Experiments on shear transfer in cracks in concrete. Part I: Description of results

DELFT UNIVERSITY OF TECHNOLOGY

DEPARTMENT OF CIVIL ENGINEERING

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Report 5-79-3

EXPERIMENTS ON SHEAR TRANSFER IN

CRACKS IN CONCRETE

PART I: DESCRIPTION OF RESULTS

Ir. J.C. Walraven

Ir. E. Vos

Dr.-Ing. H.W. Reinhardt

STEVIN LABORATORY

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Technische Universiteit Delft

Faculteit CiTG

Bibiiotiieek Civiele Techniek

Stevinweg 1

2628 CN Delft

Technische Hogeschool Bibliotheek Afdelin-: Ci • - b Techniek •^ / «/ posujus 5348 2600 GA Delft

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EXPERIMENTS ON SHEAR TRANSFER IN CRACKS IN CONCRETE PART 1: DESCRIPTION OF RESULTS

Ir. J.C. Walraven Ir. E. Vos

Dr.-Ing. H.W. Reinhardt

u

CT

Mail address: Technische Hogeschool Delft Vakgroep Betonconstructies Stevin Laboratorium

Stevinweg k

TABLE OF CONTENTS

1. INTRODUCTION

2. EXPERIMENTS ON SPECIMENS WITH EMBEDDED REINFORCING BARS 2.1. Choice of the experimental concept.

2.2. Scope.

2.3. The test specimens.

2.U. Testing arrangements and instrumentation. 2.5. Testing procedure.

2.6. Detailed description of the test results.

3. EXPERIMENTS ON SPECIMENS WITH EXTERNAL RESTRAINT BARS 3.1. Introduction.

3.2. Test specimens.

3.3. Testing arrangements and instrumentation. 3.h. Testing procedure.

3.5. Scope.

3.6. Detailed description of the test results.

h. REFERENCES

5. APPENDICES

Technische Universiteit Delft

Faculteit CiTG

Bibliotheek Civiele Techniek

Stevinweg 1

FOREWORD

The experimental investigation described in this report is a part of the project "Betonmechanica". This project aimes to increase the applica-bility and the accuracy of computor-aided calculation programs.

The experiments described here were carried out to study the mechanism of shear transfer in cracks in concrete structures. A survey of literature on this subject was presented before (Stevinreport 5-78-12 or Report A-26 79/02). An analysis of results will be presented in a next report.

The project "Betonmechanica", and as such this paxt of it, is supervised and financially supported by the CUR, the Dutch Concrete Research Foundation.

- I - Technische Hogeschool Afdelinj: Ci i::!c Techniek

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INTRODUCTION posiLus 5Ö48

2600 GA Delft To take full advantage of the modern numerical programs, developed to

calculate the behaviour of structures under several types of loading, adequate formulations of the basic material properties are requested. After an extensive study of literature, focusing on the response of cracks in concrete to combinations of shear- and normal stresses, it was concluded that the information available on this subject was not

sufficient to enable a dependable formulation. Studying the experiments, conducted in this field, and their interpretations, it appeared that in most cases the crack displacements have predominantly been related to . the shear stress and not much attention has been paid to the role of the stress normal to the plane of cracking. However, this nonnal stress,

or formulated otherwise, the restraining stiffness normal to the crack plane, plays an essential part in the whole shear transfer mechanism. Tests on specimens with external restraining bars, the stiffness of which was known, were a.o. carried out by WHITE and HOLLEY p 10 "[ and

LAIBLE, WHITE and GERGELY r^"]- The results of these tests, however,

were bound to be inserted into the calculation of reactor vessels as a conservative approximation of the real structural behaviour. There-fore the initial crack widths, chosen in the experiments, were rather great (0.25, 0.50 and 0.75 mm) and the restraining stiffness of the

external 'hars, unbonded over the full length, was low in comparison

with what could be expected in constructions with embedded bars. Furtheron in tests with external bars dowel action is absent. At the other hand experiments with embedded bars are more difficult to inter-pret, since the restraining stiffness of the reinforcement is a function of the unknown bond properties. Because these type of experiments reflect the actual mechanism of shear transfer in cracks in the most realistic way, an analysis on basis of measurements on cracks crossed by embedded reinforcement, seems to be preferable in spite of the more complicated interpretation. Experiments of this type were conducted by MATTOCK p 3 - 8 ~[ revealing interesting features of the behaviour. However, in these tests the ultimate resistance was the main object of investigation, and the deformational behaviour was only studied by the way. Measurements of the displacements were carried out, but only at one side of the specimen and only on one place, so that no high accuracy may be expected. For the initial crack widths an average value of 0.25 mm was given for all tests.

-2-Besides on the role of the restraining force normal to the crack plane, also on the fundamental behaviour of the crack interfaces, subjected to shear- and normal forces, different opinions exist. LAIBLE, WHITE and GERGELY P 2 "] distinguished crushing of matrix material and over-riding of particles; furtheron they subdivided the irregularity of the crack surface into a global and a local roughness level. Also MATTOCK p3-8j concluded from his tests that a distinction can be made between a major and a minor roughness level. On basis of the results of his experiments he pointed out that the minor roughness, being the uneveness at sand particle level, is mainly responsible for the crack opening direction, since for different concrete types, with the same major roughness but different minor roughness, different opening directions were registrated. However, only overriding was mentioned as a possible mechanism of crack opening. Also about the role of the maximum aggregate size contradictory conclusions have been drawn. FENWICK, PAULAY f 1 J and TAYLOR f 9 ~| did not find a significant influence of the maximum particle diameter, while

WHITE, HOLLEY f 10 ] and LAIBLE, WHITE, GERGELY \~2~\ reported an increase

of shear displacement when smaller aggregate particles were used. A positive relation between the maximum aggregate size and the shear transfer in cracks is also used as an argument to explain scale effects in structures subjected to shear forces. So the fact that the shear strength of a beam without shear reinforcement is not proportional to the scale of the beam but less is attributed to the decreasing ratio between aggregate diameter and crack width when the scale of the beam is enlarged. This particular phenomenon was investigated in an other research program |_ '' 1 J •

Another point of discussion concerns the question whether the displace-ment path that the crack interfaces have passed before reaching a certain position, influences the stresses inherent to that position. The fact that in most structures in which shear forces are active, the cracks open and shear simultaneously is sometimes used as an argument to doubt on the validity of constant crack width tests.

It is obvious that a number of questions still remains to be answered. In order to reveal the effect of some of the variables and combinations of them, an experimental investigation, focusing especially on the relation between the stresses in and the displacements of cracks in several types of concretes was considered to be necessary.

-3-The experimental program developed was subdivided into two parts. In a first part,tests were carried out on specimens with a single, preformed crack, crossed by various amounts of embedded reinforcement. The variables studied in this part of the program were: the roughness of the crack inter-faces, the concrete strength, the reinforcement ratio, the influence of the bar diameter at a constant reinforcement ratio, the dowel action (eliminated or not) and the angle between the reinforcement and the crack plane. In a second part, experiments were carried out on specimens with a single preformed crack, with external restraining bars. In these specimens no dowel action existed and the external restraining stiffness could be assessed by measurements. The variables studied in this part of the program were the influence of the restraining stiffness, the concrete strength, the maximum particle diameter and the initial crack width.

