cracks in RC.pdf

CRACKING IN REINFORCED CONCRETE.* B y F. G. THOMAS, B.Sc., B.Sc.(Eng.), Assoc.M.1nst.C.E. (of the Building Research Station).

T Ix'1'HOL)rCrrION.

HE problem with cracking in reinforced concrete is to elimina.te t,he formation of

cracks wherever possible and to distribute the cracking t,hat does occur so that, t,he individual cracks are not serious.

The purpose of the present paper is to indi- ca.te generally our present knowledge of crack formation and development. It em bodies some of the results that have accrued from a series of investigations relat,ing to shrinkage and strain cracking which is being carried out a t the Building Research Station under the supervision of Dr. W. H. Glanville. Parts of the work are included in the general research programme of the station while others are comprised in a scheme of co-operative research arranged with the Reinforced Concrete Associa- tion.

I ~ ( : r l ~ ~ : ~ c l ~ : ASD MEAST_-HEJII~:K'r O F (XACKS.

The Strain From the results of very Capacity of early tests of reinforced con- Concrete. crete, Considbre(l)' put forward

the hypothesis that the intro- duction of steel in a concrete member increased considerably the extension that could be under- gone by the concrete before cracking occurred. This power of extension without cracking is usually called the strain-capscity or extensibility of the concrete. In these tests, Considkre measured tensile strains in the concret,e up to two parts in a thousand (2,000 X 10 l ; ) before any cracks were noticed, whereas in parallel tests on unreinforced specimens the breaking strain was only from 0.1 to 0.2 pa.rts in :x thousand (100 to 200 X 10 l ; ) .

These results were not, however, confirmed by tests carried out by other workers a t about the same time, e.g. tests carried out for Wayss and Freytag'Y' in which the strains at the first crack were not much greater than those given by Considbre for plain concrete, and in which the quantity of reinforcement had no important influence on the strain capacity of the concrete. Similm results were ohtninetl by Kleinlogel"l', - -_ __ - - - . . . - * Crow)) copyright reserwd. t These ?lumber8 relate to the liut of refmwre*v yiven at thp

end of t?lQ papcr .

who found that for all quantities o f reinforcement the stra.in that) occurred I)efore t'he appearance of a crack was approximately the same> having LL value of from 148 to 196 X 1 0

As a result of these tests, Considkre repeat'ed his investigation(4) with larger beams, a,nd with these the observed stra.in capacity of reinforced concrete was not so great a s he had previously obta,ined. Typical strains that he obtained without cracks appearing w r c ? :-- Mernbcrs stored Ilndcr damp savks. 220 t o 500 X 10 ti.

.. . ,, wcitcr, 560 to 1.070 X 10 1;. The uncracked parts of the beam srlbjecteti

to sllch strains were cut out and test.eti, a,nd it wa.8 found that the strength was a s great as that of similar concrete that h a t 1 had no previous loading.

Bach") found tha,t in air-cured unreinforced concrete the strain capacity was from 130 to 160 x 10 Ii. With reinforced concrete the strains were in general greater. Ra,ch observed that the cracks appeared first a t t,he corners of t,he beam section, tha.t is a t t,he point, most remote from the ba.r, and then developed by extending up the beam sides and towuds the centre of the beam soffit. He gives t.he following results for a series of beams in which the distance from the corner t.0 the newest bar was compared with the resulting values of t,he strain just before a crack was observed :-- Corner Distarwe --mm. 139, 92. 46, 31. 25. 24. Strain Capavit,y- x 10 l;. 138, 139. 171, 202, 247. 241.

The strain capacity of an unreinforced member of similar concrete was 143 x 10 It will be seen, therefore, that the st,rain capacity of reinforced concrete was only increased beyond the value for phin concret,e when the corner distance was below a certain limit. .4bove t,his limit, no help was given by t,he reinforcement in resisting crack formation.

In other tests the percentage of reinforcement was varied and it. was found that, after allowing for the corner distance, t,he percentage of steel used did not materiallp affect t,he strain capacity of the concrete.

The effect of wat,er storage was found t,o increase the cracking strain as in Considbe's tests, and this effect Bach attributed to the compression stress set up in the concrete owing to the rest,raint offered by the stmeel to

('racking in Ruinforced Concretp.

J u t / . 1936 =-=--- .---- T H E S T R U C T U R A L E N G I N E E R 299

expansion. The greatest strain capacity measured was for a water stored member, reinforced with ;t steel mesh, the value being about 370 X 10';.

In all of the tests of the strain capacity that have been considered, the time factor was not introduced. Although no data are at present available as to the maximum strain that can be obtained in tension in a long time loading test, it is possible that this value will be decidedly greater than the strain capacity in a short period test. In this connection, it should be noted that at early ages when shrinkage movements are comparatively large, the creep of the concrete is also large, thus increasing the strain capacity a.t, A time when i t is most necessary.

In tests carried out at the Building Research Station, the appearance of the first crack has generally been noticed when the maximum tensile strain in the concrete due to loading reaches a value of from 150-250 X 1 0 f;. In some cases, however, the strain capacity has been little more than 100 X IO ".

Crack Unt,il it is known definitely Measure- that there is a limiting width

ment. of crack below which corrosion of thc steel does not take place,

i t is essential that the accuracy of observing crack formation and development should be the best possible. Commenting on the high values obtained by Considbre for t,he strain capacity of reinforced concrete, Bach(;') suggested that the first. crack was not observed until i t had developed considerably, owing to insufficiently accurate ohservation.

Bach himself claimed that with a smooth whitened surface, using a high powered micro- scope he could detect a crack of width l,/ZOO mm. (0.0002 in.).

H a t P used a. dye method for indicating the development of cracks. A 1 per cent. solution of methyl violet dye in alcohol was spread on part of the tension surface of the beam under test ; after cracks had opened, as indicated by the sudden increase in strain shown by extenso- meters on the beam surface, further dye was added in narrow widths for each increment of 1oa.d. Observations of the penetration of the dye on the broken sections after test determined the loads at which cracks developed.

Hatt found that with strong concrete the steel elongated when cracks developed, resulting in an immediate formation of eye-visible

Cracking in Reinforced (Toncrete.

cracks and a rapid increase in extension. With weaker concrete, the load necessary to produce cracks was not sufficient to cause elongation of the steel to the extent of eye-visible cracks in the concrete. In such cases he suggested that the use of dye would facilitate the detection of these minut,e cracks.

In other tests, Hatt used a light oil spread over the surface of the concrete to develop the appearance of cracks. In the case of repeated loading he found that the early minutme cracks that appeared even in plain concrete would open up and then spring ba.ck and close after removal of the load.

The same phenomenon was observed by Probst';) who called the opening and closing of the cracks " breat,hing." He divided t,he crack widths into two parts, viz. (i) elastic and (ii) permanent. The elastic width was the amount. tha,t the crack recovered, and the permanent width was t,he remaining widt,h, after removal of the load.

The term " elastic " is, however, not very satisfactory because it implies that the recovery in width is proportional to t,he load reduction. Probst, however, does not use it in this sense, but means the total recovery on reduction in load from one value t o another. Probst found that the " elastic " width was a high proportion, about 70-80 per cent. of the t,otal crack width.

The method of crack measurement used a t the Building Research St,ation is by means of portable microscopes with eye-piece scales fitted so that the cracks can be measured to an accuracy of about f 0.0002 in. The bea.m faces are whitened before test to help in the detection and measurement of the cracks when they appear. Various dyes are also used for showing the development. of cracks (e.g. see pa,ge 28).

