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PUDDLE D

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Originally appearing in Volume V28, Page 401 of the 1911 Encyclopedia Britannica.
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PUDDLE D LA C'CFN RET[~ 4 _~• R . A . W'OF;, EL`O'.:.'! SANDSTONE behind in the crevice. The clay roof, rather than the walls of this crevice of sand, gave way and pressed. down to fill the vacancy, and the leakage worked up along the weakened plane of tangential strain bd. On the appearance of serious leakage the overflow level of the water criginally at of was lowered for safety to gh; and for many years the reservoir was worked with its general level much below gh. The sand-filled vein, several inches in width, was found, on taking out the puddle, to have terminated near the highest level to which the water was allowed to rise, but not to have worked downwards. There can be little doubt that the puddle at the right-hand angle j was also strained, but not to the point of rupture, as owing to the rise of the sandstone base there was comparatively little room for settlement on that side. In repairing this work the perfectly safe form shown by the dotted lines ka, kj was substituted for the flat surface aj, and this alone, if originally adopted, would have pre- vented dangerous shearing strains. As an additional precaution, however, deep tongues of concrete like those in fig. 7 were built in the rock throughout the length of the trench, and carried up the sides and over the top of the ped- estal. The puddle was then replaced, and remains sensibly watertight. The lesson taught by fig. 8 applies also to the ends of puddle walls where they abut against steep faces of rock. Unless such faces are so far below the surface of the puddle, and so related to the lower parts of the trench, that no tension, and consequent tendency to separation of the puddle from the rock, can possibly take place, and unless abundant time is given, before the reservoir is charged, for the settlement and compression of the puddle to be completed, leakage with disastrous results may occur. In other cases leakage and failure have arisen from allowing a part of the rock bottom or end of a puddle trench to overhang, as in fig. 9. Here the straining of the original horizontal puddle in settling down is indicated in a purposely exaggerated way by the curved lines. There is considerable distortion of the clay, resulting from combined shearing and tensile stress, above each of the steps of rock, and reaching its maximum at and above the highest rise ab, where it has proved sufficient to produce a dangerous line of weakness ac. the tension at a either causing actual rupture, or such increased porosity as to permit of percolation capable of keeping open the wound. In such cases as are shown in figs. 8 and 9 the growth of the sand vein is not vertical, but inclined towards the plane of maximum shearing strain. Fig. 9 also illustrates a weak place at b where the clay either never pressed hard against the overhanging rock or has actually drawn away therefrom in the process of settling towards the lower part to the left. When it is considered that a parting of the clay, sufficient to allow the thinnest film' of water to pass, may start the formation of a vein of porous sand in the manner above explained, it will be readily seen how great must be the attention to details, in unpleasant places below ground, and below the water level of the surrounding area, if safety is to be secured. In cases like fig. 9 the rock should always be cut away to a slope, such as that shown in fig. to. If no considerable difference of water-pressure had been allowed between the two sides of the puddle trench in figs. 8 or 9 until the clay had ceased to settle down, ~-~—' = /jam it is probable that the /interstices, at first formed between the puddle and .—PUDDLE / -the concrete or rock, % — would have been suffici -, ~~ - ently filled to prevent in- ~, = jurious percolation at any —se~~~' future time. Hence it is' always a safe precaution to afford plenty of time :• ,r for such settlement before with water. But to all such precautions should be added the use of concrete or brickwork tongues running longitudinally at the bottom of the trench, such as those shown at a higher level in fig. 7. In addition to defects arising out of the condition or figure of the rock or of artificial work upon which the puddle clay rests, the puddle Defects ln wall itself is often defective. The original material may have been perfectly satisfactory, but if, for example, in pud the progress of the work a stream of water is allowed to wall. flow across it, fine clay is sometimes washed away, and the gravel or sand associated with it left to a sufficient extent to permit of future percolation. Unless such places are carefully dug out or re-puddled before the work of filling is resumed, the percolation may increase along the vertical plane where it is greatest, by the erosion and falling in of the clay roof, as in the, other cases cited. Two instances probably originating in some such cause are shown in fig. 11 in the relative positions in which they were found, and carefully measured, as the puddle was removed from a crippled reservoir dam. These fissures are in vertical planes stretching entirely across the puddle trench, and reaching in one case, aa, nearly to the highest level at which the reservoir had