Showing papers on "Bending moment published in 1984"

Stability of Fracturing Process in RC Beams

Abstract: A reinforced concrete beam section with a through‐thickness edge crack in the stretched part is considered. The eccentric axial force transmitted by the reinforcement to the concrete beam element, is estimated by means of a rotation congruence condition able to provide this statically undetermined reaction. In the field of linear elastic fracture mechanics, such a force increases linearly by increasing the external bending moment, until the limit force of yielding or slippage is reached. From this point on a perfectly plastic behavior of the reinforcement is considered. Once the bending moment of steel plastic flow is exceeded, the cracked beam segment presents a linear‐hardening behavior, until the concrete fracture occurs. It is shown how the stability of the process of concrete fracture and steel plastic flow depends on the mechanical and geometrical (scale included) properties of the beam cross section.

Fast continuous swimming of saithe (pollachius virens): a dynamic analysis of bending moments and muscle power

Abstract: This paper deals with the hydrodynamics and internal dynamics of fish swimming. Our analysis starts from kinematic data obtained for fast swimming saithe, and treats the fish as a flexible elongated body. The distribution along the body of the lateral bending moment and the bending power generated inside the fish are computed as well as the power spent on the water. The computed thrust implies a drag coefficient (based on wetted surface area) of about 0.007, which is probably an over-estimate. Our major result is that the bending moment does not travel as a running wave from head to tail like the lateral body curvature does, but behaves as a standing wave. The left and right sides produce alternate contractions simultaneously over the whole body length. This finding is in agreement with myographic data from the literature.

Toward a consistent beam theory

Abstract: It is well known that the Euler-Bernoulli theory of the bending of beams makes use of a contradicting assumption of zero shear strains and nonzero shear stresses. Sometimes, this type oJ assumption is also carried over to more refined shear deformation theories. This paper outlines a theory thai avoids this assumption. With the aid of the specific example of a tip loaded cantilever beam, it is shown that the present theory gives Euler Bernoulli solutions in that part of the beam where shear deformation is unimportant and a shear deformation type of solution in the pari of the beam where shear deformation is important, with transition stress patterns between the two. Numerical studies, with a shear modulus representative of sandwich beams, bring out the usefulness of the present theory for the analysis of such soft-cored beams.

Evaluation of Brassica genotypes for resistance to shatter. I. Development of a laboratory test.

Abstract: A new test procedure for measuring shatter-resistance of siliquae of Brassica spp. is described. A siliqua with its proximal end clamped is loaded as a cantilever in a testing machine. The maximum bending moment, the corresponding stiffness and the energy to cause the siliqua to rupture were taken as measures of the resistance of the siliqua to shatter. Studies showed that ranking of accessions based on either bending moment or energy closely approximated the rankings based on observations of field shatter. A reasonably high significant negative correlation was found between percentage of shattered siliquae and both bending moment and energy (r=−0.595 and −0.531 respecitvely, P=0.001). The above results indicated that bending moment and energy could be used as criteria in evaluating rapeseed genotypes for shatter-resistance in breeding programmes.

Stress analysis of rectangular walls under seismically induced hydrodynamic loads

Abstract: Seismically induced bending moments in the walls of rectangular concrete liquid storage tanks are evaluated. The tank is assumed to be subjected to simultaneous horizontal and vertical components of earthquake excitations. The liquid is assumed to be homogeneous, inviscid, and incompressible. Hydrodynamic pressures are calculated using the classical potential flow approach and are compared with those obtained from approximate analyses. Typical systems of loadings are identified and applied on the walls which are assumed to behave as elastic plates. Analytical expressions for the computation of internal moments are presented, and numerical values of moment coefficients are tabulated for use in seismic design analysis of tank walls.

Technical Theory of Beams with Normal Strain

Abstract: A new sixth order technical theory for the bending of beams is presented, which includes the influence of transverse normal strain. Appropriate boundary conditions are delineated. Application to the bending of a simple beam verifies improvement over shear deformation solution.