SHRINKAGE CRACKING. Shrinkage of concrete is probably the most

frequent cause of cracking and also the most difficult to remedy or prevent. In the case of unrestrained reinforced concrete members the stresses set up by shrinkage are compressive for the steel and tensile for the concrete, so that even before the application of any load whatsoever the tensile strength of the concrete may be reached, with consequent cracking. After formation of the first cracks the concrete stress will develop from the crack as a result of steel-concrete bond until the tensile strength is again reached, and so the process of Rhrinkage

3CO T H E S T R U C T U R A L E N G I N E E R ====_---=- July ,

cracking becomes a continuous one, being limited only by the magnitude of the shrinkage. The effect of creep of the concrete is to reduce the concrete stresses so that in this connection creep is helpful in reducing the tendency of the concrete to crack. P u t in another way, creep produces an increased extensibility. The percentage of reinforcement clearly has an important influence, the concrete stress increasing with the quantity of steel, so that the tendency to crack becomes more pronounced with high percentages of steel.

I n practice, however, some degree of end restraint is almost always present, particularly in monolithic frameworks. The resistance of a concrete to cracking under such conditions can be obtained by two methods :-

( U ) By a study of the shrinkage, creep, elasticity and strength properties of the concrete, the combined effects being estimated mathematically from the results obtained, or

( b ) By using special apparatus to impose suitable conditions of end restraint on a specimen of the concrete.

Considering first the computation of the stresses set up in a restrained member, the case of a symmetrically reinforced member will be analysed. Let a reinforced concrete member of

concrete area A,. and steel area A," ( r = t:.) be imperfectly restrained a t its ends. In general the fixity at the ends will be such that the length L of the member is allowed to decrease by an amount proportional to the load developed in the member. Let the deformation a t each end per unit load be 6.

Then with the degree of fixity the same a t both ends, if ds is the normal shrinkage of the unreinforced concrete in an interval of time dt, dc is the creep per unit stress, f p == concrete stress (tensile) a t beginning of interval, dfp = increase in concrete stress during interval, -drv = increase in compressive stress in steel, dP = increase in end load :-

( i ) From the deformations :-,

as in the case of an unrestrained member.'") (ii) From the loads :-

and d P = dff,.Af. + dL

July, 1936 - - - ~ - T H E S T R U C T U R A L E N G I N E E R 301

AGE.

Concrete. 10 days. - 1 30 days. I 60 days. fc f flfe I fc f fc flfc f ----___----

Ordinary Portland l : 2 : 4 (by weight) with clayey sand ... ... ...

480 I 660 2.13 640 300 5.45 600 110 Ditto, with washed sand ... ... 440 390 1.45 420 290 3.27 360 110

-- f l f c -- 1.13

1.37

f" = calculated shrinkage stress in lb. per sq. in. f = modulus of rupture in lb. per sq. in.

The pure tensile. strength development was not known but the modulus of rupture is a good guide to this so that the resistance to cracking increases with flfo. It is seen from the table that this ratio is definitely lower for the concrete with very clayey sand, indicating that there will be an increased tendency for such a concrete t o crack.

A similar method of comparing resistances to cracking has been used(a) to explain the increased cracking often noticed with rapid hardening Portland cement. Calculations from the known creep and shrinkage properties of the cements showed that the induced shrinkage stresses with a rapid hardening cement rise to a greater maximum than that reached with an ordinary Portland cement. The tensile strength is somewhat increased with t$e rapid hardening cement but not to the same extent as the increase in maximum shrinkage stress ; hence increased shrinkage cracking is likely with this cement.

There is one disadvantage t o the method of computation outlined above; the creep of the concrete is assumed to be proportional to the stress. Now although this has been shown to be a reasonable assumption a t working stresses, it has been found that this assumption is quite untenable a t loads. approaching the ultimate in the case of compression members. I n tension it is possible that proportionality holds t o a greater extent, but such evidence is dificult to obtain. In view of this it seemed advisable t o obtain direct experimental confirmation of the com- putations.

Concrete members were cast in a

the concrete. Removable plates were fixed in the mould during casting, and, after taking these out when the concrete had set, the reduced section of concrete at the middle of the mould was restrained from shrinkage by the outer portions of the specimen which were still securely held by the mould. To increase the anchorage, the inside of the mould widened towards the ends, where threaded bars were also provided, so that the degree of restraint offered by the mould to concrete movement was considerable, any stresses induced in the concrete being relieved by steel movement by only about 10 per cent., this relief being taken into account in the calculations. A photograph of the apparatus is given in Figure 1.

In Figure 2, the calculated curve for the development of shrinkage stress in a partially

the cross Of Figure 1. Apparatus for comparing resistances to cracking of which was nearly three times that of restrained concrete members.

Cracking in Reinforced Concrete. C 2

302 T H E STRUCTURAL E N G I N E E R July, 1936

restrained member is compared with the actual strength of the concrete. The calculated curve shown is based on the measurements of shrinkage and creep made on specimens cast at the same time as the restrained member, together with tension and compression strength specimens. The tension specimens were of the same form as the restrained member. It will be seen from the figure that a t an age of about five weeks the calculated stress reached the tensile strength of the concrete, and assuming that the theory were correct the restrained member would be expected to crack at that age. Actually, the first crack appeared on the surface of the member a .few days later.

Although the experiment just described indicates the age a t which a concrete will crack under the conditions of restraint offered by the steel mould, it does not indicate how nearly the tensile strength is approached at ages before cracking occurs. I n view also of the variability of the tensile strength of concrete it was felt that it would be better to arrange so that the actual shrinkage stresses set up could be measured continually until tensile failure, for various conditions of end restraint.

A special apparatus was therefore designed in which concrete specimens, with extenso- meters attached to the central portion, were

I 2 3

Figure 2.

maintained under tensile loads by means of springs, and these loads were adjusted periodically so that the shrinkage movements were entirely balanced by the elastic movements and creep produced by them. A photograph of the apparatus after failure of a specimen is shown in Figure 3.

The tests included concretes with clayey sand and the results for two specimens, one with a high percentage of clay in the sand and the other with washed sand, are given in Figure 4. It will be seen that the shrinkage stresses were somewhat greater with the washed sand but that the increased tensile strength more than compensated for this, the concrete with clayey sand being less resistant to cracking. This is a direct confirmation of the conclusions obtained earlier in this paper from computation based on the shrinkage and creep properties of the concretes.

The effect of rapidity of hardening is striking. I n Figures 5-7 the results are given for duplicate tests on ordinary Portland, rapid hardening Portland and High Alumina cement concretes, a 1 : 2 : 4 mix (by weight) with 60 per cent. of water being used in each case. The shrinkage stresses are initially little different for the Portland cement concretes, but as failure is approached with ordinary Portland cement the development of stress decreases

5 6 7 8 AGE - WEEKS.

Cracking of restrained concrete memberu.

Cracking in Reinforced Concrete.

July, 1936 T H E S T R U C T U R A L E N G I N E E R 303

considerably, presumably as the result of large creep movements. This effect is not so great with rapid hardening Portland cement, the stress increasing steadily until cracking occurred. With the High Alumina cement concrete there is a rapid increase in stress, the factor of safety against cracking being negligible shortly after the commencement of the test.

Other tests have indicated that an increase of water content is not necessarily followed by a greater tendency to crack ; and that the resistance to cracking is markedly affected by the type of aggregate used. Sufficient data are not, however, available to justify any general conclusions.

