PhD Summary

A thesis presented to the Faculty of Civil Engineering

of Technical University of Cluj-Napoca

In partial fulfillment

of the requirements for the degree Doctor of Philosophy

By Eng. Dumitru Vasile MOLDOVAN

A STUDY OF HIGH STRENGTH AND

PERFORMANCE CONCRETE

SUBJECTED TO UNIAXIAL

COMPRESSION AND FLEXURE

Coordonator,

Prof. Phd. Eng. Cornelia MĂGUREANU

Evaluation Committe:

CHAIRMAN: Prof. PhD. Eng. Mihai Iliescu - dean, Faculty of Civil Engineering, Technical

University of Cluj-Napoca;

MEMBERS: Prof. PhD. Eng. Cornelia Măgureanu – coodonator, Technical University of

Cluj-Napoca;

Prof. PhD. Eng. Radu PASCU - referee, Technical University of Civil

Engineering Bucharest;

Prof. PhD. Eng. Valeriu STOIAN - referee, “Politehnica” University of

Timișoara;

Prof. PhD. Eng. Zoltan KISS - referee, Technical University of Cluj-Napoca;

Acknowledgements

This paper has been made possible with the unconditioned help of my family, Crina and

Roxana, to whom it is dedicated.

The author expresses his gratitude to Prof. PhD. Eng. Cornelia MĂGUREANU,

coordinator of the present paper, teacher and life model.

The author expresses his gratitude to fellow colleagues for the help, observations and

support provided in all the various stages of writing this paper.

The author expresses his gratitude to the National Grant Agency, CNCSIS, for the

financial support that made possible the following research programmes:

Grant A, cod 1036/2004-2006, High Strength and Performance Concrete incorporating

steel or carbon fibers and rubber fume. Earthquake, aggressive enviroments, dynamic loading

and fatique behaviour. Enviromental Ecology (coord. Prof. PhD. Eng. Cornelia

MĂGUREANU);

Grant TD 280/2007-2009, Ductility of High Strength and Performance Concrete (coord.

Assist. Lect. Eng. Hegheș BOGDAN).

All support is gratefully acknowledged.

Table of Contents

[3]

I. INTRODUCTION Page [5]

A. Context and motivation Page [5]

B. Research methodology Page [5]

C. Thesis structure Page [5]

II. STATE OF THE ART Page [7]

A. Introduction Page [7]

B. Concrete matrix Page [7]

C. Conversion relationships for the characteristic compressive strength.

Establishing concrete grade Page [8]

D. Stress-strain curves for HSC Page [8]

E. Ultimate compressive strain for plain HSC Page [11]

F. Stress block parameters Page [12]

References Page [15]

III. EXPERIMENTAL INVESTIGATION Page [20]

A. Concrete properties Page [20]

a. Compressive strength Page [20]

b. Stress-strain curve Page [21]

B. Reinforcement properties Page [21]

C. Experimental programme Page [22]

D. Beam response under flexure Page [22]

IV. EXPERIMENTAL STRESS-STRAIN CURVE Page [24]

A. Proposed Definitions Page [24]

a. Stress-strain curve Page [24]

b. Concrete strain corresponding to the maximum stress Page [24]

c. Ultimate concrete strain Page [24]

d. Centroid position for the experimental stress-strain curve Page [25]

e. Stress block models Page [25]

Table of Contents

[4]

B. Resistive flexural capacity Page [25]

a. Cited models Page [25]

b. Proposed trapezoid stress block model Page [26]

c. Proposed equivalent rectangular stress block Page [26]

d. Proposed triangular stress block Page [27]

e. Stress block parameters Page [27]

V. CONCLUDING REMARKS Page [32]

A. Synthesis Page [32]

B. Observations and conclusions Page [32]

C. Recomandations Page [33]

VI. APPENDICES Page [34]

APPENDIX I – Strain development over the height of the cross section Page [34]

APPENDIX II – Experimental stress-strain curve Page [36]

APPENDIX III – Flexural resistive moment Page [38]

Eng. Dumitru Vasile MOLDOVAN [5]

I. INTRODUCTION

A. Context and motivation

It has become increasingly clear that any future development in construction should aim

at using better and better materials such as High Strength Concrete or High Performance

Concrete. The present thesis is following this trend by addressing to national and local interested

parties a call to action by presenting local gain of experience on the matter and by providing a

valid reference for introducing in common practice High Strength Concrete as a better, more cost

attractive alternative for a variety of construction projects.

B. Research methodology

The experimental programme consisted of two series of small reinforced concrete

beams (eight and six respectively) having dimensions of ( ), each series

being accompanied by corresponding standard cubic and prismatic specimens ( and

1 ). Two curing treatments were applied: standard, water submersion at

for 28 days and specific, at normal humidity and temperature, identical to the casted

beams.

Governing parameters were considered to be:

(1) ⁄ concrete grade and longitudinal rebars as PC 52 steel grade (specific national steel

grade, similar to S 400 in terms of yielding strength) for percentages of longitudinal

reinforcement of (coefficient of longitudinal reinforcement of

and mechanical coefficients of reinforcement of ;

(2) ⁄ concrete grade and longitudinal rebars as Bst 500 S (equivalent to S500 as per EC 2)

for percentages of longitudinal reinforcement of (coefficient of longitudinal

reinforcement of ) and mechanical coefficients of reinforcement of

.

C. Thesis structure

Present thesis is basically structured in two parts and a total of six chapters. The first

part, chapters 1 and 2, are introductory to the theme set here-in. In the second part, chapters 3

and 4 present the experimental programme and corresponding data. Chapter 5 presents a

A study of HIGH STRENGTH and PERFORMANCE CONCRETE...


synthesis and the concluding remarks of present study, as well as future work directions, while

the last chapter lists the appendices.

Notations adopted here-after refere to:

chapter

part

corresponding listing number.


II. STATE OF THE ART

A. Introduction

According to official definitions High Strength Concrete is the concrete having on a

cylinder specimen compressive strengths from 60 MPa to 130 MPa as per SR EN 1992-1-1:2004

(2004) [2-A-1] (Eurocod 2: Proiectarea structurilor...). Similarly High Performance Concrete is

considered to be the concrete mix having a Water/Cement ratio less than 0,40 according to CEB

(1993), [2-A-2] (Design Code...).

Other definitions refer to strength and durability characteristics that cannot be obtained

by use of common technology and constituents, see RUSSELL (1999), [2-A-3] (ACI Defines

High-Performance Concrete) which in turn means:

Higher compressive strengths are possible only for low and very low Water/Cement

ratios;

Use the latest generation of superplasticizers, water reductive and highly reductive as

well as optimized granulometry of all constituents mixed;

The obtained matrix exhibits superior durability characteristics as well as some

deficientes that have nonetheless accessible solutions;

B. Concrete matrix

The quality of the concrete mix depends on the reactivity of the cement with water

generating fast strengthening gels. Decreasing the water dosage must be balanced by the increase

in the reactivity of the added water given by a two-step process when superplasticizers are used:

(1) disperse more eficiently cement particles in the solution and (2) prevent water from

encapsulating the cement particles and thus provide additional water for the hidration process,

see TAYLOR (1997), [2-B-1] (Cement chemistry). That is why the cement and superplasticizer

must be compatible to create a proper chemical system.

Micro-cracking of concrete starts in the point of minimum strength, somewhere in the

capilar system. As it has been shown, see HSU (1984), [2-B-2] (Fatique and microcracking of

concrete), even prior to loading, concrete may have a well developed capilar system and

therefore multiple points of failure initiation. It may be concluded that although failure is a

sudden event, it is actually the result of a continuous process of cracking, capilar interconnection

and local degradation.



C. Conversion relationships for the characteristic compressive

strength. Establishing concrete grade

Characteristic strength is established with a fractile of 5%, see fib (2009), [2-C-1]

(Bulletin no. 42, Constitutive modelling...) at 28 days on cylinder specimens having (

) or cubic specimens with an edge of ( ), submerged in water or in a fog

room (at an RH ).

De LARRARD et al. (1994), [2-C-2] (Is the cube test suitable for…) propose a

( ⁄ ) conversion domain of:

[2-A]

( ) [2-B] A [2-C] A

[2-C-1]

while IMAM et al. (1995), [2-C-3] (Are current concrete strength...) propose:

[2-C-2]

both indicating that the conversion factor in the case of High Strength Concrete is superior to

that of Normal Concrete, considered to be somewhat closer to ( ).

In order to establish the concrete grade, the following where used:

(3) SR EN 1992-1-1:2004 (2004), [2-C-4] (Eurocod 2: Proiectarea structurilor...)

( ) { ( ) ( )

[2-C-3]

( ) characteristic strength of concrete on cylin er s ecimens, in MPa at age ( )

( ) mean concrete strength in MPa, at age ( )

D. Stress-strain curve for HSC

The following proposed models may be cited:

(1) JENSEN (1943), [2-D-1] (Ultimate strength of reinforced...)

{

( ⁄ )

[2-C-4]

Chapter 2. State of the art


(2) HOGNESTAD (1951), [2-D-2] (A study of combined bending...)

{

[ ( ⁄ ) ( ⁄ ) ]

[(

) (

)]

[2-C-5]

(3) DESAYI and KRISHNAN (1964), [2-D-3] (Equation for the Stress-Strain…)

( ⁄ ) [2-C-6]

(4) SARGIN and HANDA (1968), [2-D-4] (Structural Concrete and...)

( )

( ) [2-C-7]

(5) POPOVICS (1973), [2-D-5] (A numerical approach to the...)

( ⁄ ) [2-C-8]

(6) WANG et al. (1978), [2-D-6] (Stress-strain curves of normal...)

[2-C-9]

(7) CARREIRA and CHU (1985), [2-D-7] (Stress-strain relationship for plain…)

⁄

( ⁄ ) [2-C-10]

(8) THORENFELDT et al. (1987), [2-D-8] (Mechanical properties of High-Strength...)

( ⁄ ) [2-C-11]

(9) Comité Euro-International du Béton (CEB) (1990), [2-D-9] (Design Code...)

{

( ⁄ ) ( ⁄ ) ( ⁄ )

( ⁄ ) ( ⁄ )

[

(

) ] (

)

[

]

[2-C-12]

(Space intentionally left blank)



(10) LOOV (1991), [2-D-10] (A General Stress-Strain Curve for Concrete…)

( ⁄ )

( ⁄ ) ( ⁄ ) [2-C-13]

(11) MUGURUMA et al. (1991), [2-D-11] (Stress-Strain curve model for concrete…)

{

( ) ( ⁄ )

[2-C-14]

(12) HSU and HSU (1994), [2-D-12] (Complete stress-strain behaviour of…)

{

( ⁄ )

( ⁄ )

[ (

) ]

[2-C-15]

(13) WEE et al. (1996), [2-D-13] (Stress-Strain Relationship of…)

{

( ⁄ )

( ⁄ )

( ⁄ )

( ⁄ )

[2-C-16]

(14) Van GYSEL and TAERWE (1996), [2-D-14] (Analytical formulation of the…)

{

( ⁄ ) ( ⁄ ) ( ⁄ )

( ⁄ ) ( ⁄ )

[ ⁄ ⁄

]

[2-C-17]

(15) ATTARD and SETUNGE (1996), [2-D-15] (Stress-Strain relationship of confined...)

