Showing papers on "Bending moment published in 1982"

Optimal correction of mass and stiffness matrices using measured modes

Abstract: Discussion of Results The equations of motion were numerically integrated utilizing a total of 36 elements to define the geometry of the corer. The corer was allowed to free-fall for 3 s, at which time the global variables had the following values: u = 23.6 m/s, w = 2.3 m/s, 4 = 0.05 rad/s, 6 = 6.4 deg, ^=-0.8 m, Ze = 31.0 m. The corer assumed an elongated inverted-S shape. At ^ = 3 s, maximum bending moments occurred at the location of the step taper and at the junction between the afterbody and the upper portion of the barrel. The local element deflection, slope, and bending moment at these locations are given in Table 1 and are approximate due to the local variables being measured at discrete locations along the length of the corer. It is unlikely that the corer will actually experience such large bending moments during free-fall. However, it is intuitive that large bending moments will occur at the barrel/afterbody junction and may even become larger during penetration.

Toward a New Engineering Theory of Bending: Fundamentals

Abstract: The classical engineering theory of bending due to Bernoulli and Euler serves as a cornerstone for structural analysis and design. Limitations of this theory, however, become apparent in flexural wave propagation studies; it predicts infinite phase velocity as the wavelength becomes shorter. This theoretical deficiency is corrected by Timoshenko theory which accounts for transverse shear deformation. A thorough study of exact elasticity solutions reveals that there are two additional effects that are the same order as transverse shear in bending behavior. A new theory accounting for them is presented, along with several applications. The new equations are no more complicated than those of Timoshenko-ty pe theory, yet they yield solutions which are exact or indistinguishable from exact in the examples studied.

Single Pile Response to Cyclic Lateral Load

Abstract: An analysis is presented for the deflection of a pile in clay subjected to quasi-static cyclic lateral loading. This analysis is an extension of the elastic continuum analysis for static pile response, and allows for the reduction of soil modulus and yield pressure with increasing cyclic strain or deflection. A number of theoretical solutions are presented to illustrate the factors influencing the increase in deflection and bending moment in the pile with increasing cycles and cyclic load level. Some of these solutions are presented in dimensionless form as correction factors which may be applied to the computed static response of a pile. Some comparisons are made between the theoretical behaviour and that measured in field tests, and these demonstrate that the theory reproduces the observed characteristics of behaviour of the pile. They also give an indication of the order of magnitude of some of the key variables in the cyclic response analysis.

Application of the line-spring model to a cylindrical shell containing a circumferential or axial part-through crack

Abstract: An approximate solution was obtained for a cylindrical shell containing a part-through surface crack. It was assumed that the shell contains a circumferential or axial semi-elliptic internal or external surface crack and was subjected to a uniform membrane loading or a uniform bending moment away from the crack region. A Reissner type theory was used to account for the effects of the transverse shear deformations. The stress intensity factor at the deepest penetration point of the crack was tabulated for bending and membrane loading by varying three dimensionless length parameters of the problem formed from the shell radius, the shell thickness, the crack length, and the crack depth. The upper bounds of the stress intensity factors are provided by the results of the elasticity solution obtained from the axisymmetric crack problem for the circumferential crack, and that found from the plane strain problem for a circular ring having a radial crack for the axial crack. The line-spring model gives the expected results in comparison with the elasticity solutions. Results also compare well with the existing finite element solution of the pressurized cylinder containing an internal semi-elliptic surface crack.

Finite element analysis of RHS T-joints.

Abstract: The finite element method (FEM) is used to model the behavior of rectangular hollow section (RHS) T-joints beyond the elastic limit, and is applied to determine their ultimate and working strengths. Punching shear and rotational stiffnesses under branch axial force and bending moment have also been calculated. The unreinforced and haunch type joints were analyzed in the study. In both cases the chord top flange was modelled as a thin plate supported by coupled edge springs. Loading was incorporated through line loads along the perimeter of a rigid inclusion (the branch). In the elastic range, joint stiffness values were found to be in good agreement with the available test results. The sensitivity of joints to different geometric parameters, i.e., width ratio λ, haunch size λ 1 , and chord thickness t was studied using the FEM model in the elastic-plastic range. Ultimate branch moments or punching shear forces were found to be about five times the corresponding first yield values, thus indicating the need to base design loads on an ultimate strength or maximum deflection criterion.

