Concrete

Concrete, the name given to a building material consisting generally of a mixture of broken stone, sand and some kind of cement. To these is added water, which combining chemically with the cement conglomerates the whole mixture into a solid mass, and forms a rough but strong artificial stone. It has thus the immense advantage over natural stone that it can be easily moulded while wet to any desired shape or size. Moreover, its constituents can be obtained in almost any part of the world, and its manufacture is extremely simple. On account of these properties, builders have come to give it a distinct preference over stone, brick, timber and other building materials. So popular has it become that besides being used for massive constructions like breakwaters, dock walls, culverts, and for foundations of buildings, lighthouses and bridges, it is also proving its usefulness to the architect and engineer in many other ways. A remarkable extension of the use of concrete has been made possible by the introduction of scientific methods of combining it with steel or iron. The floors and even the walls of important buildings are made of this combination, and long span bridges, tall factory chimneys, and large water-tanks are among the many novel uses to which it has been put. Piles made of steel concrete are driven into the ground with blows that would shatter the best of timber. A fuller description of the combination of steel and concrete will be given later.

The constituents of concrete are sometimes spoken of as the matrix and the aggregate, and these terms, though somewhat old-fashioned, are convenient. The matrix is the lime or cement, whose chemical action with the added water causes the concrete to solidify; and the aggregate is the broken stone or hard material Constituents. which is embedded in the matrix. The matrix most commonly used is Portland cement, by far the best and strongest of them all. The subject of its manufacture and examination is a most important and interesting one, and the special article dealing with it should be studied (see Cement), Here it will only be said that before using Portland cement very careful tests should be made to ascertain its quality and condition. Moreover, it should be kept in a damp-proof store for a few weeks; and when taken out for use it should be mixed and placed in position as quickly as possible, because rain, or even moist air, spoils it by causing it to set prematurely. The oldest of all the matrices is lime, and many splendid examples of its use by the Romans still exist. It has been to a great extent superseded by Portland cement, on account of the much greater strength of the latter, though lime concrete is still used in many places for dry foundations and small structures. To be of service the lime should be what is known as “hydraulic,” that is, not pure or “fat,” but containing some argillaceous matter, and should be carefully slaked with water before being mixed with the aggregate. To ensure this being properly done, the lumps of lime should be broken up small, and enough water to slake them should be added, the lime then being allowed to rest for about forty-eight hours, when the water changes the particles of quicklime to hydrate of lime, and breaks up the hard lumps into a powder. The hydrated lime, after being passed through a fine screen to sort out any lumps unaffected by the water, is ready for concrete making, and if not required at once should be stored in a dry place. Other matrices are slag cement, a comparatively recent invention, and some other natural and artificial cements which find occasional advocates. Materials like tar and pitch are sometimes employed as a matrix; they are used hot and without water, the solidifying action being due to cooling and to evaporation of the mineral oils contained in them. Whatever matrix is used, it is almost invariably “diluted” with sand, the grains of which become coated with the finer particles of the matrix. The sand should be coarse-grained and hard. It should be free from dirt—that is to say, free from clay or soft mud, for instance, which prevents the cement adhering to its particles, or again from sewage matter or any substance which will chemically destroy the matrix. The grains should show no signs of decay, and by preference should be of an angular shape. The sand obtained by crushing granite and hard stones is excellent. When lime is used as a matrix, certain natural earths such as pozzuolana or trass, or, failing these, powdered bricks or tiles, may be used instead of sand with great advantage. They have the property of entering into chemical combination with the lime, forming a hard setting compound, and increasing the hardness of the resulting concrete.