[

( )

]

[

( )

]

(

) [2-C-18]

(16) OZTEKIN et al. (2003), [2-D-16] (Determination of rectangular stress block…)

[ ( ⁄ ) ( ) ( ⁄ ) ] [2-C-19]



(17) SR EN 1992-1-1:2004 (2004), [2-D-17] (Eurocod 2: Proiectarea structurilor...)

Non-linear model for short term uniaxial loads:

( ) | | | | [2-C-20]

Parabola-rectangular model for sectional calculus:

{ [ ( ⁄ ) ]

[2-C-21]

Trapezoid model for sectional calculus:

{ ⁄

[2-C-22]

(18) STAS 10107-0/90 (1990), [2-D-18] (Calculul and alcătuirea...)

{ [ ( ⁄ ) ] | | | |

| | | | | | [2-C-23]

E. Ultimate compressive strain for plain HSC

Str

ess (σ

c) î

n [

N/m

m2]

120

110

100

90

80

70

60

50

40

30

20

10

0

(1) Early age microcracking

(contraction, temperature variations)

(2) Load microcracking

(3) Cracking development

(4) Cracking interconnection and

failure

0 1 2 3 4 5 6 7 8 9 10

Strain (ε) [‰] Fig. [1-A]

Failure under uniaxial compression

Commom values for HSC are 2,80 [‰] ( [ ] [ ]⁄ ) for the non-linear

model and 2,60 [‰] for parabola-rectangular and trapezoid models ( [ ] [ ]⁄ ).



F. Stress block parameters

The following proposed models may be citated:

(1) J.A. PASTOR et al. (1984), [2-F-1] (Behavior of High-Strength Concrete Beams)

[2-C-24] [2-D] A [2-E] a

[2-F] a

[2-F-1.1]

{ , entr 0 MPa

[ ( )] , t. 0 MPa [2-F-1.2]

and [2-F-1.3]

[2-F-1.4]

(2) CEB (1993), [2-F-2] (Design Code...)

Parabola-rectangular model:

[2-F-2]

[2-F-2.1]

[2-F-2.2]

strain corres on ing to ma im m stress [2-F-2.3]

{ , entr

( ⁄ ) , entr [2-F-2.4]

Rectangular-equivalent model:

( ⁄ ) [2-F-2.5]

[2-F-2.6]

⁄ [2-F-2.7]

(3) Norwegian Standard NS 3473 (1995), [2-F-3] (Concrete Structures – Design and...)

Tab. [1-A] Tab. [1-B] Tab. [2] Tab. [2-A] Tab. [2-B] Tab. [2-C] Tab. [2-D] Tab. [2-E] Tab. [2-F] Tab. [2-G] Tab. [2-H] Tab. [2-I] Tab. [2-J] Tab. [2-K]

Tab. [2-K-1] Proposed values for ( ) cf. NS 3473, [2-F-3] (Concrete Structures – Design and...)

C25 C35 C45 C55 C65 C75 C85 C95 C105

εcu [-] 0,0035 0,0035 0,0035 0,0035 0,0032 0,00305 0,0029 0,0028 0,0027

η [-] 1 1 1 1 0,97 0,96 0,95 * *

λ [-] 0,80 0,80 0,80 0,80 0,80 0,78 0,76 * *

Clasa betonului

* according to experimental data



(4) AS 3600-2001 (2001), [2-F-4] (Australian Standard - Concrete Structures)

[2-F-3]

[2-F-3.1]

{ , entr 28 MPa

[ ( )] , entr 28 MPa [2-F-3.2]

[2-F-3.3]

[ ( )] t.60 MPa MPa [2-F-3.4]

(5) SR EN 1992-1-1:2004 (2004), Error! Reference source not found. (Eurocod 2:

Proiectarea structurilor de beton...)

[2-F-4]

{ , entr 0 MPa

( ) ⁄ , entr 0 MPa 0 MPa [2-F-4.1]

{ , entr 0 MPa

( ) ⁄ , entr 0 MPa 0 MPa [2-F-4.2]

{

entr 0 MPa

[ (

)

] 0 MPa 0 MPa [2-F-4.3]

(6) Halit Cenan MERTOL et al. (2005), [2-F-5] (Characteristics of Compressive Stress...)

[2-F-5]

{ , entr 6 MPa

( ) , entr 6 MPa [2-F-5.1]

{ , entr 28 MPa

( ) , entr 28 MPa [2-F-5.2]

[2-F-5.3]

(7) CSA A23.3-04 (2005), [2-F-6] (Design of Concrete Structures...) and CAN/CSA S6-06

(2006), [2-F-7] (Canadian Highway Bridge Design Code)

[2-F-6]

( ) [2-F-6.1]

( ) [2-F-6.2]

[2-F-6.3]



(8) ACI 441-R96 (2005) [2-F-8] (High-Strength Concrete Columns...)

[2-F-7]

[ ( )] entr 6 MPa [2-F-7.1]

, entr 6 MPa [2-F-7.2]

[2-F-7.3]

(9) NZS 3101: Part 1:2006 (2006), [2-F-9] (Concrete Structures Standard...)

[2-F-8]

{ , entr MPa

[ ( )] , entr MPa [2-F-8.1]

{ , entr 0 MPa

[ ( )] , entr 0 MPa [2-F-8.2]

[2-F-8.3]

(10) ACI 318 (2008), [2-F-10] (Building Code Requirements...) and AASHTO (2007), [2-F-11]

(AASHTO LRFD Bridge Design...)

[2-F-9]

[2-F-9.1]

{ , entr 0 MPa

[ ( )] , ac 0 MPa [2-F-9.2]

[2-F-9.3]

References


[2] STATE OF THE ART

[2-A] Introduction

[2-A-1] SR EN 1992-1-1:2004, Eurocod 2: Proiectarea structurilor de beton. Partea 1-1: Reguli generale and

reguli pentru clădiri, Asociaţia e Stan ar izare in România (ASRO), E iţia 1, 200 , 212 Page.

[2-A-2] Comité Euro-International du Béton, Design Code (CEB-FIP MC 90), Thomas Telford, London, 1993,

Page. [437]

[2-A-3] Henry G. RUSSELL, ACI Defines High-Performance Concrete, Concrete International, vol. 21, no. 2, 1999,

Page. [56-57], http://www.concrete.org, accesat la 8 oct. 2009

[2-B] Concrete matrix

[2-B-1] H.F.W. TAYLOR, Cement Chemistry, E iția a o a, 1 7, http://books.google.ro/, accesat la 8 oct. 2009

[2-B-2] Thomas T.C. HSU, Fatique and Microcracking of Concrete, Materiaux et Constructions, vol 17, no. 97,

1984, Page. [51-54]

[2-C] Conversion relationships for the characteristic compressive strength. Establishing concrete grade

[2-C-1] fédération internationale du béton (fib), Bulletin no. 42, Constitutive modelling of high-strength/high-

performance concrete, februarie 2009, Page. [3-4]

[2-C-2] F. De LARRARD, A. BELLOC, S. RENWEZ, C. BOULAY, Is the cube test suitable for high performance

concrete?, Materials and Structures, Vol. 27, No. 10, December 1994, Page. [580-583]

[2-C-3] M. IMAM, L. VANDEWALLE, F. MORTELMANS, Are current concrete strength tests suitable for high

strength concrete?, Materials and Structures, Vol. 28, No. 7, August 1995, Page. [384-391]

[2-C-4] SR EN 1992-1-1:2004, Eurocod 2: Proiectarea structurilor de beton. Partea 1-1: Reguli generale and

reguli pentru clădiri, Asociaţia e Stan ar izare in România (ASRO), E iţia 1, 200 , 212 Page.

[2-D] Stress-strain curve for HSC

[2-D-1] V. P. JENSEN, Ultimate Strength of Reinforced Concrete Beams as Related to the Plasticity Ratio of

Concrete, Bulletin Series, no. 345, University of Illinois, Engineering Experimental Station, Urbana-Champaign,

Illinois, 1943, Page. [1-63]

[2-D-2] E. HOGNESTAD, A study of combined bending and axial load in reinforced concrete elements, Bulletin

Series, no. 399, University of Illinois, Engineering Experimental Station, Urbana-Champaign, Illinois, 1951,

Page. [1-129], http://www.ideals.illinois.edu/handle/2142/4360, downloadat la data de 12 dec. 2009

[2-D-3] Prakash DESAYI, S. KRISHNAN, Equation for the Stress-Strain Curve of Concrete, ACI Journal

Proceedings, vol. 61, no. 3, March 1964, Page. [345-350]

[2-D-4] M. SARGIN, V. K. HANDA, Structural Concrete and Some Numerical Solutions, Proceedings of the 23rd

ACM National Conference, New York, 1968, Page. [563-574C]

[2-D-5] S. POPOVICS, A numerical approach to the complete stress strain curve for concrete, Cement and

Concrete Research, vol. 3, no. 5, 1973, Page. [583-599]

http://www.concrete.org/

http://books.google.ro/

http://www.ideals.illinois.edu/handle/2142/4360

References


[2-D-6] P.T. WANG, S.P. SHAH, A.E. NAAMAN, Stress-strain curves of normal and lightweight concrete in

compression, ACI Journal Proceedings, vol. 75, no. 62, November 1978, Page. [603-611]

[2-D-7] Domingo J. CARREIRA, Kuang-Han CHU, Stress-strain relationship for plain concrete in compression,

ACI Journal Proceedings, vol. 82, no. 6, November-December 1985, Page. [797-804]

[2-D-8] E. THORENFELDT, A. TOMASZEWICZ, J.J. JENSEN, Mechanical Properties of High-Strength

Concrete and Application in Design, Proceedings of the Symposium Utilization of High Strength Concrete,

Tapir, Trondheim, 1987, Page. [149-159]

[2-D-9] Comité Euro-International du Béton (CEB), Design Code (CEB-FIP MC 90), Thomas Telford, London,

1993, Page. [437]

[2-D-10] Robert E. LOOV, A General Stress-Strain Curve for Concrete: Implications for High Strength Concrete

Columns, 1991 Annual Conference of the Canadian Society for Civil Engineering, May 29, 1991, Page. [302-

311]

[2-D-11] H. MUGURUMA, M. NISHIYAMA, F. WATANABE, Stress-Strain curve model for concrete with a

wide-range of compressive strength, Proceedings of the Third Symposium on Utilization of High Strength

Concrete, Lillehammer, Norway, June 20-23, 1993, Page. [314-321]

[2-D-12] L.S. HSU, Thomas T.C. HSU, Complete stress-strain behaviour of high strength concrete under

compression, Magazine of Concrete Research, vol. 46, no. 169, 1994, Page. [301-312]

[2-D-13] T. H. WEE, M. S. CHIN, M. A. MANSUR, Stress-Strain Relationship of High-Strength Concrete in

Compression, ASCE Journal of Materials in Civil Engineering, vol 8, no. 2, May 1996, Page. [70-76]

[2-D-14] A. Van GYSEL, L. TAERWE, Analytical formulation of the complete stress-strain curve for high strength

concrete, Materials and Structures/Matériaux et Constructions, vol. 29, November 1996, Page. [529-533]

[2-D-15] Mario M. ATTARD, S. SETUNGE, Stress-Strain relationship of confined and unconfined concrete, ACI

Materials Journal, vol. 93, no. 5, September-October 1996, Page. [1-11]

[2-D-16] Ertekin OZTEKIN, Selim PUL, Metin HUSEM, Determination of rectangular stress block parameters for

high performance concrete, Engineering Structures, vol. 25, no. 3, February 2003, Page. [371-376]

[2-D-17] SR EN 1992-1-1:2004, Eurocod 2: Proiectarea structurilor de beton. Partea 1-1: Reguli generale and

reguli pentru clădiri, Asociaţia e Stan ar izare in România (ASRO), E iţia 1, 200 , Page. [24-31]

[2-D-18] STAS 10107/0-90, Calculul and alcătuirea elementelor structurale din beton, beton armat and beton

precomprimat, Institutul Român de Standardizare, 12 Ianuarie 1990, 115 Page.

