FACULTY OF CIVIL ENGINEERING

Eng. Attila PUSKÁS

DEFORMATIONS OF WIDE BEAMS

PhD THESIS

- ABSTRACT -

Scientific Coordinator:

Prof.Univ.PhD.Eng. Zoltán KISS

Prof.Univ.DHC.Eng. Mircea MIHAILESCU

CHAIRMAN: - Prof.Univ.PhD.Eng. Mihai Iliescu - Dean, Faculty of Civil Engineering,

Technical University of Cluj-Napoca

MEMBERS: - Prof.Univ.PhD.Eng. Zoltan KISS - Scientific Coordinator, Technical

University of Cluj-Napoca

- Prof.Univ.PhD.Eng. Radu PASCU – Reviewer, Techincal University of

Civil Engineering Bucharest

- Prof.Univ.PhD.Eng. Valeriu STOIAN – Reviewer, “Politehnica” University

of Timișoara

- Prof.Univ.PhD.Eng. Nicolae TĂRANU - Reviewer, “Gheorghe Asachi”

Technical University of Iaşi

- Prof.Univ.PhD.Eng. Adrian M. IOANI – Reviewer, Technical University of

Cluj-Napoca

- 2012 -

Deformations of wide beams

Page 1

Contents

Abstract ....................................................................................................................................... 2

Chapter 1 – Introduction............................................................................................................... 2

Chapter 2 – Considerations regarding calculus of wide beams ....................................................... 2

Chapter 3 – Numerical analysis of the wide beam ......................................................................... 3

Chapter 4 – Experimental program ............................................................................................... 5

Chapter 5 – Interpretation of results. Conclusions. ........................................................................ 7

Selective References ................................................................................................................... 10

Appendixes ................................................................................................................................ 12

I. Full papers of the author from the domain of the thesis ......................................................12

II. Design of the wide beam using FETT-Abacus software .........................................................12

III. Test of beam PA-G1 ...............................................................................................................12

IV. Test of beam PA-G2 ...............................................................................................................12

V. Test of beam PA-G1 ...............................................................................................................12

The thesis is structured in 5 chapters and 5 appendixes, with a total of 227and 63 pages respectively,

having 361 figures, 41 tables and 105 references.

The abstract retains the structure and numbering of chapters, figures, tables, relations and references.

For a better understanding it is recommended to study the full thesis.

Deformations of wide beams

Page 2

Abstract

Wide beams are horizontal structural elements presenting multiple advantages when using for

multistory building having generally larger openings.

A special case is the use of wide precast prestressed concrete beams, where excessive initial

deformations of the beam before the continuization of the structure might adversely affect

subsequent behavior of the structure.

The thesis is studying behavior of wide precast prestressed concrete beams, by mean of

analytical, numerical and experimental studies.

Chapter 1 – Introduction

As introduction the chapter presents short history of reinforced concrete frame structures,

marked by the achievements of several personalities, followed by the evolution of the

prestressed concrete and sequences in prefabrication of reinforced concrete structures.

Despite of the mechanical disadvantages of wide beams with respect to the regular ones

multi-story building having wide beams are used when complex optimization parameters are

imposed. The second part of the chapter shows the rationality of wide beams, examples of

structures using wide reinforced concrete beams, and studies on wide concrete beams,

performed by researchers as Siah et al [89], Stehle et al [91], Benavent-Climet [30] and

Sherwood [88].

Existing standard limitations of wide beams regarding their dimensions are described

afterward, and the aim of the thesis, formulated as study of the effect of width, loading pattern

and transversal reinforcement ratio of wide beams on their deformations, and evaluation of

the prestressed beam design method based on Eurocod 2 applied for designing wide beams.

Chapter 2 – Considerations regarding calculus of wide beams

Based on the influence of the cross-section dimensions presented in fig. 2.2, the author

establishes the limit of the wide beams at b/h≥1.

Fig. 2.2: Influence of the cross-section on the deformation of the beam

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0

De

flec

tio

n

h/b ratio

A - const

h - const

b - const

wide beams regular beams

Deformations of wide beams

Page 3

Work stages of reinforced concrete and prestressed concrete beams are detailed afterward.

In work stage I calculus of structural elements subjected to bending is based on simplifying

hypotheses. In case of simple loadings, based on the similarity of the wide beams to the one

way slabs, calculus of the wide beams according to the theory of elasticity can be performed

accepting the limitations for thin slabs having small displacements, even if in some situations

wide beams are beyond the mentioned limitations. For the loads corresponding to the erection

phase of the beams from the structure presented in chapter 1, longitudinal and transversal

deformations of the beam are calculated in several phases.