been worked for seventeen years after the leakage had been discovered. The larger and older of these veins was 44 ft. high, of which 14 ft. was above the original ground level, and it is interesting to note that this portion, owing probably to easier access for the water from the reservoir and reduced compression of the puddle, was much wider than below. The little vein to the left marked bb, about 31 ft. deep, is curious. It looks like the beginning of success of an effort made by a slight percolation during the whole life of the reservoir to increase itself materially by erosion. There is no reason to believe that the initial cause of such a leakage could be developed except during construction, and it is certain that once begun it must increase. Only a knowledge of the great loss of capital that has resulted from abortive reservoir construction justifies this notice of defects which can always be avoided, and are too often the direct result, not of design, but of parsimony in providing during the execution of such works, and especially below ground, a sufficiency of intelligent, experienced and conscientious supervision. In some cases, as, for example, when a high earthen embankment crosses a gorge, and there is plenty of stone to be had, it is desirable to place the outer hank upon a toe or platform of rubble stonework, as in fig. 7, by which means the height of the earthen portion is reduced and complete drainage secured. But here again great care must be exercised in the packing and consolidation of the stones, which will otherwise crack and settle. As with many other engineering works, the tendency to slipping either of the sides of the valley or of the reservoir embankment 'rtself has often given troutile, and has sometimes led to serious disaster. Carrt.cz way ezloreg Ernbcadernerrt water level ~riginatly intended top -de -Aviv ;W. i lghest working level H allowed ._ _ P, c o 20 Jo Paet 398 This, however, is a kind of failure not always attributable to want of proper supervision during construction, but rather to improper choice of the site, or treatment of the case, by those primarily responsible. In countries where good clay or retentive earth cannot be obtained, numerous alternative expedients have been adopted Dams with more or less success. In the mining districts. with dla- of America, for example, where timber is cheap, rough phragms stone embankments have been lined on the water face of wood, _ with timber to form the water-tight septum. In such steel, (ft. a position, even if the timber can be made sufficiently water-tight to begin with, the alternate immersion and exposure to air and sunshine promotes expansion and con-traction, and induces rapid disintegration, leakage and decay. Such an expedient may be justified by the doubtful future of mining centres, but would be out of the question for permanent water supply. Riveted sheets of steel have been occasionally used, and, where bedded in a sufficient thickness of concrete, with success. At the East Canon Creek dam, Utah, the height of which is about 61 ft. above the stream, the trench below ground was filled with concrete much in the usual way, while above ground the water-tight diaphragm consists of a riveted steel plate varying in thickness from -iba in. to 18r in. This steel septum was protected on either side by a thin wall of asphaltic concrete supported by rubble stone embankments, and owing to irregular settling of the embankments became greatly distorted, apparently, however, without causing leakage. Asphalt, whether a natural product or artificially obtained, as, for example, in some chemical manufactures, is a most useful material if properly employed in connexion with reservoir dams. Under sudden impact it is brittle, and has a conchoidal fracture like glass; but under continued pressure it has the properties of a viscous fluid. The rate of flow is largely dependent upon the proportion of bitumen it contains, and is of course retarded by mixing it with sand and stone to form what is commonly called asphalt concrete. But given time, all such compounds, if they contain enough bitumen to render them water-tight, appear to settle down even at ordinary temperatures as heavy viscous fluids, retaining their fluidity permanently if not exposed to the air. Thus they not only penetrate all cavities in an exceedingly intrusive manner, but exert pressures in all directions, which, owing to the density of the asphalt, are more than 40 % greater than would be produced by a corresponding depth of water. From the neglect of these considerations numerous failures have occurred. Elsewhere, a simple concrete or masonry wall or core has been used above as well as below ground, being carried up between embankments either of earth or rubble stone. This construction has received its highest development in America. On the Titicus, a tributary of the Croton river, an earthen dam was completed in 1895, with a concrete core wall ioo ft. high—almost wholly above the original ground level, which is said to be impermeable; but other dams of the same system, with core walls of less than too ft. in height, are apparently in their present condition not impermeable. Reservoir No. 4 of the Boston waterworks, completed in 1885, has a concrete core wall. The embankment is 1800 ft. long and 6o ft. high. The core wall is about 8 ft. thick at the bottom and 4 ft. thick at the top, and in the middle of the valley nearly too