Long-term deflections of reinforced concrete beams

Abstract: Synopsis Long-term static load tests were carried out on simply supported and continuous reinforced concrete beams at the N.S.W. Institute of Technology, Sydney, Australia. The instantaneous and time-dependent beam deflections were recorded, together with the time-varying strain distributions at selected cross-sections and the redistribution of bending moments due to creep and shrinkage. In this paper, the measured beam deflections are compared with values predicted by British and American design code methods and by finite element methods. The creep and shrinkage properties used in the predictions were obtained from test specimens and were also calculated in accordance with CP 110:1972, AS 1481–1978, ACI 209:1971 and the CEB–FIP 1978 Model Code. For the samples of concretes examined, the applicability of these predictive methods is discussed.

Dowel for pavement joints

Abstract: A device for transferring vertical shear stress and bending moments across transverse joints in concrete pavement slabs and the like, and for simultaneously controlling the joint gap width A dowel is formed from a continuous length of steel bar, treated to cause its outer ends to bond to concrete and its central portion treated to prevent bonding to concrete The outer ends of each bar is formed to permit the center portion to be disposed near either the top surface or bottom surface of the slab sections and the outer ends along the neutral axis of the slab sections The bars are used in pairs with one center portion adjacent the top surface and the other one adjacent the bottom surface A multiplicity of such dowels is embedded in the concrete of a continuously-poured concrete slab aligned with the roadway and in a spaced relationship across the slab The concrete is grooved before curing across the slab and over the central portions of the dowels As the concrete cures, the outer ends of the dowels bond to the concrete while the central portions remain unbonded causing a joint crack and strain produced in the concrete due to shrinkage which is partially transferred to the unbonded steel which acts as a latent spring to subsequently control the gap width The dowels additionally serve to transfer bending moments and vertical shear stresses from live loads across the pavement joint

Load Capacity of Concrete Bridge Decks

Abstract: The behavior of two reduced-scale concrete bridge decks subjected to simulated wheel loads was evaluated in a series of tests. One slab was reinforced in accordance with AASHTO requirements; the other had three areas with varying amounts of isotropic reinforcement. Results show that with either reinforcement pattern, service load bending moments are from 40 to 65 percent of those predicted by flexural theory. Failures were by punching shear rather than flexure and occurred at loads at least six times larger than design.

Transverse bulkhead connection to filament wound vehicle body sides

Abstract: Bulkhead supports (18) are integrally connected to opposite side portions of a filament wound hopper car body (16). The bulkhead supports include longitudinally spaced extensions (20, 22) extending inwardly from the car body sides. The transverse bulkheads (14) are located within the extensions on either side of the car with longitudinal clearance (31). Resilient bulkhead cushioning members (32) are located between the bulkhead and each extension. The resilient bulkhead cushioning members extend only a short distance transversely to reduce or substantially eliminate the introduction of bending moments into the car body sides when the transverse bulkheads are subjected to lading loads.

Plate reinforced square hollow section T-joints of unequal width

Abstract: The carrying capacity of square hollow structural section T-joints stiffened by a rectangular flange plate is investigated for both branch bending moment and punching shear. The ultimate moment or load is determined from the simple yield line method of which one of three failure modes is applicable depending on the plate length. A large number of combinations of branch, chord, and plate sizes are analysed to provide a statistical basis for making recommendations of optimum plate lengths and thicknesses for stiffened joints in Vierendeel truss applications.

The Large Elastic-Plastic Deflection With Springback of a Circular Plate Subjected to Circumferential Moments

Abstract: The large deflection elastic-plastic bending of a circular plate subjected to radially outward acting bending moments uniformly distributed around its circumference is analyzed, and computer programs are given to facilitate the determination of the distributions of bending moments, in-plane forces, and displacements during the bending and after unloading or springback. Computed examples are given, and the errors developed by small deflection theory are discussed.

Predicting performance of buried conduits

Abstract: The capabilities of finite element computer codes FINLIN, CANDE, SSTIP and NLSSIP were evaluated CANDE was judged to be the best over-all code for predicting performance of buried conduits A number of improvements to this code were made Example solutions are given to illustrate the effects of conduit stiffness, interface slippage, and soil properties on conduit performance It was found that conventional concepts of soil "arching" are misleading; that slippage at the soil-conduit interface strongly affect the response; and that soil behavior plays the most crucial role in conntrolling performance It was concluded that the Duncan-Chang hyperbolic model is a satisfactory representation of nonlinear soil behavior for routine studies of conduit response Further use of equivalent elastic, overburden dependent, or default values in the extended Hardin soil models is not recommended For prediction purposes, especially to investigate the effects of soil compaction and of localized shear failures, a plasticity model of soil behavior is needed Duncan's (1979) SCI procedure for design of long-span metal culverts with shallow cover was also investigated The procedure provided good estimations of maximum thrust for the problems investigated in this study; however, agreement in both the magnitude of the bending moment and in the form of the bending moment equation was found to be poor, and the proposed safety factor to guard against plastic hinging in the conduit wall is considered to be overly conservative (FHWA)