Fig. 2.33: Longitudinal deformation of the beam for the superposition of loads

Fig. 2.34: Transversal deformation of the beam for the superposition of loads

Influence of width on deformations is studied based on the calculation according to the theory

of elasticity by the presented method.

In work stage II supplementary hypotheses are necessary for the calculus of the wide beam.

When calculating prestressed beams according Eurocod 2, effect of the width is neglected,

and the actual cross section is transformed into the idealized one. The initial stage of the beam

for the experimental studies is determined based on the calculation method of the prestressed

beam. Limit of the IInd

work stage is determined by calculating the value of the ultimate

moment by the Morsch method.

Chapter 3 – Numerical analysis of the wide beam

The analysis of the wide beam is done by modeling in Abaqus the prestressed beam by the

finite element method, taking into consideration the nonlinear behavior of the used materials

(Lubliner et al [62], Lee and Fenves [62], [63]). The stress-strain relationship for the concrete

is determined based on the model proposed by Mander [65], once the compression resistance

of the concrete being determined.

Analysis of the beam is performed for reinforcement ratios ρwc=0.168% and ρwc=0.084%, for

concentrated loads applied in the middle of the opening, on the sides of the beam, and for

distributed loads, using two steps of applying the loads; the first step is used for applying the

prestressing, while the second step is used for applying the load incrementally, monotone

increasingly.

0

5

0 1.9 3.8 5.7 7.6

d [

mm

]

Beam length [m]

Latură grindă

Axul grinzii

3.957 3.888 3.957

3.00

4.00

-600 0 600

d [

mm

] Lățime grindă [mm]

I+II+III

Deformations of wide beams

Page 4

Fig. 3.6: Stress-strain relationship used for concrete modeling [65]

Comparison of the deformations for the different type of loads is done by realizing the

bending moment-deformation diagrams.

Fig. 5.10: Bending moment-deformation diagrams for the studied beams

Deformations of beams are depending on the transversal reinforcement ratio and type of

applied loading.

Fig. 5.9: Transversal deformation of beam after prestress transfer

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

60.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

σ [N

/mm

2]

ε [‰]

0

100

200

300

400

500

600

700

800

900

1000

-30 -15 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210

Ben

din

g m

om

ent

[kN

m]

Deflection [mm]

q, ρwc=0.164%

F, ρwc=0.168%

F, ρwc=0.084%

q, ρwc=0.084%

F, ρwc=0.084%, majorat

-15.916

-15.871

-15.916

-15.926 -15.896 -15.926

-15.898

-15.830

-15.898

-15.950 -15.876

-15.950 -16.00

-15.75

-600 0 600

d [

mm

]

Lățime grindă [mm]

F,δwc=0.168% F, δwc=0.084% q, δwc=0.168% q, δwc=0.084%

Deformations of wide beams

Page 5

Fig. 5.11: Longitudinal deformations of beams for F=88.42 kN and q=15.789 kN/m2 (on edges)

Fig. 5.12: Transversal deformations of beams for F=88.42 kN and q=15.789 kN/m2

Chapter 4 – Experimental program

In order to study the behavior of wide prestressed precast beams, three elements, namely PA-

G1, PA-G2 and PA-G3 were tested, loaded by concentrated loads applied on the middle of the

opening, on the sides of the beams. The differences between the beams PA-G1 and PA-G2,

and PA-G3 are in the qualities of the materials used (due to concreting in different time),

transversal reinforcement ratio (ρwf=0.084% and ρwc=0.164%, respectively), and number of

load cycles applied.

In order to compare the calculated stress loss and stress distribution in the middle section of

the beam, at the transfer phase the strain variation in the active reinforcement (4) and upper

(2) and lover (2) passive reinforcements was measured by mean of strain gages displaced on

the studied reinforcements.

Fig. 4.18: Strain gages disposal for active

reinforcement

Fig.4.22: Strain gages disposal for passive

reinforcement

Using the Hooke’s law, stress variation in reinforcements can be calculated.

