Showing papers on "Bending moment published in 1983"

Web design under compressive edge loads

Abstract: The studies on crippling of rolled beams and plate girders' webs, subjected to patch or distributed edge loading, summarized in this report. Solutions are available for the elastic critical buckling loads of idealized web panels which show little or no correlation to crippling loads determined from tests. Semi-empirical formulae are available to predict the crippling load with an accuracy that is acceptable for practical purposes. Formulae to predict the crippling load are recommended. Semi-empirical formulae to predict loads above which membrane yielding of the web becomes pronounced are also available. The effects of coexistent global bending moment or shearing force were discussed. Reduction of P sub u due to coexistent global moment has been established by the way of a formula for a reduction factor. A conservative approach is recommended. The requirements to prevent crippling given in the AISC building specification, as well as the proposed AISC LRFD specification, have to be reexamined in the light of the information in this report. (Author)

Direct shear failure in reinforced concrete beams under impulsive loading

Abstract: : An analytic procedure is developed, using classic elastic Timoshenko beam theory, to define conditions under which reinforced concrete beams and one- way slabs can fail in a direct shear mode when subjected to distributed impulsive loading. The procedure is based on the assumption that incipient failure occurs in direct shear when the beam support shear exceeds a strength threshold before the support bending moment attains its ultimate capacity. The Timoshenko theory is extended to include rotational beam-end restraint and to account for viscoelastic material response to assess qualitatively the influence of rate effects on shear and bending moment. Dynamic failure in direct shear is presumed to behave in accordance with currently accepted static shear transfer mechanisms. Dynamic failure criteria are extropolated from static criteria with the use of an enhancement factor based on increased material strengths due to load rate. Failure curves, defining peak pressure versus rise time domains where direct shear failure is possible, are compared to experimental evidence for specific beam geometries and load rates. Post failure deterministic and stochastic models are introduced as candidates for analysis beyond incipient shear failure. It is concluded that direct shear failures can be predicted for certain combinations of load parameters. Rate effects enhance shear forces more than bending moments during transient response. Strength enhancement due to load rate reduces the domain of load parameters over which a direct shear failure can take place, whereas a relaxation of beam-end restraint increases this domain considerably.

Bending properties of creased zones of paperboard related to interlaminar defects

Abstract: A parallel beam model is presented for the bending behaviour of locally delaminated zones (creased zones) of paperboard. It is shown that the bending moment and the force levels are strongly dependent on the geometry and elastic properties of the creased zone. A favourable condition for low crease stiffness is a large number of long interlaminar failures. Experimental measurements of the crease stiffness and maximum bending moment for paperboards with implanted defects of various lengths and numbers were in reasonably good agreement with the crease stiffness predicted by the parallel beam model.

Gravity stiffness of classical suspension bridges

Abstract: Although classical suspension bridges have been designed for over 70 years using the deflection theory, it is difficult to obtain from literature a clear understanding of their structural action. The all‐important “gravity stiffness” is isolated from the modifying effects due to cable extensibility, tower stiffness, and deck bending stiffness. Graphs of maximum gravity stiffness deflections and changes of slope due to concentrated and distributed loads are presented, and formula for the modifying effects are given. It is found that with flexible decks simple formula exist for the maximum bending moment and shearing force in the deck due to concentrated and distributed loads.

Process and apparatus for strip flatness and tension measurements

Abstract: A process and apparatus for on-line measurement of unflatness of hot or cold rolled strip products, wherein the longitudinal bending of a shape roll over which the strip passes provides a measure of the unflatness of the strip. Actual values of force, displacement or bending moment near the ends of the shape roll may be compared to theoretically predicted values for a flat product and for product having various out-of-flatness conditions. Preferably, the shape roll is supported at its ends by two pairs of supports, and the measurements at the supports are used in determining roll bending and then strip unflatness. Other conditions such as off-center strip and asymmetric operation of the rolling mill may also be determined from the measurement.