The commonest aggregates are broken stone and natural flint gravel. Broken bricks or tiles and broken furnace slag are sometimes used, the essential points being that the aggregate should be hard, clean and sound. Generally speaking, broken stones will be rough and angular, whereas the stones in flint gravel will be comparatively smooth and round. It might be supposed, therefore, that the broken stone will necessarily be the better aggregate, but this does not always follow. Experience shows that, although spherical pebbles are to be avoided, Portland cement adheres tightly to smooth flint surfaces, and that rough stones often give a less compact concrete than smooth ones on account of the difficulty of bedding them into the matrix when laying the concrete. In mixing concrete there is always a tendency for the stones to separate themselves from the sand and cement, and to form “pockets” of honeycombed concrete which are neither water-tight nor strong. These are much more liable to occur when the stones are flat and angular than when they are round. Modern engineers favour the practice of having the stones of various sizes instead of being uniform, because if these sizes are wisely proportioned the whole mixture can be made more solid, and the rough “pockets” avoided. For first-class work, however, and especially in steel concrete, it is customary to reject very large stones, and to insist that all shall pass through a ring 7/8 of an inch in diameter.

The water, like all the other constituents of concrete, should be clean and free from vegetable matter. At one time sea-water was thought to be injurious, but modern investigation finds no objection to it except on the score of appearance, efflorescence being more likely to occur when it is used.

Sometimes in massive concrete structures large and heavy stones as big as a man can lift are buried in the concrete after it is laid in position but while it is still wet. The stones should be hard and clean, and care must be taken that they are completely surrounded. Such concrete is known as rubble concrete.

In proportioning the quantities of matrix to aggregate the ideal to be aimed at is to get a concrete in which the voids or air-spaces shall be as small as possible; and as the lime or cement is usually by far the most expensive item, it is desirable Proportions. to use as little of it as is consistent with strength. When natural flint gravel containing both stones and sand is used, it is usual to mix so much gravel with so much lime or cement. The proportions in practice generally run from 3 to 1 for very strong work, down to 12 to 1 for unimportant work. Some engineers have the sand separated from the stones by screens or sieves and then remixed in definite proportions. When stones and sand are obtained from different sources, their relative proportions have to be decided upon. A common way of doing this is first to choose a proportion of sand to cement, which will probably vary from 1 to 1 up to 4 to 1. It then remains to determine what proportion of stones should be added. For this purpose a large can, whose volume is known, is filled loosely with stones, and the volume of the voids between them is determined by measuring how much water the can will hold in addition to the stones. It is then assumed that the quantity of sand and cement should be equal to the voids. Moreover, the volume of sand and cement together is generally assumed to be equal to that of the sand alone, as the cement to a large extent fills up voids in the sand. For example, suppose it is resolved to use 2 parts of sand to 1 of cement, and suppose that experiment shows that in a pailful of stones two-fifths of the volume consists of voids, then 2 parts of sand (or sand with cement) will fill voids in 5 parts of stones, and the proportion of cement, sand, stones becomes 1:2:5. There are several weak points in this reasoning, and a more accurate way of determining the best proportions is to try different mixtures of cement, stones and sand, filling them into different pails of the same size, and then ascertaining, by weighing the pails, which mixture is the densest.

In determining the amount of water to be added, several things must be considered. The amount required to combine chemically with the cement is about 16% by weight, but in practice much more than this is used, because of loss by evaporation, and the difficulty of ensuring that the water shall be uniformly distributed. If the situation is cool, the stone hard, and the concrete carefully rammed directly it is laid down and kept moist with damp cloths, only just sufficient to moisten the whole mass is required. On the other hand, water should be given generously in hot weather, also when absorbent stone is used or when the concrete is not rammed. In these cases the concrete should be allowed to take all it can, but an excess of water which would flow away, carrying the cement with it, should be avoided.

The thorough mixing of the constituents is a most important item in the production of good concrete. Its object is to distribute all the materials evenly throughout the mass, and it is performed in many different ways, both by Mixing. hand and by machine. The relative values of hand and machine work are often discussed. Roughly it may be said that where a large mass of concrete is to be mixed at one or two places a good machine will be of great advantage. On the other hand, where the mixing platform has to be constantly shifted, hand mixing is the more convenient way. In hand mixing it is usual to measure out from gauge boxes the sand, stones and cement or lime in a heap on a wooden platform. Then they are turned once or twice in their dry state by men with shovels. Next water is carefully added, and the mixture again turned, when it is ready for depositing. For important work and especially for thin structures the number of turnings should be increased. Many types of mixing machines are obtainable; the favourite type is one in which the materials are placed in a large iron box which is made to rotate, thus tumbling the matrix and aggregate over each other again and again. Another simple apparatus is a large vertical pipe or shoot in which sloping baffle plates or shelves are placed at intervals. The materials are fed in at the top of the shoot and fall from shelf to shelf, the mixing being effected by the various shocks thus given. When mixed the concrete is carried at once to the position required, and if the matrix is quick-setting Portland cement this operation must not be delayed.