-1;-2. EXPERIMENTS ON SPECIMENS WITH EMBEDDED REINFORCING BARS (SERIES A )

2.1. Choice of the experimental concept.

In previous investigations several types of specimens were used, the most important of -vrtiich are represented in Fig. 2.1.

1 1 1 1 1 ''. i

1

i Fenwick b Taylor

1 1

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d White

Mattock

-5-The experimental set up represented in Fig. 2.1.a and c was used in

tests, during which the crack width was kept constant by external forces. Since it was not known whether these tests give results, representative for cracks, opening and shearing simultaneously, none of these possibilities was chosen. Arrangement b, which facilitates the imposition of various

crack opening directions, was also considered not to be an undisputable solution, since it is not sure, whether the externally imposed opening direction is followed by the crack faces itself, because these may have a direction of preference. From the other possibilities the concept of e and f seemed appropriate for the aim pursued, as it gives the most

realistic representation of the object to be studied: a crack crossed by reinforcement and subjected to shear stresses. It might be advanced that in cracks in actual structures the reinforcement is generally stressed by a tensile force, acting in the direction normal to the crack plane. However, it must be pointed out that it is essentially the nonnal stress between the crack faces - which is the difference between the external stress and the internal stress, provided by the restraining action of the reinforcement - that is the factor whose

variation is decisive for the behaviour of the crack under shear forces. Variation of the normal stress can be obtained by a combination of varying external and internal forces, but also by variation of the internal forces alone, as such by choosing different reinforcement ratios. On basis of these arguments it was decided to carry out mono-axial tests on specimens of the type represented in Fig. 2.I.e. With this type of specimen the first series of tests were conducted. The subsequent series were carried out with specimens of the type repre-sented in Fig. 2.1.f. This type of specimen is more suitable for reinforcement, inclined to the crack plane, which was taken up as a part of the experimental program. All specimens were cracked prior to loading and were subsequently subjected to a monotonically increasing load. In some specimens the load was removed and the specimen was loaded for the second time, to see whether a detrimental effect of the first loading could be observed. It was decided to postpone tests under cyclic or fatigue loading to an eventual later program, when more knowledge of the mechanism would have been obtained.

-6-Scope. •

The experimental program reported in this chapter was designed to study the influence of several variables.

a. The reinforcement ratio.

A nimiber of series of specimens were tested, in which the amount of reinforcement, crossing the crack, was the only vsiriable. To obtain a systematic variation of the reinforcement ratio, all series (which

had a constant concrete quality), contained at least h specimens

reinforced with 2, U, 6 and 8 stirrups 0 8 mm, which resulted in reinforcement ratios of 0.56^, 1.12^, 1.68^ and 2.2W. In one series the range of reinforcement ratios was extended by adding a specimen with 2 stirrups 0 U mm (p = O . l W ) and one with 3 stirrups 0 l6 mm

(p = 3.35^) to the series. b. The bar diameter.

In two of the series seme additional tests were carried out with equal reinforcement ratios but different bar diameters: a specimen with 7 stirrups 0 6 mm (p = 1.10^) could be compared with a

speci-men with h stirrups 0 8 mm (p = 1.12^), and in an other case 2

stirrups 0 l6 mm could be compared with 8 stirrups 0 8 mm (both p = 2.23^). In this way it could be observed if an enlargement of the bar diameter at a constant reinforcement ratio, which leads

theoretically to a less favourable bond behaviovir (smaller restraint) and a slightly lower dowel action ( P 12 ~| , pp. ^^-1+5), would have an observable influence on the behaviour under loading.

c. The concrete strength.

To compare the influence of the concrete strength three mixes with the same maximum aggregate size of 16 mm were composed, which were used for different standard series. The cube crushing strengths of the series were 20, 30/35 and 56 N/mm^.

d. The roughness of the crack plane.

1. To check whether the accidental global structure of the crack plane influences the behaviour of the specimen, a number of similar speci-mens have been tested; when the, inevitably always different globaJ.

-7-crack structure would be an important parameter, this would result in different behaviour under shear loading.

2. To test whether the shear transfer behaviour of a crack is primarily a function of the minor roughness of the faces of the crack rather than the major roughness or uneveness, as was stated in | 5 ~| , a special gap graded concrete mixture was designed. The aggregate sieve line of the mix was discontinuous in this respect, that all particles with sizes between 0.25 mm and 1.00 mm were excluded, while quartz powder was added to obtain a feasible mixture. The cube crushing strength was f' = 30 N/mm^, so that this series could be directly compared with one of the standard series, with the same strength but a continuous sieve line.

3. To study the effect of the roughness, procured by the greater aggregate particles, a sanded lightweight concrete was used in one of the series, with a cube crushing strength of 3^ N/mm^. In this series a lower roughness of the crack planes could be expected, since the cracks pass through the lightweight particles, but around the sand particles. Also in the high strength standard series

(56 N/mm^ ) a decreased roughness might be expected, since in this concrete the bond strength between the cement paste and the aggreate particles is normally greater than the tensile strength of the

aggregate. As a result the cracks intersect both the gravel and the sand particles, due to which major and minor roughness are less than in concretes with average strengths.

e. The effect of an inclination of_the stirrups to the crack plane. To study the effect of an inclination of the reinforcement to the crack plane a series has been designed in which, at a constant cube crushing strength of 3^ N/mm^, 8 specimens contained all 2 stirrups 0 8 mm, but arranged at angles of 1+5°, 60°, 67.5°, 75°, 105°, 112.5°,

120 and 135 with the crack plane. f. The presence of dowel action.

To study the effect of elimination of dowel action one series of four specimens (with 2, U, 6 and 8 stirrups 0 8 mm) was tested, in which the reinforcing bars were covered with soft sleeves over a distance of 20 mm to both sides of the crack. These sleeves consisted of layers of tape (width UO m m ) , wrapped around the bars. The cube crushing

-8-strength was in the range of 3i+-3T N/mm^, so that a direct comparison with the corresponding standard series was possible. Of course it has also to be taJcen into account that the restraint stiffness normal to the crack plane is lowered by the absence of bond over the wrapped paj-t of the bar.

The test specimens.

The test specimens were, as stated earlier, of the push off type.

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[. 300 teflon ( ) ( ) ( ) ( ) ( ) 300 teflon

Fig. 2.2 Geometry of test specimens.

1).

In the first three series specimens as represented in Fig. 2.2-.,a were used, in the remaining part of the program specimens as in 2.2.b. The shear plane of all specimens wa^s 36000 mm^ (300 x 120 mm). When loaded as indicated by the arrows, shear without moment is produced in the shear

-9-plane. The reinforcement crossing the shear plane was in the form of closed stirrups, overlapped on one of the short sides. This was to ensure the effective anchorage of the reinforcement on both sides of the shear plane. The specimens were cast in horizontal wooden moulds on their sides, so that at the time of casting the shear plane was vertical (Fig. 2.3).

Fig. 2.3 Wooden mould just before casting.