Hysteretic Behavior of RC Beams

Abstract: A mechanical model for the cross section of a reinforced concrete beam is proposed. Attention is focused on the local phenomena relating to the cross section, while the phenomena relating to the beam element to which the section belongs is ignored. In particular the concrete fracturing mechanism and the slippage and yielding of steel are considered, while the smeared damage of concrete are not taken explicitly into account. Namely, a rigid‐plastic constitutive law is assumed for steel, while for concrete a linear elastic one. Loading and unloading processes are considered, the bending moment range being lower than that of crack extension. The phenomenon of shake‐down due to slippage or plastic deformation of the steel bars is studied. Up to a certain value of the bending moment an elastic shake‐down occurs; above this value the shakedown becomes elastic‐plastic and an hysteretic loop is described by the stressstrain diagram of steel. Thus the energy absorbed in such a dissipative phenomenon is computed fo...

Seismic Design for Highway Bridge Foundations

Abstract: This paper focuses on the determination of stiffness characteristics of piles and pile groups. Both battered and vertical pile groups are considered. Recommended methods for determining the axial and lateral stiffness of single piles are presented along with sensitivity studies to demonstrate the influence of liquefaction and strength degradation on lateral stiffness. Solutions are presented showing how axial and lateral stiffness of individual piles may be combined to represent group pile stiffness to moment and lateral loading. Significant bending moments may be induced in laterally loaded battered piles. Seismically induced moment loading on a pile group may lead to permanent axial displacements.

A refined finite element model for the analysis of elastic–plastic frames

Abstract: A finite element model for the elastic–plastic analysis of plane frames is proposed. The formulation is based on the independent modelling of the displacement and plastic strain fields; the latter is modelled both over the cross-section and along the element length as function of a finite number of parameters, which are considered as an extra set of independent variables, in addition to nodal displacements. Stress redistribution is allowed for over the cross-section, but not over the element length, where the distribution of stress resultants (axial forces and bending moments) is imposed consistently with the assumed displacement model; stress redistribution in terms of stress resultants becomes possible only because of the finite number of redundancies introduced when assembling. It is shown that the model can be formulated in such a way that not only compatibility and elasticity, but also equilibrium (in the sense of beam theory), are fully complied with and only the plastic portion of the constitutive relationship is approximately fulfilled, even if, in principle, to any desired level of accuracy. The model produces accurate results, including a detailed representation of the spreading of plastic zones, with a fairly limited number of elements.

On a variational analysis of finite deformations of prismatical beams and on the effect of warping stiffness on buckling loads

Abstract: An earlier approximate consideration of the finite-deformation problem of prismatical beams is modified through the inclusion of non-linear displacement derivative terms in the expressions for transverse shearing strains The general system of equations is specialized so as to describe the problems of lateral buckling of doubly symmetric cross section cantilever beams including warping stiffness effects While the present results agree with the earlier results for the case of a combination of end bending moment and axial end force, this is not so for the case of a transverse end force For this latter problem we now have the classical Timoshenko result as a special case, in contrast to what followed from the earlier consideration

Bending machine with numerical control

Abstract: The invention relates to a bending machine with numerical control 1 for the bending of metal sheets. Provided on the bending machine 2 is a measuring device 3 which is connected to the control 1 and which detects the actual value of the bending angle on the sprung-open bending part. The actual value is transmitted to a desired-value/actual-value comparator 4 and is compared there with a stored desired value. The bending parameters are corrected by the control 1 according to the deviation and a corrective bend is carried out.

Apparatus for precision placement and parameter measurement

Abstract: Apparatus is described for precise placement of an object or sensing or measurement of a parameter using a plurality of tilt plates in substantially parallel spaced apart relationship forming a stack. Adjacent pairs of tilt plates in the stack are joined by unitary hinge plates secured to respective edges of each adjacent pair of tilt plates on one side. Each hinge plate is constructed and arranged of rigid elastic material for controlled elastic bending and recovery under applied bending moment stress. A plurality of spreader elements are provided operatively coupled to each pair of adjacent tilt plates at the side opposite the respective hinge plate. A spreader actuator actuates the spreaders for imparting tilting motion to the respective pair of tilt plates by varying the spacing of the pair of adjacent tilt plates relative to each other at one side imparting bending moment stress to the hinge plate on the other side. An object or sensor coupled to the top or end of the stack may be precisely placed, positioned or moved by controlled actuation of the spreaders. Parameters accurately measured by using, for example, temperature sensitive, pressure sensitive or weight sensitive motional response spreader elements. Passive motion sensors or transducers may be substituted for the spreaders for sensing motin or deflection. Strain gauges may be applied to the hinge plates for the same purpose. The apparatus is applied, by way of example, in retrofitting a conventional grinder for fine adjustment and precise placement of a workpiece relative to a working tool. Other applications include work holders, manipulators, robots, measuring instruments, scales, springs, bellows and deflection devices.

