European Union – Brite EuRam III

Tensile strength as design parameter

EuroLightCon

Economic Design and Construction with

Light Weight Aggregate Concrete

Document BE96-3942/R32, June 2000

Project funded by the European Union

under the Industrial & Materials Technologies Programme (Brite-EuRam III)

Contract BRPR-CT97-0381, Project BE96-3942

The European Union – Brite EuRam III

Tensile strength as design parameter

EuroLightCon

Economic Design and Construction with

Light Weight Aggregate Concrete

Contract BRPR-CT97-0381, Project BE96-3942

Document BE96-3942/R32, June 2000

Although the project consortium does its best to ensure that any information given is accurate, no liability or responsibil-

ity of any kind (including liability for negligence) is accepted in this respect by the project consortium, the authors/editors

and those who contributed to the report.

Acknowledgements

The report has been written by Erik Thorenfeldt, SINTEF

Information

Jan P.G. Mijnsbergen, CUR, PO Box 420, NL-2800 AK Gouda, the Netherlands

Tel: +31 182 540620, Email: jan.mijnsbergen@cur.nl

Information on the EuroLightCon-project and its partners: http://www.sintef.no/bygg/sement/elcon

ISBN 90 376 02 58 4

The European Union – Brite EuRam III

Tensile strength as design parameter

EuroLightCon

Economic Design and Construction with

Light Weight Aggregate Concrete

Contract BRPR-CT97-0381, Project BE96-3942

Document BE96-3942/R32, June 2000

Selmer Skanska AS, NO

SINTEF, the Foundation for Scientific and Industrial Research at the

Norwegian Institute of Technology, NO

NTNU, University of Technology and Science, NO

ExClay International, NO

Beton Son B.V., NL

B.V. VASIM, NL

CUR, Centre for Civil Engineering Research and Codes, NL

Smals B.V., NL

Delft University of Technology, NL

IceConsult, Línuhönnun hf., IS

The Icelandic Building Research Institute, IS

Taywood Engineering Limited, GB

Lias-Franken Leichtbaustoffe GmbH & Co KG, DE

Dragados y Construcciones S.A., ES

Eindhoven University of Technology, NL

Spanbeton B.V., NL

Tensile strength as design parameter

BE96-3942 EuroLightCon 3

Table of Contents

PREFACE 4

SUMMARY 7

1 INTRODUCTION 8

2 TENSILE STRENGTH AND BRITTLENESS OF CONCRETE 10

2.1 Tensile strength of normal weight concrete 10

2.2 Tensile strength of LWA concrete 12

2.3 Brittleness 15

3 SHEAR STRENGTH OF SLABS 16

3.1 Shear capacity equations in design codes 16

3.2 Comparison with test results 17

4 BOND STRENGTH 20

5 MINIMUM REINFORCEMENT AND DETAILING OF MEMBERS 21

6 OTHER COMMENTS TO PREN1992-1 SECTION 10 - 1

ST

DRAFT 22

7 NOMENCLATURE 23

8 REFERENCES 24

APPENDIX 25

Tensile strength as design parameter

BE96-3942 EuroLightCon 4

PREFACE

The lower density and higher insulating capacity are the most obvious characteristics of Light-

Weight Aggregate Concrete (LWAC) by which it distinguishes itself from ‘ordinary’ Normal

Weight Concrete (NWC). However, these are by no means the only characteristics, which jus-

tify the increasing attention for this (construction) material. If that were the case most of the de-

sign, production and execution rules would apply for LWAC as for normal weight concrete,

without any amendments.

LightWeight Aggregate (LWA) and LightWeight Aggregate Concrete are not new materials.

LWAC has been known since the early days of the Roman Empire: both the Colosseum and the

Pantheon were partly constructed with materials that can be characterised as lightweight aggre-

gate concrete (aggregates of crushed lava, crushed brick and pumice). In the United States, over

100 World War II ships were built in LWAC, ranging in capacity from 3000 to 140000 tons and

their successful performance led, at that time, to an extended use of structural LWAC in build-

ings and bridges.

It is the objective of the EuroLightCon-project to develop a reliable and cost effective design

and construction methodology for structural concrete with LWA. The project addresses LWA

manufactured from geological sources (clay, pumice etc.) as well as from waste/secondary ma-

terials (fly-ash etc.). The methodology shall enable the European concrete and construction in-

dustry to enhance its capabilities in terms of cost-effective and environmentally friendly con-

struction, combining the building of lightweight structures with the utilisation of secondary ag-

gregate sources.

The major research tasks are:

Lightweight aggregates: The identification and evaluation of new and unexploited sources spe-

cifically addressing the environmental issue by utilising alternative materials from waste. Fur-

ther the development of more generally applicable classification and quality assurance systems

for aggregates and aggregate production.

Lightweight aggregate concrete production: The development of a mix design methodology to

account for all relevant materials and concrete production and in-use properties. This will in-

clude assessment of test methods and quality assurance for production.

Lightweight aggregate concrete properties: The establishing of basic materials relations, the

influence of materials characteristics on mechanical properties and durability.

Lightweight aggregate concrete structures: The development of design criteria and -rules with

special emphasis on high performance structures. The identification of new areas for applica-

tion.

The project is being carried out in five technical tasks and a task for co-ordination/management

and dissemination and exploitation. The objectives of all technical tasks are summarised below.