One of the few drawbacks of concrete is that, unlike brickwork or masonry, it has nearly always to be deposited within moulds or framing which give it the required shape, and which are removed after it is set. Indeed, the trouble Moulds. and expense of these moulds sometimes prohibit its use. It is essential that they shall be strong and stiff, so as not to yield at all from the pressure of the wet concrete. The moulds for the face of a wall consist generally of wooden shutters, leaning against upright timbers which are secured by horizontal or raking struts to firm ground, or to anything that will bear the weight. If a smooth and neat face is wanted other precautions must be taken. The shutters must be planed, and coated with a mixture of soap and oil, so as to come away easily after the concrete is set. Moreover, when depositing the concrete, a shovel or other tool must be worked between the wet concrete and the shutter. This draws sand and water to the face and prevents the rough stones from showing themselves. Sometimes rough concrete is rendered over with a plaster of cement and sand after the shutters have been removed, but this is liable to peel off and should be avoided.

The method of depositing depends on the situation. If for important walls, or for small scantlings such as steel concrete generally involves, the concrete should be deposited in quite small quantities and very carefully rammed Depositing. into position. If for massive walls, it is usual to tip it out in large quantities from a barrow or wagon, and simply spread it in layers about a foot thick. Depositing concrete under water for breakwaters and bridge foundations requires special skill and special appliances. It is usually done in one of three ways:—(a) By moulding the concrete ashore into large blocks, which, when sufficiently hard, are lowered through the water into position by a crane or similar machine with the aid of divers. The most notable instance of this type of construction was at the port of Dublin, where Mr B. B. Stoney made blocks no less than 350 tons in weight. Each block formed a piece of the quay wall 12 ft. long and 27 ft. high, being made on shore and then deposited in position by floating sheers of special design. (b) By moulding the concrete into what are called “bag-blocks.” In this system the concrete is filled into bags, which are at once lowered through the water like the blocks. But in this case the concrete being still wet can adapt itself more or less to the shape of the adjoining bags, and strong rough walls can be built in this way. Sometimes the bags are made of enormous size, as at Aberdeen breakwater, where the contents of each bag weighed 50 tons. The canvas was laid in a hopper barge and there filled with the concrete and sewn up. The enormous bag was then dropped through a door in the bottom of the barge upon the breakwater foundation. (c) By depositing the wet concrete through the water between temporary upright timber frames which form the two faces of the wall. In this case very great care has to be taken to prevent the cement from being washed away from the other constituents when passing through the water. Indeed, this is bound to happen more or less, but it is guarded against by lowering the concrete slowly in a special box, the bottom of which is opened as it reaches the ground on which the concrete is to be laid. This method can only be carried out in still water, and where strong and tight framing can be built which will prevent the concrete from escaping. For small work the box can be replaced by a canvas bag secured by a special tripping noose which can be loosened when the bag has reached the ground. The concrete escapes from the bag, which is then drawn up and refilled.

Concrete may be compared with other building materials like masonry or timber from various points of view, such as strength, durability, convenience of building, fire-resistance, appearance and cost. Its strength varies Strength. within very wide limits according to the quality and proportions of the constituents, and the skill shown in mixing and placing them. To give a rough idea, however, it may be said that its safe crushing load would be about ½ cwt. per sq. in. for lime concrete, and 1 to 5 cwt. for Portland cement concrete. The safe tensile strength of Portland cement concrete would be something like one-tenth of its compressive strength, and might be far less. On this account it is usual to neglect the tensile strength of concrete in designing structures, and to arrange the material in such a way that tensile stresses are avoided. Hence slabs or beams of long span should not be built of plain concrete, though when reinforced with steel it is admirably adapted for these purposes.

