of a surface point load. The reaction distribution is assumed uniform over each of the equal width annuli into which the raft is divided, and the error inherent in this approach is largely removed by extrapolation. Attention has been concentrated on the effects of variation of raft flexibility and layer depth, but the effects of variation of Poisson's ratio of the raft and of the foundation layer are also indicated. On donne une description d'une methode d'etablissement des repartitions de la reaction et du moment de flexion et des deplacements d'un radier circulaire a charge uniforme d'une flexibilite quelconq...

A refined mixed-type plate bending element.

Abstract: Triangular plate bending element using Herrmann variational method, deriving matrices for finite elements

Prestressed vertically laminated beam of wood

Abstract: DURING THE MANUFACTURE OF BEAMS, VERTICAL LAMINATIONS OF WOOD ARE HELD SECURELY IN AN OPPOSITE BENDING MOMENT TO THAT ANTICIPATED AFTER THEIR ERECTION IN A BUILDING. WHILE SO HELD, THEY ARE RELATIVELY MOVED TO RESPECTIVE SIDES OF A VERTICAL MEAL LAMINATION OR LAMINATIONS, WHICH IN TURN ARE BEING OPTIONALLY LONGITUDINALLY PULLED AT THE BOTTOM OF EACH OF THEIR RESPECTIVE ENDS. THEN ALL VERTICAL LAMINATIONS ARE MOVED TOGETHER UNDER COMPRESSIVE FORCES AND SECURED WITH FASTENERS. OPTIONALLY, THE FASTENERS MAY BE FORMED FROM AND REMAIN A PART OF THE METAL LAMINATION OR LAMINATIONS. AFTER SECUREMENT BY FASTENERS AND THEN UPON RELEASE FROM BENDING, PULLING AND COMPRESSIVE FORCES, THE DERIVED PRESTRESSED WOOD AND METAL BEAM IS READY FOR INCLUSION IN AN OVERALL STRUCTURE.

Vibration of a Combination of Circular Plates and Cylindrical Shells : 1st Report, A Cylindrical Shell with Circular Plates at Ends

Abstract: The vibrations of a cylindrical shell of which one end is built-in and the other is combined to a circular plate or of which both ends are combined to circular plates are studies. The displacements of a circular plate and a cylindrical shell which is built-in at one end are shown in graphs. The distribution of the bending moment in this cylindrical shell is also shown.

Analysis of Shear Walls with Openings

Abstract: Openings are often introduced into shear walls in multistoried buildings for either architectural or environmental reasons. These openings reduce the efficiency and change the deformation characteristics of the shear walls, depending on the distribution of the loads and the geometry of the walls with openings. Variations of the material properties also affect the stress distribution. The use of the finite-element method in analyzing these problems is found to be convenient and more accurate than conventional approximate methods. A model shear wall problem is selected and analyzed by the finite-element method and the results are presented. It was observed that local distortions occurred at the junctions of the lintel beams and the shear walls due to the bending moments, shear forces, and axial loads carried by the lintel beams. Because of these distortions, the bending moments on the lintel beams were found to be much less than the bending moments obtained from other approximate methods of analysis.

Horizontally Curved Bridges Subject to Moving Loads

Abstract: The analysis of the dynamic response of single span, horizontally curved bridges subject to moving forcing systems comprised of sprung and unsprung mass components is described. The bridge is considered to be a continuous, elastic system of thin-walled open cross section. An exact solution to the governing partial differential equations is obtained in the form of an infinite series. The solution is programmed on a digital computer, and a comparison is made between the computed and measured response of a laboratory model. The effect of the mass and velocity of the load upon the dynamic displacements and upon bending and twisting moments is analyzed.

Cutting of glass sheets

Abstract: A glass sheet is divided along a required line of break delineated by a score line on the sheet by supporting the sheet on an elongated member disposed in the region of the required line of break and making line contact with the underface of the sheet. One end of the member is then raised and a bending moment is applied across the raised end of the score line so as to effect a break which runs along the supported line.

Finite Element Plate Bending Equilibrium Analysis

Abstract: For the problem of elastic plate bending, a finite element procedure based on the minimum of complementary energy principle is developed. Primary variable of the problem is the distribution of the bending moments m x , m y and m xy . These vary parabolically inside each triangular element and have continuous values throughout the plate. In order to satisfy the equilibrium conditions, Lagrangean multipliers are introduced as secondary variables. It is then shown that these multipliers are generalized displacement parameters. The final solution will therefore provide direct information about both the stress distribution and the displaced shape of the plate. Equilibrium conditions are satisfied exactly. A strain energy bound is found. For several cases numerical results are given and compared with known solutions.