On the front and rear face metal strips were casted in, to enable the attachment of measuring devices. Two days after casting the specimens were demoulded and stored in a climate conditioned room with a constant relative humidity of 95^ and a temperature of 21° C. One day before testing the specimens were transported to the testing hall. The reinfor-cement of the specimens, provided to prevent failure in other parts of the specimens was arranged according to Fig. 2.I4.

-10-type I -10-type 2

Fig. 2.k Stirrup- and additional reinforcement in both types of specimen.

Testing arrangements and instrumentation.

Prior to the tests the specimens were cracked along the shear plane by applying line loads to their front and rear faces. These loads were

applied through steel rods, pushed in V-shaped grooves, with the specimen in horizontal position (Fig. 2.5). The displacements of the specimens across the crack plane were measured during the cracking operation,

using h strain gages, attached on steel reference points, stuck on

the surface of the concrete. These displacements were continuously monitored on two recorders. When a crack was observed the load was removed. The definite crack width and shear displacement was measured with a manuel displacement gage on four places, using metal reference points, stuck on the concrete surface. The accuracy of this measure-ment was approximately 0.01 mm. A schematical representation of all

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Fig. 2.5 Precracking of a specimen.

The actual tests were carried out using a hydraulic testing machine, to load the specimen along the shear plane, as indicated in Fig. 2.6. At the bottom the specimens were supported by a roller bearing (Fig. 2.6 and 2.7). The rollers ensured that separation of the two halves of the push off specimen was not restrained by the testing machine itself.

At the top the load was induced over a so called "knife hinge". (Fig. 2.6 and 2.8). A load cell was provided between the upper plate of the testing machine and the hinge to measure the shear force imposed to the specimen. Both the crack width and the shear displacement of the crack were measured on- both sides of the specimen (Fig. 2.2.a and b ) . For these measurements use has been made of a special device, the "plate spring gage". These devices consist of two plate springs on which four strain gages are attached (Fig. 2.9). Only a displacement normal to the springs can be measured. The maximum displacement which can be measured is 5 nm. The accuracy from 0 - 1 mm is about 0.01 mm. Between each pair of measuring points two plate spring gages were combined (perpendicular to each other) so that each set could measure both the crack width and the shear dis-placement. , •

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-13-Fig. 2.7 Roller bearing under the specimen.

Fig. 2.8 Knife hinge at the top of the specimen.

105 I, strain gages ^ _ 4 l !Z_:-.' sineshaped deflection

-^k-The position of the plate spring gages on one side of the specimen is shown in the figures 2.10 and 2.11.

Fig. 2.10 Specimen under loading. Fig. 2.11 Plate spring gages over crack.

One of the shear displacements and the load, measured by the load cell, were monitored continuously on a grafical XY-recorder. All displacements, measured by the plate spring gages, were collected by a data acquisition

system, immediately after each measurement. To control the test, the crack widths, shear displacements and load were printed immediately on a teletype. A schematical representation of the measuring system used during the tests is presented in Appendix II.

2.5. Testing procedure.

a. Precracking.

As soon as the measurements over the intended crack plane indicated that a crack was formed, the load was removed. In this way initial crack widths were obtained in the order of 0.01-0.03 mm.

-15-b. The actual test.

In the actual test the specimens were subjected to a continuously increasing load. During the first three minutes the shear displace-ment rate was 0.00i+ mm/min, which was subsequently increased to 0.02 mm/min. The ultimate load was defined as the maximum load carried by the specimen during the test. After passing the top of the load-shear displacement curve the displacement rate was increased to 0.05 mm/min. The tests were ended when the shear displacement had reached a value of 2 mm. A few specimens were deloaded after passing the top of the curve, and subsequently reloaded in order to get an impression of the behaviour at repeated loading.

Detailed description of the test results.

a. Codification.

All specimens have been assigned an identifying code indicating the type of the specimen. The first number indicates the geometry of the specimen. 1 stands for a specimen of the type of Fig. 2,2.a, 2 for the type of Fig. 2.2.b and 3 for the last type but with rein-forcing bars covered with soft sleeves over a distance of 20 mm to both sides of the crack. The second number indicates the type of the mix used:

1 = Gravel concrete, D = I6 mm, f' = 30-35 N/mm^ (cube crushing strength).

max cc 00 2 = Gravel concrete, D = I6 mm, f' = 29-30 N/mm^, discontinuous grading,

II1£LX CC 3 = Gravel concrete, D = I6 mm, f' = 5 6 N/mm^ max cc h = Gravel concrete, D = I6 mm, f' = 2 0 N/mm^ max cc 5 = Gravel concrete, D = 32 mm, f' = 3 8 N/mm^ max cc

6 = Lightweight concrete, (Korlin A ) , f' = 3^^-38 N/mm^. cc

The third number was a reserve number, used during the tests themselves, but taken 0 in this report.

The fourth number indicates the number of stirrups crossing the crack plane. The fifth and sixth number indicate the diameter of the stirrups

in mm. A full survey of all tests with a detailed description of the ••• •• variables is given in Table 2.1. In this Table the maximum nominal shear

Table 2.1. Tests on specimens with embedded 'bars 1. Reinforcement normal to the crack.

Type of aggregate Code Reinf. ratio {%) P^e (N/mm2)

Amount Diam. Mix In.crack Cube Splitt. Ult.shear of stirr. width strength strength strength stirrups (mm) (mm) (N/mm^) (N/mm^ ) (N/mm^ ) Remarks G r a v e l D = 1 6 max G r a v e l D = 1 6 max d i s c o n t . g r a d i n g G r a v e l D = 1 6 max G r a v e l D = 1 6 max 110208t 110208 110208g IIOI4O8 110608 110808t 110808 110808h 1108ü8hg 110706 21020U 210608 210216 210316 210808h 120208 120i+08 120608 120808 120706 120216 230208 230^08 230608 230808 2I+0208 2Uoiio8 2ii0608 2)t0808 0 . 5 6 0 . 5 6 0 . 5 6 1.12 1.68 2 . 2 3 2 . 2 3 2 . 2 3 2 . 2 3 1.10 O.IH 1.68 2 . 2 3 3.35 2 . 2 3 0 . 5 6 1.12 1.68 2 . 2 3 1.10 2 . 2 3 0.56 1.12 1.68 2 . 2 3 0 . 5 6 1.12 1.68 2 . 2 3 2.1*3 2.1+3 2.1+3 It.86 7 . 2 9 9 . 7 2 9 . 7 2 9 . 7 2 9 . 7 2 5.58 1.06 7 . 2 9 10.12 15.17 9 . 7 2 2.1+3 1+.86 7 . 2 9 9.72 5 . 5 8 10.12 2,1+3 U.86 7.29 9.72 2.1+3 1+.86 7 . 2 9 9 . 7 2 2 2 2 1+ 6 8 8 8 8 7 2 6 2 3 8 2 1+ 6 • 8 7 2 2 1+ 6 8 2 1+ . 6 • 8 8 8 8 8 8 8 8 8 8 6 1+ 8 16 16 8 8 8 8 8 6 16 8 8 8 8 8 8 8 8 2 2 2 2 2 2 3 3 3 3 1+ 1+ 1+ 1+ 0 . 0 3 0 . 0 2 0 . 0 9 0 . 0 3 0 . 0 1 0 . 0 5 0 . 0 2 0 . 0 1 0 . 0 7 0 . 0 2 0 . 0 8 0 . 0 0 0 . 0 2 0 . 0 2 0 . 0 2 O.OI+ O.OI+ 0 . 0 1 0 . 0 2 0 . 0 2 0 . 0 3 0 . 0 5 0 . 0 2 0 . 0 3 0 . 0 2 0 . 0 1 0 . 0 1 0.01 0 . 0 1 3 5 . 9 3 0 . 7 29.1+ 3 0 . 7 3 0 . 7 3 5 . 9 3 0 . 7 29.1+ 29.1+ 3 1 . 7 36.6 36.6 36.6 36.6 2 5 . 2 2 9 . 5 2 9 . 5 2 9 . 5 2 9 . 5 2 9 . 2 2 9 . 2 5 6 . 1 5 6 . 1 5 6 . 1 5 6 . 1 19.9 19.9 19.9 19.9 2.1+ 2.1+ 2 . 2 2.1+ 2.1+ 2.1+ 2.1+ 2 . 2 2 . 2 2 . 5 . 2 . 8 2 . 8 2 . 8 2 . 8 1.7 2 . 1 2 . 1 2 . 1 2 . 1 2 . 2 2 . 2 l+.O ^ . 0 l+.O l+.O 1.1+ 1.1+ 1.1+ 1.1+ 5 . 0 8 5.50 5 . 0 8 6.1+1+ 7 . 3 9 7 . 7 8 7 . 0 8 8.39 8 . 5 8 7 . 1 9 3.22 9 . 7 2 9 . 2 5 10.11 7.97 5.36 6.53 6.78 7 . 3 1 6 . 9 2 6 . 5 3 6 . 7 2 10.83 12.56 1I+.19 l+,65 6.01+ 6 . 5 5 6 . 2 9