It is realised that in practice complete restraint will not usually be imposed. It is possible that the relative resistances to cracking of the various concretes may be somewhat altered with the degree of fixity. For example, with a reduced degree of fixity it is possible that a rapid hardening Portland cement concrete will crack after some months, but that an ordinary Portland cement concrete will remain uncracked. Further tests are being made in which the fixity is not complete.

STRAIN CRACKING. In this section will be considered only the

condition where the tensile forces producing cracking are the outcome of directly applied loading, as in the case of tests in bending or tension. Since, also, we are primarily concerned with the effects likely to be met with in practice, consideration need be given only to such members as beams, in which cracks may be produced a t working loads.

Previous Many tests have been carried Work on out to determine the behaviour Strain of reinforced concrete beams

Cracking. under load, particularly in Germany and America, and it

is clear from these that a t design loads some cracking of the concrete is almost always present although considerable help is often given by the concrete on the tension side, particularly in the case of slabs or beams where the percentage of steel is low.

The earliest recorded work on the problem of cracking is that carried out by Consid&re(9) a t the end of the last century. Considbre tested small columns 6 cm. (2.36 in.) square and 90 cm. (35.3 in.) long, with the axes vertical,

Cracking i n Reinforced Concrete.

Fiyure 3. Measurement of shrinkage stresses in restrained concrete mem6er.s.

applying uniform bending moments throughout their length by means of cantilevered loads a t the tops of the columns, the feet being fixed. By observation of the cracks occurring when the number of reinforcing bars was increased, though keeping the total cross-sectional area of the steel the same throughout, he found that greater slip took place when the larger bars were used.

At the beginning of this century, Bach and Graf(l0) published a great deal of information on the behaviour of reinforced concrete under load. With particular reference to crack formation they tested beams with two-point loading, their results being concerned chiefly with the

304 T H E STRUCTURAL E N G I N E E R July, 1936

effects in the middle portions of the beams, where the bending moment was constant. As in the tests of Considere then, the effects of shear on the cracking were eliminated except for the shear effects of the weight of the beam itself. The beams were tested on a 2 or 3 metre (79 or 118 in.) span and the smallest cross section adopted was approximately 20 cm. X 30 cm. (7.9 in. X 11.8 in.). The ma,in results can be summarised as follows :-

(i) When the sectional area of the .tensile reinforcement was kept constant, the number of cracks increased with increase in number of bars used.

(ii) Tests to determine the effect of the steel surface showed that the cracking was greater when smooth reinforcing bars were used than when the bars were covered with mill scale. For example, in a particular case the sum of the crack widths for the same load were 4.7 mm. for the smooth .bar reinforwment and 1.2 mm.

p801 240 L

5 mol-

in the case of the beam in which the reinforcement was covered with mill scale.

(iii) Except at high loads near failure of the beam and at low loads when there was little cracking a t all, there was a rough proportionality between the width of a crack and the average distance away of the neighbouring cracks. At high loads certain cracks developed more rapidly whilst neighbouring cracks sometimes even decreased in width, and the simple relationship between crack width and distance between cracks no longer held.

(iv) It was found that the tension load carried by the concrete reached a maximum value a t the same time as the first crack appeared and then decreased to a practically constant value as the bending moment wa.s further increased.

(v) Repetition of loading. caused an increase in the number and lengths of cracks, although

OO d

2 4 6 8 70 12 / 4 16 18 20 A G E -DAYS

Figure 4 . Effect of the resistance to shrinkage cracking of clay in the sand of completely restruined rapid hardening Portland cement concrete.


J u l y , 1936 T H E STRUCTURAL ENGINEER - 305

equilibrium was reached after only a few repetitions a t design loads.

Berry), HomamP and Probst) all carried out tests to determine the efEect of repeated loading and their results confirmed those of Bach, the crack widths and lengths increasing at a decreasing rate with the number of load repetitions.

General It appears from the above Factors that the widths of cracks

Influencing formed as a result of bending Crack or pure tension in a reinforced

Formation. concrete member will depend upon the following main fac-

tors :- (a) Bar diameter = d . (b) Limiting bond stress = sbnZ. ( c ) Ratio of steel to concrete area = T . ( d ) Steel atress = t . (e) Concrete tensile strength or extensi-

The analysis of the stress distribution along the reinforcement in a cracked beam is extremely complicated and cowideration will be given first to the stresses and crack formation in a symmetrically reinforced member in which both concrete and steel are wholly in tension.

bility.

Let the number of bars = n. Area of steel = -ET- d2 = A, 4

Area of concrete = A, Distance between consecutive cracks = L

Then the steel stress will have a maximum value of t, a t the crack, decreasing with distance from the crack ; whilst the concrete stress will increase from zero at the crack to a maximum value of t, midway between cracks. The exact development of stress will depend on the way the bond stress changes along the bar. The only experimental evidence as to the bond stress distribution is that obtained a t the Building Research Station with a special tube extensometer. It was found that in general the bond stress was approximately constant over the length in which it was acting, though for a Portland cement concrete there was a tendency for the bond stress to decrease with the distance from the crack. No serious error should be involved by assuming the relation-

s, = s,,,~ ( I - $) . . . . . . . . (8) That is, the bond stress follows a parabolic

law in its relationship to x , the distance from the crack. This equation of course holds only from x = 0 to x = L/2.

Then a t a distance x from the crack, the load developed by bond will be-

,,,$,,,,(l - ~ ) d x = n ~ d s , , ( x -g:-) Cracking i n Reinforced Concrete.

3 06 -- - T H E S T R U C T U R A L E N G I N E E R July, 1936

and the corresponding steel. and concrete stresses will be

where m = EJE,. i.e., t, = t,,,, - ( 9 )

d The maximum concrete stress t,., is given

by- n x d S,, (x -- 4x3 --2) and t, = 3L

d - .

Since the steel and concrete strains tyre unequal there will be slip between the concrete and the steel, the slip E per unit length being given by :-

where E, and E, = elastic moduli of steel and concrete.

The width W of the crack at the steel is the ACE - D A M summation of the slip between cracks and there- Figure 7. Resbtance to cracking of completely fore- restrained high aluminous cement concrete.


July , 1936 T H E S T R U C T U R A L E N G I N E E R 307

- 47-8, L 3d

3t d so that L = -LE!-- . . . . . . . . . . . (13) 47-

Substituting for L inside the bracket of equation (12), we have-

L = - { t m - ?..l ( l + m r ) } . (14)

E8 8r Equations (13) and (14) give the distribution

and widths of the cracks in a symmetrically reinforced member wholly in tension. There are two effects not included in the above analysis :-

First, the concrete stress is not uniform across any section and the greatest stress, a t the steel, will be a times the average stress used above. The effect of this is to replace r in equations (13) and (14) by ar. The value of a is indeterminate but Emperger(13) states that for concrete strengths (pri8m) greater than 225 kg. per sq. cm. (3,150 lb. per sq. in.), the exposure a t the steel is equal to the outside crack width. It follows therefore that for most concretes used in practice the value of a is not far removed from unity, so that this does not appreciably affect the accuracy of the above equations.

Second, the effective elasticity of the concrete varies with the distance from the crack, the effective modular ratio m increasing as the concrete stress increases. The value of m in equation (14) is therefore the average value and may be taken approximately as 40,000 divided by the cube strength of the concrete. The value midway between cracks may be 20 or 30 per cent.'above the average value. However, the term in which the modular retio enters in equation (14) is usually small compared with the steel stress t,,,, and any error in the value of m will be relatively unimportant.

