Mohammed Raoof

Theoretical and experimental study on externally plated R.C. beams

Using theoretical parametric studies, based on a recently proposed model, the influence of various design parameters such as concrete cube strength, size and position of main embedded tensile bars, width of the beam, plate thickness, and ratio of plate/beam width, on the magnitude of ultimate plate peeling moment are investigated and some aspects of the theoretical predictions are checked against large scale test data reported by others. The theoretical model depends on the spacings of stabilized flexural cracks in the concrete cover zone, and in view of large variations (by a factor of, say, 2) in the spacings of such cracks in practice, it is argued that a unique solution for the ultimate plate peeling moment does not exist and, hence, one has to resort to theoretical upper/lower bound solutions. Moreover, the question of pre-cracking of the beams prior to upgrading them with externally bonded steel plates is discussed in some detail. It is theoretically shown that testing uncracked (i.e. as cast) beams provides results which may reasonably safely be used for predicting the behaviour of actual beams in practice which (under service conditions) are invariably pre-cracked to some degree. Finally, it is shown that if the practising engineers do not guard against the potentially dangerous brittle premature plate peeling failures, the ultimate plate peeling loads can be significantly lower than the associated ultimate (failure) loads of even unplated R.C. beams which have been designed according to the ultimate limit state code recommendations even when partial material safety factors are included in the design calculations of the unplated beams.

Simple derivation of the stiffness matrix for axial/torsional coupling of spiral strands

Abstract Coupled extensional-torsional behaviour of realistic multi-layered helical strands is addressed. Simplified routines are presented for obtaining the upper and lower bounds to various strand stiffnesses. Such straightforward formulations (aimed at practising engineers) have been derived by extensive theoretical parametric studies on a number of multi-layered spiral strand constructions covering a wide range of cable (and wire) diameters and lay angles. Numerical examples are presented to facilitate the use of the formulations, whose possible practical limitations have been critically addressed.

Behaviour of cables under dynamic or repeated loading

Abstract The paper describes the elastic properties and fatigue performance of spiral strands and wire ropes relevant to tension structures. An up-to-date literature review is followed by a discussion of the effects of the contacts between the individual wires within the cable. These contact effects are seen to influence all aspects of cable behaviour. The variation of axial stiffness and hysteresis with load amplitude and mean load is then described, and followed by a discussion of the bending of axially preloaded cable in response to environmental effects. This discussion pays particular attention to the effects of localised bending close to a termination. Fatigue performance is then discussed, concentrating on cyclic axial loading and on the resistance to repeated bending close to terminations.

Determination of wire recovery length in steel cables and its practical applications

Abstract In the presence of relatively significant states of radial pressures between the helical wires of a steel cable (spiral strand and/or wire rope), and significant levels of interwire friction, the individual broken wires tend to take up their appropriate share of the axial load within a certain length from the fractured end, which is called the recovery (or development) length. The paper presents full details of the formulations for determining the magnitude of recovery length in any layer of an axially loaded multi-layered spiral strand with any construction details. The formulations are developed for cases of fully bedded-in (old) spiral strands within which the pattern of interlayer contact forces and associated significant values of line-contact normal forces between adjacent wires in any layer, are fully stabilised, and also for cases when (in the presence of gaps between adjacent wires) hoop line-contact forces do not exist and only radial forces are present. Based on a previously reported extensive series of theoretical parametric studies using a wide range of spiral strand constructions with widely different wire (and cable) diameters and lay angles, a very simple method (aimed at practising engineers) for determining the magnitude of recovery length in any layer of an axially loaded spiral strand with any type of construction details is prestented. Using the final outcome of theoretical parametric studies, the minimum length of test specimens for axial fatigue tests whose test data may safely be used for estimating the axial fatigue lives of the much longer cables under service conditions may now be determined in a straightforward fashion. Moreover, the control length over which one should count the number of broken wires for cable discard purposes is suggested to be equal to one recovery length whose upper bound value for both spiral strands and/or wire ropes with any construction details is theoretically shown to be equal to 2.5 lay lengths.

PREDICTION OF COUPLED AXIAL/TORSIONAL STIFFNESS COEFFICIENTS OF LOCKED-COIL ROPES

Abstract The paucity of theoretical and/or experimental results for locked-coil ropes is emphasised. In locked-coil ropes, shaped wires of full-lock type (Z section) or half-lock are used to provide a final layer (or sometimes two or more final layers) over the basic spiral strand construction with round wires, resulting in a structure more resistant to corrosion, at the cost of a slight reduction in strength to weight ratio. Using an extended version of a previously reported orthotropic sheet theory, a model is proposed for predicting the patterns of interwire contact forces, wire kinematics, and the coupled axial/torsional stiffness coefficients in fully bedded-in locked-coil ropes experiencing either static monotonic axial/torsional loading or a mean axial load superimposed on which are external load perturbations. The theoretical model takes interwire contact deformations into account, and is capable of predicting the full-slip values of all the four stiffness coefficients in the stiffness matrix. The full-slip stiffnesses correspond to cases when large variations in axial and/or torsional loads take place, with their associated large changes in the contact forces between adjacent wires in various layers. Using theoretical parametric studies, simplified routines amenable to hand calculations, which are aimed at practising engineers, are developed for obtaining reasonable estimates of the full-slip stiffness coefficients in the 2×2 stiffness matrix defining the coupled axial/torsional behaviour of locked-coil ropes.