-1.5

-1.0

-0.5

0.0

0.5

0 1.9 3.8 5.7 7.6d[m

m]

Beam length [m] q, ρwc=0.168% q, ρwc=0.084% F, ρwc=0.168% F, ρwc=0.084%

0.088 0.064 0.088

0.080 0.084 0.080

0.756 0.695 0.756

0.769 0.678 0.769

0.00

0.50

1.00

-600 0 600

d [

mm

]

Lățime grindă [mm] q, ρwc=0.168%

q, ρwc=0.084%

F, ρwc=0.168%

F, ρwc=0.084%

1 2 3 4 1 2

4 3

Deformations of wide beams

Page 6

Fig. 4.20: Stress variation in tendons, at ½ section of the beam

During experiments, the beams were subjected to 3, 5, and 9 load cycles, respectively,

displacements in several points and strain variation being measured.

Fig. 4.28: Displacement transducers disposal

During experiments, the beams were subjected to 3, 5, and 9 load cycles, respectively,

displacements in several points and strain variation being measured. Differences in behavior

of the beams were remarked during the tests, due to differences in the used materials,

transversal reinforcement ratio, initial camber and load cycles applied.

Fig. 4.117: Longitudinal deformation of beams after consuming the camber

1,310

1,315

1,320

1,325

1,330

1,335

1,340

1,345

1,350

0 30 60 90 120 150 180 210

Stre

ss v

aria

tio

n[N

/mm

2 ]

Transfer time [sec]

ToronMijloc 1

ToronMijloc 2

ToronMijloc 3

ToronMijloc 4

-5

0

5

0 1.9 3.8 5.7 7.6

d [

mm

]

Beam length[m]

PA-G1, F=126.00 kN

PA-G2, F=110.00 kN

PA-G3, F=90.00 kN

Deformations of wide beams

Page 7

Fig. 4.118: Transversal deformation of beams after consuming the camber

Fig. 4.108: Strain variation on the side of the beam at the middle of the opening

Fig. 4.110: Strain variation on the upper face of the beam at the middle of the opening

Chapter 5 – Interpretation of results. Conclusions.

Influence of the width on the deflections of the beams using the principles from theory of

elasticity were established for uniform distributed loads and concentrated loads, displaced on

a transversal strip of 20 cm on the middle of the opening.

0.0

1.0

-600 0 600

De

form

atio

n [

mm

]

Beam width [mm]

PA-G1,F=126.00 kN

PA-G2,F=110.00 kN

PA-G3,F=90.00 kN

0

5

10

15

20

25

-2,000 -1,500 -1,000 -500 0 500 1,000 1,500 2,000

Be

am h

eig

ht

[cm

]

Strain[μm/m]

Ciclul 1

Ciclul 2

Ciclul 3

Ciclul 4

Ciclul 5

Cclul 6

Ciclul 7

Ciclul 8

Ciclul 9

0

200

400

600

800

1,000

1,200

1,400

1,600

-600 -400 -200 0 200 400 600

Stra

in [μ

m/m

]

Beam width [mm]

Ciclul 1

Ciclul 2

Ciclul 3

Ciclul 4

Ciclul 5

Ciclul 6

Ciclul 7

Ciclul 8

Ciclul 9

Deformations of wide beams

Page 8

Fig. 5.1: Transversal deformation of the beam with variable width, supposed to q=constant

Fig. 5.3: Relative transversal deformation of the beam with variable width, supposed to

P=constant

Using the assimilation of the wide beam with one way thin slab having small deformations for

width/height ratio smaller than 6 the relative transversal deformation of the beam is less than

1% for both layout of the service loads.

Fig. 5.15: Force-deflection diagrams for beams modeled and tested

Differences in force-deflection diagrams of the modeled and tested beams are due to time

dependent characteristics of concrete, differences of stress-strain curves for materials used in

-19.2

-19.1

-19.0

-18.9

-100 -80 -60 -40 -20 0 20 40 60 80 100d

[m

m]

Lățime grindă [mm]

b=200 cm

b=180 cm

b=150 cm

b=120 cm

b=90 cm

b=60 cm

b=40 cm

b=25 cm

-0.2

-0.1

0.0

-100 -80 -60 -40 -20 0 20 40 60 80 100

d [

mm

]

Lățime grindă [mm]

b=200 cm

b=180 cm

b=150 cm

b=120 cm

b=90 cm

b=60 cm

b=40 cm

b=25 cm

0

50

100

150

200

250

300

350

400

450

-45 -30 -15 0 15 30 45 60 75 90 105 120 135 150

Forc

e [

kN]

Deflection [mm]

ρwc=0.168%

ρwc=0.084%

PA-G1

PA-G2

PA-G3

Deformations of wide beams

Page 9

modeling and tests, and the effect of the cyclic loads, producing residual deformations even in

the elastic domain of behavior.

