US2910921A

US2910921A - Surface areas of pre-stressed concrete and their method of construction

Info

Publication number: US2910921A
Application number: US463667A
Authority: US
Inventors: Freyssinet Eugene
Original assignee: Individual
Current assignee: Individual
Priority date: 1953-10-21
Filing date: 1954-10-21
Publication date: 1959-11-03
Anticipated expiration: 1976-11-03

Description

Nov. 3, 1959 E. FREYssINET 2,910,921

SURFACE AREAS OF' PRE-'STRESSED CONCRETE AND THEIR METHOD OF' CNSTRUCTIQN Filed oct. 21, 1954 5 sheets-sheet 1 a V -L y 7 2f INVENTOR y. gjwWMv/Mi- 20a/Epu MTORNF/S Nov. 3, 1959 E FREYSSWET 2,910,921

' SURFACE AS OF PRE-STRESSED CONCRETE' AND T R METHOD OF' CONSTRUCTION Filed Oct. 21, 1954 5 Sheets-Sheet 2 IN VEN T0 R Nov. 3, 1959 E. FREYsslNr-:T 2,910,921

SURFACE AREAS OF RRE-sTREssED CONCRETE AND THEIR METHOD OF CONSTRUCTION Filed Oct. 21, 1954 5 Sheets-Sheet 3 5y/f'.- 6 7% (15 2,5 21/ 2,5 f2.9@ 2M Nov. 3, 1959 y E. FREYssINET SURFACE AREAS 2,910,921 oF PRESTRESSED coNcNET AND THEIR METHOD 0F CONSTRUCTION Filed oct. 21. 1954 5 Sheets-Shvaet 4 irraRA/Eys Nov. 3, 1959 E- FREYSS'NET 2,910,921

SURFACE AREAS OF' PRE-STRESSED CONCRETE AND THEIR METHOD OF" CONSTRUCTION l Filed Oct. 2l. 1954 5 Sheets-$11961. 5

United States Patent iice 2,910,921 Patented Nov. 3, 1959 SURFACE AREAS OF PRE-STRESSED CONCRETE AND THEIR METHOD OF CONSTRUCTION Eugene Freyssinet, Neuilly-sur-Seine, France Application October 21, 1954, Serial No. 463,667

Claims priority, application France October 21, 1953 8 Claims. (Cl. 94-8) It is known that the greatest drawbacks of laid areas of concrete which are put down at the present time arise from the necessity of dividing these areas up into separate sections by means of expansion joints. These expansion joints break the continuity of the surface of the concrete and when this latter is subjected to rolling loads, there rapidly appear, at the edges of the concrete sections and on each side of a joint, defacements which increase the discontinuity of the laid section and which tend to become more and more rapidly aggravated by the shocks to which they give rise.

In view of avoiding these drawbacks, it has already been proposed to increase the size of the pavement slabs, in order to reduce the number of the expansion joints and, even, in view of avoiding crackings of the concrete, to lay the slabs on a coextensive foundation, the upper surface of which is adapted for reducing the friction.

However, with slabs of great size, chiefly when the friction of these slabs on their foundation is reduced, the variation of breadth of the expansion joint is of great magnitude, so that each of these joints provides in the pavement a discontinuity, and the greater the size of the slabs, the wider the discontinuity.

An object of the present invention is to eliminate all .discontinuities of a concrete coating on the ground whatever be the extent thereof.

Another object of the invention is to provide a concrete coating in the major part of which any risk of cracking is absolutely avoided.

A further object of the invention is to utilize the fric- '.tion of the concrete coating on the soil foundation for .allowing the prestressing of said concrete coating and keeping this coating in good condition, whereas said fric- .tion (the main cause of the cracking in the conventional pavements) remains always an inevitable drawback of .these conventional pavements.

A further object of the invention is to provide a concrete coating of the ground wholly prestressed in two perpendicular directions, and the major part of which does not move with respect to the foundation soil, i.e a coat- .ing in which the thermic and hygrometric variations give .rise only to variation of the compression stresses of this coating about mean values without displacement of the `coating with respect to the ground.

.A further object of the invention is to provide cheap :and safe means for keeping, in a prestressed coating, a permanent compressional condition even in case of ex- .treme values of temperature or moisture which may haprpen in a given climate.