[2-E] Ultimate compressive strain for plain HSC

[2-F] Stress block parameters

[2-F-1] J.A. PASTOR, Arthur H. NILSON, Floyd O. SLATE, Behavior of High-Strength Concrete Beams, Research

Report No. 84-3, Department of Structural Engineering, Cornell University, Ithaca, New York, 1984

[2-F-2] Comité Euro-International du Béton, Design Code (CEB-FIP MC 90), Thomas Telford, London, 1993

[2-F-3] Norwegian Standard NS 3473, Concrete Structures – Design and detailing rules, The Norwegian Council

for Building Standardisation, N.B.R., Oslo, Norway, 1995

[2-F-4] Committee BD-002 (Concrete Structures), Australian Standard - Concrete Structures (AS 3600-2001),

Standards Australia, Australia, 2001, 181 Page.

References


[2-F-5] Halit Cenan MERTOL, Sami RIZKALLA, Paul ZIA, Amir MIRMIRAN, Characteristics of Compressive

Stress Distribution in High-Strength Concrete, ACI Structural Journal, vol. 105, no. 5, September-October 2008,

Page. [626-633]

[2-F-6] CSA A23.3-04, Design of Concrete Structures, Includes Update No. 1 (2005), Update No. 2 (2007), and

Update No. 3 (2009), Canadian Standards Association, 01-Jan-2005, 240 Page.

[2-F-7] CAN/CSA S6-06, Canadian Highway Bridge Design Code, 10th Edition, Canadian Standards Association,

National Standard of Canada, 01-Nov-2006, 800 Page.

[2-F-8] Joint ACI-ASCE Committee 441, High-Strength Concrete Columns: State of the Art (ACI 441-R96), ACI

Manual of Concrete Practice, Part 5, 2005, Page. [441R-1-441R-13]

[2-F-9] NZS 3101: Part 1:2006, Concrete Structures Standard, Includes Amendment No. 1 (2006) and Amendment

No. 2 (2008), Wellington, New Zealand, 2006, 646 Page.

[2-F-10] ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary,

First Printing, January 2008, Page. [1-467]

[2-F-11] American Association of State Highway & Transportation Officials, AASHTO LRFD Bridge Design

Specifications, Customary U.S. Units with 2008 and 2009 Interim Revisions, 4th Edition, Washington DC, 2007,

https://bookstore.transportation.org/item_details.aspx?ID=879, accesat la 2 febr. 2010

[2-F-12] S. SARKAR, O. ADWAN, J. G. L. MUNDAY, High strength concrete: an investigation of the flexural

behavior of high strength RC beams, The Structural Engineer, vol. 75, no.7, April, 1997, Page. [115-121]

[2-F-13] BS 8110-1: 1997, Structural use of concrete – Part 1: code of pactice for design and construction, British

Standards Institution, London, 1997, 173 Page.

[2-F-14] S. A. ASHOUR, Effect of compressive strength and tensile reinforcement ratio on flexural behavior of

high-strength concrete beams, Engineering Structures, vol. 22, 2000, Page. [413-423]

[2-F-15] H. J PAM, A. K. H KWAN, M. S. ISLAM, Flexural strength and ductility of reinforced normal- and high-

strength concrete beams, Structures & Buildings, vol. 146, no. 4, 2001, Page. [381-389]

[2-F-16] WORKING PARTY of THE CONCRETE SOCIETY, Technical Report No.49, Design Guidance for High

Strength Concrete, The Concrete Society, Slough, UK, 1998

[2-F-17] L. F. A. BERNARDO, S. M. R. LOPES, Neutral Axis Depth versus Flexural Ductility in High-Strength

Concrete Beams, ASCE Journal of Structural Engineering, vol. 130, no.3, March, 2004, Page. [425-459]

[2-G] OTHER ARTICLES

[2-G-1] T. POSTELNICU, E. LOZINCĂ, R. PASCU, The new Romanian code for seismic evaluation of existing

buildings, CONSEC’10, Si th International Conference Concrete n er Severe Con itions Environment &

Loa ing”; Meri a, Me ic

[2-G-2] C. RUSANU, A. PAPURCU, R. PASCU, Comparative study of shear design according to EN 1992-1-1

and Romanian Code, 1st International Workshop on Design of Concrete Structures using EN 1992-1-1, Prague

[2-G-3] V. POPA, D. COŢOFANĂ, R. PASCU, A. PAPURCU, Displacement Capacity of Bending Controlled RC

Columns, 4th ECEE, Ohrid, Macedonia

[2-G-4] V. POPA, D. COŢOFANĂ, R. PASCU, Precast concrete columns connections for earthquake resistance.

Experimental research, 3rd FIB International Congress, Washington D.C.

https://bookstore.transportation.org/item_details.aspx?ID=879

References


[2-G-5] T. NAGY-GYÖRGY, V. STOIAN, D. DIACONU, C. DĂESCU, D. DAN, G. SAS, M. MOŞOARCĂ,

Pereţi din Beton Armat and capete de grinzi consolidate cu Materiale Compozite – Rezultatele încercărilor,

AICPS Review 1/2007

[2-G-6] L. BEREVOESCU, V. STOIAN, D. DAN, Solutii moderne pentru îmbunatatirea performantelor energetice

ale cladirilor, Analele Universit ții in Ora ea, I. SECTION, ARCHITECTURE AND CIVIL ENGINEERING,

2007

[2-G-7] A. FABIAN, V. STOIAN, D. DAN, New tehnological solutions used for High-Rise Buildings, Analele

Universit ții in Ora ea, I. SECTION, ARCHITECTURE AND CIVIL ENGINEERING, 2007

[2-H] ARTICLES WRITEN BY THE AUTHOR ALONE OR AS PART OF A TEAM

[2-H-1] D. MOLDOVAN; E. SZABO, Efectul condițiilor de mediu asupra betonului, Sesi nea e Com nic ri

Științifice St ențești, e iția a III–a, Cluj-Napoca, 7 mai 2004, Editura UT Press Cluj-Napoca

[2-H-2] D. V. MOLDOVAN, Betoane Performante, Sesi nea Național e Com nic ri Științifice St ențești,

Secți nea Constr cții Civile, In striale and Agricole, e iția a V–a, Cluj-Napoca, 11 mai 2007, Editura UT Press

Cluj-Napoca

[2-H-3] C. MĂGUREANU, D. V. MOLDOVAN, A short introduction to load carrying capacity for high strength

concrete, Ovidius University Annals Series: Civil Engineering, Vol. 1, No. 9, November 2007, p. 45-52

[2-H-4] C. MĂGUREANU, B. HEGHEȘ, C. LEȚIA, O. CORBU, A. CHIOREAN, D. V. MOLDOVAN,

C. NEGRUȚIU, Beton Armat – Îndrumător de laborator, Editura UT Press, Cluj-Napoca, 2007

[2-H-5] D. V. MOLDOVAN, Variația eforturilor unitare în zona comprimată pentru elemente încovoiate din

betoane de înaltă rezistență, Sesi nea Național e Com nic ri Științifice St ențești, Secți nea Constr cții

Civile, Industriale and Agricole, e iția a VI–a, Cluj-Napoca, 18 aprilie 2008, Editura UT Press Cluj-Napoca

[2-H-6] C. MĂGUREANU, B. HEGHEȘ, D. V. MOLDOVAN, Deformability and loading capacity of beams

realized with high strength/high performance concrete, Proc. of the Int. Conference CONSTRUCTIONS 2008,

9-10 May 2008, Cluj-Napoca, Romania, Journal of the Tehnical University ACTA TECHNICA NAPOCENSIS

no. 51, vol. II 2008, Section: Civil Engineering-Architecture, ISSN 1221-5848; p.83-89

[2-H-7] C. MĂGUREANU, D. V. MOLDOVAN, Legea de variaţie sigma-epsilon în zona comprimată pentru

elemente încovoiate din betoane de înaltă rezistenţă, Zilele Tehnice St ențești, Timișoara, 11-18 mai, 2008

[2-H-8] C. MĂGUREANU, B. HEGHEȘ, D. V. MOLDOVAN, Behaviour and design of HSC members subjected to

flexure, Proc. of 4th Int. Conference HIGH PERFORMANCE STRUCTURES AND MATERIALS, Algavre,

Portugalia, 13-15 May, 2008

[2-H-9] R. I. CHIUZBAIAN, D. MOLDOVAN, Betonul Aparent, Sesi nea Național e Com nic ri Științifice

St ențești, Secți nea Constr cții Civile, In striale and Agricole, E iția a VIII-a, Cluj-Napoca, 6 mai 2010,

Editura UT Press, Cluj-Napoca

[2-H-10] C.-T CIOCAN, D MOLDOVAN, Betonul Permeabil, Sesi nea Național e Com nic ri Științifice

St ențești, Secți nea Constr cții Civile, In striale and Agricole, E iția a VIII-a, Cluj-Napoca, 6 mai 2010,

Editura UT Press, Cluj-Napoca

[2-H-11] D. MOLDOVAN, Scurtă analiză a costurilor elementelor realizate din Betoane de Înaltă Rezistență,

Conferința Național ȘTIINȚA MODERNĂ AND ENERGIA: PRODUCEREA, TRANSPORTUL AND

References


UTILIZAREA ENERGIEI, E iția 2 , Cl j-Napoca, 20-21 mai 2010, RisoPrint Cluj-Napoca, ISSN 2066-4125,

p. 401-407

[2-H-12] D. MOLDOVAN; C. MĂGUREANU, Static Modulus of Elasticity of High Strength Concrete, 8th Int.

Sym osi m COMPUTATIONAL CIVIL ENGINEERING, May 28th, 2010, Technical University “Gh. Asachi”

Iaand, România

[2-H-13] D. MOLDOVAN; C. MĂGUREANU, Stress-Strain Diagram For High Strength Concrete Elements In

Flexure, Proc. r Int. Conference „ADVANCED COMPOSITE MATERIALS ENGINEERING” COMAT

2010, 27- 29 October 2010, Brasov, Romania, Transilvania University Press of Brasov, Page. 137-142

[2-H-14] D. MOLDOVAN; C. MĂGUREANU, Modulus of Elasticity For High Strength Concrete, Proc.

of the Int. Conference MINERAL RESOURCES AND ENVIROMENT, E iția a 2-a, 28 – 30

octombrie 2010, Baia Mare, România, North University of Baia Mare Publishing House

(ABSTRACT), Page. 61; Scientific Bulletin of the North University of Baia Mare, Series D, Vol.