second loading after 1+ months initial loading rate too high failure by secondairy cracks

second loading after 5 months

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concrete strength too low by malfvinction of climate room

second loading after 5 months second loading after 5 months

second loading after 5 months

x) only the T -values for the

U

Tests on specimens with embedded bars (contd) Type of a g g r e g a t e Gravel D = 3 2 max L i g h t -weight ( K o r l i n ) Code 250208 250I1O8 250608 250808 260208 260I+O8 260608 260808 260208h 26o8o8h 310208 3IOI+08 310608 310808 R e i n f . r a t i o {%) 0 . 5 6 1.12 1.68 2 . 2 3 0 . 5 6 1.12 1.68 2 . 2 3 0.56 2 . 2 3 0 . 5 6 1.12 1.68 2 . 2 3 P^e (N/mm^) 2.1+3 1+.86 7 . 2 9 9 . 7 2 2.1+3 1+.86 7 . 2 9 9 . 7 2 2.1+3 9 . 7 2 2.1+3 U.86 7 . 2 9 9.72 Amount of St i r r u p s 2 h 6 8 2 1+ 6 8 2 8 2 1+ 6 8 Diam. s t i r r . (mm) 8 8 8 8 8 8 8 8 8 8 8 8 8 8 Mix 5 5 5 5 6 6 6 6 6 6 1 1 1 1 I n . c r a c k w i d t h (mm) 0.01 0.01 0 . 0 1 0 . 0 1 0 . 0 1 0 . 0 1 0.01 0.01 O.OI+ 0.02 O.OI+ 0 . 0 2 0 . 0 2 0 . 0 1 Cube s t r e n g t h (N/mm^) 3 8 . 2 3 8 . 2 3 8 . 2 3 8 . 2 3I+.I+ 3k.k 3I+.I+ 31+.1+ 3 8 . 1 3 8 . 1 3 6 . 1 3 6 . 1 3 6 . 1 3 6 . 1 S p l i t t . s t r e n g t h (N/mm^) 3.0 3 . 0 3 . 0 3.0 2 . 9 2 . 9 2 . 9 2 . 9 2 . 5 2 . 5 _ — -U l t . s h e a r s t r e n g h t (N/mm2) 6.83 8.69 9.65 9.91+ 6.52 1 8.62 9.79 10.36 J I+.09 8.87 5.95 1 8.15 8.81 8.91+ Remarks R e s u l t s i n f l u e n c e d by • m a l f u n c t i o n of t h e t o p h i n g e Soft s l e e v e s around r e b a r s 20 mm t o b o t h s i d e s of , t h e c r a c k i;^ '

2. Reinforcement inclined to the plane of cracking.

Type of a g g r e g a t e Gravel D = 1 6 Code 21.01+5 2 1 . 0 6 8 21.112 2 1 . 1 3 5 2 1 . 0 6 0 21.075 2 1 . 1 0 5 2 1 . 1 2 0 R e i n f . r a t i o

i%)

1.12 1.12 1,12 1.12 1.12 1.12 1.12 1.12 P^e (N/mm2) 2.1+3 2.1+3 2.1+3 2.1+3 2.1+3 2,1+3 2.1+3 2.1+3 Amount of St i r r u p s 2 2 2 2 2 2 2 2 Diam. s t i r r . (mm) 8 8 8 8 8 8 8 8 Angle w i t h Mix I n . c r a c k c r a c k p l a n e

^5°

67.5° 112.5° 135° 60° '^^o 105° 120° w i d t h (mm) 1 0 . 0 6 1 0 . 0 2 1 0 . 0 2 1 0 . 0 5 1 0 . 0 1 1 0 . 0 1 1 0 . 0 1 1 0 . 0 1 Cube s t r e n g t h (N/mm2 ) 3I+.2 3I+.2 3I+.2 3I+.2 37.6 37.6 37.6 37.6 S p l i t t . s t r e n g t h (N/mm2 ) 2 . 9 7 2 , 9 7 2 , 9 7 2 . 9 7 2.61+ 2.61+ 2.61+ 2.61+ U l t . s h e a r s t r e n g t h (N/mm2) 6 . 9 7 6 , 8 3 1+.81 2 , 9 2 7.59 7 . 2 5 5.96 l+,l+6 Remarks R e s u l t s i n f l u e n c e d by m a l f u n c t i o n of t o p h i n g e

-18-b, Materials,

For the stirrup reinforcement crossing the crack plane use has been made of Hi-Eond steel (defonned). The stress-strain diagrams for the different bar diameters are represented in Fig, 2,12,

For the concrete glacial river aggregate was used. The lightweight concrete was composed with Korlin A, an expanded clay, in combination with sand. In all mixes as cement type Portland B was used. Detailed data of the mix compositions for all concrete types (1-6) are presented in Appendix IV,

c. Presentation of results.