Starting point of the project, the project baseline, are the results of international research work

combined with the experience of the partners in the project whilst using LWAC. This subject is

dealt with in the first task.

Tensile strength as design parameter

BE96-3942 EuroLightCon 5

Tasks 2-5 address the respective research tasks as mentioned above: the LWA itself, production

of LWAC, properties of LWAC and LWAC structures.

Sixteen partners from six European countries, representing aggregate manufacturers and suppli-

ers, contractors, consultants research organisations and universities are involved in the Eu-

roLightCon-project. In addition, the project established co-operation with national clusters and

European working groups on guidelines and standards to increase the benefit, dissemination and

exploitation.

At the time the project is being performed, a Working Group under the international concrete

association fib (the former CEB and FIP) is preparing an addendum to the CEB-FIP Model Code

1990, to make the Model Code applicable for LWAC. Basis for this work is a state-of-the-art

report referring mainly to European and North-American Standards and Codes. Partners in the

project are also active in the fib Working Group.

General information on the EuroLightCon-project, including links to the individual project part-

ners, is available through the web site of the project: http://www.sintef.no/bygg/sement/elcon/

At the time of publication of this report, following EuroLightCon-reports have been published:

R1 Definitions and International Consensus Report. April 1998

R1a LightWeight Aggregates – Datasheets. Update September 1998

R2 LWAC Material Properties State-of-the-Art. December 1998

R3 Chloride penetration into concrete with lightweight aggregates. March 1999

R4 Methods for testing fresh lightweight aggregate concrete, December 1999

R5 A rational mix design method for lightweight aggregate concrete using typical UK ma-

terials, January 2000

R6 Properties of Lytag-based concrete mixtures strength class B15-B55, January 2000

R7 Grading and composition of the aggregate, March 2000

R8 Properties of lightweight concretes containing Lytag and Liapor, March 2000

R9 Technical and economic mixture optimisation of high strength lightweight aggregate

concrete, March 2000

R10 Paste optimisation based on flow properties and compressive strength, March 2000

R11 Pumping of LWAC based on expanded clay in Europe, March 2000

R12 Applicability of the particle-matrix model to LWAC, March 2000

R13 Large-scale chloride penetration test on LWAC-beams exposed to thermal and hygral

cycles, March 2000

R14 Structural LWAC. Specification and guideline for materials and production, June 200

R15 Light Weight Aggregates, June 200

R16 In-situ tests on existing lightweight aggregate concrete structures, June 200

R17 Properties of LWAC made with natural lightweight aggregates, June 2000

R18 Durability of LWAC made with natural lightweight aggregates, June 2000

R19 Evaluation of the early age cracking of lightweight aggregate concrete, June 2000

R20 The effect of the moisture history on the water absorption of lightweight aggregates,

June 2000

R21 Stability and pumpability of lightweight aggregate concrete. Test methods, June 2000

R22 The economic potential of lightweight aggregate concrete in c.i.p. concrete bridges,

June 2000

R23 Mechanical properties of lightweight aggregate concrete, June 2000

Tensile strength as design parameter

BE96-3942 EuroLightCon 6

R24 Prefabricated bridges, June 2000

R25 Chemical stability, wear resistance and freeze-thaw resistance of lightweight aggregate

concrete, June 2000

R26 Recycling lightweight aggregate concrete, June 2000

R27 Mechanical properties of LWAC compared with both NWC and HSC, June 2000

R28 Prestressed beams loaded with shear force and/or torsional moment, June 2000

R29 A prestressed steel-LWAconcrete bridge system under fatigue loading

R30 Creep properties of LWAC, June 2000

R31 Long-term effects in LWAC: Strength under sustained loading; Shrinkage of High

Strength LWAC, June 2000

R32 Tensile strength as design parameter, June 2000

R33 Structural and economical comparison of bridges made of inverted T-beams with top-

ping, June 2000

R34 Fatigue of normal weight concrete and lightweight concrete, June 2000

R35 Composite models for short- and long-term strength and deformation properties of

LWAC, June 2000

R36 High strength LWAC in construction elements, June 2000

R37 Comparison of bridges made of NWC and LWAC. Part 1: Steel concrete composite

bridges, June 2000

R38 Comparing high strength LWAC and HSC with the aid of a computer model, June 2000

R39 Proposal for a Recommendation on design rules for high strength LWAC, June 2000

R40 Comparison of bridges made of NWC and LWAC. Part 2: Bridges made of box beams

post-tensioned in transversal direction, June 2000

R41 LWA concrete under fatigue loading. A literature survey and a number of conducted

fatigue tests, June 2000

R42 The shear capacity of prestressed beams, June 2000

R43 A prestressed steel-LWA concrete bridge system under fatigue loading, June 2000

Tensile strength as design parameter

BE96-3942 EuroLightCon 7

SUMMARY

Tensile strength values associated with the characteristic compressive strengths classes are ex-

plicitly defined in most codes. However, the application of the tensile strength as design pa-

rameter in international design codes varies. The tensile strength of LWAC is usually defined by

a modification of the tensile strength of NWC as a function of the oven dry density. The cali-

bration of such functions should take into account, not only results of material tests, but also the

influence on the predicted behaviour and safety of the structure. In addition to the decrease of

the tensile strength also the increased brittleness of LWA concrete is expected to influence the

behaviour of structural members.

On this background a review of the application of tensile strength as design parameter in inter-

national codes is performed. Of special interest is the recently published first draft of the new

Eurocode 2 (prEN 1992-1). Special emphasis is put on ultimate limit state.