Tension stiffening model for reinforced concrete members

Abstract: The principal difficulty in modelling the moment-curvature relationship for a reinforced concrete element is the influence of flexural cracking, the tensile strength of the concrete between the cracks, bond slip and the non-linear stress-strain relationship of the concrete especially as influenced by creep. A simple theory based on the deformation and equilibrium at a cracked cross-section may be easily derived if the influence of the tension stiffening of the concrete between cracks is taken into account by a hypothetical stress-strain curve for the reinforcement. Typical curves have been obtained from experimentally observed values of bending moment, curvature and compressive concrete strain using the calculus of variations. (Author/TRRL)

On the Characteristic of a Bolted Joint Subjected to an External Bending Moment : the case where clamped parts are circular flanges

Abstract: In designing a bolted joint, it is important to estimate the force ratio. But this force ratio is the factor to be considered in the case where a load is applied only in the axial direction, but it is not considered when an external bending moment is applied on an assembly. In the previous paper, in the case of T-flanges, a force ratio for the external bending moment, which is the ratio of the increment of bolt axial force to the external bending moment, is introduced. In this paper, the force ratio for the external bending moment is analyzed in the case of circular flanges. The effect of the circular pitch diameter on the force ratio for the external bending moment is discussed. In addition, the stresses produced in bolts are analyzed. Then, in order to verify these analyses, experiments are carried out. Comparing these results, they are in a fairly good agreement.

Strength of Lumber under Combined Bending and Compression.

Abstract: : Wood members under combined bending and compression occur as structural elements in several important applications: as the top chords of trusses, as wall studs, as frame members in towers, and in other rigid frame structures. While strength in bending alone and compression have been extensively studied, the interaction of these two modes of failure is poorly understood, particularly for dimension lumber of common construction grades. The aim of this study was to define a failure locus in the plane of bending moment (M) versus compressive force (C). Attention was restricted to that portion of the plane where bending stress exceeds compressive stress since that is the region of greatest importance in the design of wood frame structures and trussed roofs. In order to limit the scope of the study, only one species (Western Hemlock) and one size (nominal 2 x 6) were studied.

Force measuring apparatus mounted on tractor including Hall sensor detecting deformation of flex rod to control tractor power hoist

Abstract: A force measuring procedure and a force measuring apparatus are used to control the power hoist of an agricultural tractor. The force measuring procedure operates in such a manner that the relative displacement of a point on an elastic system is detected by at least one Hall sensor disposed on either the elastic system or on the fixed frame with the Hall sensor being located in a magnetic field with a predeterminable magnetic flux. For this the force measuring apparatus has a flex rod attached to at least one of a pair of lower hitches which indicates the bending moment, and the Hall sensor is mounted with its detector surface essentially in the primary plane of bending deformation of the flex rod and is connected to the control circuit of the power hoist. The described force measuring procedure and the force measuring apparatus operating with this procedure produce the particular advantage that the mounting of the parts needed for the apparatus becomes extremely simple, with a resulting high degree of measuring precision and operating reliability assured for the apparatus. The force measuring procedure and the force measuring apparatus can thus be used to particular advantage whenever the objective is to continuously monitor the construction elements of a mass produced mechanical system.

External Pressure and Sectional Behavior of Fabricated Tubes

Abstract: The effect of external hydrostatic pressure on the cross sectional behavior of fabricated tubular columns is studied analytically using tangent stiffness approach. The moment-curvature behavior of a short column is of prime importance in the analysis of any long beam-column. The results will be applied to study the effect of external pressure on the strength and behavior of long beam-columns. The fabricated tubular column contains imperfections such as out-of-roundness and longitudinal and transverse residual stresses. These imperfections combined with the effect of external pressure are studied in the present analysis. Tresca yield criterion is used for elements in biaxial stress state, which is induced by the interaction of axial stress and longitudinal and transverse residual stresses and magnified by external pressure. A computer program has been developed to obtain numerical results from which practical design formulas are derived for cross-sectional capacity of fabricated tubular columns subjected to axial force, bending moment and external hydrostatic pressure.