XXIV nr. 2, Page. 141-150

[2-H-15] D. MOLDOVAN, Concrete Grade Influence on the Bearing Capacity of Flexural Members,

Proc. of the Int. Scientific Conference PEOPLE, BUILDINGS AND ENVIRONMENT 2010

[2-H-16] 10-12 November 2010, Krtiny, Czech Republic, Akademicke Nakladatelstvi Cerm, s.r.o. Brno,

Page. 218-223

[2-H-17] D. MOLDOVAN; C. MĂGUREANU, Flexural behaviour and design of High Strength Concrete

Members, Int. Scientific Conference CIBv 2010, Braşov 12-13 November 2010, România, Transilvania

University Press of Brasov, Page. 209-214

[2-H-18] O. CORBU, C. MĂGUREANU, D. MOLDOVAN, H. SZILAGYI, Ultra-High Strength And Performance

Concrete Properties, Proc. of fib Symposium PRAGUE 2011, 8-10 June 2011 Prague, Czech Republic, vol. I,

Page. 495-498

[2-H-19] O. CORBU, D. MOLDOVAN, Ultra High Performance Steel Fiber Reinforced Concrete, Conferinta

CONSTRUIESTE CU STEEL, Cluj-Napoca 20-21 mai 2011, România

[2-H-20] O. CORBU, D. MOLDOVAN, C. MĂGUREANU, H. SZILAGYI, O. CAZAC, Innovative green concrete

mixes by use of glass by-products, Proc. of 7rd CCC CONGRESS BALATONFÜRED 2011, INNOVATIVE

MATERIALS AND TECHNOLOGIES FOR CONCRETE STRUCTURES, 22–23 September 2011,

Balatonfüred, Hungary, Balazs – Lubloy 2011, Page. 211-214

[2-H-21] C. MĂGUREANU, B. HEGHEȘ, H. CONSTANTINESCU, D. MOLDOVAN, Betoane de Înaltă

Performanță. Capacitate portantă and deformabilitate, Conf. Naț. INGINERIA CLĂDIRILOR, Secț.

MATERIALE AND TEHNOLOGII ACTUALE PENTRU REALIZAREA CLĂDIRILOR, 2 –30 Sept. 2011,

B c rești, România, E . Cons ress, B c rești, Page. 274-281


III. EXPERIMENTAL INVESTIGATIONS

A. Concrete properties

a. Compressive strength

Tab. [3]

Tab. [3-A-1] Mix proportions

Cement CEM I

(52,5 R)

Aggregate

(8-16)

Aggregate

(4-8)

Sand

(0-4)

Silica

fumeWater

[kg/mc] [kg/mc] [kg/mc] [kg/mc] [kg/mc] [l/mc] Type [l/mc]

I 480 706 530 530 48 13,5 RAVENIT 152 C60

BH 520 706 530 530 52 13,5 AC 30 152 C80

SuperplasticizerSeries

Concrete

grade

Tab. [3-A-2] Chararteristic compressive strength (statistical analysis)

Indi

vidu

al

Com

pres

sive

St

reng

th

SUM

of

indi

vidu

al

valu

es

Mea

n St

reng

th

Off

sets

fro

m

mea

n va

lue

Min

imum

O

ffse

t

Max

imum

O

ffse

t

Squa

re o

f O

ffse

t V

alue

s

SUM

of

Squa

re

Off

sets

Stan

dard

D

eriv

atio

n

Var

iatio

n C

oeff

icie

nt

Cha

ract

eris

tic

Stre

ngth

fci Σ fci fcm Δ fcm Δ fcm, min Δ fcm, max (Δ fcm)2 Σ (Δ fcm)2 Sn cv fck,cube

[N/mm2] [N/mm2] [N/mm2] [N/mm2] [N/mm2] [N/mm2] [N/mm2] [N/mm2] [N/mm2] [-] [N/mm2]

I 1-1 75,556 1,086 1,180

I 1-2 75,556 1,086 1,180

I 2-1 73,333 -1,136 1,290

I 2-2 73,333 -1,136 1,290

I 3-1 77,778 3,309 10,947

I 3-2 77,778 3,309 10,947

I 4-1 72,889 -1,580 2,497

I 4-2 80,444 5,975 35,704

BH 1-2 106,089 10,228 104,615

BH 1-1 88,671 -7,190 51,691

BH 2-2 95,400 -0,461 0,212

BH 3-1 96,662 0,801 0,642

I 1-1 92,444 7,636 58,314

I 1-2 92,444 7,636 58,314

I 2-1 91,111 6,303 39,728

I 2-2 84,444 -0,364 0,132

I 3-1 70,222 -14,586 212,747

I 3-2 85,778 0,970 0,940

I 4-1 86,667 1,859 3,454

I 4-2 92,889 8,081 65,299

BH 2-2 99,107 -3,449 11,895

BH 3-1 104,267 1,711 2,928

BH 3-2 103,080 0,524 0,275

1,967 0,019 99,644

Bea

m

1340,444 74,469 -4,691 5,975 210,261 3,517 0,047 69,264

8,987 0,094 82,560

615,333 102,56 -3,449 1,711 19,346

7,142 0,084 74,237

90 days

28 days

1865,778 84,808 -14,586 8,081 1071,264

862,747 95,861 -18,994 10,228 646,097


Chapter 3. Experimental Investigations


b. Stress-strain curve

Experimental strains were measured using digital transducers having a precision of

( ) under constant deformation load of ( ) on prismatic samples of

( ), subjected to uniaxial compression load on a 3000 kN compression

frame and precision class 1 connected to an Advantest 9 type loading machine.

The experimental load-deformation curves obtained were downsized to 15 curves for

each series and converted to stress-stain curves than enabled the determination of a mean curve

based on the following procedure:

(a) The maximum stress-strain curve was identified along with any other curve having a

maximum negative offset of 5% from this upper limit;

(b) The minimum stress-strain curve was identified along with any other curve having a

maximum positive offset of 5% from this lower limit;

(c) Those curves (9 for series C60 and 7 for series C80) were removed at this stage of

the procedure;

(d) An additional curve in series C80 (8 curve remaining) exhibited offsets values in

terms of strains domain and it was also removed;

(e) Remaining curves were used to calculate the mean curve for each series.

B. Reinforcement properties

Rebars for the main longitudinal reinforcement are either local available PC 52 (Mechel

Cîmpia Turzii) or Bst 500 S imported from Hungary with sizes starting with 12, 14, 16 and 18

[mm], in various layout, on one or two rows. Constructive longitudinal top reinforcement is from

local available size 6 [mm] OB 37 just as the stirrups evenly spaced at [300 mm] along the end

thirds of the beam to prevent shear failure close to the supports.

Reinforcement properties were established on a VEB ZD 10/90-1976 loading machine

having force transducers with a precision of 0,03 [kN], displacement transducers with a precision

of 0,03 [mm] and real time CATMAN acquisition software from HBM.

Modulus of Elasticity is considered to be the prescribed ( ).

(Space inetntionally left blank)



Tab. [3-B]

Tab. [3-B-1] Reinforcement properties

Type ft [MPa] fy [MPa] fy/ft k = ft /fy Ductility Class

PC 52 534,80 392,00 0,706 1,410 C

Bst 500 S 642,25 553,00 0,861 1,160 C

C. Experimental programme

The facilities used in this research are those available in the Reinforced and Prestressed

Structural Concrete Laboratory as part of the Central Laboratory of the Faculty of Civil

Engineering of Technical University of Cluj-Napoca.

D. Beam response under flexure

I 1-1 and I 1-2, I 2-1 and I 2-2, I 3-1 and I 3-2, I 4-1 and I 4-2,

BH 1-1 and BH 1-2,

BH 2-1 and BH 2-2,

BH 3-1 and BH 3-2,

Fig. [1- B] Fig. [1- C] Fig. [2] Fig. [3] Fig. [3-A] Fig. [3- B] Fig. [3- C] Fig. [3-D]

Reinforcement layout

Chapter 3. Experimental Investigations


Beams were loaded at 90 days on a 3000 kN maximum load and precision class 1

loading machine type WPM 262/6-1977 with a constant loading speed of ( ⁄ ). Each

load step was calculated to be 1/10 of the expected maximum flexure resistive moment and took

about ( ) to fully record data. The beams were simply supported with a span of

3,00 [m] in a four points test setup. Critical sections (middle and where the two concentrated

force where applied) are equipped with digital transducers to record concrete strains over the

height of the cross section.

For each beam two diagrams were later drawn to showcase the variation in time of the

strains over the height of the cross section presented in Chapter 6, Appendix I.

Tab. [3-C] Tab. [3-D]

Tab. [3-D-1] Experimental data

Beamfci,med

(MPa)b (mm) h (mm)

d

(mm)

As

(mm2)

fy

(MPa)ρ ω

Force

(kN)

Moment

(kNm)

Force

(kN)

Moment

(kNm)

I 1-1 92,4 125,00 240,00 191 628 392 0,0263 0,1113 32,38 32,38 49,75 49,75

I 1-2 92,4 125,00 240,00 191 628 392 0,0263 0,1113 29,19 29,19 50,00 50,00

I 2-1 92,4 130,00 240,00 191 735 392 0,0296 0,1255 35,62 35,62 67,00 67,00

I 2-2 85,1 130,00 245,00 196 735 392 0,0289 0,1329 36,15 36,15 66,00 66,00

I 3-1 85,1 130,00 245,00 194 817 392 0,0323 0,1490 33,04 33,04 73,50 73,50

I 3-2 76,7 130,00 245,00 194 817 392 0,0323 0,1652 32,81 32,81 67,50 67,50

I 4-1 76,7 125,00 245,00 193 911 392 0,0378 0,1933 37,83 37,83 77,50 77,50

I 3-2 89,9 130,00 240,00 188 911 392 0,0374 0,1629 38,46 38,46 72,50 72,50

BH 1-1 102,4 122,75 249,00 215 355 553 0,0134 0,0725 21,26 21,26 48,00 48,00

BH 1-2 97,0 124,75 248,50 215 355 553 0,0132 0,0755 23,22 23,22 48,00 48,00

BH 2-1 100,3 126,50 252,50 205 452 553 0,0175 0,0964 29,56 29,56 55,00 55,00

BH 2-2 100,3 124,00 252,25 204 452 553 0,0179 0,0985 28,73 28,73 54,50 54,50

BH 3-1 103,7 124,75 241,25 195 575 553 0,0236 0,1259 31,61 31,61 62,00 62,00

BH 3-2 103,7 124,75 241,25 195 575 553 0,0236 0,1259 38,58 38,58 62,50 62,50

Mechanical and geometrical parameters Yielding Failure


IV. EXPERIMENTAL STRESS-STRAIN CURVE

A. PROPOSED DEFINITIONS

a. Stress-strain curve

Based on the cited 22 models with 26 relationships a number of ( ) for

series and ( ) for series calculated stress-strain curves lead to a new stress-

strain definition as:

[3]

( )

( )

[4] A

[4-A-1]

The above cited ”a”, ”b” and ”c” parameters were established on a quality based criterio

and permitted the fabrication of calculated stress-strain curves as presented in Chapter 6,

Appendix II.

b. Concrete strain corresponding to the maximum stress

Tab. [4]

Tab. [4-A-1] Experimental values for (notation as per SR EN 1992-1-1:2004)

0 1 2 3 4 5 6 7

[10-3] [10-3] [10-3] [10-3] [10-3] [10-3] [10-3] [10-3] [10-3]

C60 2,017 2,117 1,568 1,341 1,273 2,162 1,712 1,741

C80 1,123 1,156 1,289 0,907 0,885 0,955 0,852 1,042 1,026

Concrete Grade

Experimental Curve Mean value

{ ( )

( ) [4-A-2]

c. Ultimate concrete strain

Tab. [4-A-2] Experimental values for (notation as per SR EN 1992-1-1:2004)

0 1 2 3 4 5 6 7

[10-3] [10-3] [10-3] [10-3] [10-3] [10-3] [10-3] [10-3] [10-3]

C60 3,224 2,661 2,180 2,042 1,667 2,887 2,444 2,444

C80 1,500 1,462 1,806 1,588 2,073 1,420 1,585 1,633 1,633

Concrete Grade

Experimental Curve Mean Value

{ ( )

( ) [4-A-3]

Chapter 4. Experimental Stress-Strain Curve


d. Centroid position for the experimental stress-strain curve

The mathematical relations used are:

[4-A-4]

∫

[4-A-4.1]

∫ ( ) [4-A-4.2]

centroi osition from the ne tral a is [ ]

concrete strain [ ]

( ) stress f nction [MPa]

area of the integral of the stress f nction [MPa]

which were them referenced to the most compressed fiber using:

[4-A-4.3]

ltimate concrete strain [ ]

concrete strain corres on ing to the osition of the ne tral a is [‰]

e. Stress block models

Two stress block models were established in present study:

(1) An equivalent rectangular model similar to national code provisions;

(2) A triangular model, sometimes considered to be more appropriate for HSC.

B. Resistive flexural capacity

a. Cited models

In order to evaluate flexural capacity the following procedure is implemented:

(1) Known values for ( ) the coefficient of the effective height of the stress block and ( ) the

coefficient for the effective concrete stress are extracting according to the model cited;

(2) The tensile resultant in the reinforcement ( ) is calculated based on the reinforcement area

( ) and the effective yielding strength of the reinforcement ( ) (similarly for the calculated

yielding strength of the reinforcement ( ));

(3) The compressive resultant in concrete ( ) is calculated based on the width of the cross

section ( ), the effective concrete compressive strength ( ) and the corresponding



coefficient ( ) as a multiple of ( ) (similarly for the calculated concrete compressive strength

( ));

(4) Product ( ) is evaluated from ( );

(5) The neutral axis position is calculated by dividing the above ( ) to the known values for

( );

(6) Lever arm is calculated next;

(7) Finally the resitive capacity is flexure is ( ) (for effective strengths of the

materials) and 𝑀𝑅𝑑 𝐴𝑠𝑙 𝑓𝑦𝑑 𝑧 respectively (for the calculated strengths of the materials).

b. Proposed trapezoid stress block model

A trapezoid stress block as per [4-C-4] and [4-C-1] is proposed:

( )

(

)

respectiv

Parameters for the trapezoid stress block

[4-B] A [4-C]

{ ( ⁄ )

( ) [4-C-1.1]

{ ( ) t.

( ) t.

– strain corres on ing to ma im m stress( )

[4-C-1.2]

{ ( ) t.

( ) t. – ltimate strain

[4-C-1.3]

c. Proposed equivalent rectangular stress block

The following algorithm is implemented:

(a) The neutral axis position in [mm] is considered to be equal to half the sum of the

ultimate strain ( ) and the one corresponding to the maximum stress ( );

(b) That proportion is used to convert ( ) and ( ) from [ ] to

[ ] and thus determine the position of the compression centroid ( ) in [ ];

(c) Finally calculate ( ) and ( ) for this model.

Chapter 4. Experimental Stress-Strain Curve


Resistive flexural moment is calculated in tabel [4-B-3].

d. Proposed triangular stress block

Based on the same algorithm, the resistive flexural moment is calculated in tabel [4-B-

4].

e. Stress block parameters

[4-C-2]

{ ( ) t. istrib ția re t nghi lar echivalent t. istrib ția tri nghi lar

[4-C-2.1]

{ ( ) t. istrib ția re t nghi lar echivalent t. istrib ția tri nghi lar

[4-C-2.2]

Sintesys for flexural moment values

Sintez moment încovoietor (e erimental și e calcul utilizand valorile rezistentelor efective)

Experimental [E]

SR EN 1992-1-1 : 2004 (2004) [N]

Propunere distrib.

drept.-echiv. [P1] Propunere distrib.

triung. [P2]

80

75

70

65

60

55

50

45

40

35

M [kNm]

0,060 0,100 0,140 0,180 0,190 0,230 0,270 0,310

ω

50 [E]

67 [E]

73,5 [E]

77,5 [E]

49,75 [E]

66 [E]

67,5 [E]

72,5 [E]

48 [E]

55 [E]

62,5 [E]

54,5 [E]

62 [E]

43,82 [N]

50,49 [N]

54,66 [N]

60,18 [N]

40,22 [N]

46,99 [N]

59,19 [N]

44,47 [P1]

51,21 [P1]

55,35 [P1]

61,43 [P1] 61,21 [P1]

40,7 [P1]

47,72 [P1]

60,46 [P1]

40,64 [P1]

47,66 [P1]

ω = 0,1 ω = 0,22 ω = 0,2 ω = 0,281 ω = 0,107 ω = 0,1 6 ω = 0,18

Seria ”I”

Seria ”BH”

43,65 [P2]

50,04 [P2]

53,75 [P2]

59,72 [P2] 59,43 [P2]

40,26 [P2]

47 [P2]

59,32 [P2]

40,18 [P2]

46,93 [P2]


Drd. Ing. Dumitru Vasile MOLDOVAN [28]

Tab. [4-B]

Tab. [4-B-1] Resistive flexural moment as per literature proposed models

ρ ω MExp,u MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc

[-] [-] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm]

I 1-1 0,025 0,190 49,750 43,649 35,324 43,289 35,401 43,735 35,401 43,575 35,091 43,529 34,995 43,780 35,378 43,231 35,401 43,707 35,234 43,478 35,114 43,792 35,401 I 1-1

I 1-2 0,025 0,190 50,000 43,649 35,324 43,289 35,401 43,735 35,401 43,575 35,091 43,529 34,995 43,780 35,378 43,231 35,401 43,707 35,234 43,478 35,114 43,792 35,401 I 1-2

I 2-1 0,029 0,223 67,000 50,037 40,581 49,923 40,686 50,274 40,686 49,994 40,262 49,905 40,130 50,313 40,655 49,440 40,686 50,185 40,459 49,899 40,293 50,369 40,686 I 2-1

I 2-2 0,029 0,223 66,000 50,037 40,581 49,923 40,686 50,274 40,686 49,994 40,262 49,905 40,130 50,313 40,655 49,440 40,686 50,185 40,459 49,899 40,293 50,369 40,686 I 2-2

I 3-1 0,033 0,250 73,500 53,862 44,100 54,124 44,230 54,238 44,230 53,782 43,707 53,630 43,544 54,257 44,192 52,927 44,230 54,047 43,949 53,713 43,745 54,387 44,230 I 3-1

I 3-2 0,025 0,250 67,500 53,862 44,100 54,124 44,230 54,238 44,230 53,782 43,707 53,630 43,544 54,257 44,192 52,927 44,230 54,047 43,949 53,713 43,745 54,387 44,230 I 3-2

I 4-1 0,025 0,281 77,500 59,430 48,014 58,870 48,176 59,676 48,176 59,303 47,525 59,191 47,322 59,759 48,128 58,527 48,176 59,589 47,826 59,116 47,572 59,807 48,176 I 4-1

I 4-2 0,037 0,281 72,500 59,721 48,014 59,182 48,176 59,957 48,176 59,599 47,525 56,139 47,322 60,038 48,128 58,852 48,176 59,874 47,826 59,419 47,572 60,083 48,176 I 4-2

BH 1-2 0,013 0,107 48,000 40,255 31,661 39,777 31,708 N/A 31,772 40,185 31,661 40,165 31,625 40,280 31,780 40,011 31,450 40,252 31,729 40,109 31,638 40,264 31,808 BH 1-2

BH 1-1 0,013 0,107 48,000 40,176 31,661 39,838 31,708 40,197 31,772 40,114 31,661 40,094 31,625 40,231 31,780 39,922 31,450 40,193 31,729 40,044 31,638 40,228 31,808 BH 1-1

BH 2-2 0,018 0,146 55,000 46,997 36,883 46,326 36,958 N/A 37,062 46,883 36,883 46,859 36,823 47,054 37,076 46,604 36,540 47,003 36,993 46,762 36,844 47,036 37,122 BH 2-2

BH 2-1 0,018 0,146 54,500 46,930 36,883 46,246 36,958 N/A 37,062 46,815 36,883 46,790 36,823 46,989 37,076 46,530 36,540 46,937 36,993 46,691 36,844 46,971 37,122 BH 2-1

BH 3-1 0,023 0,184 62,000 59,317 46,376 58,014 46,497 N/A 46,665 59,137 46,376 59,082 46,280 59,363 46,687 58,695 45,822 59,295 46,554 58,945 46,313 59,313 46,761 BH 3-1

BH 3-2 0,023 0,184 62,500 59,317 46,376 58,014 46,497 N/A 46,665 59,137 46,376 59,082 46,280 59,363 46,687 58,695 45,822 59,295 46,554 58,945 46,313 59,313 46,761 BH 3-2

BeamE

xp

eri

men

tal

flex

ura

l m

om

en

tBeam

Co

eff

icie

nt

of

lon

git

ud

inal

rein

forc

em

en

t

Mech

an

ical

co

eff

icie

nt

of

lon

git

ud

inal

rein

forc

em

en

t AZIZINAMINI et al. (1994) (Seismic

Behavior of Square High-Strength...)

Raghu PENDYALA si Priyan MENDIS

(1997) (A Rectangular Stress-

block Model..)

Hisham H. H. IBRAHIM si James G. MacGREGOR

(1997) (Modification of

the ACI Rectangular Stress

Block...)

Mario M. ATTARD si Mark

G. STEWART (1998) (A Two

Parameter Stress...)

Ertekin OZTEKIN et al. (2003)

(Determination of rectangular stress

block...)

Sungjin BAE si Oguzhan

BAYRAK (2003) (Stress Block

Parameters for...)

Togay OZBAKKALOGL

U si Murat SAATCIOGLU

(2004) (Rectangular

Stress Block for...)

Teng-Hooi TAN si Ngoc-Ba

NGUYEN (2005) (Flexural Behavior

of Confined...)