A further object of the invention is to provide a con- 4crete coating of the ground, prestressed in two perpenconcrete coating on the ground; the coating is transversely divided by at least one gap remote from said abutments and adapted to receive, on the one hand, means for thrusting apart the edges of said gap and intended to put under compression the part of the coating situated on each side of said gap up to the abutments which resiliently yield, and, on the other hand, incompressible wedging members intended to maintain the compression thus obtained in the coating and to close said gap.

This arrangement of abutments at the extremities of the concrete coating, has the effect of permitting, in the case of expansion, a displacement of the extremities of the coating against the pressure of the saidelastic abutments.

It is to be noted that the expansion, properly so-called, that is to say the Variation in dimension, is only associated with a relatively short portion of the coating in the vicinity of each abutment, since the expansion of the major portion of the concreted area is absorbed by friction and does not give rise to any variations in dimension, but only in the state of elastic strain of the `concrete of this coating.

The greater the coefficient of friction between the coating and the ground, the smaller the length of coating which, starting from the extremities supported by the elastic abutments, moves with respect to the ground due to variations of its thermo-hygrometric state and, as a result, the amplitude of the movement of the extremities is also reduced. But in that part of the concrete coating which remains fixed with respect to the ground, the variations of the pre-stress, due to the expansion and contraction are not compensated by a movement of the coating, and are therefore at their maximum values.

Conversely, the smaller the coecient of friction, the greater is the length of coating, measured from its extremities, which moves with respect to the ground, and the greater the amplitude of displacement of the elastic abutments.

In very long concrete coatings (longer than one kilometer), the central portions thereof will, in any case, be subjected to the maximum variations of stress. In this case, it is useless to increase the cost of the foundations of the concrete coating by a special arrangement of the surface of these foundations, nor is it useful to increase the cost of the elastic abutment members by increasing the possible amplitude of their movement. It will then be suicient to make the value of the coefficient of friction uniform by a careful levelling of the ground, on which a thin layer of sand, preferably sand with sharp grains, is spread in order to perfect the levelling. In this Way, there may be obtained a practically uniform coefficient of friction of the order of 01.5 to 0.8.

The description which follows below with respect to the attached drawings (which are given by way of example only and not in any sense by way of limitation) will make it quite clear how the invention may be carried into effect, the special features which are brought out, either in the drawings or in the text, being understood to form a part of the said invention.

Fig. l shows in vertical cross-section and at right angles to its general direction, an abutment comprising an inlinitely flexible spring.

Fig. 2 shows as a similar vertical cross-section, an abutment provided with springs constituted by parallel steel wires.

Fig. 3 shows in vertical cross-section the general arrangement of an elastic abutment with parallel steel wires.

Figs. 4a and 4b are two possible cross-sections following the line VII-VII of Fig. 6.

Fig. 5 shows an alternate form of elastic abutment, in vertical cross section.

Fig. 6 is similar to Fig. l and is a diagrammatic plan View of a concrete layer provided with divisions for the application of temporary pre-stresses.

Fig. 7 shows a vertical cross-section, of a device for applying either. temporary.- or final pre-stress to a concret'elayer.

Fig- 8y shows a cross-section similar to that given in Fig- 7 and relating to a device for applying temporary prestress.

Fig. 9A is a vertical cross section through a further form of' elastic abutment.

Fig: l is a vertical cross-section of a further device for applying final pre-stress comprising rods anchored in the ground.

Fig. 1.1 is an alternative'form ofthe arrangement shown in Fig.`

` Fig. 12 shows a plan View of a concrete layer arranged so as to make its method of construction understood.

Fig. 1'3 is a cross-section along the line XXXl-XXXi of Fig. 30, during the execution of the concrete work.

Fig. 14v is a diagrammatic View in plan of a curved sectionof a concrete layer.

Fig. shows the application of the present invention to a curved` concrete layer.

In the drawings, Figs. 1 to 5 show, amongst the very many possible embodiments, a few practical forms of con struction of elastic abutments, Fig. 4 corresponding to the case of an abutment having a perfect spring.

In this figure, the end portion 21 of the concrete layer, is supported against the abutment 1 through `the intermediary of a hat bag 4. ln order that this bag may nevertheless supply the necessary thrust to the layer without the necessity of using an excessive internal pressure, the extremity of this layer is made thicker by a progressively rounded portion 6 on its lower face, so that the thickness of the layer at the point of the abutment is n times greater than the normal thickness of the layer. The pressure obtaining in the bag may thus be n times smaller than that which would be necessary if the thrust wereV applied to the normal thickness of the layer. lnside the block of the abutment, there is provided an inspection passage 7 which enables the bags to be repaired or changed in case of bursting; in this case, wedges are arranged inthe space 8 so as to enable the state of compression of the layer to be maintained.