ft. in height. At irregular intervals of 150 ft. or more buttresses 3 ft. wide and t ft. thick break the continuity on the water side. That this work has been regarded as successful is shown by the fact that Reservoir No. 6 of the same waterworks was subsequently constructed and completed in 1894 with a similar core wall. There is no serious difficulty in so constructing walls of this kind as to be practically water-tight while they remain unbroken; but owing to the settlement of the earthen embankments and the changing level of saturation they are undoubtedly subject to irregular stresses which cannot be calculated, and under which, speaking generally, plastic materials are much safer. In Great Britain masonry or concrete core walls have been generally confined to positions below ground. Thus placed, no serious strains are caused either[DAMS by changes of temperature or of moisture or by movements of the lateral supports, and with proper ingredients and care a very thin wall wholly below ground may be made water-tight. The next class of dam to be considered is that in which the structure as a whole is so bound together that, with certain reservations, it may be considered as a monolith subject chiefly to the overturning tendency of water- Mgams.ry pressure resisted, by the weight of the structure itself ason and the supporting pressure of the foundation. Masonry dams are, for the most part, merely retaining walls of exceptional size, in which the overturning pressure is water. If such a dam is sufficiently strong, and is built upon sound and moderately rough rock, it will always be incapable of sliding. Assuming also that it is incapable of crushing under its own weight and the pressure of the water, it must, in order to fail entirely, turn over on its outer toe, or upon the outer face at some higher level. It may do this in virtue of horizontal water-pressure alone, or of such pressure combined with upward pressure from intrusive water at its base or in any higher horizontal plane. Assume first, however, that there is no uplift from intrusive water, As the pressure of water is nil at the surface and increases in direct proportion to the depth, the overturning moment is as the cube of the depth; and the only figure which has a moment of resistance due to gravity, varying also as the cube of its depth, is a triangle. The form of stability having the least sectional area is therefore a triangle. It is obvious that the angles at the base of such a hypothetical dam must depend upon the relation between its density and that of the water. It can be shown, for example, that for masonry having a density of 3, water being t, the figure of minimum section is a right-angled triangle, with the water against its vertical face; while for a greater density the water face must lean towards the water, and for a less density away from the water, so that the water may lie upon it. For the sections of masonry dams actually used in practice, if designed on the condition that the centre of all vertical pressures when the reservoir is full shall be, as hereafter provided,-at two-thirds the width of the base from the inner toe, the least sectional area for a density of 2 also has a vertical water face. As the density of the heaviest rocks is only 3, that of a masonry dam must be below 3, and in practice such works if well constructed vary from 2.2 to 2.6. For these densities, the deviation of the water face from the vertical in the figure of least sectional area is, however, so trifling that, so far as this consideration is concerned, it may be neglected. If the right-angled triangle abc, fig. 12, be a profile i ft. thick of a monolithic dam, subject to the pressure of water against its vertical side to the full depth ab = d in feet, the horizontal a pressure of water against the section of the dam, in- creasing uniformly with the depth, is properly repre- sented by the isosceles right-angled triangle abe, in which be is the maximum water-pressure due to the 1ar18uthr, m full depth d, while the area abe=- is the total hori- / zontal pressure against the dam, generally stated in FIG. 1a.-Diagram of Right-Angled cubic feet of water, acting Triangle Dam. at one-third its depth above dQ . the base. Then 2 is the resultant horizontal pressure with an over-turning moment of (t) If x be the width of the base, and p the density of the masonry, the weight of the masonry in terms of a cubic foot of water will be PZ acting at its centre of gravity g, situated at Ix from the outer toe, and the moment of resistance to overturning on the outer toe, px32d (2) ds - Equating the moment of resistance (2) to the overturning moment (I), we have px'd _ d_' 3 6 and d x='I2p.. That is to say, for such a monolith to be on the point of overturning under the horizontal pressure due to the full depth of water, its base must be equal to that depth divided by the square root of twice the density of the monolith. For a density of 2.5 the base would there-fore be 44.7 % of the height. We have now to consider what are the necessary factors of safety, and the modes of their application. In the first place, it is out of Factors of the question to allow the water to rise to the vertex a safety, of such a masonry triangle. A minimum thickness must be adopted to give substance to the upper part; and where the dam is not used as a weir it must necessarily rise several feet above the water, and may in either event have to