The report reveals that the modification coefficient for the tensile strength of LWAC in different

codes varies by 6 –20 % depending on the density of the concrete. This is partly due to the use

of different reference density, varying between 2200 and 2400 kg/m

3

. A compromise using

2300 kg/m

3

, which is not far from the expected oven dry density of NWC, is suggested.

Investigation of the expressions for shear strength of members without shear reinforcement re-

veals that calibration of the tensile strength parameter with respect to shear strength of LWA

concrete members will depend very much on the format of the shear strength formula.

Comparison with test result indicate that the suggested modification of the shear strength in

prEN1992, where a direct mult iplication of the shear strength by the tensile strength modifica-

tion coefficient is applied, seems to function quite well despite that the general formula predicts

a dependence of the square root of the tensile strength for NWC. A further reduction of the

modification coefficient for ALWAC with light weight aggregate in all fractions is suggested.

The design bond strength defining the development length of deformed bars is assumed propor-

tional to the tensile strength in European codes. Modification by a conservative density depend-

ent coefficient for LWA concrete seems to give satisfactory predictions. A more strict limita-

tion of the use of large diameter bars in LWA concrete should be considered.

Further comments to the application of the tensile strength parameter in design of minimum re-

inforcement and detailing and general comments to prEN1992 with respect to LWAC is in-

cluded in section 7 and 8 . Detailed result of shear test are given in Appendix.

Keywords

Light weight aggregate; concrete; tensile strength; brittleness; shear strength; bond strength;

design codes.

Tensile strength as design parameter

BE96-3942 EuroLightCon 8

1 INTRODUCTION

The tensile strength of concrete is used directly or indirectly as design parameter in different

ways in design codes. Tensile strength values associated with the characteristic compressive

strengths classes are explicitly defined in most codes. Even so, the direct application of the ten-

sile strength as design parameter varies. Direct application are mainly used in the following de-

sign situations:

Ultimate limit state:

Shear strength and punching shear strength of slabs

Bond anchorage and overlap splicing of reinforcement

Shear transfer in cracks

Minimum reinforcement

Service limit state:

Crack formation

Crack spacing

Tension stiffening

Analysis

Tensile stress-strain relationship in non linear finite element analysis

When the tensile strength is applied as a design parameter in the ultimate limit state, the major

concern is to maintain adequate safety.

It is generally realized that the effective minimum tensile strength of concrete members may be

substantially reduced by environmental effects (restrained shrinkage and temperature differ-

ences ) , construction joints and other crack initiators. Transfer of longitudinal force resultants

by the tensile strength of plain concrete is therefore usually not relied upon. However, in cases

where the average tensile strength in a certain volume is decisive such as for anchorage of rein-

forcement, and/or when the tensile stresses are oriented in directions where the concrete is more

protected from detrimental effects, such as in slabs subjected to shear, the tensile strength is re-

liable and should be recognized as a basic strength parameter in ultimate limit state.

The tensile strength of normal weight concrete is usually defined in codes by a simple function

of the compressive strength. It is well known that tensile strength is more variable than the

compressive strength. It is more influenced by the shape and surface texture of the aggregates

than the compressive strength. It is, however, also observed that for example the shear resis-

tance of slabs without shear reinforcement made of concrete with increasing strength cannot be

satisfactory expressed by the increase of the tensile strength alone. It may be assumed that also

the increasing brittleness of concrete of increasing strength has a certain influence on the resis-

tance.

Tensile strength as design parameter

BE96-3942 EuroLightCon 9

This can be taken into account either by defining a modified function of the compressive

strength with more moderate increase of the tensile strength or by substit uting the tensile

strength with a different formula in the shear resistance equation.

In general, LWA concrete is more brittle than normal weight concrete. In certain laboratory

conditions the tensile strength may be only moderately lower than the strength of normal weight

concrete with equal compressive strength. With lower E-modulus and lower fracture energy the

characteristic length expressing the relation between the elastic energy per unit volume and the

fracture energy per unit crack area will be substantially reduced.

These considerations should also be taken into account when introducing standard conversion

functions for the tensile strength of LWA concrete as a function of the oven dry density.

The main questions are therefore:

Should the conversion function express the average observations under laboratory condi-

tions, or should a possible increased sensitivity to environmental conditions be taken into

account?

Should possible effects of the increased brittleness in ultimate limit states be accounted for?

On this background a review of the application of tensile strength as design parameter in inter-

national codes is performed. Of special interest is the recently published first draft of the new

Eurocode 2 (prEN 1992-1). Special emphasis will be put on ultimate limit state.

Tensile strength as design parameter

BE96-3942 EuroLightCon 10

2 TENSILE STRENGTH AND BRITTLENESS OF CONCRETE

2.1 Tensile strength of normal weight concrete

The tensile strength of normal weight concrete of equal compressive strength may vary within a

wide range depending, among other parameters, on the shape and surface texture of the aggre-

gate.

In CEB-FIP Model Code 1990 the usual range of the tensile strength associated with the differ-

ent strength classes defined by the required characteristic compressive cylinder strength are as

shown in Figure 1.

Figure 1 Usual range of tensile strength given in Model Code 90

In MC90 it assumed that the average compressive strength is about 8 MPa higher than the speci-

fied characteristic strength.