In regard to durability good Portland cement concrete is one of the most durable materials known. Neither hot, cold, nor wet weather has practically any effect whatever upon it. Frost will not injure it after it has once set, though Durability. it is essential to guard it from frost during the operations of mixing and depositing. The same praise cannot, however, be given to lime concrete. Even though the best hydraulic lime be used it is wise to confine it to places where it is not exposed to the air, or to running water, and indeed for important structures the use of lime should be avoided. Good Portland cement is so much stronger than any lime that there are few situations where it is not cheaper as well as better to use the former, because, although cement is the more expensive matrix, a smaller proportion of it will suffice for use. Lime should never be used in work exposed to sea-water, or to water containing chemicals of any kind. Portland cement concrete, on the other hand, may be used without fear in sea-water, provided that certain reasonable precautions are taken. Considerable alarm was created about the year 1887 by the failure of two or three large structures of Portland cement concrete exposed to sea-water, both in England and other countries. The matter was carefully investigated, and it was found that the sulphate of magnesia in the sea-water has a decomposing action on Portland cements, especially those which contain a large proportion of lime or even of alumina. Indeed, no Portland cement is free from the liability to be decomposed by sea-water, and on a moderate scale this action is always going on more or less. But to ensure the permanence of structures in sea-water the great object is to choose a cement containing as little lime and alumina as possible, and free from sulphates such as gypsum; and more important still to proportion the sand and stones in the concrete in such a way that the structure is practically non-porous. If this is done there is really nothing to fear. On the other hand, if the concrete is rough and porous the sea-water will gradually eat into the heart of the structure, especially in a case like a dam, where the water, being higher on one side than the other, constantly forces its way through the rough material, and decomposes the Portland cement it contains.

As regards its convenience for building purposes it may be said roughly that in “mass” work concrete is vastly more convenient than any other material. But concrete is hampered by the fact that the surface always has to Convenience and appearance. be formed by means of wooden or other framing, and in the case of thin walls or floors this framing becomes a serious item, involving expense and delay. In appearance concrete can rarely if ever rival stone or brickwork. It is true that it can be moulded to any desired shape, but mouldings in concrete generally give the appearance of being unsatisfactory imitations of stone. Moreover, its colour is not pleasing. These defects will no doubt be overcome as concrete grows in popularity as a building material and its aesthetic treatment is better understood. Concrete pavings are being used in buildings of first importance, the aggregate being very carefully selected, and in many cases the whole mixture coloured by the use of pigments. Care must be taken in their selection, however, as certain colouring matters such as red lead are destructive to the cement. One of the great objections to the appearance of concrete is the fact that soon after its erection irregular cracks invariably appear on its surface. These cracks are probably due to shrinkage while setting, aggravated by changes in temperature. They occur no less in structures of masonry and brickwork, but in these cases they generally follow the joints, and are almost imperceptible. In the case of a smooth concrete face there are no joints to follow, and the cracks become an ugly feature. They are sometimes regulated by forming artificial “joints” in the structure by embedding strips of wood or sheet iron at regular intervals, thus forming “lines of weakness,” at which the cracks therefore take place. A pleasing “rough” appearance can be given to concrete by brushing it over soon after it has set with a stiff brush dipped in water or dilute acid. Or, if hard, its surface can be picked all over with a bush hammer.

At one time Portland cement concrete was considered to be lacking in fireproof qualities, but now it is regarded as one of the best fire-resisting materials known. Although experiments on this matter are badly needed, there is little Resistance to fire. doubt that good steel concrete is very nearly indestructible by fire. The matrix should be Portland cement, and the nature of the aggregate is important. Cinders have been and are still much favoured for this purpose. The reason for this preference lies in the fact that being porous and full of air, they are a good non-conductor. But they are weak, and modern experience goes to show that a strong concrete is the best, and that probably materials like broken clamp bricks or burnt clay, which are porous and yet strong, are far better than cinders as a fireproof aggregate. Limestone should be avoided, as it soon splits under heat. The steel reinforcement is of immense importance in fireproof work, because, if properly designed, it enables the concrete to hold together and do its work even when it has been cracked by fire and water. On the other hand, the concrete, being a non-conductor, preserves the steel from being softened and twisted by excessive temperature.