The form of equation (14) shows that the crack width is proportional to the increase in maximum steel stress beyond a certain value. This value, which is the extrapolated steel stress for zero crack width, is not the stress a t which cracking commences, since a crack will on formation have a definite width which may be considerable, particularly in the case of beams with low percentages of steel. The

position of the stress-crack width curve is, however, most readily given by the point of intersection of the curve and the stress axis. The value of the extrapolated steel stress for zero crack width is given by-

( ~ + m r ) . . . . . r

where ecm is the maximum tensile strain in the concrete between cracks. It appears therefore that the extrapolated steel stress for zero crack width may be considered as partly dependent on the tensile strength of the concrete and partly on the extensibility. For low percentages of steel the strength becomes the more important factor, but for high percentages the extensibility is the deciding factor.

In a reinforced concrete beam the problem is complicated by two main issues, (i) the effect of varying tensile stresses across a section and (ii) the influence of shear. Considering first the effect of the varying tensile forces, no analysis is possible until the distribution of tensile stress is known for all sections bet,ween cracks. It seems reasonable to assume that for the part of a member under constant bending moment the cracking at the level of the steel will be similar to that in a member under pure tension except that the percentage of reinforcement should be based on the area of concrete in tension, and a correction made for the increased ratio a of the maximum to the mean concrete stress for any section. In the case of a rectangular beam with a steel percentage p in which the ratio of the depth of the neutral axis to the effective depth of the beam is n, the equivalent ratio of steel to concrete area may be taken as-

For a T- beam of flange breadth 6, and rib breadth 6,. the ratio is-

0 . 0 1 ~ b r = ~ x - 2 . . . . . . . (1 7 4 l - nl 6,. The cracking of a reinforced concrete beam

under constant bending moment can be given roughly as-


308 T H E S T R U C T U R A L E N G I N E E R July, 1936

where r is given by equation (17) or (1 7a) above. The value of a cannot be calculated exactly with our present knowledge of the subject, but a rough estimate indicates that it will normally lie between about 1.3 and 1.8. With regard to the effect of shear, no analysis will be put forward a t present. It seems reasonable to suppose that the increased bond stresses resulting from shear will lead to increased crack widths. In the case of a simply supported beam under uniform loading this effect will tend to make the widths of the cracks more nearly equal throughout the length of the beam since the shear is a maximum when the bending moment is a minimum and vice versa.

In view of the complicated nature of the problem the use of equations (18) and (19) quantitatively will lead to a rough approxima- tion only of the cracking in a reinforced concrete beam under constant bending moment. However, the equations indicate the way in which the various factors influence the crack width. Combining equations (18) and (19) we have-

d Sb,,, r

W a 5 . -- . (t,,,, - itsrn) . . . . . (20) It is seen that if the percentage of steel is

kept constant, the crack widths are directly proportional to the diameter of the bars used. This is in agreement with the tests already mentioned.

The effect of increased bond obtained with certain bar surface conditions is to reduce the crack width, the distance between cracks being less.

The effect of increasing the percentage of steel is to distribute the cracking along the beam, individual cracks being finer. At the same time the extrapolated steel stress for zero crack width is reduced. It is seen from equation (17a) that the effect of using a T- shaped beam instead of a rectangular beam is to lead to earlier cracking, but the increase of crack width with steel stress is smaller. This appears to be a definite advantage obtained by this type of beam.

It is interesting t o expand equation (20) a little further. We have, substituting for r , if the effective depth of a rectangular beam is h-

But if C is the curvature a t the cracked section, then-

C = 28, EA1 - n1)h

. . . . . . . . . . (22) so that

Equation (23) indicates that although curvature does affect the cracking it is not so important as the steel stress. It is seen also that it is an inverse effect, i.e., increased curvature for a particular steel stress tends to distribute the cracking rather than widen individual cracks.

Building Although the appearance and Research development of cracks have Station been carefully observed in Tests. many tests on reinforced con-

crete made at the Building Research Station, these observations were usually subsidiary to the determination of other factors such as stress and deformation, and until 1933 very few measurements were made of crack widths. I n all tests on reinforced concrete members now being made, however, the widths of cracks are measured and it is hoped that at a later date a complete analysis of these measurements will provide considerable information on strain cracking. Certain general results are already available and a few of the tests in which crack measurements have been made are described below.

In one test, the beam was rectangular ip section, 4 in. wide and S& in. deep, and 7 f t . long. The tensile reinforcement consisted of two mild steel bars of 8 in. diameter a t an effective depth of 7 in., and suitable stirrup reinforcement was provided to resist shear. The beam was loaded a t third points on a 6 f t . span, the arrangement a t the loading points being such that no resistance was offered to rotation or longitudinal movement of the beam a t these points.

The side surfaces of the beam were whitened before test in order to facilitate the inspection of cracks. The appearance and progress of cracks up the side of the beam were carefully observed by eye, and the widths of each crack near the bottom of the beam and at the level of the steel were measured for every increment of


July, 1936 T H E STRUCTURAL ENQINEER 309

TOTAL CRACU WIDTH.

? a 2 5

0.25

r" U

Figure 8. Recovery of cracks.

load by means of portable microscopes with which an accuracy of about f 0.0002 could be obtained. The widths of the cracks measured near the bottom of the beam were usually 0.0003 in. on first being observed although cracks about 0.0001 in. wide could be detected by eye. The widths of all cracks were measured in order that an idea might be obtained of the general development of cracking for the beam as a whole.

The load was first increased steadily to the calculated working load and this load was maintained for 21 hours. After this period the load was gradually removed. The results of the crack measurements are shown in Figure 8. It will be seen from this figure that the total crack width (i.e., the sum of the widths of all cracks) increases to some exfent during the period under sustained load, and that on removal of the load, there is a partial recovery in crack width. It is rather interesting that on reducing the load slightly from the working value, the total crack width increased somewhat, and one or two cracks increased slightly in length.

The recovery in crack width on removal of the load is what Probst calls the " elastic


width " of the crack. In the present test the " elastic width " was on the average just over one-half of the actual width of crack. However, the term " elastic " must be used with caution for it is seen from Figure 8 that the recovery does not take place uniformly on reduction of the load, but the crack width remains practically constant during the early stages of un- loading. It is clear that before recovery can take place the slip mechanism at the steel has to be reversed and tbis reversal requires a substantial load change. The action is of course' very similar to the movements of mechanisms in which frictional resistance is bigh, when the direction of motion is altered by an external force.

The beam was left without load only for sufficient time to measure the crack widths, and was then steadily loaded to a value of l+ times the working load. This load was sustained for 44 hours, during which period very little increase of cracking occurred. The load waB then increased until failure of the beam resulted from yield of the steel.

In Figure 9, the maximum crack width a t the level of the steel has been compared with the steel stress, computed from the usual

310 T H E XTRUCTURAL E N G I N E E R July, 1936

-0 -002 -001 '906 -008 -010 -012 -014 rcMYlMUM CRACK WfDTH AT LEVEL W STEEL - INCHES

Figure 9. Dependence of maximum crack width on steel stress.

sfraight line-no tension theory. I n this figure the effects on removing the load have not, however, been included. It will be seen that there is a rough linear relationship between the crack width and the steel stress, and that the crack width is inappreciable on &st loading until a stress of about 12,000 lb. per sq. in. The relationship is of the same form as that indicated by equation (20).