The functions relating the tensile strength to the compressive strength are usually of the follow-

ing format:

f

ct

= k (f

c

)

p

Different exponents are used in various codes. In MC90 p = 2/3 is applied. In other codes p=

0,6 and p = 1/2 occur.

The choice of the exponent has a significant influence on the predicted tensile strength of high

strength concrete.

Tensile strength in Model Code 90

0,00

1,00

2,00

3,00

4,00

5,00

6,00

7,00

8,00

0 20 40 60 80 100

Characteristic compressive strength (MPa)

Tensile strength (MPa)

fctmax

fctm

fctmin

fctd

Tensile strength as design parameter

BE96-3942 EuroLightCon 11

Figure 2 Tensile strength relative to the strength of concrete C20

In figure 2 the effect of using different exponents in the strength formula is shown.

Exponent p = 1/3 is included because this is sometimes used in substitute functions for shear

strength (MC90 and prEN1992 draft).

A modified design tensile strength with a reduction of the tensile strength of high strength con-

crete is sometimes introduced.

The modification in prEN 1992-1-1 for concrete strength higher than 50 MPa and the corre-

sponding design tensile strength are shown in Fig 3.

The assumed characteristic tensile strength, modified structural strength and corresponding de-

sign tensile strength in NS3473 are shown in Fig 4.

The modification in the Norwegian code is calibrated with respect to the use of the tensile

strength in resistance calculation in ultimate limit state. A further reduction by 15 % is applied

for LWAC with lightweight aggregate in all fractions. (ALWAC)

Relative tensile strength

0

0,5

1

1,5

2

2,5

3

0 20 40 60 80 100

Compressive strength

Relative strength

fct/fct20

p=2/3

p=0,6

p=1/2

p=1/3

Tensile strength as design parameter

BE96-3942 EuroLightCon 12

Figure 3 Design tensile strength in prEN 1992-1-1-Draft.

Figure 4 Modified design tensile strength in NS3473 – 1998.

2.2 Tensile strength of LWA concrete

The usual formula relating the tensile strength of LWA concrete to the tensile strength of nor-

mal weight concrete (i.e. with the same compressive strength) have the form:

f

ct LWAC

/ f

ct NWC

= a + (1-a)

o

/

1

Tensile strength in prEN 1992-1-1 Draft

0,00

1,00

2,00

3,00

4,00

5,00

6,00

0 20 40 60 80 100

Characteristic compressive strength (MPa)

Tensile strength (MPa)

fctm

fctm mod

fctk 005

fctd

Tensile stength in NS3473-98

0,00

1,00

2,00

3,00

4,00

5,00

6,00

0 20 40 60 80 100

Characteristic cylinder strength (MPa)

Tensile strength (MPa)

ftk

ftn

ftd

Tensile strength as design parameter

BE96-3942 EuroLightCon 13

where

a is constant 0,5 < a < 0

o

is the oven dry density

1

is a reference density 2400

1

2200

The influence of using different constants and reference densities is shown in Figures 5 and 6

Figure 5 Tensile strength reduction factors as function of oven dry density

Figure 6 Tensile strength reduction factors as function of oven dry density

Tensile strength of LWA concrete

= 2200 kg/m

3

0,5

0,6

0,7

0,8

0,9

1

1,1

800 1000 1200 1400 1600 1800 2000 2200 2400

Oven dry density (kg/m

3

)

Relative strength

fctLWA/fctND

a = 0.40

a = 0.30

a = 0.15

Tensile strength of LWA concrete

= 2400 kg/m

3

0,5

0,6

0,7

0,8

0,9

1

800 1000 1200 1400 1600 1800 2000 2200 2400

Oven dry density (kg/m

3

)

Relative strength

fctLWA/fctND

a = 0.50

a = 0.40

a = 0.30

Tensile strength as design parameter

BE96-3942 EuroLightCon 14

Figure 7 Tensile strength reduction factors for LWAC in various codes

Figure 7 shows the different reduction factors for tensile strength of LWA concrete applied in

existing codes. NS3473* refers to the new edition of the Norwegian code issued in 1998.

The reduction factor varies between 0,94 – 1,0 for

o

= 2200 kg/m

3

and 0,54 – 0,66 for

o

=

1000 kg/m

3.

A simple comparison of the resulting design tensile strength in ultimate limit state i

different codes can be made if a reasonable relation between the oven dry density and the com-

pressive strength is chosen. For this purpose the relation

o

= 550 f

ck

0,3

is selected, which is

valid for LWAC with rather high strength/density ratios. The resulting design strength in ULS

according to Model Code 90, prEN1992-draft and NS3473 are shown in Fig 8.

Figure 8 Design tensile strength of LWAC in various codes

Figure 8 illustrate the modification of the tensile strength for high strength LWAC in the new

draft of prEN1992 compared to Model Code 90. This modification is even more pronounced in

the Norwegian code, which also include a further reduction for all-lightweight aggregate con-

crete.