Buckling of a beam on a Wieghardt-type elastic foundation

Abstract: The paper gives a computation of the buckling load for a rod with pinned ends and elastic embedding according to Wieghardt The influence of shearing stresses on the bending is taken into account The result is compared with the buckling load holding for elastic embedding according to Winkler The important differences in the results of two theories are emphasized

Tests of A Two-Way Reinforced Concrete Floor Slabs

Abstract: Construction and testing of a nine-panel two-way reinforced concrete floor slab are described. The panels were 5 ft sq. Stresses, strains, deflections, and cracking observed during the tests are described. Bending moments derived from measured strains are presented and are shown to be substantially different than the design moments at many design sections. The measured beam moments were appreciably lower than the design moments, but many of the slab sections were underdesigned. The slab design load was 145 psf and the failure load with all panels loaded was 537 psf. This compared favorably with the 529 psf predicted for the same failure mechanism by means of yield-line analysis methods.

Prestressed concrete prisms as reinforcement for crack control

Abstract: A MEANS OF REINFORCING THE DECK CONCRETE FOR CONTINUITY AND CRACK CONTROL IS "AUXILIARY PRESTRESSING". PART OR ALL OF THE DECK REINFORCEMENT IS REPLACED BY LONG PRECAST PRISMS OF CENTRALLY PRESTRESSED CONCRETE. WHEN THIS IS DONE, LIMITED PAST EXPERIENCE HAS SHOWN THAT THE CAST-IN-PLACE CONCRETE SURROUNDING THE PRECOMPRESSED CONCRETE PRISMS IS RESTRAINED FROM CRACKING. THE STRUCTURE BEHAVES AS THOUGH IT WERE PRESTRESSED. DEFORMED BAR REINFORCEMENT, COMBINATIONS OF DEFORMED BARS AND PRESTRESSED CONCRETE PRISMS, AND OF DEFORMED BARS AND PRESTRESSING STEEL WERE COMPARED IN TESTS OF SEVEN T-BEAMS WITH THREE DIFFERENT SETS OF CROSS SECTIONS. THE PRISMS WERE EITHER 1-1/2 X 1-1/2 IN. OR 2 X 2 IN. IN CROSS SECTION AND CONTAINED EITHER A 0.162-IN. WIRE OR A 1/4-IN. PRESTRESSING STRAND. THE T-BEAMS WERE TESTED IN NEGATIVE MOMENT BENDING OVER A CENTRAL SUPPORT. COMPARISONS WERE BASED ON CRACKING MOMENT, CRACK WIDTH, DEFLECTION, AND ULTIMATE STRENGTH. PRESTRESSED CONCRETE PRISMS PLACED AS PART OF THE REINFORCEMENT IN THE DECK OVER SUPPORTS OF T- BEAMS WERE FOUND IN THE TESTS REPORTED HERE TO ACT AS PRESTRESSING REINFORCEMENT. THE BENDING MOMENT AT FIRST CRACKING WAS INCREASED BY THE PRESENCE OF THE PRESTRESSED CONCRETE PRISMS. THE OVERALL EFFECT WAS SIMILAR TO THAT OF DIRECTLY PRESTRESSING THE DECK CONCRETE. ULTIMATE STRENGTH OF THE SEVEN TEST BEAMS WAS SATISFACTORILY PREDICTED BY EQUATIONS GOVERNED BY YIELDING OF THE FLEXURAL REINFORCEMENT. IT IS BELIEVED THAT THIS NEW TECHNIQUE IS READY FOR FIELD TRIAL.

An investigation of the utility of computer simulation to predict ship structural response in waves

Abstract: Methods of computer simulation of ship structural response in waves are described, with emphasis given to the slowly varying bending moments due to waves and to slamming responses. Analog, digital, and hybrid computer systems are analyzed, and results obtained by use of the most efficient computational procedures for each type of structural response. The vertical and lateral bending moments due to waves are determined by use of a digital computer, and sample computations illustrated for determin- ing frequency domain outputs. Time history outputs of vertical bending moments due to nonlinear slamming are obtained using a modal model of the ship structural dynamic representation, together with time histories of the wave-induced vertical bending moment due to the same wave system. The capabilities of various computer systems to obtain the required responses, the form of the mathematical model appropriate for computational means, and the time requirements for carrying out the operations are also presented. The rapid assessment of spectral responses and their related statistical properties by means of digital computation, together with time history responses at rates faster than real time, provides a useful tool for determin- ing many aspects of ship structural response characteris- tics by means of computer simulation.