Only very general remarks can be made on the subject of cost, as this item varies greatly in different situations and with the market price of the materials used. But in England it may be said that for massive work such as big walls Cost. and foundations concrete is nearly always cheaper than brickwork or masonry. On the other hand, for reasons already given, thin walls, such as house walls, will cost more in concrete. Steel concrete is even more difficult to generalize about, as its use is comparatively new, but even in the matter of first cost it is proving a serious rival to timber and to plate steel work, in floors, bridges and tanks, and to brickwork and plain concrete in structures such as culverts and retaining walls, towers and domes.

Artificial Stones.—There are many varieties of concrete known as “artificial stones” which can now be bought ready moulded into the form of paving slabs, wall blocks and pipes: they are both pleasing in appearance and very durable, being carefully made by skilled workmen. Granolithic, globe granite and synthetic stone are examples of these. Some, such as victoria stone, imperial stone and others, are hardened and rendered non-porous after manufacture by immersion in a solution of silicate of soda. Others, like Ford’s silicate of limestone, are practically lime mortars of excellent quality, which can be carved and cut like a sandstone of fine quality.

Fig. 1.—Expanded Steel Concrete Slab.

Steel Concrete.—The introduction of steel concrete (also known as ferroconcrete, armoured concrete, or reinforced concrete) is generally attributed to Joseph Monier, a French gardener, who about the year 1868 was anxious to build some concrete water basins. In order to reduce the thickness of the walls and floor he conceived the idea of strengthening them by building in a network of iron rods. As a matter of fact other inventors were at work before Monier, but he deserves much credit for having pushed his invention with vigour, and for having popularized the use of this invaluable combination. The important point of his idea was that it combined steel and concrete in such a way that the best qualities of each material were brought into play. Concrete is readily procured and easily moulded into shape. It has considerable compressive or crushing strength, but is somewhat deficient in shearing strength, and distinctly weak in tensile or pulling strength. Steel, on the other hand, is easily procurable in simple forms such as long bars, and is exceedingly strong. But it is difficult and expensive to work up into various forms. Concrete has been avoided for making beams, slabs and thin walls, just because its deficiency in tensile strength doomed it to failure in such structures. But if a concrete slab be “reinforced” with a network of small steel rods on its under surface where the tensile stresses occur (see fig. 1) its strength will be enormously increased. Thus the one point of weakness in the concrete slab is overcome by the addition of steel in its simplest form, and both materials are used to their best advantage. The scientific and practical value of this idea was soon seized upon by various inventors and others, and the number of patented systems of combining steel with concrete is constantly increasing. Many of them are but slight modifications of the older systems, and no attempt will be made here to describe them in full. In England it is customary to allow the patentee of one or other system to furnish his own designs, but this is as much because he has gained the experience needed for success as because of any special virtue in this or that system. The majority of these systems have emanated from France, where steel concrete is largely used. America and Germany adopted them readily, and in England some very large structures have been erected with this material.

Expanded Metal.

Section through Intersection. Fig. 2.

The concrete itself should always be the very best quality, and Portland cement should be used on account of its superiority to all others. The aggregate should be the best obtainable and of different sizes, the stones being freshly crushed and screened to pass through a 7/8 in. ring. Very special care should be taken so to proportion the sand as to make a perfectly impervious mixture. The proportions generally used are 4 to 1 and 5 to 1 in the case of gravel concrete, or 1:2:4 or 1:2½:6 in the case of broken stone concrete. But, generally speaking, in steel concrete the cost of the cement is but a small item of the whole expense, and it is worth while to be generous with it. If It is used in piles or structures where it is likely to be bruised the proportion of cement should be increased. The mixing and laying should all be done very thoroughly; the concrete should be rammed in position, and any old surface of concrete which has to be covered should be cleaned and coated with fresh cement.