Transversal deformation of beams compared for tests and models for loads close to the

reference load shows differences smaller than 1 mm, for both transversal reinforcement ratio.

Fig. 5.16: Relative transversal deformation of beams at tests and in modeling for load close

to the reference load

Values of ultimate loads obtained during the experiments are 7÷13% higher than the value of

the calculated ultimate load according to Eurocod 2. Even if neither the longitudinal

compression stress nor the transversal tension stress achieves the ultimate limit, failure of

concrete appears in the axis on the upper face of beam in the middle of the opening, due to the

effect of the biaxial effort (longitudinal compression and transversal tension).

Fig. 5.20: Beam failure at biaxial effort (longitudinal compression & transversal tension)

Taking into account the results obtained in modeling and tests, appropriate behavior of the

wide precast prestressed beam dimensioned according Eurocod 2 can be remarked even if

concentrated load is applied.

The obtained results permits considering the method presented in Eurocod 2 for prestressed

beam appropriate and sufficient for dimensioning wide prestressed beams due to transversal

deformations smaller than 1% for b/h ratios less than 6. For this situation the relative

displacements of the edges with respect to the axis of the beams are sufficiently small, even in

0.704

0.000

0.510

0.692

0.000

0.552 0.360

0.000

0.680

0.122

0.000

0.122

0.139 0.000 0.139

0.00

0.25

0.50

0.75

-600 0 600

d [

mm

]

Beam width [mm] PA-G1, F=126.00kN

PA-G2, F=110.00kN

PA-G3, F=90.00kN

Model ρwc=0.168%

Model ρwc=0.084%

Deformations of wide beams

Page 10

case of loads close to the ones causing failure, so that they fit in permissible deviations set out

in NE 012/2 – 2010 [9], permitting neglecting the width influence for prestressed beams

having b/h<6.

Transversal deformation of the beam is produced even in case of uniform distributed load, not

only in case of concentrated loads applied on the sides. It was remarked that longitudinal

concave deformation is producing transversal convex deformation, and vice-versa.

Initial camber of the prestressed beams has major influence on the deformation of the beams

and on the crack appearance. By prestressing the beam transversal convex deformation is

obtained, thus limiting the relative deflection of the edges to the axis for loads at work stage I,

obtaining relative transversal deformations of neglecting size.

The experiments and models show influence of the load pattern on the actual ultimate loads

and on the failure modes, but also proper behavior of the beams even in case of concentrated

loads applied in the middle of the opening.

The most important conclusion of the thesis is that designing wide precast prestressed beams

neglecting the influence of the width can be applied for beams having b/h<6, due to relative

transversal deformations smaller than 1%, the relative displacement of the edges to the axis

being smaller, even in the middle of the opening, than the permissible deviations established

in NE 012/2 – 2010 [9].

Selective References

[1] *** ACI-318: Building code requirements. Michigan, USA, American Concrete Institute, 1999.

[3] *** CEB-FIB Model Code 2010, Federation Internationale du Beton, 2010

[4] *** Ceb-Fip no.43, Structural connections for precast concrete buildings’, Guide to good practice, ISBN

978-2-88394-083-3, February 2008;

[5] *** CSA A23.3-04/2005, Design of Concrete Structures, Canadian Standards Association

[6] *** DIN-1045, German code for the design of concrete structures. 2008

[7] *** fib bulletin 45: Practitioners’ Guide to Finite Element Modelling of Reinforced Concrete Structures,

Fédération Internationale du Béton, 2008.

[9] *** NE 012/2 - 2010: Normativ pentru producerea betonului și executarea lucrărilor din beton, beton armat

și beton precomprimat. Partea 2: Executarea lucrărilor din beton

[10] *** NE 013-2002: Cod de practică pentru execuția elementelor prefabricate din beton, beton armat și

beton precomprimat

[12] *** NZS3101: The New Zealand standard for the design of concrete structures. Wellington, New Zealand:

Standards New Zealand; 1995

[13] *** P100-1/2006: Cod de proiectare seismică — Partea I — Prevederi de proiectare pentru clădiri

[17] *** SR EN 1992-1-1. Eurocod 2: Proiectarea structurilor de beton, 2004

[21] Abaqus Cae, Analysis Manual

[23] K. Abdouka, H. Goldsworthy: Seismic effects on wide band beam construction in Australia, 15th