The bag, which may be of any elastic material providedv that it is capable of resisting the applied pressure, isconnected to a source 9 of fluid under pressure which provides, in this case, a constant pressure. Such a constant pressure may be obtained from a hydraulic accumuIator or from a liquid or `gas pump controlled by a ypressostat. Y

Asv in the case of all the other figures which will be described. in the pages following, the concrete layer rests on the ground with the interposition of a layer of sand 10,. and a layer of anti-friction material l1, for example pitch, acts as an intermediary for the support of the `layer on the block of the abutment, so as to permit the free action of the spring constituted by the bag 4.

In the form of construction shown in Figs. 2 and 3, the elastic coupling between the abutment and the layer is efected by means of stretched wires 12 which are anchored, for example in the same way as the usual prestressing cables, by means of cones 13 at one of their extremities in the layer and at the other extremity in the:v abutment. The layer slides, through the medium of coatings 14, of pitch for example, on a platform 15 serving as a support for its extremity. The cables 12, the

` .lengthof which is of the order of 100 metres in the .ex-

ample'ehosen,l are free to move inside the channel through which" they pass, this channel'being formed in the concrete or being constituted by steel sheet; they are protected` against, rusting by a layer of pitch. Between the platform 15 and the concrete layer, these cables pass through Van open space which permits of movement with respect to the abutment and in this space, they are prod tected by elastic sleeves 16. The right-hand extremity of the cables shown in Fig.` 2 may be anchored in an abutment of any kind arranged underneath the concrete layer.

It is convenient, as shown in Fig. 3, to use the sheaths of concrete which enclose the cables 12 to form the resisting block of the abutment. These cables are spread out inside a transverse block of concrete 18 from the ends of the sheaths, and the sheaths and the block are weighed by means of an embankment i9, the weight of which gives the desired resistance to the abutment.

As shown in Fig. 4a, the sheaths 17 may be quite separate from each other and each housed in. a` trench, 20 which is then filled with earthing material 21, or even with concrete, or alternatively as shown in Fig. 7b, all the sheaths 17 may be solidly connected together by a covering of concrete 22, on which the embankment 19 is supported through the medium. ofy a layer of sand 23 which is intended to distribute evenly the pressure of the embankment.

The elastic abutments which have just beenl described are far from beingthe only ones suitable to be used.

In the thick extremity of the concrete layer 21, shown in Fig, 5, are sunk theends of steel piles 24 (or concrete) which are driven obliquely into the ground. The piles shown in full line are compressedl by the thrust of the concrete layer, whilst the piles shown in dotted lines, and which are located in front of or behind the iirst piles, are put in tension. An elastic abutment of this kind is capable of absorbing a very large amount of energy of deformation.

The abutment shown in. Fig. 9V is similar in its main lines to that shown in Fig. 3; it is however designed to withstand" very much higher thrusts. The abutment is constituted by a curved curtain 94 of concrete, either continuous or made in separate elements, at the upper part of which the cables 12a, which are free inthe di'- rcction of their length and are slightly inclined to thehorizontal, may play the part of springs.

The lower extremities 9i? of these cables `12a are anchored in the intermediate' block 96. This block is: itself anchored by the cables 12b which cross over the cables 12a, to the mass of concrete 18a. Contrary to the cables 12u, the cables lib may be made rigid by in jection of concrete into the part of the curtain in which they are enclosed. By means of its curved shape, the radius of curvature of which is preferably decreasing from the horizontal portion to the vertical portion, this abutment converts the horizontal thrusts which are applied to it into vertical 'forces of smaller value because of the 'friction of the concave face of the curtain on the ground. These vertical stresses are carried by the Weight of earth which serves as a load on the anchorage mass Finally, it will be noted thatit is not necessary for the abutments to be perpendicular to the largest dimension of the concrete layer. They may be arranged in any way whatever, provided that the resultants of the stresses which they transmit to the extremity of the concrete layer, are applied along the largest dimension of this latter.

ln the description given in respect of Figs. 2 and 3, it has been supposed that the concrete was stable; however, in practice, it is advisable to take account of shrinkage. A iirst means of avoiding the results of shrinkage consists in forming, during the pouring of the concrete layer, and at a few metres ifrom each other, lshrinkage divisions which are intended to prevent the concrete from forming cracks spontaneously. The shrinkage is then allowed to proceed and this has the effect of en- .larging the said divisions, after which the latter are filledin with rammed mortar. The whole of the concrete layer is then in the condition postulated and the 'linal pre-stress may then be applied to it.