Fig. 3.—Hennebique System.

The reinforcement mostly consists of mild steel and sometimes of wrought iron: steel, however, is stronger and generally cheaper, so that in English practice it holds the field. It should be mild and is usually specified to have a breaking (tensile) strength of 28 to 32 tons per sq. in., with an elongation of at least 20% in 8 in. Any bar should be capable of being bent cold to the shape of the letter U without breaking it. The steel is generally used in the form of long bars of circular section. At first it was feared that such bars would have a tendency to slip through the concrete in which they were embedded, but experiments have shown that if the bar is not painted but has a natural rusty surface a very considerable adhesion between the concrete and steel—as much as 2 cwt. per sq. in. of contact surface—may be relied upon. Many devices are used, however, to ensure the adhesion between concrete and bar being perfect. (1) In the Hennebique system of construction the bars are flattened at the end and split to form a “fish tail.” (2) In the Ransome system round bars are rejected in favour of square bars, which have been twisted in a lathe in “barley sugar” fashion. (3) In the Habrick system a flat bar similarly twisted is used. (4) In the Thacher system a flat bar with projections like rivet heads is specially rolled for this purpose. (5) In the Kahn system a square bar with “branches” is used. (6) In the “expanded metal” system no bars are used, but instead a strong steel netting is manufactured in large sheets by special machinery. It is made by cutting a series of long slots at regular intervals in a plain steel plate, which is then forcibly stretched out sideways until the slots become diamond-shaped openings, and a trellis work of steel without any joints is the result (fig. 2).

Fig. 4. Hennebique System.

The structures in which steel concrete is used may be analysed as consisting essentially of (1) walls, (2) columns, (3) piles, (4) beams, (5) slabs, (6) arches. The designs differ considerably according to which of these purposes the structure is to fulfil.

The effect of reinforcing walls with steel is that they can be made much thinner. The steel reinforcement is generally applied in the form of vertical rods built in the wall at intervals, with lighter horizontal rods which cross the vertical ones, and thus form a network of steel which is buried in the concrete. These rods assist in taking the weight, and the whole network binds the concrete together and prevents it from cracking under a heavy load. The vertical rods should not be quite in the middle of the wall but near the inner and outer faces alternately. Care must be taken, however, that all the rods are covered by at least an inch of concrete to preserve them from damage by rust or fire. In the Cottancin system the concrete is replaced by bricks pierced with holes through which the vertical rods are threaded; the horizontal tie-rods are also used, but these do not merely cross the vertical ones, but are woven in and out of them.

Fig. 5.—Steel and Concrete Pile (Williams System).

Fig. 6.

Fig. 7.

Columns have generally to bear a heavier weight than walls, and have to be correspondingly stronger. They have usually been made square with a vertical steel rod at each corner. To prevent these rods from spreading apart they must be tied together at frequent intervals. In some systems this is done by loops of stout wire connecting each rod to its neighbour, and placed one above the other about every 10 in. up the column (figs. 3 and 4). In other systems a stout wire is wound continuously in a spiral form round the four rods. Modern investigation goes to prove that the latter is theoretically the more economical way of using the steel, as the spiral binding wire acts like the binding of a wire gun, and prevents the concrete which it encloses from bursting even under very great loads.

Fig. 8.

Fig. 9.

Fig. 10.

Fig. 11.

That steel concrete can be used for piles is perhaps the most astonishing feature in this invention. The fact that a comparatively brittle material like concrete can be subjected not only to heavy loads but also to the jar and vibration from the blows of a heavy pile ram makes it appear as if its nature and properties had been changed by the steel reinforcement. In a sense this is undoubtedly the case. A. G. Considère’s experiments have shown that concrete when reinforced is capable of being stretched, without fracture, about twenty times as much as plain concrete. Most of the piles driven in Great Britain have been made on the Hennebique system with four or six longitudinal steel rods tied together by stirrups or loops at frequent intervals. Piles made on the Williams system have a steel rolled joist of I section buried in the heart of the pile, and round it a series of steel wire hoops at regular intervals (fig. 5). Whatever system is used, care must be taken not to batter the head of the pile to pieces with the heavy ram. To prevent this an iron “helmet” containing a lining of sawdust is fitted over the head of the pile. The sawdust adapts itself to the rough shape of the concrete, and deadens the blow to some extent.