Australasian conference on the Mechanics of Structures and Materials, Melbourne, Australia, Balkema, 1997

(pg. 311-316)

[24] R. Agent, T. Postelnicu: Îndrumator pentru calculul și alcătuirea elementelor din beton armat, Editura

Tehnică București 1992

[26] C. Avram, C. Bob, R. Friedrich R., Stoian V.: Structuri din beton armat, Metoda elementelor finite. Teoria

echivalentelor, Editura Academiei Republicii Socialiste România, București,1984

Deformations of wide beams

Page 11

[29] A. Benavent-Climent: Influence of hysteretic dampers on the seismic response of reinforced concrete wide

beam–column connections, Engineering Structures 28, 2005

[30] A. Benavent-Climent: Shaking table tests of reinforced concrete wide beam–column connections,

Earthquake Engng Struct. Dyn. 2005; 34:1833–1839

[31] A. Benavent-Climent, X. Cahís, J.M. Vico: Interior wide beam-column connections in existing RC frames

subjected to lateral earthquake loading, Bulletin of Earthquake Engineering, Volume 8, Number 2, pp. 401-420,

2009

[33] P. Bhatt: Prestressed Concrete Design to Eurocodes, Taylor & Francis, 2011

[34] C. Bia, V. Ille, M.V. Soare: Rezistenţa materialelor şi teoria elasticităţii, Ed. Didactică și Pedagogică,

București, 1983

[36] I. Bucur Horvath: Épiteszet mérnökszemmel, Editura Kriterion, București, 1995

[37] I. Cadar, T. Clipii, A. Tudor: Beton armat, Editura Orizonturi Universitare Timișoara, 1999

[40] C.G. Chiorean: Aplicaţii Software pentru Analiza Neliniară a Structurilor în Cadre (Software Applications

for Non-linear Analysis of Frame Structure), UTPress, Cluj-Napoca, 2006

[45] K.S. Elliot: Precast Concrete Structures, Butterworth-Heinemann, Woburn, 2002

[48] T.R. Gentry, J.K. Wight: Reinforced concrete wide beam–column connections under earthquake-type

loading, USA, The University of Michigan, 1992 [Report no. UMCEE 92-12]

[49] A. Ghali, A. Neville: Structural analysis: a unified classical and matrix approach, E&FN Spon, 1997

[51] H. Hatamoto, S. Bessho, Y. Matsuzaki: Reinforced concrete wide beam-to-column subassemblages

subjected to lateral load. Design of beam–column joints for seismic resistance, SP123. Jirsa, J. Detroit,

Michigan: American Concrete Institute; 1991. p. 291–316.

[53] M.K. Hurst: Prestressed Concrete Design, E&FN Spoon, 2003

[54] A.M. Ioani: Structuri cu dale, Ed. Dacia, Cluj-Napoca, 1994

[56] Z. Kiss, K. Bálint, A. Puskás: Steel or concrete structure – prefabricated or cast in situ? The design of a

multistory building in Bucharest for Kika, III, Medunarodna Savetovanke, Subotica, 8-9. Octobar 2009, p. 79-93

[57] Z. Kiss, K. Bálint, A. Puskás: High-efficiency reinforced concrete floor systems for multy-storey buildings,

Medunarodna Savetovanke, Subotica, 8-9. Octobar 2009, p. 171-180

[58] Z. Kiss, T. Oneț: Beton armat, Editura U.T. Press, Cluj-Napoca, 1999

[59] Z. Kiss, T. Oneț: Proiectarea structurilor din beton dupa SR-EN 1992-1, Editura Abel, Cluj-Napoca, 2008

[60] Z. Kiss, A. Puskas, K. Balint: Planșee performante pentru clădiri multietajate, Simpozionul Naţional – Noi

reglementări pentru Beton, Ed. Conspress, Bucureşti, 2009, pp. 94-102.

[61] J.M. LaFave, J.K. Wight: Reinforced concrete exterior wide beam–column-slab connections subjected to

lateral earthquake loading, ACI Structural Journal 1999;96(4):577–585.