The yield of the steel is shown in Figure 9 by the very sharp bend in the curve a t a stress of 47,000 lb. per sq. in. The deflection of the beam also increased rapidly at this load, but in cases where more than one layer of fer sile reinforcement is used it has been found

that the crack widths are a much better guide to the yield point of the steel than the deflection. This point was shown up well in some recent tests at the Building Research Station on two-span continuous beams. The results for one test are shown in Pigure 10. From the crack width diagrams it is seen that the yield point loads a t both the central support and in the span are quite clearly defined, but there is no definite indication of the value of these loads from the deflection curve. It is seen therefore that in such tests the measurement of the crack widths will help materially in the analysis of the test.

The effect of the percentage of the steel on the crack width when the bar size is kept constant was investigated in some tests on a high tensile steel. Ten beams were tested, all of length 9 ft. 6 in. and overall depth 103 in. Five different widths were used varying from 63 in. to 144 in., two beams of each width being tested. The tension reinforcement consisted in all cases of two compound bars each of which was made up of two 4 in. diameter round bars tw5sted together helically ; the percentage of steel varied therefore from about 0.6 to 1.4.

The beams were tested by loading a t two points symmetrically 2 f t . 6 in. apart on a span of 9 f t . The results of the measurements of the crack widths in the parts of the beams

Figure 10. Maximum crack width as guide to steel yield.

Cracking in Reinforced Concrete:.

July , 1936 - THE STRUCTURAL ENGINEER 311

AGE AT 7F.T - 14 DAn. 0 - 0 -010 e 020

Figure 11. Effect of steel percentage on crack widths.

under constant bending moment (no shear) are shown in Figure 11. The experimental points have been omitted for the sake of clearness. The following points should be noted :-

(i) The relationship between steel stress and crack width is not wholly linear. The probable reason for this is that the slope of the stress- strain curve for the steel is' not, constant for the high tensile steel tested but decreases a t high stresses.

(ii) In general, the extrapolated stress for zero crack width increases as the percentage of steel decreases. The values for this stress were :- Percentageof Steel 1.38 1.19 0.98 0.78 0.59 SteelStressforZero

CRACK WID rn - wcn

Crack Width- lb. per sq. in. ... 5,900 4,600 8,900 10,oOO 13,500 This effect tends to keep the cracks small a t

working stresses for low percentages of steel. (iii) The rate of increase of crack width with

stress is greater for low percentages of steeI. The increases in crack width between 18,000 and 40,000 lb. per sq. in. were :- Percentage of Steel 1.38 1.19 0.98 0.78 0.59 Increase in Crack

Width-in. X 10-3 3.9 5.2 6.4 7.3 8.1 This effect tends to make the cracks bigger

for low percentages of steel, particularly when the stresses are increased. beyond the values now used in design. If, therefore, for high


tensile steel, higher steel stresses are allowed leading to decreased percentages, the cracking will be increased as a result of both the increased stress and the decreased percentage if the bar size is unaltered. It should be remembered at the same time that the percentage increase of cracking is decidedly greater than the percentage increase in working stress in the steel.

It will be seen that the results of these tests are in general agreement with those expected from the use of equations (18) and (19).

Effect of An increase with time of the Prolonged widths of cracks may result

Loading on from two effects ; first, the Cracking. increase in steel stress due to a

continuous breakdpwn of the concrete in tension and to the creep of the concrete ; and second, a creep in bond causing increased slip of the concrete along the steel away from the crack. The magnitude of this second effect is unknown, but it has been shown by Shank(14) and also by Davis(15) that creep in bond exists. Shank carried out direct tests to measure such creep, but the movement on a gauge length of 20 in. was only about 200 x

in. after a year's sustained loading. On the other hand Davis measured continuous slip near the ends of loaded reinforced concrete columns amounting on a gauge length of 10 in. to nearly 8,000 X 10 in. in a year in the case of a weak concrete used with a high percentage of steel.

Measurements have been made a t the Build- ing Research Station of the increase of cracking in reinforced concrete beams, and the results for one series of tests are given in Figure 12. High tensile steel was used for two of the beams (19N and 24N) and ordinary mild steel used in the others. A t an age of 12-13 days the beams were loaded so that the theoretical maximum steel stress was 20,000 lb. per sq. in. for the plain bars and 27,000 lb. per sq. in. for the high tensile bars. The load was maintained for 6 weeks, and was then altered so that the theoretical steel stresses were increased by 50 per cent. This load was sustained for a further period of six weeks before the beams were tested to destruction. It will be seen from Figure 12 that the crack widths increased by about 50 per cent. during the early stages of the test when the cracks were extending up the sides

312 T H E STRUCTURAL ENGINEER July, 1936

of the beams and the concrete creep was comparatively large ; and that at a later age, even a t a higher steel stress, the change in crack width with time was small. PRETENSIONING OF THE REINFORCEMENT

AS A PREVENTATIVE OF CRACKING. It has been noticed in a previous section that

the strain capacity is greater in water-cured concrete than in air-cured concrete. The reason for this is clearly that the expansion of the concrete in water lead? to tension stresses in the steel reinforcement, which restricts the concrete movement, and balancing compression stresses in the concrete. This compression must therefore be destroyed before the concrete on the tension side is actually stressed in tension, and the strain capacity is evidently the sum of the strain due to the initial compression and the normal extensibility of a similar concrete without initial internal stress.

It is apparent that the higher the initial compressive stress in the concrete, the greater will be the applied bending moment necessary to produce sufficient tension to cause cracking. The possibility, therefore, of preventing cracking a t working loads by artificially obtaining

an initial concrete compression has frequently been advocated, notably by Freyssinet.(ls)

The method has been applied in the com- mercial production of precast concrete floor slabs. The tension reinforcement is stressed by means of springs or levers before the concrete is cast. The pretensioning apparatus is left in position until the concrete has sufficiently hardened to take the stresses induced in it when the forces in the reinforcing bars are allowed to be taken up by adhesion between concrete and steel. The object of this pretensioning is to reduce the normal cracking and deflection of the slabs without necessarily increasing the failing strength, and without increasing the amount of reinforcement and concrete required to withstand a given load. Since the practical usefulness of a slab is often determined by its resistance to deflection rather than its ultimate strength, it follows that successful pretensioning is of importance.

There are, however, certain difficulties. Immediately the steel load is transferred from the pretensioning apparatus to the concrete section, there is a compressive strain in the concrete resulting in a release of tensile load


July, 1936 ~ T H E S T R U C T U R A L E N G I N E E R 313

in the steel. At the same time there will be slip a t the ends of the bars over the distance required to develop the maximum steel stress, and it would be wise therefore to delay the removal of the pretensioning device until the bond strength is sufficient to reduce this distance to a fraction of the whole length of the slab. However, in the cwe of simply supported slabs, it is sufficient to ensure that the initial stresses increase from the end a t such a rate that at no point is the ratio of initial stress to the stress due to the applied working load less than that decided upon for the centre of the span.

Between the time of removing the pretensioning apparatus and applying the working load, the concrete continues to deform as a result of the creep of the concrete under the action of the internal load, and also through the normal shrinkage of the concrete. Since shrinkage tends to decrease the strain capacity of all air cured concrete, this factor does not enter into a comparison between members with and without pretensioning, but in calculating the pretension necessary to prevent cracking under a 'given bending moment the effect of shrinkage must certainly be considered. It should be noticed that since moist curing conditions reduces the creep of the concrete* and at the same time increases the extensibility, this method of curing will tend to give the best results with pretensioned beams since the decrease in the initial internal stresses will be a minimum.