This method of procedure has, however, a number of disadvantages: before the concrete layer can be put into service, it is necessary to wait until the shrinkage has been almost wholly completed; in addition, this method complicates the construction. Finally, each of the divisions creates a break in the uniformity of the concrete layer which may adversely effect its ultimate behaviour under pre-stress.

In order to annul the effects of this shrinkage tension, it is first of all advisable to apply a compression acting in compensation for the shrinkage of the concrete as soon as the latter begins to shrink and, in addition, to increase the final compression by the value of the shrinkage tension remaining eifective at the moment at which this final compression is carried out.

Now it has been shown that the arrangement of a concrete layer in accordance with the invention, enables very high values of compression to be utilised. There is therefore an advantage in reaching the state of final compression with as few intermediate stages as possible. Thus, there may be applied from the moment at which the concrete has set, a compression Pn which is intended to compensate the shrinkage up to the time t1 and then at that moment, the compression Pr1 having disappeared, there is applied the nal compresison increased by Pff-Pn. The concrete layer will thus be definitely usable at the time f1 (which is of the order of a few weeks). If a; method were followed involving more progressive compressions at longer intervals of time, for example withthe intermediate stages P'11 and Prz, the concreted area would not be definitely available for use until the time t2, which may correspond to several months.

However, by applying at a given moment, a pre-stress of pre-determined value P11 to a concrete layer in a state of shrinkage, it -is not certain that this shrinkage, together -with the contraction of the concrete under thermo-hygrometric influences will not cause the total disappearance of this temporary prestress, and this would lead to cracking of the concrete before the final prestress were applied.

It is thus preferable, as shown in Fig. 6, to arrange, in the concrete layer, divisions which are sufficiently numerous (by local interruptions in the concreting) for the portions of the concrete layer which they de-limit to be able to be displaced on the ground by a relatively small force. Thus, by permanently applying this force to the portions of the concrete layer, it isV certain that all the shrinkage will be compensated. i

If W is the weight per square metre of a concrete layer having a thickness e, and gb is the coefficient of friction with the ground, in order to displace a length L of this layer, the thrust per square centimetre on the division of this layer will be greater than kg.A Taking once more the example chosen, the maximum permanent pre-stress necessary for the compensation of all shrinkage must thus be at least equal to 0.16 kg. X L kg. per sq. cm. The pre-stresses for compensating shrinkage, on the condition that they are permanent, may thus have values which ldecrease as the lengths of the concrete layer concerned become shorter.

As Vthe difficulties of producing pre-stresses increase even more quickly than the values of these pre-stresses, there is thus an advantage in increasing the number of divisions intended for carrying out these temporary prestresses, Within the limits of the cost and the depreciation of the jacks (which are recoverable) and of the labour `required for putting them into operation. For example,

of a strip of indefinite length which is supported at one of its extremities by an elastic abutment 1, and is divided up by divisions perpendicular to its greatest dimension, 3a, 3b, etc. which are intended for the application of a temporary pre-stress for compensating shrinkage. The layer comprises, in addition, the divisions such as 31 already referred to and which are intended for the application of the final pre-stress.

The divisions 3a, etc. are uniformly spaced apart at a relatively lshort distance from each other, for example less than metres; they are quite simply formed by an interruption in the concreting which can be carried out in a continuous manner starting from one of the extremities of the layer to the other.

The divisions such as 31 are more dilicult to anrange, and this maybe carried out as shown in Figs. 10 and 11. As soon as the concrete has set, and at .the latest on-the day following the pouring of this concrete, a provisional pre-stress is applied to each of the elements 21a and 2lb, etc. which are bounded by the

divisions

3a, 3b, etc. To this end, as shown in Fig. 7, there may be arranged against the edges of the lips of the division, steel section members 60 intended to distribute the pressure, and between which are mounted at intervals, ordinary hydraulic jacks 61. i

In view of the small unit pressure Which is to be employed, as has been stated above, the jacks 61 may be spaced apart fairly widely. All these jacks: are connected to a hydraulic accumulator 62 having a fairly large volume, and which is intended to supply the jacks at a constant pressure. Thus, the jacks apply to the concrete elements located oneach side ofthe division, 211, and 21c in the case considered, a constant thrust which tends to force them apart. The pressure in the jacks is then progressively increased until the opposite extremities of the concrete sections 211, and 21c (which form one of the edges of the

adjacent slots

3a and 3c) begin to move. At this moment, the pressure is kept steady in the said jacks; thus the total extent of the concrete sections 211, and 21c is in a state of compression and this compression exactly balances the passive force due to friction.