Halit Cenan MERTOL et al.

(2005) (Characteristics of

Compressive Stress...)

Bing LI et al. (1994) (Strength and Ductility of

Reinforced Concrete...)

Observations

First column of each model (subscript ”eff”) corresponds to effective strength for concrete under compression ( ) and for steel under tension ( ).

Second column of each model (subscript ”calc”) corresponds to calculus strength for concrete under compression ( ) and for steel under tension ( ).

Both cases use known values for the coefficient of the effective height of the stress block ( ) and for the coefficient for the effective concrete stress ( ) according to the cited model.

N/A is the short for ”Not Available” and corresponds to those situations in which a model is not defined for the specific effective strength of concrete under compression ( ).


Chapter 4. Stress-strain curve under compression


Tab. [4-B-2] Resistive flexural moment as per code proposed models

ρ ω MExp,u MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc MRd,eff MRd,calc

[-] [-] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm] [kNm]

I 1-1 0,025 0,190 49,750 44,524 34,929 42,249 32,916 44,061 34,281 44,524 34,929 44,061 34,281 43,817 34,735 43,459 33,232 43,981 35,201 44,061 35,401 I 1-1

I 1-2 0,025 0,190 50,000 44,524 34,929 42,249 32,916 44,061 34,281 44,524 34,929 44,061 34,281 43,817 34,735 43,459 33,232 43,981 35,201 44,061 35,401 I 1-2

I 2-1 0,029 0,223 67,000 51,288 40,040 48,347 37,285 50,626 39,153 51,288 40,040 50,626 39,153 50,489 39,775 49,846 37,718 50,535 40,413 50,626 40,686 I 2-1

I 2-2 0,029 0,223 66,000 51,288 40,040 48,347 37,285 50,626 39,153 51,288 40,040 50,626 39,153 50,489 39,775 49,846 37,718 50,535 40,413 50,626 40,686 I 2-2

I 3-1 0,033 0,250 73,500 55,458 43,432 51,874 40,031 54,551 42,337 55,458 43,432 54,551 42,337 54,665 43,106 53,604 40,565 54,461 43,893 54,551 44,230 I 3-1

I 3-2 0,025 0,250 67,500 55,458 43,432 51,874 40,031 54,551 42,337 55,458 43,432 54,551 42,337 54,665 43,106 53,604 40,565 54,461 43,893 54,551 44,230 I 3-2

I 4-1 0,025 0,281 77,500 61,321 47,183 56,570 42,952 60,320 45,821 61,321 47,183 60,320 45,821 59,906 46,777 59,061 43,616 60,159 47,756 60,320 48,176 I 4-1

I 4-2 0,037 0,281 72,500 61,539 47,183 56,971 42,952 60,577 45,821 61,539 47,183 60,577 45,821 60,179 46,777 59,366 43,616 60,422 47,756 60,577 48,176 I 4-2

BH 1-2 0,013 0,107 48,000 40,766 31,639 39,244 30,334 40,496 31,324 40,766 31,639 40,496 31,324 40,222 31,324 40,098 30,706 40,436 31,749 40,496 31,869 BH 1-2

BH 1-1 0,013 0,107 48,000 40,707 31,639 39,238 30,334 40,426 31,324 40,707 31,639 40,426 31,324 40,218 31,324 40,039 30,706 40,371 31,749 40,426 31,869 BH 1-1

BH 2-2 0,018 0,146 55,000 47,819 36,847 45,439 34,726 47,383 36,334 47,819 36,847 47,383 36,334 46,990 36,334 46,759 35,331 47,292 37,026 47,383 37,220 BH 2-2

BH 2-1 0,018 0,146 54,500 47,769 36,847 45,341 34,726 47,325 36,334 47,769 36,847 47,325 36,334 46,923 36,334 46,688 35,331 47,232 37,026 47,325 37,220 BH 2-1

BH 3-1 0,023 0,184 62,000 60,620 46,318 56,673 42,893 59,930 45,490 60,620 46,318 59,930 45,490 59,186 45,490 58,901 43,869 59,774 46,606 59,930 46,921 BH 3-1

BH 3-2 0,023 0,184 62,500 60,620 46,318 56,673 42,893 59,930 45,490 60,620 46,318 59,930 45,490 59,186 45,490 58,901 43,869 59,774 46,606 59,930 46,921 BH 3-2

Beam

Ex

per

imen

tal

flex

ura

l

mo

men

tBeam

Co

effi

cien

t o

f lo

ng

itu

din

al

rein

forc

emen

t

Mec

han

ical

co

effi

cien

t o

f

lon

git

ud

inal

rei

nfo

rcem

ent

CEB (1993) (Design Code,

CEB-FIP MC 90)

EC 1992-1-1 (1993) (Eurocode

2: Design of concrete

structures...)

BS 8110-1:1997 (1998) (Structural use of concrete

Part 1...)

AS 3600-2001 (2001) (Australian

Standard - Concrete

Structures)

SR EN 1992-1-1:2004 (2004)

(Eurocod 2: Proiectarea

structurilor...)

CSA A23.3-04 (2005) (Design of

Concrete Structures...) si

CAN/CSA S6-06 (2006) (Canadian Highway Bridge

Design Code)

NZS 3101: Part 1:2006 (2006)

(Concrete Structures

Standard...)

ACI 318:2008 (2008) (Building

Code Requirements...)

STAS 10107-0/90 (1990) (Calculul si

alctuirea...)

Observations

First col mn of each mo el (s bscri t ”eff”) corres on s to effective strength for concrete n er com ression ( ) and for steel under tension ( ).

Secon col mn of each mo el (s bscri t ”calc”) corres on s to calc l s strength for concrete n er compression ( ) and for steel under tension ( ).

Both cases use known values for the coefficient of the effective height of the stress block ( ) and for the coefficient for the effective concrete stress ( ) according to the cited model.




Tab. [4-B-3] Resistive flexural moment for proposed equivalent rectangular stress block

Raport

Înăl

țim

ea u

tilă

Rez

iste

nța

efec

tiv

ă

Mo

men

tul

înco

vo

ieto

r

Mo

men

tul

înco

vo

ieto

r

Ex

per

imen

tal/

Ca

pab

il

fci,cube fck,cil fcd,cil b h d Asl fyd ρ ω λ η Fs Fc λ·x x z MRd MExp,y MExp,u MExp,u/MRd

[MPa] [MPa] [mm] [mm] [mm] [mm2] [MPa] [-] [-] [-] [-] [kN] λ·x [kN] [mm] [mm] [m] [kNm] [kNm] [kNm] [-]

I 1-1 92 125 240 191,429 628,32 392 0,026 0,111 0,840 0,980 246,301 11,324 21,749 25,892 180,554 44,471 32,385 49,750 1,119 I 1-1

I 1-2 92 125 240 191,429 628,32 392 0,026 0,111 0,840 0,980 246,301 11,324 21,749 25,892 180,554 44,471 29,186 50,000 1,124 I 1-2

I 2-1 85 130 240 191,000 735,13 392 0,030 0,136 0,840 0,980 288,172 10,843 26,576 31,639 177,712 51,212 35,615 67,250 1,313 I 2-1

I 2-2 85 130 245 191,000 735,13 392 0,030 0,136 0,840 0,980 288,172 10,843 26,576 31,639 177,712 51,212 36,146 66,000 1,289 I 2-2

I 3-1 77 130 245 189,250 816,81 392 0,033 0,170 0,840 0,980 320,191 9,777 32,750 38,988 172,875 55,353 33,041 74,000 1,337 I 3-1

I 3-2 77 130 245 189,250 816,81 392 0,033 0,170 0,840 0,980 320,191 9,777 32,750 38,988 172,875 55,353 32,813 67,500 1,219 I 3-2

I 4-1 90 125 245 187,588 911,06 392 0,039 0,169 0,840 0,980 357,136 11,016 32,420 38,595 171,378 61,205 37,830 78,500 1,283 I 4-1

I 4-2 90 130 240 187,588 911,06 392 0,037 0,163 0,840 0,980 357,136 11,457 31,173 37,111 172,002 61,428 38,459 72,500 1,180 I 4-2

BH 1-2 102 123 249 215,467 355,00 553 0,013 0,072 0,800 0,960 196,315 12,067 16,269 20,337 207,332 40,702 21,261 48,000 1,179 BH 1-2

BH 1-1 97 125 249 215,467 355,00 553 0,013 0,075 0,800 0,960 196,315 11,615 16,901 21,127 207,016 40,640 23,222 49,000 1,206 BH 1-1

BH 2-2 100 127 253 201,000 452,39 553 0,018 0,098 0,800 0,960 250,171 12,183 20,535 25,668 190,733 47,716 29,558 55,000 1,153 BH 2-2

BH 2-1 100 124 252 201,000 452,39 553 0,018 0,100 0,800 0,960 250,171 11,942 20,949 26,186 190,526 47,664 28,727 54,500 1,143 BH 2-1

BH 3-1 104 125 241 202,963 574,91 553 0,023 0,121 0,800 0,960 317,926 12,416 25,606 32,008 190,160 60,457 31,614 62,000 1,026 BH 3-1

BH 3-2 104 125 241 202,963 574,91 553 0,023 0,121 0,800 0,960 317,926 12,416 25,606 32,008 190,160 60,457 38,582 65,000 1,075 BH 3-2

I 1-1 60 40 125 250 201,429 628,32 305 0,025 0,190 0,840 0,980 191,637 39,110 46,559 181,874 34,854 32,385 49,750 1,427 I 1-1

I 1-2 60 40 125 250 201,429 628,32 305 0,025 0,190 0,840 0,980 191,637 39,110 46,559 181,874 34,854 29,186 50,000 1,435 I 1-2

I 2-1 60 40 125 250 201,000 735,13 305 0,029 0,223 0,840 0,980 224,215 45,758 54,474 178,121 39,937 35,615 67,250 1,684 I 2-1

I 2-2 60 40 125 250 201,000 735,13 305 0,029 0,223 0,840 0,980 224,215 45,758 54,474 178,121 39,937 36,146 66,000 1,653 I 2-2

I 3-1 60 40 125 250 199,250 816,81 305 0,033 0,250 0,840 0,980 249,128 50,843 60,527 173,829 43,306 33,041 74,000 1,709 I 3-1

I 3-2 60 40 125 250 199,250 816,81 305 0,033 0,250 0,840 0,980 249,128 50,843 60,527 173,829 43,306 32,813 67,500 1,559 I 3-2

I 4-1 60 40 125 250 197,588 911,06 305 0,037 0,281 0,840 0,980 277,874 56,709 67,511 169,234 47,026 37,830 78,500 1,669 I 4-1

I 4-2 60 40 125 250 197,588 911,06 305 0,037 0,281 0,840 0,980 277,874 56,709 67,511 169,234 47,026 38,459 72,500 1,542 I 4-2

BH 1-2 80 53 125 250 216,467 355,00 435 0,013 0,107 0,800 0,960 154,425 24,129 30,161 204,402 31,565 21,261 48,000 1,521 BH 1-2

BH 1-1 80 53 125 250 216,467 355,00 435 0,013 0,107 0,800 0,960 154,425 24,129 30,161 204,402 31,565 23,222 49,000 1,552 BH 1-1