Tensile strength of LWA concrete

0,5

0,6

0,7

0,8

0,9

1

1,1

800 1000 1200 1400 1600 1800 2000 2200 2400

Oven dry density (kg/m

3

)

Relative strength

fctLWA/fctND

CUR

ENV1992

BBK 94

NS3473*

prEN1992

Design tensile stength of LWA concrete

550 f

ck

0,3

0

0,5

1

1,5

2

2,5

0 20 40 60 80 100

Characteristic cylinder strength f

ck

(MPa)

Tensile strength f

ctd

(MPa)

Model Code

prEN1992

NS3473

NS ALWA

Tensile strength as design parameter

BE96-3942 EuroLightCon 15

2.3 Brittleness

The brittleness of concrete may be characterised by the characteristic length given in a simple

form by:

l

ch

= G

f

E

c

/ f

ct

2

where:

G

f

= fracture energy (Nmm/mm

2

)

E

c

= modulus of elasticity (N/mm

2

)

f

ct

= tensile strength (N/mm

2

)

Table 1 Characteristic length of concrete

Concrete ref f

cm

f

ctm

E

cm

G

f

l

ch

NWC 1) 28 2,2 26.000 0,060 322

NWC 1) 58 4,1 33.000 0,105 206

NWC 1) 88 5,6 38.000 0,135 163

LWAC 6) 67 4,4 26.000 0,068 91

LWAC 7) 52 3,0 18.000 0,034 68

ALWAC 7) 40 2,9 15.500 0,032 59

Table 1 shows typical mechanical properties, fracture energy and resulting characteristic length

of normal weight concrete according to Model Code (1) compared to selected test results for

LWA concrete.

The table reflects the expected decreasing characteristic length of NWC with increasing strength

indicating increased brittleness of high strength concrete. The characteristic length of LWAC is

systematically shorter. The selected results indicate, however, an opposite tendency that the

characteristic length is decreasing with decreasing compressive strength. The example in the

last line of the table indicate that especially short characteristic lengths with brittle behaviour

should be expected for ALWAC with light weight aggregate also in the sand fraction.

Tensile strength as design parameter

BE96-3942 EuroLightCon 16

3 Shear strength of slabs

3.1 Shear capacity equations in design codes

Note: In the following expressions for the shear resistance of slabs without shear reinforcement

the notation without index means the ratio of longitudinal reinforcement = A

s

/bd.

ENV 1992-1-4: V

Rd1

= 0,25 (

1

f

ctk

/

c

)(1.6 – d) (1,2 + 40 )b

w

d

1

= (0,4 + 0,6

o

/2200)

The shear resistance according to ENV 1992 is proportional to the tensile strength. The modif i-

cation factor for LWA concrete in ENV 1992-1-3 will affect the shear strength directly.

prEN 1992-1 1

st

draft Dec 1999:

V

lRd,ct

= 0,12

1

k (100 f

lck

)

1/3

b

w

d

1

= (0,4 + 0,6

o

/2400)

The shear resistance of slabs without normal force according to prEN 1992 is a function of

(f

ck

)

1/3

If the tensile strength is approximated by the formula f

ct

= k(f

ck

)

2/3

this indicate that the

shear strength of normal weight concrete slabs is assumed to be proportional to the square root

of the tensile strength (f

ct

= k (f

ck

)

1/3

). However, introduction of the external factor

1

means that the modification of the tensile strength of LWA concrete will affect the shear

strength proportionally.

CEB-FIP MC90 : NWC: V

Rd1

= 0,12 (100 f

ck

)

1/3

b

r

d

fib TG 8.1: LWAC: V

Rd1

= 0,10 (100 f

ck

)

1/3

b

r

d

1

1

= (0,4 + 0,6

o

/2200)

The format of the shear strength formula and the modification for LWA concrete suggested by

the task group TG 8.1 is in principle the same as suggested in prEN 1992. The modification

factor is slightly different. It is not known whether the reduction of the general factor from 0,12

to 0,10 is intentional or just a misprint.

ACI: V

c

= (f

c

’/6) b

w

d

The shear resistance according to ACI is a function of (f

ck

)

1/2

Simplified reduction factors

0,85 for sand-lightweight concrete and 0.75 for All-lightweight-concrete are introduced.

NS: V

co

= 0.3(

1

f

tn

+ 100)(1,5 – d)b

w

d/

c

< 0,6

1

f

tn

(1,5 – d)b

w

d/

c

1

= (0,15 + 0,85

o

/2200)

Tensile strength as design parameter

BE96-3942 EuroLightCon 17

In the Norwegian code a modification of the tensile strength (f

tn

) will influence the upper limit

proportionally. The effect on the resistance of slabs with less reinforcement will depend on the

relative magnitude of f

tn

and 100

It may be concluded that calibration of the tensile strength parameter with respect to shear

strength of LWA concrete slabs will be dependent on the format of the shear strength formula.

3.2 Comparison with test results

Table 2 shows the main results of a comparison of design shear capacities according to the

Norwegian code and two versions of Eurocode 2 and observed shear cracking strength in three

test series with beams made of three different types of LWA concrete. All beams were without

shear reinforcement and constant gross section b/h = 150/250 mm, but the shear span from the

supports to the symmetrical twin point loads and longitudinal reinforcement amount were var-

ied. The detailed measures and results are given in tables A1 – A3 in the Appendix.

Table 2 include the number of test results (N) in each series, the compressive cylinder strength

(f

cyl

) and the oven dry density (

o

).

Table 2 Ratio of observed shear cracking strength to design shear capacity

Ref/type N Str. dens.