carry a roadway. Moreover, considerable mass is required to reduce the internal strains caused by changes of temperature. In the next place, it is necessary to confine the pressure, at every point of the masonry, to an intensity which will give a sufficient factor of safety against crushing. The upper part of the dam having been designed in the light of these conditions, the whole process of completing the design is simple enough when certain hypotheses have been adopted, though somewhat laborious in its more obvious form. It is clear that the greatest crushing pressure must occur, either, with the reservoir empty, near the lower part of the water face ab, or with the reservoir full, near the lower part of the outer face at. The principles hitherto adopted in designing masonry dams, in which the moment of resistance depends upon the figure and weight of the masonry, involve certain assumptions, which, although not quite true, have proved useful and harmless, and are so convenient that they may be continued with due regard to the modifications which recent investigations have suggested. One such assumption is that, if the dam is well built, the intensity of vertical pressure will (neglecting local irregularities) vary nearly uniformly from face to face along an horizontal plane. Thus, to take the simplest case, if abce (fig. 13) represents a rectangular mass already designed for the superstructure a e .. + of the dam, and g its centre of gravity, the centre of pressure upon the base will be vertically under g, that is, at the centre of the base, and the load will be properly represented by the rectangle bfgc, of which the area represents the total load and the uniform depth of its uniform intensity._ At this high part of the structure the intensity of pressure will of course be much less than its permissible intensity. If now we assume the water to have a depth d above the base, the total water pressure represented by the triangle kbh will have its centre at d/3 from the base, and by the parallelogram of forces, assuming the density of the masonry to be 2.5, we find that the centre of pressure upon the base bc is shifted from the centre of the base to a point i nearer to the outer toe c, and adopting our assumption of uniformly varying intensity of stress, the rectangular diagram of pressures will thus be distorted from the figure bfgc to the figure of equal area bjlc, having its centre o vertically under the point at which the resultant of all the forces cuts the base bc. For any lower lever the same treatment may, step by step, be adopted, until the maxi• mum intensity of pressure cl exceeds the assumed permissible maximum, or the centre of pressure reaches an assigned distance from the outer toe c, when the base must be widened until the maximum intensity of pressure or the centre of pressure, as the case may be, is brought within the prescribed limit. The resultant profile is of the kind shown in fig. 14. Having thus determined the outer profile under the conditions hitherto assumed, it must be similarly ascertained that the water face is everywhere cap- able of resisting the vertical pressure of the masonry when the reservoir is empty, and the base of each compartment must be widened if necessary in that direction also. Hence in dams above loo ft. in height, further adjustment of the outer profile may be required by reason of the deviation of the inner profile from the vertical. The effect of this process is to give a series of points in the horizontal planes at which the resultants of all forces above those planes respectively cut the planes. Curved lines, as dotted in fig. 14, drawn through these points give the centre of pressure, for the reservoir full and empty respectively, at any horizontal plane. These general principles were recognized by Messrs Graeff and Delocre of the Ponts et Chaussees, and about the year 1866 were put into practice in the Furens dam near St Etienne. In 1871 the late Professor Rankine, F.R.S., whose remarkable perception of the practical fitness or unfitness of purely theoretical deductions gives his writings exceptional value, received from Major Tulloch, R.E., on behalf of the municipality of Bombay, a request to consider the subject generally, and with special reference to very high dams, such as have since been constructed in India. Rankine pointed out that before the vertical pressure reached the maximum pressure permissible, the pressure tangential to the slope might do so. Thus conditions of stress are conceivable in which the maximum would be tangential to the slope or nearly so, and would therefore increase the vertical stress in proportion to the cosecant squared of the slope. It is very doubtful whether this pressure is ever reached, but such a limit rather than that of the vertical stress must be considered when the height of a dam demands it. Next, Rankine pointed out that, in a structure exposed to the overturning action of forces which fluctuate in amount and direction, there should be no appreciable tension at any point of the masonry. But there is a still more important reason why this condition should be strictly adhered to as regards the inner face. We have hitherto considered only the horizontal overturning pressure of the water; but if from originally defective construction, or from the absence of vertical pressure due to weight of masonry towards the water edge of any horizontal bed, as at ab in fig. 14, water