A.11 measurements have been worked out to grafics. From all tests a set of grafics is given; several relations are presented:

1, The average shear stress on the crack plane as a function of the average shear displacement,

2, The average shear stress on the crack plane as a function of the average crack width,

3, The relation between the displacements in normal and parallel direction (crack opening path),

All relations have been represented twice, both for small and for large displacements. This seemed to be usefull since the maximum load is generally reached at a crack width of only about 0,1+ mm, Not only because the load increase is confined to the range of crack widths between 0 and 0,1+ mm, but also since the utmost part of the cracks in actual structures, even in the ultimate loading state, is restricted to this range, it seemed to be worthwhile to focus specially on this area. In the other grafics, presenting the whole extent of displacements passed through in the tests, also the behaviour of the cracks after yielding of the steel can be studied. Note: In the grafics the term separation is used for the displacement

normal to the crack plane and slip for the displacement parallel to the crack plane,

o N/mm' _ 600 V 5 ' 0 400 200 ^

j

1

a r * 800 6 0 0 A 00 200

r

1

9 6 30 iO E in •/_ e in •/., 30 (THlam^ •00 600 CTg 4 6 0 4 0 0 200 10 / / / ^

___H

_{- ^} 0 6 20 Cr N/mm' C, 4 50 400 200 / / # 1 6 ^ ' 10 20 30 VO I E in •/„ £ in */.

-20-d. Obsei-vations during the tests.

In the first tests the reinforcement in the top and bottom parts of the specimens appeared to be too low. As a result secondary cracks were formed in the specimens with the highest amoimts of reinforcement. In one specimen (IIO808) failure occurred due to these secondary cracks, before the shear capacity of the crack plane was reached. In the next tests additional reinforcement was applied, so that none of the re-maining specimens failed before the top of the load-shear displacement

curve was reached.

In some tests of the lightweight concrete series and some of the series with inclined reinforcement malfunction of the top hinge influenced the results. This was caused by the fact that these tests were carried out in another testing machine, with only a spherical hinge at the top (Fig, 2.6). It appeared that this hinge had a frictional resistance, due to which a moment was induced on the crack plane. The points at which the frictional resistance was exceeded are characterized by short falling branches in the load-displacement curves (Fig. 2.33 and 2.35). The tests which were disturbed by this phenomenon are indicated in Table 2.1. This illustrates the sensibility of this type of tests for the loading conditions.

In none of the specimens short cracks, inclined to the main crack plane - as reported in | 5 I for similar tests - were observed. Even for 3 stirrups 0 16 mm, corresponding with a reinforcement ratio p = 3.35^, no inclined cracks were found,

o

In some of the more heavily reinforced specimens (p > ^.5%) compression

s p a l l i n g a t t h e ends of t h e crack plajie was observed ( F i g . 2 . 1 3 ) .

compression ~spaliing

Fig, 2.13 Compression spalling at the end of the cracks as observed in some specimens,

-21-The total region of spalling (top + bottom) was always smaller than 60 mm,

For the grafics the average values of the shear displacements and the crack widths were used. It appeared that, during loading, the side which was at the top during casting, exhibited a crack width which was about 20$ greater than that of the other side. For the shear

displacement no systematical difference could be observed. The measure-ments at both sides of the specimen individually did not show any

-21b-For easier reading of the grafics one set is explained below as an example: left page shear stress vs.slip: region \mtil 0.5 mm shear stress vs.separation: region until 0.5 mm right page shear stress vs.separation: whole range s l i p v s . separation: small range ' s l i p v s . s e p a r a t i o n ; whole range shear stress vs.slip : whole range

2 2 -iA 12 10

I'

£ ^ / ^ ^ ^

t

""^ M020S t X ' 1 12 10 0.1 0.2 • A (mm)slip 0.3 04

r

r ^ ^

/1

1 1 •

"T^

/ / 110208 t 0.5 0.1 0.2 W ( m m ) separation 03 0.4 0.5 » W ( m m) separation 0.1 0.2 0 3 0.4 0.5 0.6 0.7 | 0 . , < 0.3 0.4 0.5 — 0.6 0.7

N^

— -— \ 1 i X" \ \^ \ \ >\ \

1

1

\--r

\^1020^t ' W(mm) separation 0.5 1.0 1.5 2.0. < a 0.5 1.0 1 5 2.0 2.5 \ ^ \ 1 ' i 1

2 3 -14 12 10 ^ * E e Z 2

^r

[^

IJ

^010208 t • 05 W(mm) separation 1.0 1.5 2.0 2 5

m

IJ» UI ,^ £ E z M 12 10 8 6 4 2 . y'"'^ , / " / 1 /

/ /

/ / /

/

/ / '

f / '^ JT02081 ' " " ' — • * * » . . ^ • 1 05 A (mm) slip 1.0 1.5 2.0 2.5

-2k-u 12 10

I'

B E z 2 / / ___^ 110208

A'

/ / /

ÓY

12 10 r / / / / A ' * / / ^11020» 0.1 0 2 • A (mm)slip 0.3 04 0.5 0.1 0.2 0.3 W (mm) separation 0.4 0.5 . W(mm) separation 0.1 0,2 0 3 0.4 0.5 0.6 0.7 > W(mm) separation 0.5 1.0 1.5 2.0 < a 0.5 1.0 1.5 2.0 2.5 \ \ i i o 209 • : • 1 1 I .

i \ '

• ! j • ' i ! !

2 5 -1 4 12 10 8 6 4 2 / ^ 1 0 2 1

\ l

/• / / / ƒ / IS .—

-1

1 1

1 !

0.5 W(mm) separation 1.0 2.0 2 5 12 10 3 \ 6 (A 3 «< 4 Ê E z 2 > •

ri

/ / 1

i

' / ' ' 0208 1

1

0.5 A (mm) slip 1.0 1.5 2.0 2.5

F i g . 2,15 Specimen type 1, mix 1, f^^ = 30,7 N/mm^, 2 s t i r r u p s 0 8 mm,

2 6 -12 8 l/l uï 2 A

1

/l

/

y ^

h

/ n040« , / < / / 14 12 10

X

/ / ^,0,"'^ /

L

—^—\ / noios 1 _^,^ / 1 1 1 1 f / 1 / \ a i 0.2 • A (mm)slip 0.3 0.4 as 0.1 0.2 03 W (mm) separation 0.4 0.5 'W(mRi) separation 0.5 1.0 1,5

2 7 -14 12 10 «1 R IA o f. 4 £ £ z 2 noios

l/"!'

\ f'

nr

/ " ^ • ^ • -^ -^ 1 0 4 0 » * 05 W(mm) separation 1.0 1.5 2.0 2S 1 ( 12 10 l 6 E E z 2 noiOi / / / / ' ' ' / / /

1 l//y

0^

il

1

1 1 t \ ~'~-—mtoat 1 0.5 A (mm) slip 1.0 1.5 2.0 2.5

Fig. 2,16 Specimen type 1, mix 1, f' = 30.7 N/mm^, 1+ stirrups 0

cc mm.