Method for correcting the bending line of the bending tool of a bending press, in particular a folding press

Abstract: The invention relates to a method for correcting the bending line of the bending tool of a bending press, in which the bottom tool is divided in the direction of the bending line and the tool halves divided into tool segments are adjustable transversely to the bending line. The bending line of the top tool is measured in the vertical plane by means of a plurality of measured-value transmitters. The tool segments of the bottom tool are adjusted in partially motorised fashion in the horizontal plane in accordance with the measured values determined to form a taper or narrowing of the bending gap corresponding to the bending line, automatic determining and correction of the bending line thus being guaranteed.

Charts for Seismic Design of Frame-Wall Systems

Abstract: Charts are presented for the seismic design by the response spectrum method of fixed-based multistory buildings consisting of solid shear walls and frames, symmetrically arranged in plan and having constant properties along the height. The building is treated as a continuum with the frames modelled as a single shear beam, and the first three normal modes of the building are utilized for evaluating various modal responses, namely, the bending moments and the shear forces in the wall, the shear force in the frame and also the top deflection, the contribution of only the fundamental mode being considered for the last named response. The charts present the distributions of the modal moments and shears along the height of the building, which should allow the quantity of reinforcements to be varied for achieving economy. The results are presented for practical values of the nondimensional parameter which incorporates all the geometric and material properties governing the behaviour of the system. The use of the design charts is illustrated by an example of a 15 storied building.

Pipe bending method

Abstract: PURPOSE:To prevent the reduction in thickness of the outside of a bending pipe caused at the time of a pipe being work with a high frequency bender by giving a brake force, bending moment and bending stress to the piping at pipe bending time and by controlling the pushing force constantly by these three powers. CONSTITUTION:A high frequency bender of a push bending type is composed of an arm 4 having the rotary center on the different position O' from the bending center O of a pipe, a clamping part 5 holding a part of the piping 1 which is on the arm 4 thereof, a rotation supporting stand 9 giving a rotation power to the clamp part 5 thereof, a sliding base 10 moving the rotation supporting base 9 thereof in a body with the clamp part 5 in a longitudinal direction of the arm 4 and the brake device 11 giving a braking force to the arm 4. At the pipe bending time, then a brake force F, bending moment M and bending stress W are given and the push force is controlled constantly by these three forces.

Stamping rectangular plates into doubly-curved dies

Abstract: Shallow spheroidal shell segments have been press formed from rectangular plates by stamping between a die and matching punch that have two degrees of curvature. Experiments on mild steel, copper and aluminium plates that were not clamped in the die have measured the punch force, contact regions and final curvature distribution; and have observed plate buckling for a range of die curvature ratios and plate sizes. An analysis based on a rigid/plastic material idealization and decoupled in-plane forces and bending moments has been correlated with these experiments. The sequence of deformation modes has been identified; initially these are bending but in later stages, in-plane forces predominate.

Mixed Boundary Value Problem of Plate with Crack

Abstract: A semi‐infinite plate, of which a part on the boundary is rigidly stiffened and in which a crack initiates from an end of the stiffened edge as a problem of a mixed boundary value of thin plate bending, is analyzed. The problem is solved by a complex variable method which uses a rational mapping function. Two analytical methods are described: one method can apply to general loads and the other can apply when the free boundary, even partially, exists. These methods give a solution in a closed form for a shape represented by the rational mapping function. Uniform bending and torsion are considered as loads. Bending moment distributions before and after crack initiation, and the stress intensity factor are investigated for crack length, stiffened edge length, and the Poisson's ratio.