Differential pressure vortex sensor

Abstract: A differential pressure sensor (10) adapted specifically for use with vortex shedding flowmeters which can be used in small spaces, uses a bending beam (60) for providing an electrical signal proportional to differential pressures between two oppositely facing diaphragms (40A, 40B). The diaphragms deflect under differential pressure and cause the beam (60) to be bent. The diaphragms have low mass and have a support structure (43) between them, carrying spring clips (50) which load one end of the bending beam (60). The other end of the bending beam (60) is then supported so it cantilevers from its mounting or support (61, 62) and upon movement of the diaphragms under differential pressure the beam (60) will bend. The signal can be derived by using a bending element made of a piezoelectric "bimorph" beam, which provides a voltage output as it bends, a strain gauge sensor on a beam, or an optical sensor, such as a fine fiber which deflects and provides an optical output may be used, as well as similar devices. Preferably, the sensor is a piezoelectric bimorph beam because of the direct electrical signals provided, which result from bending of the beam (60).

Post-Buckling Behavior of Tubular Beam-Columns

Abstract: Behavior of fabricated tubular steel beam-columns as commonly used in offshore structures is studied for the entire range of monotonic loading up to ultimate load including the post-buckling branch of unloading, using assumed deflection method. In the present approach, equilibrium is established only at a critical section of a beam-column using closed form analytical expressions for moment-curvature-thrust relationship of a fabricated tube. The computer model developed on the basis of this approximation is compared with tests and other analytical methods, and it is found that the assumed deflection method predicts the behavior of actual tubes with good accuracy, yet it simplifies the analysis drastically. A considerable amount of data has been obtained and presented concerning the behavior of cylindrical tubular beam-columns. It is concluded from this numerical study that initial imperfection (out-of-straightness), lateral load at mid-span, and bending moment at ends affect the behavior of a beam-column in a similar manner. As these values increase, the ultimate strength is reduced significantly while their associated load-deflection or shortening relations become flatter.

Postbuckling behavior of a thick plate

Abstract: The postbuckling behavior of a simply supported rectangular thick plate subjected to arbitrary loading conditions is investigated. The applied stress is taken to be a combination of a pure bending stress plus an extensional stress in the plane of the plate. Governing equations based on von Karman assumptions are used to solve the postbuckling problem by the Galerkin method. Buckling loads are obtained to compare with the results of Brunelle and Robertson. Postbuckled deflection is shown to increase with the transverse isotropic coefficient 5, and the effects of the in-plane bending stress are found to be quite significant for a thick plate.

Thermoelastic bending of the lithosphere: implications for basin subsidence

Abstract: Summary. Thermoelastic stresses are capable of producing significant lithospheric deflection. A systematic approach to modelling this effect is presented, in which the lithosphere is presumed to behave as a thin, elastic (or viscoelastic) plate on a fluid substrate, and lateral variations in basal heat flow induce both vertical buoyant loads and thermoelastic bending moments. The amount of uplift or subsidence produced by a given heat source depends on a number of factors, including the strength, duration and lateral extent of the thermal anomaly, and the thickness, density, rigidity and viscosity of the plate. The mechanical response of the plate is characterized by two distinct length scales (one for shearing, the other for bending) and the deformation produced depends critically on the scaled width of the heat source. The plate acts as a low pass spatial filter in response to thermal loads, but has a narrow band pass filter response to applied moments. The temporal response to an abrupt change in basal temperature or heat flow also depends on the ratio of the thermal diffusion time for the plate versus the viscoelastic relaxation time of the material. A rapid, localized increase in basal heat flow will initially produce a central depression and a peripheral uplift. Thus, while it is often assumed that the main depositional phase in platform basins is associated with the cooling and contraction of the lithosphere following an earlier thermal doming event, it is shown that, if conditions are right, a basin may also form in direct response to the initial heating event. Either way, subsequent thermal equilibration and viscous stress relaxation will tend to modify the initial deflection profile.

Design of Floor Slabs Coupling Shear Walls

Abstract: A finite element analysis is made of the bending moments and shear forces in a floor slab coupling a pair of laterally loaded plane shear walls in order to give guidance on the design of the slab. Contour diagrams and design curves showing the variation of critical bending moment factors are presented to facilitate a rapid evaluation of the slab stresses induced by coupling action. Based on an appraisal of the interactive shear forces between wall and slab, a design procedure is suggested for checking against punching shear failure in the slab.