Bibliotheek

afd. Civiela Tschniek T.H. SïGvirr.vcg 1 - Delft

2 8 -u 12 10 o «f CS E E z / / / / / / / / / / / / 110608 1 / ^ / ƒ ' / / / / f * / 01 0.2 0.3 04 • A (mm )sllp 14 12 10 ^ /' /

1

/

/ / / / ' 110606 1 1 1 05 0.1 0.2 03 W (mm ) separation 0.4 05 . W(mm>separation 0.1 0.2 0.3 0.4 . 0.5 0.6 . 0.7 < o. 0.3 0.4 0.5 0.6 0.7 \ ~. — -• -• J ^ • • ^ ? ^ •^ ^ \ n o , -• ~ -- . J 6 0 0 _ . -1 — . W(mm) separation 0.5 1.0 1.5 2.0 o. 0.5 1.0 1 5 2 0 2.5 \ ^ ^ 1 1 0 6 >• ! ' 1 ! 1 ' t ! 1 i i 1 1 i

2 9 -14 12 10 m e in o — "0609 / / ; / 1 / ; / / / ' /

1 J

0.5 W(mm) separation 1.0 1.5 2.0 2 5 14 12 10 8 • — 1I060»

/ 1

/ ; / / • 0.5 A (mm) slip 1.0 1.5 2.0 2.S

3 0 -u 12 10 £ E z 2 /

/

/

/

1/

^jj^^füt 808 110808 h< 110808 h 110208 g [ 01 0.2 0.3 A (mm)slip 12 10

/

/

^

1

/ 68 ^

/ / /

\ 110808 h 9 ^ --"_——. 1 ^ ^ 11080811 110208 q 04 0.5 0.1 0.2 W (mm ) separation 03 0.4 0.5 > W(m m) separation 0.1 0.2 0 3 >W(mm) separation 0.5 1.0 1.5 2.0 o. 0.51 1.0 1.5 2.0 2.5 ^ ^ ^ H 1 0 6 0 8 110808)^ v \ i _i 1 \ n 0 8 0 8 b g \ A t A 1 A i 1 1 Vl0208g

3 1 -14 12 10 • X - ? ' ' » 1 nnavat

r

\\f

₁

1

110808 ho Max ~-' 112208 a •

1.

0.5 W(mm) separation 1.0 1.5 2.0 2 5 K 12 -10 E E z 2 /6oao8

1

1

" ! 110208 a 05 A (mm) slip 1.0 1.5 2.0 2.5

Fig, 2.18 Specimens type 1,

110808 : mix 1, f' = 3 0 , 7 N/mm^, cc 110808h : mix 1 , f' = 29.^+ N/mm^, 8 cc 110808hg: mix 1 , f' = 29-1+ N/mm^ , 8 cc 110208g : mix 1 , f' =29-1+ N/mm^,

stirrups 0 8 mm, (secondary cracks). stirrups 0 8 mm,

stirrups 0 8 mm, stirrups 0 8 mm,

3 2 -12 10

I'

IN E E • — ^ ^

f\

i ; T10708 / f / / / / / / / / / w 1 / / r

f

0.1 0.2 ' A (mm )$tlp 12 10 / / /

x

/

A

ih

110706

71

K-/

A

1

' / 1

/> / / / / / / 0.3 04 0.5 0.1 02 03 W (mm ) separation 0 4 0.5 • W(mm) separation 0.5 1.0 1.5

-33-14 12 — 10 f. 4 E E z 2 110706

II

/!' '

\ w

/ ' ~ - \ _{^ - ^ 1 0 7 0 6 *} 1 1 i 05 W(mm) separation 1.0 1.5 2.0 2 5 U 12 10 in 4 110706 / / * / /

il'

w"

1 ' 11 1 ; ( \ 1 1 . . . 1 ^.. —_____ 11070S* 0.5 A (mm) slip 1.0 1.5 2.0 2.5

Fig, 2.19 Specimen type 1, mix 1, f' = 3 1 , 7 N/mm^, 7 stirrups 0 6 mm,

cc

slip A ( mm )4 21020 4 \ A yZ i

1

1 A

7

.. /

jy

JA

^

' / S l i p A ( m m ) . P 3 3 Q -1 t o r . T (N/mm2) shear stress 3 S 3 1^ to I *:-• X ( N/mm ^) Shear stress o t ui -o _ft , « ^ 3 lA A « 5' 3 p O p O o \ \ .

\j

•^ \

3 5 -1 * 12 10 a

i '

n * 5 * E £ Z 2 H . .

f /

1 ' /I

/ / , — _ao204 •-. • 05 W(mm) separation 1.0 1.5 2.0 2.5 12 10

f r

'J

• — - ^ 210704 ^ • — ™ ^ . . ^ _ ^ ^ _ _ ^ 0.5 A (mm) slip 1.0 1.5 2.0 2.5

Fig, 2,20 Specimen type 2, mix 1, f• = 3 6 , 6 N/mm^, 2 stirrups 0 k

-36-1 « 12 10 8 6 £

1'

z 2 w

r

y

/ •

A

/ / I

A

_{J •} 1 In / * / 5 z t-»

i

14 12 ,10 / ' ^ . — i y

i 1/

1 ^ / /

y

^ J10601

7

01 0.2 • A (mm)slip • 0.3 04 0.5 0.1 0.2 0.3 W(mm) separation 0.4 0.5 . W(mm) separation 0.1 0.2 0.3 0.4 0.5 05 0.7 • W(mm) separation 0.5 1.0 1.5 2.0 < o. 0.5 1.0 1.5 2.0 2.5 \ \ . • i \ i ^ 0 6 0 8 i \ ! i :

-37-14 12 10 •? 4 E £ z 2 / 1

l n

/ / / / /

V

no608 ^^^^ 05 W(mm) separation 1.0 1.5 2.0 2 5 12 10 £ E z 2 0.5 A (mm) stip 1.0 1.5

1 /

k

V

/l

^ _ a 0 6 0 8 _ f / : ~ - - ^ i 2.0 2.5

Fig, 2,21, Specimen type 2, mix 1, f' = 36,6 N/mm^, 6 stirrups 0

-38-12 10 3 6 5 2 Ik

I

f

'

^^

/

.

^

• _ 210216

, / ,

0.1 0.2 ' A (mm)slip 12 10 ^ /

ƒ

\ , / / ^ ^ 210216 / / .

/j

/ 1

/

/i

\ / 0.3 0 4 0 5 0.1 0.2 03 W(mm) separation 0.4 0.5 , W(mm) separation 0.1 0.2 0 3 0.4 0.5 OB 0.7 0.1 : Q . 2 0.3 0.4 0.5 0.5 0.7

\

s \ 1

- - —

> \ \ \ - 1 \ \ 210219 1

\

'

\

>W(mm) separation . 0.5 1.0 1.5 2.0 £ _£ < a 0.5 1 0 1.5 2.0 2.5 \ \ \

\

\2102,6 \

3 9 -14 12 10 E £ z 2

/ i

i

ƒ / ï r ' ~~~-2l02I6 , • 05 W(mm) separation 1.0 1.5 2.0 2 5 U 12 10 «1 4 E E Z 2

/ i

\ 1

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Ir^

1

1

1 - - ^ - ^ « 0.5 A (mm) slip 1.0 1.5 2.0 2.5

-kQ-14 12 10 / / / / " / / / / / / 210318 / ^ i 0.1 0.2 03 0.4 0.5 W (mm) separation . W(mm) separation 0.1 0.2 0.3 0.4 0.5 0.6 0.7 < CL 0.3 0.4 0.5 0.6 0.7

.-X

_^^\. \ 21031 5

-V

1

1 \ 1 >W(mm) separation 0.5 1.0 1.5 2.0 E < a.0.5 1.0 1.5 2 0 2.5 \210316 _. 1 ~

l n

-12 10 € i £ E Z 2 — ^ 210316

T

1

0.5 W(mm) separation 1.0 1.5 2.0 2 5 U 12 10 ,-."— / L 2 1 0 3 1 /

/ i

/ 1

1

\j

i y 0.5 A (mm) stip 1.0 1.5 2.0 2.5

1 + 2 -12 10 3 6 «A

1

1'