NS3473 prEN1992 ENV1992

f

cyl

o

(Vcr/Vd)m

(Vcr/Vd)k

(Vcr/Vd)m

(Vcr/Vd)k

(Vcr/Vd)m

(Vcr/Vd)k

8/ LWAC 10 58 1900

1,39 1,18 1,70 1,41 1,43 1,08

10/LWAC

11 36,6

1600

1,69 1,24 1,76 1,48 1,66 1,27

9/ALWAC

18 42,5

1320

1,47 1,05 1,31 1,16 1,18 0,93

The ratios of observed to calculated shear strength in Table 2 and Fig. 9 are given both in terms

of mean values and a formal characteristic value calculated simply as:

(Vcr/Vd)k = (Vcr/Vd)m – 1,4 s

where (s) is the standard deviation of the ratios within each test series.

It can be observed from tables A1-A3 in the appendix that the new draft of Eurocode 2

(prEN1992) gives satisfactory low variability of the calculated ratios with coefficient of varia-

tion between 0,08 and 0,12. The other two investigated codes give less satisfactory variation

coefficients between 0,11 and 0,21.

The desired characteristic ratios are a matter of discussion. However, ratios comparable to the

partial factor

c

for concrete in ultimate limit state seems reasonable. It should be mentioned that

the final shear failure load are much higher than the diagonal cracking load in beams with small

shear span ratios, and especially so for LWA concrete beams. The general tendency is that this

margin decreases with increasing shear span. In some cases with shear span ratio a/d = 4,0 di-

agonal cracking lead almost immediately to failure. Observing that the widths of diagonal shear

cracks in specimens without shear reinforcement are usually very large, and that the final failure

loads are very variable, the diagonal cracking is defined as the primary failure criterion.

On this background the ratios 1,41 and 1,48 calculated with prEN1992 for the first two series

with LWAC have the desired order of magnitude. However, the ratio 1,16 for the tests with

Tensile strength as design parameter

BE96-3942 EuroLightCon 18

ALWAC with light weight aggregate in all fractions (last line in Table 2 depicted with oven dry

density 1320 kg/m

3

in Fig 9) does not seem to give adequate safety.

The results indicate that an extra reduction factor should be introduced for ALWA concrete with

respect to shear capacity.

Figure 9 Ratio of observed shear cracking strength to design shear capacity

The basic reduction factor for tensile strength of LWAC in prEN1992 is:

1

= (0,4 + 0,6

o

/2400)

It may be more convenient to use a reference oven dry density which is more realistic for ordi-

nary normal weight concrete. The formula will then probably give a better fit to modified nor-

mal weight concrete where only a part of the coarse aggregate is substituted with LWA.

Figure 10 Ratio of observed shear cracking strength to design shear capacity according to

a modified version of prEN1992, Draft, section 10

0,80

1,00

1,20

1,40

1,60

1,80

1200 1400 1600 1800 2000

Oven dry density (kg/m

3

)

Ratio Vcr/Vd

prEN mean

prEN kar

NS mean

NS kar

ENV mean

ENV kar

Modified prEN 1992

0,80

1,00

1,20

1,40

1,60

1,80

1200 1400 1600 1800 2000

Oven dry density (kg/m

3

)

Ratio Vcr/Vd

prEN mean

prEN kar

Tensile strength as design parameter

BE96-3942 EuroLightCon 19

A modified version of formula for shear capacity prEN1992 using

1

= (0,3 + 0,7

o

/2300)

with an additional reduction factor

2

= 0,85 for ALWAC has been applied in Fig 10.

It can be seen that characteristic ratios within the range of 1,4 –1,5 have been obtained for all

three test series.

Tensile strength as design parameter

BE96-3942 EuroLightCon 20

4 Bond strength

The expressions for the design bond strength for reinforcing bars in various codes:

ENV 1992-1-4: f

bd

=

1

2

3

f

ctd

(0,4 + 0,6

o

/2200)

1

considers the type of reinforcement = 2,25 for ribbed bars

2

considers the position of the bar during concreting

3

considers the bar diameter, i.e. a reduction factor less than 1,0

for bar diameters larger than 32 mm

prEN 1992-1

1

st

draft Dec 1999: f

bd

= 2.25

2

3

f

lctd

f

lctd

= f

ctd

(0,4 + 0,6

o

/2400)

Limitation: Unless the concrete tensile strength can be shown to be grater than that calculated

for f

ck

= 55 MPa, it should be limited to that value.

CEB-FIP MC90 : NWC: f

bd

=

1

2

3

f

ctd

fib TG 8.1: LWAC: Void

ACI: Basic development length in LWAC: 1.3 0,02 A

b

f

y

/f

c

’

design bond strength: 0,77 f

c

’ /(0,02 )

The increase of the development length by a factor of 1,3 for reinforcement in LWA concrete,

corresponds to a decrease of the bond strength by a factor of 0,77. The values of f

c

’ should be

limited to 8,3 MPa, i.e. f

c

’ 70 MPa.

NS: f

bd

= k

1

k

2

f

tn

(1/3 + 2/3 c/) (0,15 + 0,85

o

/2200)

The design bond strength of reinforcement in LWAC is modified proportionally by the oven dry

density dependent tensile strength modification factor in all reference codes except ACI, where

a constant factor is applied.

Tests with lap splices in tension specimens made of relatively high strength LWAC (11) indi-

cated that the modification of the tensile strength related to the density will give reasonable pre-

diction of the bond strength, but that scatter of the results was larger than in comparative tests

with NWC. This was mainly due to the gradual decrease of the average bond strength with in-

creasing lap length of 32 mm bars. The conclusion was that the this reflects the lower ability of

the brittle LWA concrete to redistribute high local stresses causing splitting before a uniform

bond stress distribution is established. It was recommended that the limitation of the bar diame-

ter should be more restrictive in LWAC.