intrudes beneath that part of the masonry more readily than it can obtain egress along be, or in any other direction towards the outer face, we shall have the uplifting and overturning pressure due to the full depth of water in the reservoir over the width ab added to the horizontal pressure, in which case all our previous calculations would be futile. The condition, therefore, that there shall be no tension is important as an element of design; but when we come to construction, we must be careful also that no part of the wall shall be less permeable than the water face. In fig. 13 we have seen that the varying depth of the area bjlc approximately represents the varying distribution of the vertical stress. If, therefore, the centre of that became so far removed to the right as to make j coincident with b, the diagram of stresses would become the triangle j'l'c', and the vertical pressure at the inner face would be nil. This will evidently happen when the centre of pressure i' is two-thirds from the inner toe b' and one-third from the outer toe c'; and if we displace the centre of pressure still further to the right, the condition that the centre of figure of the diagram shall be vertically under that centre of pressure can only be fulfilled by allowing the point j' to cross the base to j" thus giving a negative pressure or tension at the inner toe. Hence it follows that on the assumption of uniformly varying stress the line of pressures, when the reservoir is full, should not at any horizontal plane fall outside the middle third of the width of that plane. Rankine in his report adopted the prudent course of taking as the safe limits certain pressures to which, at that time, such structures were known to be subject. Thus for the inner face he took, as the limiting vertical pressure, 320 ft. of water, or nearly 9 tons per sq. ft.. and for the outer face 250 ft. of water, or about 7 tons per sq. ft. . (3) fc 19 J." GiJ'~•• F'et 'y pressure in Masonry Dam. For simplicity of calculation Rankine chose logarithmic curves for both the inner and outer faces, and they fit very well with the conditions. With one exception, however—the Beetaloo dam in Australia 1 1 0 ft. high—there are no practical examples of dams with logarithmically curved faces. After Rankine, a French engineer, Bouvier, gave the ratio of the maximum stress in a dam to the maximum vertical stress as i to the cosine squared of the angle between the vertical and the resultant which, in dams of the usual form, is about as 13 is to 9. During the last few years attention has been directed to the stresses—including shearing stresses—on planes other than horizontal. M. Levy contributed various papers on the subject which will be found in the Cam ptes rendus de l Acadimie des Sciences (1895 and 1898) and in the Annales des Ponts et Chaussees (1897). He in- vestigated the problem by means of the general differential equations of static equilibrium for dams of triangular and rectangular form considered as isotropic elastic solids. In one of these papers Levy formulated the requirement now generally adopted in France that the vertical pressure at the upstream end of any joint, calcuated by the law of uniformly varying stress, should not be less than that of the water pressure at the level of that joint in order to prevent intrusive water getting into the structure. These researches were followed by those of Messrs L. W. Atcherley and Karl Pearson, and by an approximate graphical treatment by Dr W. C. Unwin, F.R.S.2 Dr Unwin took two horizontal planes, one close above the other, and calculated the vertical stresses on each by the law of uniformly varying stresses. Then the differ- ence between the normal pressure on a rectangular RERERVOIR element in the lower plane and that on the upper plane is the weight of the element and the difference between the shears on the vertical faces of that element. The weights being known, the principal stresses may be determined. These researches led to a wide discussion of the sufficiency of the law of uniformly varying stress when applied to horizontal joints as a test of the stability of dams. Professor Karl Pearson showed that the results are dependent upon the assumption that the distribution of the vertical stresses on the base of the structure also followed the law of uniformly varying stress. In view of the irregular forms and the uncertainties of the nature of the materials at the foundation, the law of uniformly varying stress was not applicable to the base of the dam. He stated that it was practically impossible to determine the stresses by purely mathematical means. The late Sir Benjamin Baker, F.R.S., suggested that the stresses might be measured by experiments with elastic models, and among others, experiments were carried out by Messrs Wilson and Gore 2 with indiarubber models of plane sections of dams (including the foundations) who applied forces to represent the gravity and water pressures in such a manner that the virtual density of the rubber was increased many times without interfering with the proper ratio between gravity and water pressure, and by this means the strains produced were of sufficient magnitude to be easily measured. The more important of their results are shown graphically in figs. 15 and 16, and prove that the law of uniformly varying stress is generally applicable to the upper two-thirds of a dam, but that at parts in or near the foundations