£ E z 2 . 1

Z ^

14 12 10 / / • 210808 h ..^iwawH 0.1 0.2 0.3 0.4 0.5 ' A (mm )sllp 0.1 0.2 0.3 0.4 0.5 W (mm ) separation . W(mm) separation 0.1 0.2 03 0.4 0.5 0.6 0.7 | 0 . 1 < _{a .} 0.3 0.5 0.6 \ ' '' \ \ 1 \ i — \ . _ . . _ . , . . . _ _ . -. -.-.-. \ i 1 . . _ ' \210aO8 1 • W(mm) separation 0.5 1.0 1.5 2.0 < Q.0.5 1.0 1.5 2.0 2.5

k

! \21O8O8 h • i j 1 i

1

-1;3-14 12 10 E e z 2 H / " / 210808 h 0.5 W(mm) separation 1.0 2.0 2.5 U 12 10 in 4 E E z 2 ^

y

/ /

I

„^joeoöh 0.5 A (mm) slip 1.0 1.5 2.0 2.5

-kk-14 12 10

r

_£ £

y

/ ^ ^ — /

/A

120:

Ï

110W6 ' 12 10 0.1 0.2 • A (mm)stip / ^ / / ^ ^ t2ii209 y"^

A7

/ /

(A~'

f

J'

0.3 04 0.5 0.1 0.2 W(mm) separation 0.3 0.4 0.5 . W ( m m ) separation 0.1 0.2 0 3 0.4 0.5 0.6 0.7 | o . i < o. 0.3 0.4 0.5 0.6

X

. \ 1

N.

'v ^ N^ 1208 \ \ r V \ ' > 208" \ 'S E < a 0.5 1.0 1.5 2.0 2.5 'W(mm) separation 0.5 1.0 \ \ \

-V

\ 1.5 120208 2.0

-1;5-u 12 10 UI o •S 4 — • 120208 ,

1'

"••^ ..^j2ojoe* i 05 W(mm) separation 1.0 1.5 2.0 2 5 14 12 10 8 -in 4 £ E Z 2 0.5 A (mm) stip j2i2aja_ 1.0 1.5 2.0 2.5

Fig. 2.25 Specimen type 1, mix 2 (discontinuous grading), f' = 29.5 N/mm^, 2 stirrups 0 8 mm, second loading after 5 months (-,-,-.-),

U 6 -14 12 10

I'

£ E z 2 / / / / 1 j 1 1

j

1

/ / y / / / ^ / l . " f -120*08 -ia r ;

Jr /<

A f < / \ / / / / / / / / . / ' / / / / / 1 / 1 1/ \ 1 /. ' / ' . > / ^' L- - * 1 12 10 0.1 0.2 A (mm)slip 0.3 04 / / .

Z'

^ / 1 120401 1200)8 y

71'

//

7/ • 1

-V-y-A

1 1 ' *-» 0 5 0.1 02 W ( m m ) separation 0.3 0.4 0 5 , W(mm) separation 0.1 0.2 03 0.4 0.5 Ofi 0.7 < ï O - 2 0.3 0.4 0.5 0.6 0.7 \

N

N

k

^ \

k

• V I i i 1 !

1

^ 4 2 0 4 0 8 * \ , W(mm) separation 0.5 1.0 1.5 2.0 a 0.5 1.0 1.5 2.0 2.5 ^ ^ 2 0 i O N 8

K i

\ ! '

-1+7-14 12 10 ^ 4 t»4gjii /

/ M

1

7

IA.'

K"

-^-• m 05 W(mm) separation 1.0 1.5 2.0 2 5 14 12 10 £ E z 2 «0408

/ h:

/ >i\ / '!' ƒ f tl , \ 1 II 1 f II 1 1 ' 1

1

i

^ ^ ^ - _{^ — — a o « o a *} 0.5 A (mm) slip 1.0 1.5 2.0 2.5

Fig. 2.26 Specimen type 1, mix 2 (discontinuous grading), f' = 29.5 N/mm^

cc

-kQ-12 10 8 6 4 2 / /

j

/ / / 1 ^20608 1

i,

'( / / / ^ / i / /

W JA!

/ / / ^ /i 01 0.2 0.3 04 14 12 10 / / / A 1 1 1 120^8

/]

/l />

(i

\f

-05 ' A (mm)slip 0.1 0.2 W (mm) separation 0.3 0.4 0.5 • W(mm) separation 0.1 0.2 0.3 0.4 0.5 06 0.7 'W(mm) separation 0.5 1.0 < o. ^ 0 - 2 0.3 0.4 0.5 0.6 0.7 — \ , \ X \ ^ \^20608 i

1

— u _H

-1

1 1 i 1.5 2.0 E < a 0.5 1 0 1,5 2.0 2.5 "^i^aoa ia 1 ! i ! 1 1 1 i

1

1 1

-k9-1 * 12 UI e N E £ H 120608

X i

/f

/ / '

Ijj

0.5 W(mm) separation 1.0 1,5 2.0 2 5 14 12 10 120608 / 1

il

_i

0.5 A (mm) slip 1,0 1.5 2.0 2.5

Fig. 2.27 Specimen type 1, mix 2 (discontinuous grading), f' = 29.5 N/mm^. 6 stirrups 0 8 nim.

5 0 -12 10 6 W s I 4

A

\ /

L

/ ^ / / / / / / / / >• 12C808 - I 1 ' 1 > 1 ( ( ; /120216 ' i j 0;i 0.2 0.3 04 A ( m m ) s l i p 12 10 3 6 4 2

A

/ / • 1208 18 , ; ; : : = ? -/ -/ / /

^ 1

1 1 f f f / / / t ^ 1 2 0 2 1 6 > 0 5 0.1 0.2 0.3 W ( m m ) separation 0.4 0.5 > W(mm) separation 0.1 0.2 03 0.4, 0.5 0J6 0.7 , • ^ 0 1 g0.1 < o. ^ 0 - 2 0.3 0.4 0.5 0.6 n T

A I ' '

X

V\

-X

— _ \ ^ ^ \ j 9 0 i . — ;.-.. ,, . ₁ ! . •* "• — « " •

1

i 1 — 1 -[ • 1 ->W(mm) separation 0.5 1.0 1.5 2.0 < Q.0.5 1.0 1,5 2.0 2.5 ^ ^ 2 0 8 0 8 • • 1 i 1 i

i

5 1 -14 12 10 •ü 4 • ,120808 / / '

f//

/ / 16 • , • 05 W(mm) separation 1.0 1.5 2.0 2 5 14 12 10 "1 6 Al O £ E z 2 120808

AAf^

V

II

t / / 16 • 0.5 A (mm) slip 1.0 1.5 2.0 2.5

Fig, 2,28 Specimens type 1, mix 2 (discontinuous grading}, 120808: f' = 29.5 N/mm^, 8 stirrups 0 8 mm,

cc "cc

5 2 -14 12 10

I'

£ E / / / ^

A

/ y' ^ 120708 r / I _ ^

7A7.