Effect of construction joints on the performance of reinforced concrete structures

Abstract: 1. Construction joints cause reduction of the loading required to induce failure by 15% to 20% below the computed value for the subject section. Compared with a monolithic beam, the actual strength of beams having a construction joint was found to be 15% lower. On the basis of the results, obtained and until more detailed investigations are carried out, for structures provided with block joints and the usual reinforcement, it can be recommended that the strength loss be accounted for by applying a coefficient of 0.85. 2. For a beam having a construction joint and subjected to a bending moment and a transverse force, the strength is determined by the strength of the concrete compression zone. A low bond strength across the construction joint initiates early crack formation at this section, a wider opening of the joint, and generally larger beam deformations. After the crack has formed, the frictional forces transferred to the compressed zone and the normal component of both the reinforcement shear and that of the remaining part of the compressed concrete generate an oblique crack which is directed from the joint toward the support, and along which the beam failure occurs. 3. The strength of oblique sections in beams with construction joints can be computed by the equations presented in this article. The values of inclination angle α of oblique cracks, for different ratios of M and Q, classes of concrete, layouts of joints, and bond strengths, must be established by tests. 4. To ensure that beams with construction joints will have adequate strength, the concrete compression zone in the joint region must be provided with oblique reinforcement.

Deflection of Beams

Abstract: Consider a short length of beam δx, under the action of a bending moment M. If δ is the bending stress on an element of the cross-section of area δA at a distance y from the neutral axis, the strain energy of the length δx is given by But hence

Skew reinforcement of concrete slabs against bending and torsional moments

Abstract: A METHOD IS DESCRIBED FOR PROPORTIONING STEEL REINFORCEMENT IN GIVEN, POSSIBLY SKEW, DIRECTIONS, TO RESIST BENDING AND TORSIONAL MOMENTS AT A POINT IN A CONCRETE SLAB. A FORMULA IS OBTAINED FOR THE STRENGTH OF AN UNDER-REINFORCED SLAB WITH KNOWN AREAS OF STEEL; THIS FORMULA IS THEN USED TO FIND THE REINFORCEMENT NECESSARY TO RESIST A GIVEN SET OF BENDING AND TORSIONAL MOMENTS, USING THE MINIMUM TOTAL AMOUNT OF STEEL. SAMPLE DESIGN CHARTS ARE PRESENTED AND THE PROCESS OF DESIGN IS DESCRIBED FOR BOTH A SINGLE SET OF MOMENTS AND MULTIPLE SETS DUE TO DIFFERENT LOADING CASES. /RRL/AUTHOR/

Measuring device for monitoring stresses of a tool

Abstract: A device for measuring stresses, including torque and bending moment of a tool, is disclosed wherein a rotor member operatively associated with the tool has strain gauges disposed thereon substantially parallel to the longitudinal axis to sense the bending moment at a tool and strain gauges disposed at an angle to the longitudinal angle to sense torque at the tool. Slots are provided in the rotor member to make it spring in the axial direction. The outputs of the strain gauges are sensed to provide an indication of the torque and bending moment operative on the tool.

Load Carrying Capacity of Simple Composite Columns

Abstract: A computer program based on a finite difference method of analysts has been developed for determining load deformation relationships to failure for pin-ended eccentrically loaded steel columns encased in concrete. The solutions obtained are the most accurate yet determined and take into account both the linear and nonlinear ranges of the two materials; comparisons have been made with the results of tests on both small and full scale columns. Quantitative Information obtained from the computer program has been used to examine critically existing and other likely design criteria applicable to columns of both British Standard and Universal sections. It is demonstrated that the simple interaction formula used in some design codes to determine permissible combinations of axial force and bending moment, leads to variations in load factor which are irrational. Consideration is also given to the control of the incidence of cracking of concrete under working conditions.

Photoelastic Study of Beams on Elastic Foundations

Abstract: The bending of beams supported by an elastic medium is analyzed using photoelasticity. Four models were considered: (1) A model representing a beam of infinite length with a concentrated control load; (2) a finite beam with a central load; (3) a finite beam with a load at the quarter point; and (4) a finite beam with two concentrated loads at the two quarter points. The bending moments, shears and contact pressures were obtained and compared with corresponding values for beams resting on a Winkler-type foundation. Several alternative ways of determining the pressure distribution at the surface of contact are presented. The analysis includes the stress distribution in the elastic medium.

Analysis and interpretation of full-scale data on midship bending stresses of dry cargo ships

Abstract: : Results of the analysis of stress data from full-scale measurements on two C-4 type cargo vessels are presented in the form of histograms and cumulative distributions, which together with previously analyzed full-scale data cover a total of five years of normal ship operation in the North Atlantic Two rational techniques are given for the extrapolation of full-scale data to longer periods of time, in order to predict extreme bending stresses (or bending moments) in service Recommendations are made for more data collection from different ships on different routes, for investigation of other statistical techniques, and for development of methods for model predictions of long-term trends (Author)

Apparatus for bending metal

Abstract: Metal bending apparatus is provided for progressively bending metal products such as sheets, strips, flat bars, and the like, to a predetermined angle by simple hand pressure, by pivotally moving a bending lever or arm into a wedge-shaped upper surface of a supporting bed. The pivotal mounting of the forward end of the bending arm is made resilient so that the pivoting portion of the bending arm automatically elevates in response to the thickness of the material being bent to minimize the variation which occurs in the angle of the bend along the length thereof.