The pressure thus regulated is admitted to the jacks which are arranged in asimilar way inside the

divisions

3a and 3c on each side of the division 3b. In this way, in spite of the effects of expansion and contraction, it is certain that, on the one hand the concrete sections 211, and 21c will remain permanently compressed, which will avoid any tensile stress due to shrinkage, `and in consequence, all tendency to crack and on the other hand,in spite of the expansion, the pre-stress of these sections will not increase since this expansion can be absorbed by the effect of -the jacks supplied at a constant pressure.

As shown in Fig. 8, the same result may be obtained by using simple tubes of elastic material in place of the jacks, for example tubes 63 of rubber reinforced with canvas. Beams 64, of wood for example, will be adequate in this case to distribute the pressure over the edges ofthe concrete sections `formed by the divisions.

The divisions 31, which are intended for the application of thelfnal pre-stress, are preferably arranged in such a Way that the variations in dimensions due to shrinkage do not affect them. For this purpose, a division 31 may be provided` with two shiinkage divisions disposed one on each side of it, for example as shown in Fig. 6, and wedges may be temporarily arranged in this division 31 so that the separation and the division of its edges are not modified by the action of the jacks used for applying the temporary pre-stress in the neighbouring divisions. After the shrinkage compensation has been obtained in the way described, the temporary jacks are taken down and the slots employed for the temporary pre-stress are carefully filled in with concrete.

The means for forcing apart the slots of the concrete layer such as 31, 32 (see Fig. 6) intended for the creation of the final pre-stress may be constituted by jacks'of any kind whatever. The calculations which have been made in connection With the abutments show that, in

vibration and .its final smoothing.

the case of vslots spaced apartby several hundred metres, it is rsufficient to provide jacks, the travel of lwhich 'is 'only a "few centimetre's;v In 'this way, the jacks maybe arranged at intervals in the same slot, the jacks are put in action and when the desired separation Yhas been ob'- tained, this may be maintained lby'wed'gin'g,"r`or example by a packing of concrete, placed between 'the various jacks.

Figs. 'l0 and l1 show arrangements 'designed to prevent the lifting of the lips in a more economical manner. In the oppositely-facing edges of the lips, there are fixed the upper extremities of vertical cables 80 which are anchored in the iground at their lower ends. 'To this end, the cables are 'housed lin a pit 81 at the bottom of which their lower extremities have been embedded in a fairly Afluid mass of concrete `82; at the `same time, there is placed :at the 'bottom of 'this pit a small charge of explosive 84, 'the initial profile of the pit being shown in ychain dotted lines 83. `When this charge explodes vinside the plastic concrete with which the pit has been filled, a 'chamber is created at the bottom of -the pit, and Vthis chamber is subsequently filled with fluid concrete after the residual gases from the explosion have been condensed and absorbed.

When the concrete 82 has hardened and the `jack 39 is put under pressure, the flips are forced apart and the cables vv80 become placed in .tension as they are moved apart with the lips, and the lifting of the lips is thus prevented. In order to reduce the size of the pit`81, the upper 'extremities of the cables 80 maybe anchored in the block jack 39 itself, as shown in Fig. ll. In this case, these cables do not directly prevent 'the lifting of .the lips, rbut they neutralise the vertical components of 'thrust which are likely to arise in the block jack '39.