Creep in Continuous Beam Built Span-by-Span

Abstract: The long-term variation of bending moment distribution caused by creep in a continuous beam errected sequentially in span-length sections with overhangs is analyzed. A linear aging creep law is assumed. The problem involves changes of the structural system from statically determinate to indeterminate, a gradual increase in the number of redundant moments, and age differences between various cross sections. A system of Volterra integral equations for the history of support bending moments is derived. By considering infinately many equal spans, which is good enough whenever there are many spans, one can take advantage of a periodicity condition for the construction cycle; this reduces the problem to a single equation which is of a novel type in creep theory—an integral-difference equation involving time lags in the integrated unknown. The solution exhibits sudden jumps at times equal to multiples of the construction cycle. The jumps decay with time roughly in a geometric progression. Approximation of time integrals with finite sums yields a large system of simultaneous linear algebraic equations. These equations cannot be solved recurrently, step-by-step. By solving the large equation system with a computer, the effects of the duration of the construction cycle, of concrete age at assembly of span from segments and of the overhang length are studied numerically.

Investigation of the Effect of Blade Sweep on Rotor Vibratory Loads.

Abstract: The effect of helicopter rotor blade planform sweep on rotor vibratory hub, blade, and control system loads has been analytically investigated. The importance of sweep angle, sweep initiation radius, flap bending stiffness and torsion bending stiffness is discussed. The mechanism by which sweep influences the vibratory hub loads is investigated.

Experimental and Theoretical Approach to the Estimation of Non-Linear Vertical Wave Loads

Abstract: Accurate estimation of wave loads acting on a ship is a long-lasting task for naval architects. Recently, a new approach for the investigation of non-linear characteristics of wave loads was introduced; namely, combination of experiments using “elastic model” and non-linear digital simulation.In this paper, at first, possible construction techniques of “elastic model” are examined. Adopting “backbone model” composed of segmented hulls and a metal backbone representing ship's longitudinal rigidity, two series of model experiments were carried out for a high-speed cargo vessel with different values of backbone's rigidity.Application of “backbone model” makes it easy to change model's longitudinal rigidity. Using as high rigidity backbone as possible, vibration response components can be reduced and responses almost as a rigid body can be measured. Replacing the backbone with the one having corresponding rigidity to the full scale ship, approximate responses of the ship can be measured.By the examination of dynamic characteristics of the model, vibration modes and modal damping coefficients were obtained, and the damping coefficients were found to be very close to those of full scale ships. It means that close correspondence between model experiments and full scale phenomena can be obtained.A digital simulation program was developed for the estimation of nonlinear heave and pitch motions, vertical bending moment and shearing force. Compared with the results measured through the model test, calculated results seem to predict non-linear characteristics fairly well.

A study of the inelastic seismic response of reinforced concrete coupled frame-shear wall structures

Abstract: Three 12 storey frame-shear wall buildings with varying wall size were designed according to capacity design principles. Their response to the El Centro NS 1940 and Pacoima Dam S15°W 1970 accelerograms was investigated using a 2-dimensional nonlinear dynamic analysis program. Particularly significant observations were the high levels of wall shear forces and generally low levels of column bending moment encountered. Wide spread beam flexural yielding involving moderate levels of inelastic deformations and interstorey drifts controlled by the walls indicate the potentially desirable inelastic performance of these hybrid structures. Design schemes are proposed whereby improved estimation of maximum inelastic actions can be made using the traditional elastic analysis for equivalent lateral static loading on the structure.

Comparison of radiographic images. A new method for analysis of very small movements.

Abstract: A new method, shift comparisoN, for comparing 2 radiographic images is described. The method may be used for many purposes, but is particularly suitable for detecting small provoked motions between skeletal parts. Defective union in fractures or osteotomies is easily diagnosed by such a comparison. Films are exposed before and during the application of force to one of the fragments. By examining the films in the Shift Comparator small movements caused by the force may be detected. The technique has also been used for measuring the development of stability of union of tibial fractures by determining th deflection of the fracture caused by a bending moment.