 

Fig. 12.

Fig. 13.

Fig. 14.—Stirrup (Hennebique System).

Fig. 15.

But it is in the design of steel concrete beams that the greatest ingenuity has been shown, and almost every patentee of a “system” has some new device for arranging the steel reinforcement to the best advantage. Concrete by itself, though strong in compression, can offer but little resistance to tensile and shearing stresses, and as these stresses always occur in beams the problem arises how best to arrange the steel so as to assist the concrete in bearing them. To meet tensile stresses the steel is nearly always inserted in the form of bars running along the beam. Figs. 6 to 9 show how they are arranged for different loading. In each case the object is to place the bars as nearly as possible where the tensile stresses occur. In cases where all the stresses are heavy, that portion of the beam which is under compression is similarly reinforced, though with smaller bars (figs. 10 and 11). But as these tension and compression bars are generally placed near the under and upper surface of the beam they are of little use in helping to resist the shearing stresses which are greatest at its neutral axis. (See Bridges.) These shearing stresses in a heavily loaded beam would cause it to split horizontally at or near the centre. To prevent this many ingenious devices have been introduced. (1) Perhaps one of the most efficient is a diagonal bracing of steel wire passing to and fro between the upper and lower bars and firmly secured to each by lapping or otherwise (fig. 12); this device is used in the Coignet and other French systems. (2) In the Hennebique system (which has found great favour in England) vertical bands or “stirrups,” as they are generally called, of hoop steel are used (fig. 13). They are of U shape, and passing round the tension bars extend to the top of the beam (figs. 14 and 3). They are exceedingly thin, but being buried in concrete no danger of their perishing from rust is to be feared. (3) In the Boussiron system a similar stirrup is used, but instead of being vertical the two parts are spread so that each is slightly inclined. (4) In the Coularon system, the stirrups are inclined as in fig. 15, and consist of rods, the ends of which are hooked over the tension and compression bars. (5) In the Kahn system the stirrups are similarly arranged, but instead of being merely secured to the tension bar, they form an integral part of it like branches on a stem, the bar being rolled to a special section to admit of this. (6) In many systems such as the “expanded metal” system, the tension and compression rods together with the stirrups are all abandoned in favour of a single rolled steel joist of I section, buried in concrete (see fig. 16). Probably the weight of steel used in this way is excessive, but the joists are cheap, readily procurable and easy to handle.

Floor slabs may be regarded as wide and shallow beams, and the remarks made about the stresses in the one apply to the other also; accordingly, the various devices which are used for strengthening beams recur in the slabs. But in a thin slab, with its comparatively small span and light load, the concrete is generally strong enough to bear the shearing stresses unaided, and the reinforcement is devoted to assisting it where the tensile stresses occur. For this purpose many designers simply use the modification of the Monier system, consisting of a horizontal network of crossed steel rods buried in the concrete. “Expanded metal” too is admirably adapted for the purpose (fig. 1). In the Matrai system thin wires are used instead of rods, and are securely fastened to rolled steel joists, which form the beams on which the slabs rest; moreover, the wires instead of being stretched tight from side to side of the slab are allowed to sag as much as the thickness of the concrete will allow. In the Williams system small flat bars are used, which are not quite horizontal, but pass alternately over and under the rolled joists which support the slabs.

Fig. 16.

A concrete arch is reinforced in much the same way as a wall, the stresses being somewhat similar. The reinforcing rods are generally laid both longitudinally and circumferentially. In the case of a culvert the circumferential rods are sometimes laid continuously in the form of a spiral as in the Bordenave system.

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