Bending stresses in subducted lithosphere

Abstract: Summary. The flow of the mantle near subducted lithosphere applies a force (dynamic load) to the slab which has a normal component as well as a shear component. In addition, the greater density of the slab compared to the surrounding mantle results in a downward force (negative buoyancy) which also has a component normal to the slab. Because the slab is long compared to its thickness, the stresses in the slab due to the normal components of the loads are accurately estimated from the bending moment. We have used previous estimates of the loads to compute the bending moment in the slab as a function of distance down the slab. Our results indicate that the loads applied to the slab are large compared to its strength; bending moments due to normal loads will not be transmitted over the length of the slab. Instead, the slab will deflect so that the normal loads are balanced locally.

Stochastic Theory of the Slamming Response of Marine Vehicles in Random Seas

Abstract: A stochastic theory is developed for the dynamic response of marine vehicles to slamming loads in random seas. Based on slamming observations and records, the slams are temporally represented as a train of Poisson impulses of random intensity occurring at random time intervals. Model analysis is used to derive the impulse response and system functions of the marine vehicle. The probability density functions, spectral densities, autocorrelation functions, and other relevant statistics of both the imput slams and the output vehicle response are developed and discussed. Special attention is given to the bending moment response. A numerical examaple is pres- ented in the last section in order to illustrate the application of the theory covered by the Authors. In this example, the mean square of the bending moment response of a Mariner-class ship is calculated.

Device for measuring flow speed and flow rate

Abstract: PURPOSE:To improve an S/N ratio and to obtain the device having excellent vibration resistance and rigid structure, in the device for measuring the flow speed and flow rate utilizing K arm an vortex, by mechanically separating a vortex generating body and shaft, and detecting respective stresses. CONSTITUTION:A stress detecting part 3a has a shape whose central part is blanked as shown in Figure B, and provided in the vicinity of a part where signal moment is maximum. A numeral 5 is a shaft which is inserted into a concave part 22 of the vortex generating body 2a with a gap 51 provided. One end of the shaft is supported 52 by the vortex generating body 2, and the other end is fixed to a pipe 1. Therefore, when the fluid under test flows in the pipe 1 and the arm an vortex is generated, bending moment acts on the vortex generating body 2a by the vortex lift, but it does not act on the shaft 5 and the bending moment becomes zero. Since the stress detecting part 3a, which measures the vortex signal, can be arbitrarily placed at the position where the stress is large, the large detected signal can be obtained.

Rotary bending machine

Abstract: The rotary bending machine comprises a drive spindle which is rotatably mounted in a fixed bearing block and has a clamping device for the end of a specimen to be tested for its fatigue strength under reverse bending stresses. The other end is clamped in a loading bearing on which a force which produces a bending moment in the specimen acts via a lever arm. To decouple the loading from the intrinsic weight of the loading bearing, the force which produces the loading bending moment acts on the associated lever arm of the loading bearing in a horizontal plane which extends through the axis of rotation. The intrinsic weight of the loading bearing is absorbed by a supporting bearing having horizontal mobility, for example as a result of one or more horizontal sliding surfaces. Two equally large, parallel loading forces are able to act via one lever arm in each case in the opposite direction so that no axial force is exerted on the specimen. To produce a specified loading bending moment, a loading force parallel to the axis can be produced by dimensioning the lever arm. At that end of the specimen which is remote from the drive shaft, a braking device can be provided to make it possible to produce a torsional stress in the specimen in addition to the bending stress.

Structural element models for hull strength analysis, Final Report to U.S. Coast Guard, September 1982. (NTIS DTCG-23-81-C20068)

Abstract: Hethods for reliably computing the maximum bending moment of a ship hull girder depend on the knowledge of the nonlinear behavior of the component structural elements. To be practically efficient, definition of this behavior should be in the form of compact algorithms (analytical computational models) rather than separate large computer programs. Analytical computational models were developed for the axial load vs. axial deformation relationship of single plates and of stiffened plates (longitudinal stiffeners with tributary plates). Both models were developed by using multi-variable regression analysis of the load-deformation curves available from tests, published in literature, or computed specifically for • this study by using large computer programs. These models are applicable to the preand post-ultimate ranges of deformation. Typical practical values of initial imperfections and of r~sidual stresses were incorporated into the models. The models are presented in the form of sets (matrices) of constants which, for a particular combination of material and geometric properties, are reduced to expressions which give the axial stress as a continuous analytical function of the axial deformation (strain). The input parameters for the plate model are: length, width, thickness, yield stress, and modulus of elasticity. The input parameters for the stiffened plate are: length, plate width, plate thickness, stiffener area, stiffener flange area, radius of gyration o.f the combined section, modulus of elasticity, yield stresses of plate, stiffener web, and stiffener flange. Standard deviation with respect to the data used in the development of the models is 8.1% for plates and 7.8% for stiffened plates. ·