that law is departed from in a way which will be best understood from the diagrams. Fig. 15 shows a section of the model dam. The maximum principal stresses are represented by the directions and thicknesses of the two systems of intersecting lines mutually at right angles. Tensile stresses (indicated by broken lines on the diagram) are shown at the upstream toe notwithstanding that the line of resistance is well within the middle third of the section. It is important to notice that the maximum value of the tension at the toe lies in a direction approximately at 45° to the vertical, but at points lower down in the foundation this tension, while less in magnitude, becomes much more horizontal. This feature indicates that in the event of a crack occurring at the upstream toe, its extension would tend to turn downwards and follow a direction nearly parallel with the maximum pressure lines, in which direction it would not materially affect the stability of the structure. As a matter of fact, the foundations of most dams are carried down in vertical trenches, the lower part only being in sound materials so that actual separation almost corresponding with the hypothetical 1On Some Disregarded Points in the Stability of Masonry Dams, Drapers' Company Research Memoir (London, 1904). 2 Engineering (May 12th, 1905). 2 Proceedi.sgs of the Institution of Civil Engineers, vol. 172, p. 107. crack is allowed in the first instance with no harmful effects. Similar experiments upon models with rounded toes but otherwise of the same form showed a considerable reduction in the magnitude of the tensile stresses. On examining the diagram it will be observed that the maximum compressive stresses are parallel to and near to the down stream face of the section, which values are approximately equal to the maxi-mum value of the vertical stress determined by the law of uniformly varying stress divided by the cosine squared of the angle between the vertical and the resultant. The distributions of stress on the base line of the model for " reservoir empty " and " reservoir full " are shown in fig. i6 by ellipses of stress and by diagrams of stress on vertical and horizontal sections. Arrow heads at the ends of an axis of an ellipse indicate tension as distinct from compression, and the semi-axes in magnitude and direction represent the principal stresses. It is obvious that experiments of the kind referred to cannot take into account all the conditions of the problem met with in actual practice, such as the effect of the rock at the sides of the valley and variations of temperature, &c., but deviations in practice from the conditions which mathematical analyses or experiments assume are nearly always present. Such analyses and experiments are not on that account the less important and useful. So tar we have only considered water-pressure against the reservoir side of the dam; but it sometimes happens that the water and earth pressure against the outer face is considerable enough to modify the lower part of the section. In dams of moderate height above ground and considerable depth below ground there is, moreover, no reason why advantage should not be taken of the earth resistance due either to the downstream face of the trench against which the foundations are built, or to the materials excavated and properly embanked against that face above the ground level or to both, We do not always know the least resistance which it is safe to give to a retaining wall subject to the pressure of earth, or conversely, the maximum resistance to side-thrust which natural or embanked earth will afford, because we wisely neglect the important but very variable element of adhesion between the particles. It is notorious among engineers that retaining walls designed in accordance with the well-known theory of conjugate pressures in earth are unnecessarily strong, and this arises mainly from the assumption that the earth is merely a loose granular mass without any such adhesion. As a result of this theory, in the case of a retaining wall supporting a vertical face of earth beneath an extended horizontal plane level with the top of the wall, we get Pwx2.i-sine 2 I +sin ca' The two systems of lines mutually at right angles show the directions of the maximum and minimum stresses respectively. Such stresses are termed principal stresses. Tension is indicated by broken lines and compression by full lines. The shearing stresses are zero along the lines of principal stress and reach a maximum on lines at as° thereto. The magnitudes of the maximum shearing stresses are indicated by the algebraic differences of the thicknesses of the lines of principal stress. Line ab is in such a position that the stresses along and above it are not,materially affected by the more irregular stresses below that line produced by the sudden change in section at the base of the dam. The vertical distance above the line ab of any point in the dotted line dc is proportional to the vertical com- ponent of the compressive stress on the line ab assumed to vary uniformly from face to face. and similarly the vertical distance of any point in the 3-dot-and-dash line ae above the line ab is proportional to the vertical component of the stress determined ex- perimentally. The vertical component diagrams abed and abea are drawn to a larger scale than ass-set the lines indicating the principal r stresses.
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