The general method of construction of a large concre'ted .area under pre-stress, Vfor example the 'take-off runway of an aerodrome for 'heavy aircraft, is shown in Figs. l2 and 113, This runway of considerable width, is supported at its extremities by means of abutments 1 of the kind previously described. It is constructed in par- 'allel strips arranged side by side on a ground surface which 'has 'been previously rammed 'flat .and .covered with a `layer of sand. 'This strip is constructed in a continurous process in known manner, by means of a succession of machines 'for carrying out pouring of 'fresh concrete, the levelling-off of the poured layer .of concrete, its 'The first strip "211, 2,1, etc., which forms one of `the edges of 'the runway, is poured by means of two girder sections such as 44 .straightened and placed in line 4to form rails for the movement of the yconcreting machines such as 45, and, at the same time, they provide ra lateral cofferng for Ithe said strip. In the case of the `other strips, as shown in 13, the edge of the llast strip poured 2n serves as a lateral coffering for -one of the edges of the strip 21141-1, and a single rail only 44 .lis then necessary. In order provisionally to ensure that the two coupled strips are independent, that is to say so as to avoid 'them' being Welded together, a very thin separating layer 46, for example a layer of paper stuck to the side of 'the preceding strip or a thin strip of steel sheet, is interposed between two consecutive vconcrete strips. Each of these strips ymay thus be put in compression, independently of the others, in its 'longitudinal sense, by means of jacks inserted in 'the transverse slots formed by interruptions of the concreting.

The temporary application of ,pre-stress may follow immediately after the progress of concreting o'f each strip. During pouring of -the concrete, vthe passage of the cables 47 which apply -the transverse pre-stress vis formed in the strips by means of mandrels 4S which are engaged by one .of their extremities 'in the orifice of 'the channel 49 already formed in the preceding 'strip 2n .and in holes 8 gitudina'll-y. Furthermore, in order tofacilitate 'the alignment Vof the series of channels formed in the strips, it is advisable to identify the position of some of these mandrels by means of amark 4on `the surface of the concrete. ln addition, in the outer strips, an emplacement 50 for the anchorage of the cables 47 is` formed.

'In the longitudinal sense, shrinkage is -compensated for 'by theja'cks. This shrinkage however, Vtakes place freely in the .transverse sense of the strips, and this has 11o-drawbacks `in view of 'the small width of each o'f the strips. However, has valready been indicated, in-order te avoid the accumulation of hard grains or dust in the -space which opens between two consecutive strips, this space is Vcovered over by an elastic strip l51. When all -the strips 'have lbeen poured kand the concrete Yhas approximately reached the same condition in all the strips (the age of 'the concrete -of each of the ystrips Yis,'in fact, very nearly the same in view ofthe fact that, because of the speed of modern lconcreting plant, hardly a few days sep- Varate the `pouring of the 'first strip land that of ythe last) 'the `pre-stressing cables 47 are passed through "the aligned channels and these cables are then tensioned -by supporting them `against the sides of the outer strips. As -these strips may also slide transversely with respect to .the ground, the spaces which have appeared lbetween the strips are thus re-closed, and in practice, if the separating members 46 are removed, there is effected a real welding by the Aeffect of the vpre-stress of the 'adjoining strips.

An important special case of a concrete layer is that `of roadways in which `the width is small compared with the length. "In this case, vit vwill in general 'not -be useful to provide elastic abutments Vin the straight portions but konly 'slots for the application of longitudinal compression arranged at regular intervals. `For each straight section of road, the abutment yconstituted by the mass Aof the road ron each side of this section, together with the friction, is suiiicient to maintain the longitudinal prestress, the transverse pre-stress being economically 'obtained by'means of cables. This condition will not apply in the case `of the bends `in which the elastic abutments provide 'their full measure of advantage, both for Vthe `maintenance of the pre-stress of Vthe straight sections connected together `by these bends, Aand for the maintenance 'of the pre-stress in the bends themselves.

'lf a section of road on a 'bend is considered (see Fig. 14) comprised between the transverse lines MN and N and longitudinally pre-stressed valong its curvature. This section of road is urged towards the Iouter side kof the 'bend bythe force V being the total compression in the sense of the curvature and R the radius of the bend. This force is for the moment considered as lbalanced by the friction of'tl're roadon 0its foundation. When the roadway expands, it tends `at the same time to move yas va whole and to ibecome wider. This expansion, however, does not take place from the axis XX of the road `but from a certain line GG which is fixed with respect to the ground, so that the frictional forces having a centripetal Adirection which act lover the width -h, reduced by the frictional vforces having a centrifugal direction and which act yover the Width k, balancethe force of the thrust which acts in a-centripetal direction. GG is thus within the line XX and this line is then moved towards the outer sideof the bend 'druringthe expansion.