Effect of mean axial load on axial fatigue life of spiral strands

A previously reported theoretical model for estimating the axial fatigue life to first outer (or inner) wire fracture of spiral strands is used to throw some light on the effect of mean axial load on the axial fatigue life of large diameter steel helical strands. Using theoretical parametric studies as applied to three realistic types of 127 mm diameter spiral strand constructions with lay angles of 12°, 18° and 24° which cover the full manufacturing limits, the plausibility of using an equivalent stress range based on the Goodman and/or Gerber approaches for plotting the axial fatigue data is critically examined. Despite previous claims, it is theoretically demonstrated that the use of a Goodman and/or Gerber transformation does not lead to a significant improvement in the fit of the fatigue data to a straight line and despite the additional computational efforts, such approaches do not provide any practical advantages over the traditional approaches which present the axial fatigue data in terms of stress range vs cycles to failure. The paper also examines the effect of mean axial load on the endurance limit of spiral strands and uses numerical studies to show that (within the practical range) endurance limit increases with increasing levels of strand mean axial load.

Influence of variations in the axial stiffness of steel cables on vertical deflections of cable trusses

Abstract The practical implications of using the no-slip axial stiffnesses (as opposed to the full-slip values), as permitted by the Pre-standard ENV 1993-2, Eurocode 3, for analysing certain characteristics of cable structures under serviceability loading conditions are addressed, in the context of the structural behaviour of a two-dimensional cable truss. To this end, the practical implications of changes in the lay angle of the supporting spiral strands (with this parameter controlling the variations in the no-slip and full-slip strand axial stiffnesses) in terms of, for example, estimates of the vertical deflections of the truss will be examined. It is theoretically demonstrated that, in view of the rather small axial load perturbations (cf. mean axial loads) under serviceability state conditions, use of the more appropriate no-slip stiffness (as opposed to the traditionally used full-slip value) leads to practically significant reductions in the estimated values of the vertical deflections of the cable truss.

Application of nonlinear finite strip technique to concrete deep beams

Abstract The salient features of an alternative version of the nonlinear finite strip method for analysing reinforced concrete elements is presented. Unlike the conventional finite strip models which can only handle structures whose geometry does not change in one direction, the newly developed finite strip model can analyse certain structures whose geometry (although still fairly simple) can change along their length such as deep beams with local changes of crosssection along their span(s). Moreover, unlike the conventional finite strip models, the new alternative model has the desirable feature of being able to incorporate any desired boundary conditions and different number of harmonics in various strips with minimal effort. Although the proposed model may, in certain cases, suffer when compared with the conventional alternatives, from the potential drawback of an increased number of strips with associated increases in computer storage, the present model needs many less displacement parameters at each nodal line because of the often substantially shorter lengths of the finite strips (cf. conventional strips) and, hence, needs a much narrower half-bandwidth (HBW) in the stiffness matrix with obvious savings in the subsequent computer running time. Very encouraging correlations have been found between predictions based on the present model and some recently reported test data on deep beams: these include continuous RC deep beams with changes of cross-sections over the supports and also simply supported RC deep beams covering a wide range of design parameters. In addition, the present method has been used to analyse data from a series of tests on RC deep beams with fixed-fixed boundary conditions. The numerical results for deep beams with fixed-fixed boundary conditions based on the present model provide a desirable double check on the validity of a recently reported, largely hand-based, method and should be valuable in identifying the areas in which further work may be required.

Isoparametric finite strip element

Abstract For many structures having regular geometric plans and simple boundary conditions, the traditional finite strip method offers advantages over the finite element technique especially in terms of the computational costs. The present paper presents formulations for a number of isoparametric finite strip elements which include elements with three or two comers and those which can cater for cases involving use of adjacent finite strip elements with different ‘lengths’. The proposed formulations extend the range of applications of the finite strip technique to cases involving structural elements with non-rectangular and/or curved boundaries. In particular, as discussed elsewhere, unlike the traditional finite strip techniques in which implementation of boundary conditions different from the simply supported case is difficult, the present formulations can cater for different types of boundary conditions with relative ease. Very encouraging correlations have been found between numerical data based on the proposed formulations and previously reported elastic results for a number of structural forms.

Flexural Strength and Stiffness of High Strength Concrete Beams with Exposed Main Steel

In a number of previous publications, results were reported for a series of extensive and carefully conducted tests on large scale reinforced concrete (R.C.) beams with various extents of loss of concrete cover and exposure of main reinforcement along their spans, with such areas of simulated damage being located within their regions which are dominated by either shear or flexure. These tests on R.C. beams made with normal strength concrete have covered a wide range of first order beam design parameters, with their results used to verify the generality of various theoretical models. In the present paper, much attention will be devoted to various structural characteristics (such as ultimate strength, flexural stiffness, etc.) of similar damaged R.C. beams with the proviso that, instead of the previously used normal strength concrete, the beams are made with high strength concrete. No such results (for high strength R.C. beams) have previously been reported in the public domain.