[62] J. Lee, G.L. Fenves: Plastic-Damage Model for Cyclic Loading of Concrete Structures, (ASCE) 0733-

9399(1998)124:8(892), American Society of Civil Engineers, 1998

[64] J. Lubliner, J. Oliver, S. Oller, E. Oñate: A plastic-damage model for concrete, International Journal of

Solids and Structures, Volume 25, Issue 3, 1989, Pages 299-326

[65] J. B. Mander, M.J.N. Priestley, R. Park: Theoretical Stress-Strain Model For Confined Concrete, Journal of

Structural Engineering, 1988

[66] I. Marțian: Teoria elasticității și plasticității pentru constructori, Atelier de multiplicare UTC-N, 1999

[72] W.H. Mosley: Reinforced Concrete Design, Palgrave, 2007

[73] E. Mörsch: Concrete-Steel Construction (der Eisenbetonbau), University of Michigan Library, 2009

[74] E. O'Brien, A. Dixon, E. Sheils: Reinforced and Prestressed Concrete Design to EC2: The Complete

Process, Taylor & Francis; 2011

[75] T. Oneț, R.I. Olar: Beton precomprimat, U.T.Press, Cluj-Napoca, 2007

Deformations of wide beams

Page 12

[78] E. Panțel, C. Bia: Metode numerice în Proiectare. Metoda elementelor finite, Atelier de multiplicare UTC-

N, 1993

[80] A. Pauser: Beton im Hochbau, Verlag Bau+ Technik, 1998

[81] E.P. Popov, E. Cohen, K. Koso-Thomas, K. Kasai: Behavior of interior narrow and wide beams, ACI

Structural Journal, 1992;89(6):607–16.

[84] A. Puskás, Z. Kiss: Testing of a wide reinforced concrete beam, Innovative Materials and Tehnologies for

Concrete Structures – fib Congress, Balatonfüred, 22-23 September 2011, pg. 315-318

[85] A. Puskás, Z. Kiss, K. Balint: Grinzi late, ca opțiune, Conferința internațională de Știința Construcțiilor

ÉPKO 2011, Societatea Tehnico-Stiintifica Maghiara din Transilvania, Sumuleu-Ciuc, 2-5 iunie 2011, pp. 426-

431.

[86] B.V. Rangan, A.S. Hall: Moment and shear transfer between slab and edge column, ACI Struct J

1983;80(3):183–91.

[87] J.N. Reddy: Solutions manual for an introduction to the Finite Element Method, McGraw-Hill, New York,

2005

[88] E.G. Sherwood: One-Way Shear Behaviour of Large, Lightly- Reinforced Concrete Beams and Slabs, PhD

Thesis, University of Toronto, 2008

[89] W.L. Siah, J.S. Stehle, P. Mendis, H. Goldsworthy: Interior wide beam connections subjected to lateral

earthquake loading, Engineering Structures 25 (2003) 281–291

[90] J.S. Stehle, K. Abdouka, H. Goldsworthy, O. Mendis.: The seismic performance of reinfoerced concrete

frames with wide band beams, Second international symposium on earthquake resistant structures, Catania, Italy,

1999, WIT Press, pg. 113-122.

[91] J.S. Stehle, H. Goldsworthy, O. Mendis.: Reinforced concrete interior wide-band beam–column connections

subjected to lateral earthquake loading. ACI Structural Journal 2001;98(3):270–9.

[92] A. Steinle, V. Hahn: Bauen mit Betonfertigteilen im Hochbau, Ed. Züblin AG, Berlin, 1988

[94] I. Tertea.: Betonul precomprimat, Ed. Tehnică, 1981

[96] I. Tertea, T. Oneț, M. Viorel, V. Păcurar, Z. Kiss, C. Măgureanu: Proiectarea betonului precomprimat, At.

de Multiplicare al Institutului Politehnic Cluj-Napoca, 1986

[97] C.G. Quintero-Febres, J.K. Wight: Investigation on the seismic behavior of RC interior wide beam–column

connections, USA, University of Michigan, 1997 [Report no. UMCEE 97-15].

[98] I. Yamaguchi, O. Katsuya, O. Haruhiko, Y. In Tanaka: The behavior of prestressed concrete wide flat

beam-reinforced concrete column joints subjected to lateral loads, Tokyo, Takenaka Technical Research

Laboratory; 1985. p. 117–26 [Report no. 34].

[99] O.C. Zienkiewicz: The Finite Element Method in Engineering Science, McGraw-Hill London, 1972

Appendixes

I. Full papers of the author from the domain of the thesis

II. Design of the wide beam using FETT-Abacus software

III. Test of beam PA-G1

IV. Test of beam PA-G2

V. Test of beam PA-G1