BH 2-2 80 53 125 250 202,000 452,39 435 0,018 0,146 0,800 0,960 196,789 30,748 38,435 186,626 36,726 29,558 55,000 1,498 BH 2-2

BH 2-1 80 53 125 250 202,000 452,39 435 0,018 0,146 0,800 0,960 196,789 30,748 38,435 186,626 36,726 28,727 54,500 1,484 BH 2-1

BH 3-1 80 53 125 250 203,963 574,91 435 0,023 0,184 0,800 0,960 250,086 39,076 48,845 184,425 46,122 31,614 62,000 1,344 BH 3-1

BH 3-2 80 53 125 250 203,963 574,91 435 0,023 0,184 0,800 0,960 250,086 39,076 48,845 184,425 46,122 38,582 65,000 1,409 BH 3-2

Valori experimentale

Rupere

Grinda

Curgere

Valori efective pentru rezistentele betonului si armaturii

Rez

ult

anta

de

com

pre

siu

ni

din

bet

on

Înăl

țim

ea u

tilă

a

vo

lum

ulu

i d

e

ten

siu

ni

Po

ziți

a ax

ei n

eutr

e

Bra

țul

de

pâr

gh

ie

Valori de calcul pentru rezistentele betonului si armaturii

4,900

6,400

Mo

men

tul

înco

vo

ieto

r ca

pab

il

Caracteristici mecanice și geometrice

Grinda Rez

iste

nța

ind

ivid

ual

ă p

e cu

b

resp

ecti

v

cara

cter

isti

că p

e

Rez

iste

nța

de

calc

ul

la c

om

pre

siu

ne

pe

cili

nd

ruSecțiune de

calcul

Înălțimea

utilă

Ari

a d

e ar

măt

ură

lon

git

ud

inal

ă

Rez

iste

nța

de

calc

ul

la î

nti

nd

ere

Co

efic

ien

t d

e

arm

are

Co

efic

ien

t m

ecan

ic

de

arm

are

Coeficient pentru

Rez

ult

anta

de

înti

nd

eri

din

arm

ătu

ră

Valori calculate

Chapter 4. Stress-strain curve under compression


Tab. [4-B-4] Resistive flexural moment for proposed triangular stress block

Raport

Înăl

țim

ea u

tilă

Rez

iste

nța

efec

tiv

ă

Mo

men

tul

înco

vo

ieto

r

Mo

men

tul

înco

vo

ieto

r

Ex

per

imen

tal/

Ca

pab

il

fci,cube fck,cil fcd,cil b h d Asl fyd ρ ω λ η Fs Fc λ·x x z MRd MExp,y MExp,u MExp,u/MRd

[MPa] [MPa] [mm] [mm] [mm] [mm2] [MPa] [-] [-] [-] [-] [kN] λ·x [kN] [mm] [mm] [m] [kNm] [kNm] [kNm] [-]

I 1-1 92 125 240 191,429 628,32 392 0,026 0,111 1,000 1,000 246,301 11,556 21,314 21,314 177,219 43,649 32,385 49,750 1,140 I 1-1

I 1-2 92 125 240 191,429 628,32 392 0,026 0,111 1,000 1,000 246,301 11,556 21,314 21,314 177,219 43,649 29,186 50,000 1,145 I 1-2

I 2-1 85 130 240 191,000 735,13 392 0,030 0,136 1,000 1,000 288,172 11,064 26,045 26,045 173,637 50,037 35,615 67,250 1,344 I 2-1

I 2-2 85 130 245 191,000 735,13 392 0,030 0,136 1,000 1,000 288,172 11,064 26,045 26,045 173,637 50,037 36,146 66,000 1,319 I 2-2

I 3-1 77 130 245 189,250 816,81 392 0,033 0,170 1,000 1,000 320,191 9,976 32,095 32,095 167,853 53,745 33,041 74,000 1,377 I 3-1

I 3-2 77 130 245 189,250 816,81 392 0,033 0,170 1,000 1,000 320,191 9,976 32,095 32,095 167,853 53,745 32,813 67,500 1,256 I 3-2

I 4-1 90 125 245 187,588 911,06 392 0,039 0,169 1,000 1,000 357,136 11,241 31,772 31,772 166,407 59,430 37,830 78,500 1,321 I 4-1

I 4-2 90 130 240 187,588 911,06 392 0,037 0,163 1,000 1,000 357,136 11,690 30,550 30,550 167,222 59,721 38,459 72,500 1,214 I 4-2

BH 1-2 102 123 249 215,467 355,00 553 0,013 0,072 1,000 1,000 196,315 12,569 15,619 15,619 205,054 40,255 21,261 48,000 1,192 BH 1-2

BH 1-1 97 125 249 215,467 355,00 553 0,013 0,075 1,000 1,000 196,315 12,099 16,225 16,225 204,650 40,176 23,222 49,000 1,220 BH 1-1

BH 2-2 100 127 253 201,000 452,39 553 0,018 0,098 1,000 1,000 250,171 12,690 19,713 19,713 187,858 46,997 29,558 55,000 1,170 BH 2-2

BH 2-1 100 124 252 201,000 452,39 553 0,018 0,100 1,000 1,000 250,171 12,440 20,111 20,111 187,593 46,930 28,727 54,500 1,161 BH 2-1

BH 3-1 104 125 241 202,963 574,91 553 0,023 0,121 1,000 1,000 317,926 12,933 24,582 24,582 186,575 59,317 31,614 62,000 1,045 BH 3-1

BH 3-2 104 125 241 202,963 574,91 553 0,023 0,121 1,000 1,000 317,926 12,933 24,582 24,582 186,575 59,317 38,582 65,000 1,096 BH 3-2

I 1-1 60 40 125 250 201,429 628,32 305 0,025 0,190 1,000 1,000 191,637 38,327 38,327 175,877 33,705 32,385 49,750 1,476 I 1-1

I 1-2 60 40 125 250 201,429 628,32 305 0,025 0,190 1,000 1,000 191,637 38,327 38,327 175,877 33,705 29,186 50,000 1,483 I 1-2

I 2-1 60 40 125 250 201,000 735,13 305 0,029 0,223 1,000 1,000 224,215 44,843 44,843 171,105 38,364 35,615 67,250 1,753 I 2-1

I 2-2 60 40 125 250 201,000 735,13 305 0,029 0,223 1,000 1,000 224,215 44,843 44,843 171,105 38,364 36,146 66,000 1,720 I 2-2

I 3-1 60 40 125 250 199,250 816,81 305 0,033 0,250 1,000 1,000 249,128 49,826 49,826 166,033 41,363 33,041 74,000 1,789 I 3-1

I 3-2 60 40 125 250 199,250 816,81 305 0,033 0,250 1,000 1,000 249,128 49,826 49,826 166,033 41,363 32,813 67,500 1,632 I 3-2

I 4-1 60 40 125 250 197,588 911,06 305 0,037 0,281 1,000 1,000 277,874 55,575 55,575 160,538 44,609 37,830 78,500 1,760 I 4-1

I 4-2 60 40 125 250 197,588 911,06 305 0,037 0,281 1,000 1,000 277,874 55,575 55,575 160,538 44,609 38,459 72,500 1,625 I 4-2

BH 1-2 80 53 125 250 216,467 355,00 435 0,013 0,107 1,000 1,000 154,425 23,164 23,164 201,024 31,043 21,261 48,000 1,546 BH 1-2

BH 1-1 80 53 125 250 216,467 355,00 435 0,013 0,107 1,000 1,000 154,425 23,164 23,164 201,024 31,043 23,222 49,000 1,578 BH 1-1

BH 2-2 80 53 125 250 202,000 452,39 435 0,018 0,146 1,000 1,000 196,789 29,518 29,518 182,321 35,879 29,558 55,000 1,533 BH 2-2

BH 2-1 80 53 125 250 202,000 452,39 435 0,018 0,146 1,000 1,000 196,789 29,518 29,518 182,321 35,879 28,727 54,500 1,519 BH 2-1

BH 3-1 80 53 125 250 203,963 574,91 435 0,023 0,184 1,000 1,000 250,086 37,513 37,513 178,954 44,754 31,614 62,000 1,385 BH 3-1

BH 3-2 80 53 125 250 203,963 574,91 435 0,023 0,184 1,000 1,000 250,086 37,513 37,513 178,954 44,754 38,582 65,000 1,452 BH 3-2

Rez

ult

anta

de

înti

nd

eri

din

arm

ătu

ră

Valori calculate

Ari

a d

e ar

măt

ură

lon

git

ud

inal

ă

Rez

iste

nța

de

calc

ul

la î

nti

nd

ere

Co

efic

ien

t d

e

arm

are

Co

efic

ien

t m

ecan

ic

de

arm

are

Coeficient pentru

Rez

iste

nța

ind

ivid

ual

ă p

e cu

b

resp

ecti

v

cara

cter

isti

că p

e

Rez

iste

nța

de

calc

ul

la c

om

pre

siu

ne

pe

cili

nd

ruSecțiune de

calcul

Înălțimea

utilă

Valori de calcul rezistentele betonului si armaturii

5,000

6,667

Valori experimentale

Rupere

Grinda

Curgere


Rez

ult

anta

de

com

pre

siu

ni

din

bet

on

Înăl

țim

ea u

tilă

a

vo

lum

ulu

i d

e

ten

siu

ni

Po

ziți

a ax

ei n

eutr

e

Bra

țul

de

pâr

gh

ie

Mo

men

tul

înco

vo

ieto

r ca

pab

il


Grinda


V. CONCLUDING REMARKS

A. Sintesys

Present study focused on HSC used for casting members subjected to flexure and

samples subjected to uniaxial compression. Cited models and relations include both previous

research such as MERTOL et al. (2005) and TAN and NGUYEN (2005) or code provisions such

as ACI 318:2008 (2008) and SR EN 1992-1-1:2004 (2004).

Properties of the HSC matrix were analysed, relations for cylinder to cubic samples

conversion were investigated, ultimate concrete compression strain and other parameters that are

part of a proposed stress-strain curve were established. New values were proposed for the stress

block either equivalent rectangular or triangular.

B. Observations and conclusions

(1) Literature models are more suited than code models to evaluate the resistive capacity in

flexure while also exhibiting less offset values;

(2) The calculated neutral axis position has a large offset domain from the experimental values

regardless of the stress block model used for this computation. Still, similar resistive flexural

moments (10% difference from minimum to maximum) are calculated so it seem the neutral axis

position is not the most important parameter in evaluating the resistive capacity in flexure;

(3) În ciuda acestui gra mare e îm r știere a valorilor aferente oziției a ei ne tre, moment l

încovoietor capabil se sit eaz în aceeaand ban e valori ( iferențele s nt mai mici e 10% )

atât pentru propunerile avansate în literatura de specialitate cât and pentru cele consacrate la

nivel e norm ;

(4) ACI 318:2008 (2008) (Building Code Requirements...) model code is frequently the closest to

experimental values perhaps due to a two step process: on one hand, the calculated concrete

strength is higher than as per national code provisions SR EN 1992-1-1:2004

(2004) (Eurocod 2: Proiectarea structurilor...) for example and on the other hand the stress

block parameters seem to be better evaluated. The latter is demonstrated by the fact that although

NZS 3101: Part 1:2006 (2006) (Concrete Structures Standard...) operates with the same values

for the compressive strength the resistive flexural capacity is the first after the American code;

Chapter 5. Concluding remarks


(5) Halit Cenan MERTOL et al. (2005) (Characteristics of Compressive Stress...) proposed

model seems to calculate most frequently the closest values to the experimental ones in terms of

flexural moment;

(6) Since previous national code STAS 10107-0:90 did not have concrete grade superior to Bc60

(equivalent to C50/60 as per SR EN 1992-1-1:2004) the corresponding model is not suited for

present study and in particular for the C80 series (”BH” beams);

(7) Since SR EN 1992-1-1:2004 does not have steel grade Pc52 (close to S400 in terms of

yielding strength but not evuivalent to this lower admisable limit for steel grades) the

corresponding model is not suited for present study an in artic lar for the C60 series (”I”

beams).