' A /

/y

: A

77

14 12 10 . «I /

I-I

I

I CM E E ; 2 0.1 0.2 • A (mm)slip 0.3 04 • • / ' / / A 12(9706 1 ^ ^ ^ _ .

77

/ /

(A

/

// A • 05 0.1 0.2 03 W ( m m ) separation 0.4 0.5 , W(mm) separation 0.1 0.2 0.3 0.4 0.5 0.6 0.7 • W(min) separation 0.5 1.0 • 1.5 I 0.1 < a. ^ 0 - 2 0.3 0.4 0.5 — 0.6 0.7 \

^N

> \ - "--\ "--\ 3 ^ 0 7 0 6 I

A '

2.0 <3 a 0.5 1.0 1,5 2.0 2.5 \ ^ 2 0 7 t

-53-14 12 10 m R I» " •fE 4 120706

7

1

JA

y " ' '~'~ / 1 1 / 1 ) " ~ ~ ^ - ^ 1 2 0 7 0 6 * -0 5 W(mm) separation 1.0 1.5 2.0 2 5 12 10. E E z 2 12070

( l

A

/ * ' / / ''

h' A

l' 1/ / ; / / J201D6* ' 0.5 A (mm) slip 1.0 1.5 2.0 2.5

Fig, 2,29 Specimen type 1, mix 2 (discontinuous grading), f' = 29.2 N/mm^, 7 stirrups 0 6 mm, second loading after 5 months (-,-,-.-).

-5k-14 12 10 8 6 8! s

1'

<M £ £ z 2

A

A

r ^ ^ y ^ ^ " ^ r ^ ^ 230608 230408 •<._230208 0.1 0.2 0.3 0.4 ' A (mm)slip 05 0.1 0.2 0.3 0.4 W (mm) separation 05 . W(m m) separation 0.1 0.2 • 03 0.4 0.5 :0.1 •=0.2 0.3 0.4 0.5 \ \ \ \ ^

V

230<OI 1208 |\23060a \ \ 230808 'W(mm) separation 0.5 1.0 1.5 2.0 < a 0.5 2.0 2.5 \

YT ^

V ^ 230808 \ \23O6O8 1 \j ^230408 ! 1230208 ! 1

: " 1

1 1 i 1 0 1 5 f —

-55-14 12 10 •5 4 E E z 2 /

•//A\

/ / / ^

1/ "^

/ ^ \ 230808 \ \ \

v ^ 1

V 230606 ^ 2 3 0 4 0 8 • • üolOi • 05 W(mm) separation 1.0 1.5 2.0 2.5 14 12 10 8 1 6 uï 3 .c m 4 £ £ Z 2 .^ *^ / ^

7

// / /

f'

/

/AA

/ " ^ 1 ^

A

^ 2 3 0 8 0 8 - ^ , , _ ^ > . ^ ^ ^ _ ^ ~ ~ ~ ~ - J _{..^___} • 230606 - 2 3 0 4 0 6 ' • 230208 0.5 A (mm) slip 1.0 1.5 2.0 2.5

Fig. 2.30 Specimens type 2, mix 3, f' = 56.1 N/mm^, 230208: 2 stirrups 0 8 mm,

230li08: 1+ stirrups 0 8 mm, 230608: 6 stirrups 0 8 mm, 230808: 8 stirrups 0 8 mm.

-56-14 12 10 a OJ E £

r

^ ^ ^ 240408n 240206 1 ^!4080a 14 12 10 0.1 0.2 A (mm)slip •k 4 ^

f1

'

€>

I'OCOO j4(luM 240208. 0.3 04 0.5 0.1 0.2 0.3 W ( m m ) separation 0.4 0.5 W(mm) separation 0.1 0.2 0.3 0.4 0.5 :0.1 • = 0 2 0.3 0.4 0.5 \

1

^ ^

k

A

240801 ' Y V 2 « ) 2 0 8 \ ^ • W(mm) separation 0.5 1.0 1,5 2.0 < a 0.5 1.0 1.5 2.0 2.5 7 i / i n n a » ^

1

\ \ \ \ 2403 0« 08

-57-14 12 10 -<: 4 • 7 - ^ 8 0 8

r

-I ^""^

f

• , 2 4 0 6 0 8 " ^240408 240 208 05 W(mm) separation 1.0 1.5 2.0 _2.5 14 12 10 ' 1 ^^^=^240806

r7\

! -"-^

ï

—.^240608 "^ . • 240408 240206 0.5 -A (mm) slip 1.0 1.5 2.0 _2.5 F i g . 2 . 3 1 Specimens t y p e 2 , mix U, f' = 1 9 . 9 N/mm^, 2I+O208: 2 s t i r r u p s 0 8 mm, 214-01+08: k s t i r r u p s 0 8 mm, 2U0608: 6 s t i r r u p s 0 8 mm, 2I+O808: 8 s t i r r u p s 0 8 mm.

-58-14 12 10

I*

£ £ z 2 ^ ^

A

(A

\

r l ^

250608 250608 230406 L 25020» 0.1 0.2 • A (mm)slip 12 10 ^ ^ /

1

A^

AA

250606 ' 250606 2S040S , ' I 1 2S0208 0.3 0.4 05 0.1 0.2 03 W (mm) separation 0.4 0.5 • W(mm) separation 0.1 0.2 03 0.4 0.5 , W(min) separation 0.5 1.0 1.5 < a. «0-2 0.3 0.4 0.5

\

_s^

N

\

251 <

A

2.0 < a.0.5 1,0 1,5 2.0 2.5 2 5 0 8 0 ^ ^

\

\ \

\

\

2 5 0 4 0 8 \ 250208\ •

5 9 -250808 ^ A " ^ 25060 ^ 6 250408 ~ ~ ~ 250208 0.5 1.0 1.5 2.0 2.5 > W(mm) separation 250808

[AT-

t/Y-f

^A:::^

« . ^ ^ - 2 5 0 6 0 8 ^ • 251 408 250208 0.5 1.0 1.5 2.0 2.5 » A (mm) stip

32 Specimens type 2, mix 5, f' =38.2 N/mm^ (D = 3 2 mm),

CC SICLJC 250208: 2 s t i r r u p s 0 8 mm, 250U08: k s t i r r u p s 0 8 mm, 250608: 6 s t i r r u p s 0 8 ram, 250808: 8 s t i r r u p s 0 8 mm. Bibüotheok

afd. Civiela Tschniek T.H. Stevinweg 1, - Delft

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Fig. 2,33 Specimens type 2, mix 6, lightweight concrete, 260208 : f' = 31^.1+ N/mm^, 2 stirrups 0 8 mm, 260U08 260608 cc cc co 3l*,l+ N/mm^, k stirrups 0 8 mm, 3^,1^ N/mm^, 6 stirrups 0 8 mm, 260808 : f' = 3U,1+ N/mm^, 8 stirrups oc mm, mm, influenced by malfunction of top hinge 260208h: f^^ = 38.1 N/mrn^, 2 stirrups 0 8 26o8o8h: f' = 38.1 N/mm^, 8 stirrups 0 8 mm,