In connection with some tests on a particular lightweight aggregate, four beams have been tested to determine the effect of pretensioning the tension reinforcement. The beams were 6 ft. long and of rectangular section, 4$ in. wide by 64 in. deep, with two 2 in. diameter high tensile steel bars as tension reinforcement and two 4 in. diameter mild steel bars as compression reinforcement. The concretes used were :-

Beams PT1 and PT2. Rapid hardening Portland cement concrete, 1 : 1i : 1% by volume, 1 : 0.55 : 0.54 by weight, water/ cement ratio 0.53 by weight, with foamed slag aggregate of maximum size & in. -

* Thia does not apply to Hlgh Alumina cement concretes, in which, however, the creep is m U in any m e . See Building Research Technical Paper No. 12, '' The Creep 07 Plow of Concrete under Load," by W . H . Cflanville.


Beams PT3 and PT4. As above, except that the proportions were 1 : 24 : 34 by volume, 1 : 1.10 : 1.09 by weight, water/cement ratio 0.80 by weight.

The tension bars of beams PT1 and PT4 only were stressed to an initial tension of 40,000 lb. per sq. in. before placing the concrete, and the pretensioning apparatus was left in position until an age of 14 days. All specimens were stored under damp sacks for 4 days and subsequently in air a t 64" F. and 64 per cent. relative humidity. At an age of 14 days the pretensioning device was removed from the two beams so that the steel load was transferred to the concrete. All beams were tested at an age of 28 days by loading at third points on a 5 f t . span. A very high tensile steel was used, the failing strength being 120,000 lb. per sq. in. (based on original area) ; there was no clearly defined yield point but the stress corresponding to a permanent deformation of 0.2 per cent. was 100,000 lb. per sq. in.

In the case of the first pair of beams, the yield load of the steel was not reached owing to premature bond failure of the tension bars, but for the second pair additional anchorage was provided at the ends of the beam fo prevent this. The failing loads were :-

Beam PT3 (without pretension) . . . 2.25 tom Beam PT4 (with pretension) ... 2.33 tone

equivalent to theoretical steel stresses of 104,000 and 108,000 lb. per sq. in. The pretensioning had thus no effect on the failing strength of the beam. This is in agreement with the results of previous tests at the Building Research Station on pretensioned beams.

The results of the deflection and crack width measurements for the second pair of beams are given in Figures 13 and 14. It will be seen that the pretensioning of the steel in beam PT4 markedly affected the deformations of the beam. Similar results were obtained for beams PT1 and PT2 except that steel failure in tension was not reached. The main results for all beams are given in Table 1. At a steel stress of 25,000 lb. per sq. in., calculated according to the usual no-tension theory, there were no cracks in the pretensioned beams but those in the other beams had reached widths of 0.003 and 0.005 in. The deflection a t this stress was reduced as a result of the pretension to 6 and $ of the deflection of the beams without pretension. In order to obtain the same deflection and crack widths as those

314 Z- - T H E S T R U C T U R A L E N G I N E E R - July, 1936

S" k h4 g 0 1

2-16

I I I 0 0 10 0 200 300 400 500 600 700 800

X-X ~ r 4 . Q-Q PT3

DEFLECTION AT MID-SPAN. - INCH x IOe3 Figure 13. Effect of pretensioning on deflection.

CRA CK WID m - / N c H Figure 14. Efect of pre:ensioning on crackvac.


July, 1936 T H E STRUCTURAL ENGINEER 315

that were in the beams without pretension a t a steel stFess of 25,000 lb. per sq. in., the pretensioned beams had to be loaded to about twice- this value.

It is clear therefore that pretensioning of the reinforcement is extremely useful in reducing deflection and cracking. It will be noticed, however, that the increase in stress to give the aame conditions as in the beams without pretension was about; 25,000 lb. per sq. in., and not 40,000 lb. per sq. in. which was the original pretension applied to the steel. Less than two thirds of the nominal pretension was effective at the time of loading. The reason for this is that the initial strain in the steel is reduced as a result of concrete. deformation when the load is transferred from the pretensioning apparatus to the concrete and by subsequent creep of the concrete. The concrete strengths (see Table I) were high compared with those usually obtained with light weight aggregates so that the reduction in pretension resulting from concrete deformation must be seriously considered when estimating the efficiency of pretensioning when such aggregates are to be used. It is interesting to note that quite strong concrete was obtained in these tests with a reduction in concrete weight of over 20 per cent. below that normally obtained in reinforced concrete work (see Table I).

THE POSSIBILITY OF CORROSION OF THE REINFORCEMENT AS A RESULT OF CRACKING.

It is evident that cracking will be present to some extent in most reinforced concrete members subjected to bending and the question arises as to whether such cracking is in any way harmful. Some cracking may be so developed as to be unsightly and for this reason alone cannot be tolerated, but what of the smaller cracks which can be seen only on close inspection of the member or even those which can be discovered only with a micro- scope ?

In a report by Faber on the effectiveness of various steels for road slab reinforcement(17), he stated that there is a limiting width of crack below which attack of the reinforcement is prevented, and although evidence was not a t the time given, it certainly seems reasontlble to suggest that many very fine cracks that occur in reinforced concrete are in no way harmful.

It is of importance to limit the size of cracks, and from an earlier section of this note it is clear that this can to some extent be effected by :-

(i) Increasing the surface area of the reinforce-

(ii) Increasing the bond resistance between con- ment, or

crete and steel.

TABLE I.-EFFECT OF PRETENSIONING REINFORCEMENT OF FOAMED SLAG CONCRETE BEAMS. -

BEAM NO. 1 PT1* PT2 PT4* PT3 sq. in. . . . . . . . . . . . . . . . . . . . . . . . . inch I o 0.005 0 0.003

Crack width at steel stress, due to external load, of 25,000 lb. per

Steel stress at which cracking started . . . . . . . . . lb./sq. in. I 35,000 Steel stress in pretensioned beam to give same crack widths as in

14,000 35,000 17,000

beam without pretension at 25,000 lb. per sq. in.. .. lb./sq. in. i 55,000 - - I 52,000 Deflection at mid span at steel stress of 25,000 lb. per sq. in. inch , 0.019 i 0.054 1 0.018

Steel stress in pretensioned beam to give same deflection as in beam !

0.080

Weight of concrete per cubic foot . . . . . . . . . . . . lb. -i 115 Concrete strength (4 in. cube) . . . . . . . . . . . . Ib./sq. in. Average bond strength obtained with a t in. high tensile steel bar 14 days 330

lb.!sq. in. ; 28 days 320

without pretension at 25,000 lb. per sq. in. ... lb./sq. in. 48,000 I - 1 47,- ll0 4,900 i 310

l

-

3,800

embedded in concrete cylinder, 3 in. diameter, 6 in. long 350

~- I-__ - _~ * With tension steel pretensioned to 40,000 lb. per sq. in. (nominal).


316 - T H E STRUCTURAL E N Q I N E E R July, 1936

That is to say, the use of rough bars of small section will tend to distribute the cracking throughout the member, the individual cracks being finer. The exact extent to which cracking may be permitted without detriment to the structure is, however, unknown at the present moment and can only be determined as the result of further investigation.