A numerical investigation of the retaining walls of the bell common tunnel

Abstract: In this report a class `a' prediction for the behaviour of the instrumented section of one of the retaining walls of the Bell Common cut and cover tunnel on the M25 motorway at Epping, Essex is presented. This prediction is based on complex finite element calculations simulating the construction procedure and assuming the soil to behave in an elasto-plastic manner. Predictions of wall displacements and bending moments, soil movements and total horizontal stresses in the soil are presented. These are given at the proposed locations of the measurement stations to be employed in the field instrumentation and will therefore ease later comparisons between predictions and field observations when the latter data becomes available. In addition, a parametric study investigating the sensitivity of the analysis to the input assumptions is reported. The predictions have been made well in advance of completion of tunnel construction. (Author/TRRL)

Yield Surface for Thin Bars with Warping Restraint

Abstract: A procedure is described for deriving yield surface equations for thin‐walled open cross sections for cases in which Saint Venant torsion is small compared to warping torsion. The yield surface equations are expressed in terms of an axial force, bending moments in two planes, and the warping moment or bimoment. Equations are derived for the specific case of a Z‐section. These equations are shown to satisfy the uniqueness theorem of plastic analysis thereby furnishing the correct yield surface within the limits of validity of the assumptions made. The applicability and accuracy of the proposed equations are indicated.

Connecting work for pile and footing

Abstract: PURPOSE:To reduce and relax bending moment to be applied to the head of a pile by a method in which concrete is placed to form a footing in such a way as to enable an inversed container-shaped partition case covered on the pile head to serve as a part of the footing. CONSTITUTION:An inversed container-shaped partition case 13 is covered on a pile head 11a projecting from the bottom G.L of foundation. Then, leveling concrete 14 is placed to form a footing 12 in such a way as to enable the partition case 13 to serve as a part of the footing 12. Thus, since the connection between the pile head 11a and the footing 12 is in a pinned state under a boundary condition where a horizontal force, or the force of earthquake, is applied, the application of bending moment to the pile head 11a can be reduced and relaxed as much as possible.

Flexural Strength of Square Spread Footing

Abstract: The collapse load of a reinforced concrete square spread footing under column load is derived by using the theory of plasticity. Several upper bound solutions corresponding to different yield line patterns are obtained. Since the footing slab is rigidly connected to the column end, only the so‐called rigid collapse modes are considered. The solution having the lowest collapse load gives a bending moment at the face of the column equal to that used in American practice. Lower bound solutions are also developed which together with the upper bound solutions show where the exact solution might be. The influence of nonuniform soil pressure under the footing slab upon its carrying capacity is also investigated. A comparison between the theoretical results and existing test data indicates the average measured collapse load is higher than the least upper bound which may partly be attributed to the change in contact pressure, especially near failure. It also proves the bending moment used in some foreign design co...

Effect of Axial Loads on Radial Stress in Curved Beams

Abstract: Radial tension failures have occurred in some curved glulam beams. Radial stresses in curved beams are generally computed using only the bending moment, e.g., Wilson's equation. This work was performed to provide additional insight into the effect on the radial stresses due to the axial loads that are present in the curved beams. Equations of tangential, radial, and shear stress were developed for curved beams under an axial load. The theory of elasticity with polar coordinates for plane stress applied to an orthotropic material was used. Two loblolly pine glulam specimens (orthotropic) and one aluminum specimen (isotropic) with sharp radii and high d/R ratios were tested for the purpose of verifying the theoretical tangential and radial stress distributions that were predicted by the equations. In the aluminum specimen test, theoretical and experimental values compare favorably. In the glulam specimem tests, a favorable agreement was obtained for the tangential stress between the theoretical and experimental values, while the experimental radial stress values were about 2 to 4 times larger than the theoretical values. The theoretical radial stresses predicted by Wilson's equation were verified by a rigorous theory of elasticity solution as both solutions gave almost identical results. Since the elasticity solution included the effect of axial load, we conclude that the effect of axial load on the radial stress in curved beams is small.