Tensile strength as design parameter

BE96-3942 EuroLightCon 21

5 Minimum reinforcement and detailing of members

In prEN1992, Draft Section 10 it is explicitly stated that the relevant sections for NWC with

respect to minimum reinforcement and detailing of members can be applied to LWAC without

modifications.

The required minimum reinforcement in beams and slabs is proportional to the tensile strength

f

ctm

(or f

ct,eff

at the time of cracking). Application of the strength reduction factor

1

for LWAC

in this case will relax the required minimum reinforcement of LWAC members compared to

NWC members with equal compressive strength.

The modification of the tensile strength is introduced in a general clause in section 10. The ap-

plication of this modification is however not repeated in sections concerning minimum rein-

forcement to obtain ductile behaviour and control of cracks. It is therefore not quite clear

whether the modification should be applied, or if unmodified tensile strength as for NWC

should be used to be on the safe side.

The most convenient approach will be to apply the modified tensile strength in all relevant sec-

tions. Taking into account that the tensile strength of relatively high density LWAC sometimes

may be as high as NWC of equal compressive strength, one should be careful not to underesti-

mate the effective tensile strength especially in cases control of the cracking due to imposed

deformations is important. The use of the (modified) upper characteristic tensile strength in such

cases should be considered.

Tensile strength as design parameter

BE96-3942 EuroLightCon 22

6 Other comments to prEN1992-1 section 10 - 1

st

draft

Table 10.2 Stress and deformation characteristics for LWAC :

For each strength class defined by the characteristic cylinder strength f

ck

exactly the same corre-

sponding characteristic cube strength f

ck,cube

is defined for LWAC as for NWC in Table 3.1.

It is well known that the f

ck,cube

/ f

ck

ratio is lower for LWAC than for NWC. Documentation of a

lower ratio and thereby a lower cube strength for a certain strength class and actual type of con-

crete should be allowed.

The strain limits given i Table 10.2 are exactly the same as in Table 3.1, despite that it is stated

in clause 10.3.1.5 that the strain values given in relevant figures for NWC should be substituted

by the values from Table 10.3.1. There is probably a double misprint: The name of the Table

10.2 should be changed to 10.3.1, and the strain values in this table should be altered.

The reference density value in the equations defining the modification coefficients

E

for the

modulus of elasticity and

1

for the tensile strength is 2400 kg/m

3

. It would be more logical,

and probably give a better fit to the test results if a more representative value of the oven dry

density of NWC in the order of 2200-2300 kg/m

3

were chosen as reference. ENV1992-1-4 use

2200. A possible compromise is to apply 2300 kg/m

3

as reference oven dry density.

There are some printing errors:

Expression (10.6.4): The correct ratio should be (2,5d/a

v

), not (2,5/a

v

d).

10.8.4.1 (2) Substitute f

cd

by f

ctd

and f

lcd

by f

lctd

Tensile strength as design parameter

BE96-3942 EuroLightCon 23

7 NOMENCLATURE

LWA Lightweight aggregate

LWAC Lightweight aggregate concrete

NWA Normal weight aggregate

NWC Normal weight concrete

w/b water binder ratio

w/c water cement ratio

CEB Comité Euro-international du Béton

CEN Comité Européen de Normalisation

CTR Cost Time Resources (form)

EN European Standard

FIB Féderation Internationale du Béton

FIP Féderation Internationale de la Précontrainte

TC Technical Committee (CEN)

Tensile strength as design parameter

BE96-3942 EuroLightCon 24

8 REFERENCES

1. CEB-FIP MODEL CODE 1990 Bulletin D’information No 213/214 May 1993

2. fib TG 8.1 Lightweight Aggregate Concrete

Recommended extensions to Model Code 90 , Final Draft Dec 1999, revised Jan 2000.

3. Eurocode 2: Design of Concrete Structures – Part 1: General rules and rules for buildings

Part 1-4 Lightweight aggregate concrete with closed structure.

ENV 1992-1-4, 1994

4. Eurocode 2: Design of Concrete Structures – Part 1: General rules and rules for buildings.

Section 10: Lightweight aggregate concrete structures.

prEN 1992-1 1

st

draft, December 1999.

5. NS 3473

6. High strength Concrete, Report 4.11 Effect of moisture on the mechanical properties

STF65 F91012, 1991

7. Lightcon Rapport 2.1 Mekaniske egenskaper. Dokumentasjon av LC40 1994

8. Drangsholt, G., Thorenfeldt E.: Shear Capacity of High Strength Concrete Beams SINTEF

Report STF65 F88006, Feb 1988

9. Stemland H., Thorenfeldt E.: Skjærkapasitet av bjelker uten skjærarmering

Lightcon DP3, SINTEF Report STF70 F85046, Aug 1995

10. Stemland H., Thorenfeldt E.: Skjærkapasitet av lettvektsbetongbjelker uten skjærarmering,

Lettkonstruksjonsbetong DP 2.3 SINTEF Report STF22 A99735, Jul 1999

11. Thorenfeldt E., Assved Hansen E.: Tension lap splices and crack widths. SINTEF Report

STF70 F93131, Dec 1993

Tensile strength as design parameter

BE96-3942 EuroLightCon 25

Appendix

Table A1 Diagonal cracking shear strength of beams b/h = 150/250 mm Ref 8)