The uae of deformed bars may in some cases help by providing an increased bond resistance, but in the case of several types of deformed bars the local increases in stress intensity a t sharp bends or corners tend to produce cracks a t these points, thereby increasing the cracking and at the same time reducing the bond between bar and concrete.

A type of reinforcement which has met with favour on the Continent consists of two mild steel bars twisted together. It is claimed that this treatment increases the yield point of the steel, and the bond strength when embedded in concrete, and distributes the cracking along the member, so that the individual crack widths are smaller than those obtained with ordinary bar reinforcement. Tests at the Building Research Station on this steel have shown, however, that although there is a marked increase in yield stress, the difference between the cracking obtained with this steel and that obtained with ordinary mild steel for the same steel stress is not pronounced until the ultimate stress is approached.

It has been suggested that with this steel, the fine cracks (0.002 to 0.003 in.) that occur a t 27,000 lb. per sq. in. do not penetrate to the steel. I n order to test this idea, two bars were specially tested at the Building Research Station. Each bar was embedded in concrete, using a cover equal to the diameter of the bar (4 in. and in.). The embedded bars were loaded to a stress of 27,000 lb. per sq. in. and a container was then fixed round the centre of the specimen and a green dye (naph- thol green) poured in. This dye was allowed to penetrate the cracks in the concrete for a period of about 30 minutes and was then removed. The specimen was left for 90 minutes to allow the dye to dry and the load was then continued until yield of the steel. On the removal of the specimen from the testing machine and breaking the concrete away from the bar, it was found that the dye had pene- trated the cracks in the concrete and had reached the steel, actually leaving a green stain on the bar. The assumption that the dye

had dried out before the load was increased was justified by the fact that when the concrete was broken, the dye was absolutely dry and the time of loading from 27,000 lb. per sq. in was only a few minutes. The dye was not absorbed by the concrete and only appeared. along the sides of a crack. Similar results were later obtained from tests on plain bars a t a stress of 20,000 lb. per sq. in., for crack widths of about 0.002 in. even when the time of drying out was increased to 4 days. This is direct evidence that cracks a t working loads in reinforced concrete penetrate right to the steel ; that is, there is some slip a t the bar surface.

Kriiger(lR) reports the results of exposure tests on some reinforced concrete T-beams left in the open for over 10 years. The beams were 20 cm. deep with flange and rib widths of 16 and 8 cm. respectively. The beams were supported on a span of 160 cm. at an age of 3 days and at 28 days were loaded to twioe the design load giving a theoretical steel stress of 28,000 lb. per sq. in. Two arrangements of reinforcement were used : in one type, one bar of 1 cm. diameter was used with a vertical and horizontal cover of 3.5 cm. and in the other type two bars of 0.7 cm. diameter were used with only 1 cm. cover. In all cases rusting of the steel was apparent after a few years, but even after ten years when the reinforcement was exposed the rusting'had clearly had no appre- ciable weakening effect on the steel. The rusting was about the same for the two types of reinforcement. However, it is possible that the effect of using smaller bars in the second type was counterbalanced by the decreased cover. The load was applied a t the centre of the span and this is a definite disadvantage in a'itest on cracking since the reduction in stress from midspan outwards is too rapid, particularly when, as in this case, the ratio of span to beam depth is low, the number of cracks being less than would be obtained with two point or uniform loading. The greatest disappointment with regard to the tests, however, is that no measurements of the widths of the cracks were apparently made, so that there is no direct guide as to the safe limit of cracking.

In an accelerated corrosion test, Rengers(lY) measured the widths of cracks remaining in a hollow pile after testing it transversely. He submitted the pile to repeated immersion in a 1 per cent. brine solution with intermittent periods of dry storage. After five months'


July, 1936 T H E STRUCTURAL ENGINEER 317

treatment in this way the pile was examined. It was found that rusting did not occur in the case of three cracks less than about 0.004 in. wide, that there was definite indication of corrosion in the case of one crack of width varying from 0.012 to 0.04 in. although there was no corrosion with another crack of width 0.02 in., and that rusting was pronounced with a large crack of width 0.04-0.08 in.

Probst(20) also carried out accelerated tests, using rectangular beams which were loaded in a special apparatus in which corrosive gases could be passed over the beams. During the day-time the beams were submitted to the combined action of steam, oxygen and carbon dioxide and the beams were removed a t night and left with the cracks exposed to the air. After some days of this treatment, the steel was exposed and carefully examined. Probst found that up to a given load, corresponding to a steel stress of about 35,000 lb. per sq. in., the corrosive substances used in the tests had no effect on the steel. A rusting effect was obtained only when the failing load was approached. The rusting was sometimes con- centrated along the lines where the cracks crossed the steel ; in other cases the rust

spread over the reinforcement and was not confined to the lines of the cracks. It is un- fortunate that here, as in Kriigers tests, no crack widths are given. J

It is felt that the only satisfactory method of obtaining the limiting crack width below which the possibility of corrosion can be ignored is by actual exposure tests on reinforced concrete members in which the widthe of all cracks are measured periodically. A series of such teats has already been started at the Building Research Station but useful results are not likely to become available for some considerable time.

HEALING OF CRACKS. We have seen in an earlier section that it has

been stated that cracking, due to direct stress, is to some extent elastic, i.e., the cracks recover when the load is removed, or, as Probst says, the cracks breathe. Tests at the Building Research Station have shown however that this idea of elasticity of cracking must be treated with caution.

I n practice it has been noticed that cracks do in some cases tend to heal with time. For example, if concrete specimens are tested to failure but not to absolute collapse and after-


:3 l 8 THE STRUCTURAL E N G I N E E R - July, 1936

-wards allowed to remain under no load for some time and then retested, the specimen may be found to have a strength even greater than its original strength. Some striking figures in this

.connection were put forward by Professor Duff AbramsC2l) a few years ago. He had -tested a number of concrete cylinders to failure, and retested them after a period of 'sdme years ; they not only took as much load as they had originally taken, but gave values from 167-379 per cent. of the original 28-day strength. Abrams' opinion was that -the small cracks which opened up at the time of the original test were actually welded together by the subsequent depositing of the soluble materials from the cement and aggregate. It -was actually a healing process, and the concrete -gained in strength much as it would if it had not been subjected to its original load.

Tests carried out at the Building Research ,Station have confirmed the results of Abrams .cited above. The tests were on 8 in. X 4 in. -cylinders which were retested a t quite short periods of either water, damp sand or air

istorage after loading to failure. The cylinders were tested in a hydraulic teeting machine and were not shattered under test. The results of a few of the tests which may be -regarded as typical are given in Figure 15. I n this figure which relates to Portland

*cement concretes of various consistencies, the strengths obtained on first testing are com- -pared with the strengths on retesting after a period of 7 days and again at 28 days from the initial test. From this figure it will be seen

.that the healing is greater for concrete initially

.crushed a t early ages than for older concrete. I n most cases a period of only 7 days is sufficient for the concrete to heal sufficiently to bear a t least the load that caused failure originally and that only in the case of concrete initially

-tested a t 90 days is the period of 28 days insufficient, and even here the difference in .ultimate strengths is not very much.

Similar results were obtained with several batches of cement including aluminous cement. I n general, it was found that : ( a ) the leaner and more permeable the mix, the greater the amount of healing, and ( 6 ) the wetter the mix, the greater the amount of healing.

In tests carried out some years ago on the .effect of impact on small reinforced concrete members i t was found that the shrinkage stresses set up in a member were reduced ,considerably by impact loads. In almost

all cases, the shrinkage stress was actually reduced to zero after a few hundred blows, applied longitudinally or transversely.