When the roadway contracts, it tends to shrink, but as the direction of `the frictional forces have changed, the line fixed with respect .to the ground has moved to GG", so .that lthe frictional forces, which are now centripetal, and which act over the width k1, are thus subtracted from the centrifugal forces which act over the width h1 again balance the centripetal thrust The line GG is thus, this time, beyond the axis XX and this axis again tends to move outwards towards the outer side of the bend.`

It will thus be seen that, in the caseV of a concrete layer which is curved in plan, and which is subjected to a pre-stress following this curvature, any yvariation of its thermo-hygrometric state tends to displace the axis of the concrete layer towards the outer side of the curvature, and thus to cause the pre-stress to disappear. It is thus advisable, by means of elastic abutments, to subject the portions of the concrete layer which are curved in plan, to a centripetal force which balances out the radial component of compression reduced by the frictional forces.

The problem is thus the same as in the case of the end abutments, with this difference that the forces supplied by the abutments must be directed radially instead of being parallel. With this single exception, the solutions described in the previous description will be applicable.

Fig. 15 shows a construction of this kind. In the outer edge of the curved concrete layer 54 are anchored at 55 stretched cables 56, the length of which is free to vary. The other extremity of these cables is anchored to an abutment block 57 which may be common to all the cables because of their convergence. It will be understood that this arrangement is applicable whatever may be the angle `at the centre of the curved portion, which may in some cases reach 360 in the base of circular tracks or runways which are closed on themselves.

In the case of roadways, it may however happen that, on the contrary to what has been indicated, the prole in length has a curvature such that lifting is to be feared at the summit of the hump-backof this profile. In this case, as the concrete layer may'be considered` as fixed with respect to the ground, the layer may be 4held in contact with the ground by means of vertical cables anchored at their lower ends in the bottom of a pit and at their upper ends to the said concrete layer. The necessary force applied by these cables is clearly equal to the quotient of the total thrust by the convex radius of curvature of the profile in length, -less the weight of the concrete layer itself.

It will of course, be `understood that modifications may be made to the forms of construction which have been described above, in particular by the substitution of equivalent technical means, without thereby departing from the spirit or from the scope of the present invention.

What I claim is:

l. A prestressed elongated rectilinear ground coating of concrete yof substantially uniform thickness without expansion joints and comprising means interposed between said coating and the ground for producing a u-niform coefficient of friction between the undersurface of said coating `and the upper surface of said means, at least one transverse Igap formed in said layer substantially at right angles to its greatest dimension, rigid spacing means inserted in said gap, and resiliently compressed elastic abutment means anchored in the ground for supporting the extremities of said coating in the direction of the said greatest dimension, each said elastic abutment comprising a lconcrete mass anchored in the ground beneath said coating and a plurality of freely-tensioned metal wires extending substantially parallel to the greatest dimension of said coating, one of the extremities of each said wire being anchored to the said mass and ythe 1@ other extremities being anchored in the end portion of said coating adjacent said mass.

2. A concrete coating as claimed in claim 1, in which the said endportion is'thickened at its extremity, said coating further comprising a concrete platform laid under the said end-portion, said` platform comprising two staggered horizontal parts separated by a transverse step for supporting respectively said thickened extremity and the adjacent coating portion, anti-friction means interposed between said platform and said end-portion, at least one passage formed in said thickened extremity, corresponding passages formed in the higher part of said platform through which pass the said tensioned wires, and elastic sleeves for protecting said wires within the transverse space between said step and said thickened extremity.

3. A concrete coating as claimed in claim` 1, further comprising lat least one elongated, longitudinally recessedconcrete member extending from said m-ass and integral therewith, towards the extremity of said end portion and earthy material loading said mass and said concrete member whereby said wires pass through said longitudinal recess for free variation of tension thereof.. j

4. A prestressed elongated rectilinear ground coating of concrete of` substantially uniform thickness without expansion joints and comprising means interposed between said coating and the ground for producing a uniform coefficient of friction between the undersurface of said coating and the upper surface of said means, at least one transverse lgap formed in said layer substantially at right angles lto its greatest dimension, rigid spacing means inserted in said gap, and resiliently compressed elastic abutment means anchored in the ground for supporting the extremities of said coating in the direction ofthe said greatest dimension, the said elastic abutments each comprising a concrete curtain formed in the ground under each` end-portion ofthe coating in parallel relationship with the extremity thereof, the saidvcurtain being curved downwards from the horizontal to the vertical with its concave surface directed towards the ground, and being provided with elongated recesses located in vertical parallel planes perpendicular to said extremity, tensioned cables passing freely in the upper part of said recesses, one extremity of which is anchored in the said end portion, the other extremity being anchored to the central part of said curtain, and further tensioned cables adapted to cross-over in part the said first-mentioned cables passing through the lower part of said recesses and being anchored respectively to the said central part and to the lower extremity of said curtain.