Ref 8) LWAC

Strength f

cyl

58

Density

o

1900

NS3473 prEN1992 ENV1992

Strength f

ct

:

1,60 1,66 1,93

Beam no d a/d

=

As/bd

Vcr Vd Vcr/Vd Vd Vcr/Vd Vd Vcr/Vd

B31 221 3 1,82 53,22 36,94 1,44 32,10 1,66 42,44 1,25

B31 221 3 1,82 53,22 36,94 1,44 32,10 1,66 42,44 1,25

B32 221 2,3 1,82 46,29 36,94 1,25 32,10 1,44 42,44 1,09

B32 221 2,3 1,82 53,15 36,94 1,44 32,10 1,66 42,44 1,25

B33 207 4 3,23 58,20 47,11 1,24 36,99 1,57 41,65 1,40

B33 207 4 3,23 63,11 47,11 1,34 36,99 1,71 41,65 1,52

B34 207 3 3,23 58,10 47,11 1,23 36,99 1,57 41,65 1,39

B34 207 3 3,23 63,10 47,11 1,34 36,99 1,71 41,65 1,51

B35 207 2,3 3,23 67,85 47,11 1,44 36,99 1,83 41,65 1,63

B35 207 2,3 3,23 82,57 47,11 1,75 36,99 2,23 41,65 1,98

Average 1,39 1,70 1,43

STD 0,15 0,21 0,25

VAR. 0,11 0,12 0,18

Table A2 Diagonal cracking shear strength of beams b/h = 150/250 mm Ref 10)

Ref 10) LWAC

Strength f

cyl

36,6

Density

o

1600

NS3473 prEN1992 ENV1992

Strength f

ct

: 1,11 1,05 1,29

Beam no d a/d

=

As/bd

Vcr Vd Vcr/Vd Vd Vcr/Vd Vd Vcr/Vd

B2 220 2,3 1,22 39,20 25,09 1,56 21,96 1,79 24,81 1,58

B2 220 2,3 1,22 39,20 25,09 1,56 21,96 1,79 24,81 1,58

B3 220 4 1,22 33,80 25,09 1,35 21,96 1,54 24,81 1,36

B3 220 4 1,22 31,90 25,09 1,27 21,96 1,45 24,81 1,29

B5 220 2,3 1,83 49,00 28,09 1,74 25,13 1,95 28,39 1,73

B5 220 2,3 1,83 46,60 28,09 1,66 25,13 1,85 28,39 1,64

B6 220 4 1,83 38,20 28,09 1,36 25,13 1,52 28,39 1,35

B8 205 2,3 3,23 58,80 26,48 2,22 28,80 2,04 27,68 2,12

B8 205 2,3 3,23 58,30 26,48 2,20 28,80 2,02 27,68 2,11

B9 205 4 3,23 49 26,48 1,85 28,80 1,70 27,68 1,77

B9 205 4 3,23 49 26,48 1,85 28,80 1,70 27,68 1,77

Average 1,69 1,76 1,66

STD 0,32 0,20 0,28

VAR. 0,19 0,11 0,17

Tensile strength as design parameter

BE96-3942 EuroLightCon 26

Table A3 Diagonal cracking shear strength of beams b/h = 150/250 mm Ref 9)

Ref 9) ALWAC

Strength f

cyl

42,5

Density

o

1320

NS3473 prEN1992 ENV1992

Strength f

ct

: 0,88 1,08 1,30

Beam no d a/d

=

As/bd

Vcr Vd Vcr/Vd Vd Vcr/Vd Vd Vcr/Vd

B1 221 2,3 1,82 34,30 22,43 1,53 24,14 1,42 28,55 1,20

B1 221 2,3 1,82 33,30 22,43 1,48 24,14 1,38 28,55 1,17

B2 221 3 1,82 28,90 22,43 1,29 24,14 1,20 28,55 1,01

B2 221 3 1,82 29,40 22,43 1,31 24,14 1,22 28,55 1,03

B3 207 2,3 3,23 39,20 21,24 1,85 27,82 1,41 28,02 1,40

B3 207 2,3 3,23 44,10 21,24 2,08 27,82 1,59 28,02 1,57

B4 207 3 3,23 35,80 21,24 1,69 27,82 1,29 28,02 1,28

B4 207 3 3,23 41,70 21,24 1,96 27,82 1,50 28,02 1,49

B5 207 4 3,23 37,20 21,24 1,75 27,82 1,34 28,02 1,33

B5 207 4 3,23 37,2 21,24 1,75 27,82 1,34 28,02 1,33

B7 221 4 1,82 29,4 22,43 1,31 24,14 1,22 28,55 1,03

B7 221 4 1,82 28,9 22,43 1,29 24,14 1,20 28,55 1,01

B9 221 2,3 1,22 27,9 22,30 1,25 21,13 1,32 25,00 1,12

B9 221 2,3 1,22 27,9 22,30 1,25 21,13 1,32 25,00 1,12

B10 221 3 1,22 26 22,30 1,17 21,13 1,23 25,00 1,04

B10 221 3 1,22 25 22,30 1,12 21,13 1,18 25,00 1,00

B11 221 4 1,22 26,5 22,30 1,19 21,13 1,25 25,00 1,06

B11 221 4 1,22 26,5 22,30 1,19 21,13 1,25 25,00 1,06

Average 1,47 1,31 1,18

STD 0,30 0,11 0,18

VAR. 0,21 0,08 0,15

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