Although the steel gradually increased in length to its natural value, there was, however, no relative movement between the concrete and steel a t the ends of the member. It followed therefore that the stress release had occurred by movement or slip in the length, probably in all cases, and definitely in some, a t cracks. Such cracks are a common occurrence when impact loads are applied to reinforced concrete members in which the shrinkage stresses are high. It is interesting to note, however, that if fine cracks occur a t an early age as a result of impact they will tend to heal with time provided that the loading conditions are subsequently less severe, For example, in a reinforced concrete pile, fine cracks almost always appear during driving, but these are in general not serious, as they will gradually heal under the subsequent conditions of practically static loading. Certain tests have been made at the Station to investigate this matter. Small piles were cracked in a testing machine before subjecting to severe sea-water conditions. After a period of four years no sign of corrosion a t the cracks has appeared and except for the location marks applied at the beginning of the test it would be impossible to locate them.

SUMMARY.

Incidence The strain capacity of con- and Crete, i.e., the extension that

Measurements can occur without the forma- of Cracks. tion of cracks, has been deter-

mined by many investigators with widely different results. The lack of agreement is probably due to two main reasons : (i) variation in the initial stress conditions in the members before test, and (ii) variation in the accuracy of observing the appearance of cracks.

It appears that the effect of reinforcing steel is normally to increase the strain capacity of the concrete by only a small amount ; when reinforced concrete members are stored in air, tensile stresses are set up in the concrete as a result of shrinkage, with an adverse effect on the subsequent strain capacity when the member is loaded. On the other hand, the presence of the reinforcement may lead to a considerable increase of the effective strain capacity under conditions of moist curing.


July, 1936 -- T H E S T R U C T U R A L E N G I N E E R 3 19

It is likely that the apparent increase in strain capacity due fo the reinforcement observed by some workers was partly the result of insufficiently accurate observation of the appearance of the first crack. In tests at the Building Research Station, with a smooth whitened surface it has been found possible to detect cracks 0.0001 in. in width by eye, though normally the cracks are a little wider when they first appear. Crack widths are measured in all tests on reinforced concrete members, using portable microscopes with eye- piece scales.

Shrinkage A method has been devel- Cracking. oped whereby the shrinkage

stresses in restrained concrete members can be measured until cracking occurs. It has been shown that there is a tendency for the resistance to cracking to decrease as the rapidity of hardening of the cement used increases. The type of aggregate used has an important influence on the likeli- hood of cracking ; but variations of the cement or water contents within practical limits for reinforced concrete work do not appear to affect shrinkage cracking appreciably.

Strain Early tests on reinforced Cracking. concrete members indicated

that reduction of the size of individual cracks could be effected by using smaller bars with a high bond resistance. This is shown to be in agreement with a simple theory of cracking given in the paper. This theory indicated that, for a particular bar size, the crack widths would increase with steel stress more rapidly for low percentages of steel and this has been verified by tests on beams with high tensile steel reinforcement.

The increase in crack width that would result from an increase in the working stresses in the tension steel may proportionately be considerably greater than the increase in stress, particularly as the percentages of steel normally used would tend to be reduced. The adverse effect of the reduced percentage can, however, be nullified by the use of smaller bars.

The suggestion put forward by several investigators that cracks are to some extent " elastic "-that is, they recover somewhat when the load is removed-has been confirmed, but it is clear that the term " elastic " is not very satisfactory. The cracks do recover when


the load is completely removed but the recovery is not proportional to the reduction in load. In fact, a reduction of one half .of the load may cause no change a t all in the crack widths, owing to the hysteresis due to the change in direction of the slip mechanism at the steel- concrete interface.

It has been found that there is a considerable development of cracking in beams submitted to sustained loading, though a state of equili-, brium is reached after a few weeks from loading. This development is probably the combined effect of the increase in steel stress resulting from creep of the concrete, and of creep in bond.

Pre- The possibility of preventing tensioning. cracking at working loads by

pretensioning the reinforcement has frequently been advocated, notably by Freyssinet. Tests made a t the Building Research Station, in which an initial pretension of 40,000 lb. per sq. in. was applied to the tension steel of beams, have shown that the effect of the elastic and inelastic movements of the concrete may reduce appreciably the effectiveness of pretensioning. I n the particular tests cited, the pretensioning apparatus was removed at an age of 14 days, and the beams were loaded at an age of 28 days. The effective pretension had during the intervening period been reduced by concrete deformation to only about two-thirds of its original value. This reduction must be seriously considered when using pretensioning as a means of preventing cracking.

Corrosion. It has been suggested that there is a limiting width of

crack below which corrosion of the reinforcement will not take place. Although this seems reasonable, satisfactory evidence on this point has yet to be obtained. It is felt that the best way to do this is by actual exposure tests on loaded reinforced concrete beams, and such tests have been started at the Building Re- search Station, measurements being made of the progressive cracking of the beams. The usefulness of exposure tests by certain other investigators has been severely restricted owing to the lack of data with regard to the widths of the cracks.

Healing of The autogenous healing of Cracks. cracks has been investigated

by several writers, and a series of tests has been made a t the Building Re-

320 T H E S T R U C T U R A L E N G I N E E R July, 1936

search Station which indicated that fine cracks in concrete members often heal completely with time. The healing process takes place to some extent in air, but is more complete in moist curing conditions. It seems likely that fine cracks formed at an early age as a result of impact (e.g., in reinforced concrete piles) are not in general serious, as they will gradually heal under the subsequent conditions of practically static loading. Cracks formed in piles at the Building Research Station before subjecting them to severe sea-water conditions had no adverse effect on the piles and after four years could not be detected.

REFERENCES. 1. Considdre, A . Influence of metallic reinforce-

ments on the properties of mortars and concretes : GBnie Civil, 1898-9, 34 (14), 213-6 ; (15)

2. Tests for Ways8 und Freytag, A . G. See Morsch, E., Der Eisenbetonbau. 6th edition, 1923, 1,

3. Kkinlogel, A . Extensibility of plain and reinforced concrete due to bending stresses. Beton und Eisen, 1904, 3 (2), 89-98, or Forscherarbeiten aus dem Gebiet des Eisenbetons, 1904 (1).

4. C&dre, A . Extensibility of reinforced concrete. Beton und Eisen, 1905, 4 (3), 58-9.

5. Bach, C. Mitt. uber Forschungsarbeiten, 1907 (pp. 39, 45-7), and see Stuttgarter Versuche uber die Dehnungsfiihigkeit des Betons, in Morsch, E., Der Eisenbetonbau, 6th edition, 1923, 1 (l), 111.

6. H&, W . K . Extensibility of Concrete. Am. Conc. Inst. Proc. 1926, 22, 364-85.

7. Probet, E . The Influence of Rapidly Alternating Loading on Concrete and Reinforced Concrete. Struct. Eng., 1931, 9, (12), 410-32.

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MNEMONIC NOTATION FOR ENGINEERING FORMULFE.

The above report, which was drawn up in engineering are printed on pages 25, 26 and 1918 by the Science Committee of the Concrete 27. The few cases where this Institution Institute, has now been withdrawn from the uses symbols or abbreviations which vary list of publications of the Institution. In from those contained in the British Standard British Standard Specification No. 560/1934 Specification, are set out in a note a t the foot the standard symbols to be used in structural of page 27 of the Specification.


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