5. A prestressed elongated rectilinear ground coating of concrete of substantially uniform thickness without expansion joints and comprising means interposed between said coating and the ground for producing a uniform coefficient of friction between the undersurface of said coating and the upper surface of said means, at least one transverse gap formed in said layer substantially at right angles to its greatest dimension, rigid spacing means inserted in said gap, and resiliently compressed elastic abutment means anchored in the ground for supporting the extremities of said coating in the direction of the said greatest dimension, the said elastic abutments each comprising a concrete endslab in contact relationship with the extremity of said end portion and oblique elongated and resilient anchoring means for said slab :arranged below said slab in vertical planes substantially parallel to the greatest dimension of the said coating, the said anchoring means being fast at one of their extremities with the said slab, and at their other extremities with the ground.

6. A prestressed elongated rectilinear ground coating of concrete of substantially uniform thickness without expansion joints and comprising means interposed between said coating and the ground for producing a uniform coefficient of friction between the undersurface of said coating and the upper surface of said means, at least one transverse gap formed in said layer substantially at right angles `to its-greatestl dimension, rigid spacingmeans inserted in said gap, and resiliently compressed elastic abutment means anchoredT in the groundv for supporting the extremities of said coating in ythe direction' of the said greatest dimension, including vertical pits inthe ground below said coating inthe vicinity of the gap thereof and further comprising substantially vertical cables disposed in said pits under the said' coating, the upper extremities of said cables being anchored .to the edges of `the coating adjacent the said vtransverse gap, and their lower extremities being anchored to the bot'- toms ofthe said pits.

7. A prestressed elongated rectilinear ground coating of concrete of substantially uniform thickness withoutexpansion joints and comprising meansl interposed between said coating and the ground for producing a uniform coefficient of friction between the under-surface of said coating and the upper surface cf said means, at least one transverse gap formed in said layer substantially ati right angles` to its greatest dimension, rigid spacing means inserted in said gap, and resiliently compressed elastic abutment means' anchored in ythe ground for supporting the extremities of said coating in the direction of the said` greatest dimension, at least one of the end-portions of the said coating being curved, the external edge of said-curved end portion being supported at right angles to the tangents to the said external edge by at least one elastic abutment, each of said elastic abutments comprising a plurality of Itensioned cables radially disposed with respect tothe curved external edge of said layer, one extremity of said cables being `anchored to the said external edge andl `a mass of concrete anchored inthe ground `and located near the center of curva-ture of said external edge in which lthe other extremities of said cables are anchored.

8. A method of construction of a coating of prestressed concrete on an elongated rectilinear ground area comprisingthe steps of anchoring inthe ground a resilient abutment extending generally transversely of said rectilinear area vat each end thereof, coveringY thev ground between said abutments with a leveledrlayer of material having a determined coefficient of friction with concrete, casting a concrete coating strip having definite thermal and moisture coeiiicients of expansion on said layerbetween said resilient abutments and' iny contact therewith while providing. in said coating strip substantially regularly spaced apart parallel. transverse gaps, the utmost gaps being spaced from the respective abutments by a distance which is about half the distance of two consecutive transverse gaps, exerting expanding forces in each gap, the forcesv being substantially equal yfor all the gaps, to force apart both edges of each gap until there is obtained, taking account of said coefcientof friction, resilient compression of said abutments and a longitudinall shortening of each portion of concrete strip starting from a gap and having a length substantially equal to half the distance between two consecutive gaps, which shortening is greater than the shortening ofthe said strip portion under the lowest expected thermal and'moisture conditions, and closing said gaps while in enlarged conditionv with substantially incompressible material, said concrete strip being made of adjacent elemental strips, and further comprising the steps of providing ineach elemental strip regularly spaced apart and registering transverse channels and between two adjacent elemental strips a thin wall for preventing adhesion between the said strips, providing in each elemental strip portion further transverse gaps diyiding said elemental strip portion in longitudinall sections;

References Cited in the le of this patent UNITED STATES PATENTS 2,226,201 Freyssinet Dec. 24, 1940 2,251,672 Friberg Aug. 5, 1941 2,329,189 Dill Sept. 14, 1943- 2,590,685. Coff Mar. 25, 1952 2,645,115- Abeles July 14, .1953

n FOREIGN PATENTS 623,729 Great Britain May 23, 1949