C. RECOMMANDATIONS

Since the compressive strength increases more for HSC than for Normal Strength

Concrete, after the technological conditions allow for constantly obtaining proper HSC mixes,

the use in design of a partial coefficient of safety of ”1, ” to affect the characteristic strength of

concrete may be more than necessary. Therefore it may be better to use a coefficient of ”1,3”

(

vs.

giving a reduction of

, less than the

increase in strength from 28 days to 90 days as established in present study). Supplementary,

HSC are more compact than NSC and have an inner structure increasingly similar as concrete

grade increases to that of steel for which a partial coefficient of safety of ”1,1” is used.

APPENDIX I – Strain development over the height of the cross section


Beams I 1 (C60 – PC 52) – selected readings Beams I 1 (C60 – PC 52) – final reading Fig. [4] Fig. [5]

Strain development over the height of the cross section for the failure cross section

h [mm]

255 240 220

130

40

0

Ceas 1 Fibra s erioar Ceas 2

Ceas 3

Ceas 4

Fibra inferioar

ε [‰] (-) ε [‰] (+)

-5 -4 -3 -2 -1 0 1 2 3 4 5

h [mm]

240 220

130

40

0

Fibra s erioar Ceas 2

Ceas 3

Ceas 4

Fibra inferioar

Xu = 36 [mm]

0.06 (F) 0,16 0,26 0.60 (C) 0,68 0,76

0,84 0,90 0,92 0,95 0,98 1.00 (R)

h [mm]

255 240 220

130

40

0

Ceas 1


Ceas 3

Ceas 4

Fibra inferioar

ε [‰] (-) ε [‰] (+)

-5 -4 -3 -2 -1 0 1 2 3 4 5

h [mm]

240 220

130

40

0


Ceas 3

Ceas 4

Fibra inferioar

Xu = 36 [mm]

1.00 (R)

Capitolul 6. Anexe


Beams BH 1 (C80 – Bst 500S) – selected readings Beams BH 1 (C80 – Bst 500S) – final reading

Strain development over the height of the cross section for the failure cross section

h [mm]

264 249

225

170

90

25

0

Ceas 1

Fibra s erioar

Ceas 2

Ceas 3

Ceas 4

Ceas 5

Fibra inferioar

ε [‰] (-) ε [‰] (+)

-5 -4 -3 -2 -1 0 1 2 3 4 5

h [mm]

249

225

170

90

25

0

Fibra s erioar

Ceas 2

Ceas 3

Ceas 4

Ceas 5

Fibra inferioar

Xu = 38 [mm]

0.23 (F) 0,30 0.46 (C) 0,51 0,61

0,69 0,86 0,91 0,92 0.97 (R)

h [mm]

264 249

225

170

90

25

0

Ceas 1

Fibra s erioar

Ceas 2

Ceas 3

Ceas 4

Ceas 5

Fibra inferioar

ε [‰] (-) ε [‰] (+)

-5 -4 -3 -2 -1 0 1 2 3 4 5

h [mm]

249

225

170

90

25

0

Fibra s erioar

Ceas 2

Ceas 3

Ceas 4

Ceas 5

Fibra inferioar

Xu = 38 [mm]

0.97 (R)

APPENDIX II – Experimental stress-strain-curve


Tab. [5] Tab. [6] Tab. [6-A] Tab. [6-B]

Tab. [6-B-1] Selected parameters of the the stress-strain curve ( ) - concrete grade

( )

Experimental stress-strain curve ( )

Compression stresses volume (area) Compression centroid position

Capitolul 6. Anexe


Tab. [6-B-2] Selected parameters of the the stress-strain curve ( ) - concrete grade

( )

Experimental stress-strain curve ( ) Experimental stress-strain curve ( )

Compression stresses volume (area) Compression centroid position Compression stresses volume (area) Compression centroid position

APPENDIX III – Flexural resistive moment


Tab. [6-B-3] Resistive flexural moment as per SR EN 1992-1-1:2004 (2004) (Eurocod 2: Proiectarea structurilor...)

{

, entr 0 MPa

, entr 0 MPa 0 MPa

{

, entr 0 MPa

, entr 0 MPa 0 MPa

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fci,cube fck,cil fcd,cil b h d Asl fyd ρ ω λ η Fs Fc λ·x x z MRd εyd MExp,y εcu εs MExp,u MExp,u/MRd

[MPa] [MPa] [mm] [mm] [mm] [mm2] [MPa] [-] [-] [-] [-] [kN] λ·x [kN] [mm] [mm] [m] [kNm] [‰] [kNm] [mm/m] [‰] [kNm] [-]

I 1-1 92 125 240 191,429 628,32 392 0,026 0,111 0,694 0,788 246,301 9,103 27,056 38,993 177,90 43,817 32,3846 3,500 13,683 49,750 1,135 I 1-1

I 1-2 92 125 240 191,429 628,32 392 0,026 0,111 0,694 0,788 246,301 9,103 27,056 38,993 177,90 43,817 29,1860 3,500 13,683 50,000 1,141 I 1-2

I 2-1 85 130 240 191,000 735,13 392 0,030 0,136 0,712 0,824 288,172 9,122 31,591 44,355 175,20 50,489 35,6154 3,500 11,571 67,250 1,332 I 2-1

I 2-2 85 130 245 191,000 735,13 392 0,030 0,136 0,712 0,824 288,172 9,122 31,591 44,355 175,20 50,489 36,1463 3,500 11,571 66,000 1,307 I 2-2

I 3-1 77 130 245 189,250 816,81 392 0,033 0,170 0,733 0,866 320,191 8,642 37,049 50,534 170,73 54,665 33,0410 3,500 9,608 74,000 1,354 I 3-1

I 3-2 77 130 245 189,250 816,81 392 0,033 0,170 0,733 0,866 320,191 8,642 37,049 50,534 170,73 54,665 32,8125 3,500 9,608 67,500 1,235 I 3-2

I 4-1 90 125 245 187,588 911,06 392 0,039 0,169 0,700 0,800 357,136 8,997 39,696 56,694 167,74 59,906 37,8298 3,500 8,081 78,500 1,310 I 4-1

I 4-2 90 130 240 187,588 911,06 392 0,037 0,163 0,700 0,800 357,136 9,357 38,169 54,513 168,50 60,179 38,4592 3,500 8,544 72,500 1,205 I 4-2

BH 1-2 102 123 249 215,467 355,00 553 0,013 0,072 0,669 0,738 196,315 9,276 21,163 31,634 204,89 40,222 21,2609 3,500 20,340 48,000 1,193 BH 1-2

BH 1-1 97 125 249 215,467 355,00 553 0,013 0,075 0,683 0,765 196,315 9,257 21,208 31,073 204,86 40,218 23,2222 3,500 20,770 49,000 1,218 BH 1-1

BH 2-2 100 127 253 201,000 452,39 553 0,018 0,098 0,674 0,748 250,171 9,498 26,341 39,069 187,83 46,990 29,5575 3,500 14,506 55,000 1,170 BH 2-2

BH 2-1 100 124 252 201,000 452,39 553 0,018 0,100 0,674 0,748 250,171 9,310 26,872 39,857 187,56 46,923 28,7273 3,500 14,151 54,500 1,161 BH 2-1

BH 3-1 104 125 241 202,963 574,91 553 0,023 0,121 0,666 0,732 317,926 9,462 33,599 50,463 186,16 59,186 31,6140 3,500 10,577 62,000 1,048 BH 3-1

BH 3-2 104 125 241 202,963 574,91 553 0,023 0,121 0,666 0,732 317,926 9,462 33,599 50,463 186,16 59,186 38,5821 3,500 10,577 65,000 1,098 BH 3-2

I 1-1 201,429 628,32 0,025 0,190 191,637 40,345 52,058 181,26 34,735 32,3846 3,500 10,043 49,750 1,432 I 1-1

I 1-2 201,429 628,32 0,025 0,190 191,637 40,345 52,058 181,26 34,735 29,1860 3,500 10,043 50,000 1,439 I 1-2

I 2-1 201,000 735,13 0,029 0,223 224,215 47,203 60,907 177,40 39,775 35,6154 3,500 8,050 67,250 1,691 I 2-1

I 2-2 201,000 735,13 0,029 0,223 224,215 47,203 60,907 177,40 39,775 36,1463 3,500 8,050 66,000 1,659 I 2-2

I 3-1 199,250 816,81 0,033 0,250 249,128 52,448 67,675 173,03 43,106 33,0410 3,500 6,805 74,000 1,717 I 3-1

I 3-2 199,250 816,81 0,025 0,250 249,128 52,448 67,675 173,03 43,106 32,8125 3,500 6,805 67,500 1,566 I 3-2

I 4-1 197,588 911,06 0,025 0,281 277,874 58,500 75,484 168,34 46,777 37,8298 3,500 5,662 78,500 1,678 I 4-1

I 4-2 197,588 911,06 0,037 0,281 277,874 58,500 75,484 168,34 46,777 38,4592 3,500 5,662 72,500 1,550 I 4-2

BH 1-2 216,467 355,00 0,013 0,107 154,425 27,251 37,588 202,84 31,324 21,2609 3,500 16,656 48,000 1,532 BH 1-2

BH 1-1 216,467 355,00 0,013 0,107 154,425 27,251 37,588 202,84 31,324 23,2222 3,500 16,656 49,000 1,564 BH 1-1

BH 2-2 202,000 452,39 0,018 0,146 196,789 34,728 47,900 184,64 36,334 29,5575 3,500 11,260 55,000 1,514 BH 2-2

BH 2-1 202,000 452,39 0,018 0,146 196,789 34,728 47,900 184,64 36,334 28,7273 3,500 11,260 54,500 1,500 BH 2-1

BH 3-1 203,963 574,91 0,023 0,184 250,086 44,133 60,873 181,90 45,490 31,6140 3,500 8,227 62,000 1,363 BH 3-1

BH 3-2 203,963 574,91 0,023 0,184 250,086 44,133 60,873 181,90 45,490 38,5821 3,500 8,227 65,000 1,429 BH 3-2

250 435 0,725 0,850 5,66780 53 125

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Valori de calcul pentru rezistentele betonului si armaturii

60 40 125 250 305 0,775 0,950 4,750 1,525


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