Multiple fractures produced by the bending of brittle beams

Abstract: This paper describes experiments where the bending of beams results in two or more fractures being formed, apparently simultaneously. This is explained in terms of the stress waves emitted by the initial fracture process. It is shown that three separate types of secondary fracture may occur as a result of the interaction between the stress pulses produced by the initial fracture and the loading stresses already present in the beam. In treating these problems it has been found helpful to use an analytical solution for the bending wave propagated when a semi-infinite beam, which is subjected to a constant bending moment, is suddenly unloaded at the free end. In modelling the longitudinal stress pulse produced by the fracture we have used a simplified model which assumes that the forcing function on the fracture plane is a force field equal to the resultant force acting on the unbroken portion of the fracture surface prior to the onset of fracture.

Wind‐Buckling Approach for RC Cooling Towers

Abstract: The equations of the bending and stability theories for the orthotropic shell are solved using the finite element method (FEM). A biaxial material law for concrete and a nearly bilinear stress‐strain diagram for reinforcing steel were considered. Taking a layered ring element the influence of bending moments together with the membrane forces can be followed under increasing load up to the failure of concrete or steel. At each level the buckling factor can be calculated considering the stress dependent orthotropic buckling stiffness. The method of calculation developed is applied to two large cooling tower shells, one under wind load according to German code DIN 1055 and the other one under unusually high wind pressures, as those considered in the U.S.A. According to the wall thickness taken the buckling load factor drops to half or less of the value obtained assuming a linear elastic behavior. This high reduction is mainly due to orthotropy and the descending tangent modulus near the ultimate load.

Vertical motions of high-speed boats in head sea and wave loads

Abstract: In this paper, the authors investigate into vertical motions of a high-speed boat travelling in head sea and wave loads acting on it, taking account of the effects of non-linear hydrodynamic forces and dynamic lift in waves. A series of tests was carried out to measure heave and pitch, bow acceleration, vertical bending moment and shearing force at the midship section of a segmented model. The experimental results were compared with theoretical values predicted in the following three different ways : (A) linear calculation, that is to say, the Ordinary Strip Method applied to the running condition at travelling in a calm water, (B) non-linear calculation in which the effects of time-varying sectional hydrodynamic forces were taken into account, and (C) non-linear calculation taking account of the effects of planing at a high-speed as well as the effects of time-varying sectional hydrodynamic forces. As the result of comparison, it was shown that vertical motions and wave loads of high-speed boats can be evaluated by the method presented in this paper with accuracy enough for practical use, and that the method may be applied to the case of travelling at a higher speed than that considered in this paper if the sectional hydrodynamic forces will be appropriately evaluated when travelling at that speed.

Improvements to Frequency-Domain Riser Programs

Abstract: This paper develops and demonstrates the improvements to frequency domain riser analysis obtained by including a wave surface correction and by calculating forces at the displaced riser position. The range of validity is extended to higher waves without a significant increase in program running costs. Comparisons of running costs and results are made against two time domain programs. Significant improvements to the bending moment range are obtained and therefore to the fatigue damage estimates for regular waves.

Dynamometer having a bending beam

Abstract: A dynamometer is provided with a testing member having a bending beam. The bending beam has an end embedded in a support and is elastically deformable in bending under the influence of a force Q applied to its opposite end. The dynamometer further comprises a sensor for detecting the deformation of the beam. Anchorage zones are defined in the material of the beam, for receiving four rows of windings of prestressed gauge wire having their principal strands directed approximately perpendicularly to the force Q. The principal strands remain in close contact with the beam in the bending zone. Two of the rows of windings have their principal strands arranged along the tensioned fibres of the beam and the other two have their main strands arranged along the compressed fibres of the beam. The four rows of windings form an electrical bridge assembly.

Dynamics of a bar of asymmetric cross-section

Abstract: An elastic bar of asymmetric cross-section is supported at two points and loaded by constant gravity force and axial force. The principal bending moments are assumed to be proportional to the principal curvatures, and the torque proportional to the twist. The equations of motion reduce to the sine-Gordon equation. The solutions corresponding to one soliton and to the collision of two solitons are given.