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1
Reinforced Concrete
Structures 1 - Eurocodes
RCS 1
Professor Marwan SADEK
https://www.researchgate.net/profile/Marwan_Sa...
2
RCS1
M. SADEK
Ch 1 : Generalities – Reinforced concrete in practice
Ch 2 : Evolution of the standards – Limit states
Ch ...
3
Selected References
French BAEL Code (91, 99)
 Règles BAEL 91 modifiées 99, Règles techniques de conception et de calcu...
4
In addition to Eurocodes, the references that are mainly
used to prepare this course material are :
 Thonier 2013
 Per...
5
CHAPTER III
Mechanical Characteristics of Materials
Behaviour Constitutive Law
M. SADEK
1. Concrete
2. Steel
Annexes
6
Concrete compressive strength - Test
M. SADEK
 France : Cylindrical Concrete specimen, H/D = 2
(diameter16 cm, height 3...
7
M. SADEK
Concrete compressive strength - Test
1. Concrete 2. Steel  Annexes
8
M. SADEK
 fcm : Mean value of concrete cylinder compressive strength
 fck : Characteristic compressive cylinder streng...
9
Concrete compressive strength
1. Concrete 2. Steel  Annexes
10
> 200 MPa
 Ultra high performance concrete
Fiber Reinforced Concrete
1. Concrete 2. Steel  Annexes
11
fcm(t) = cc x fcm
 Normal Concrete
(t < 28 jours)
 fcm(t) is the mean concrete compressive strength at an age of t d...
12
M. SADEK
 fcd : Design value of concrete compressive strength
cc= 1 (ANF)
C = 1.5 (persistent situation) ; 1.2 (acci...
13
Another test for tensile strength of Concrete
 The tensile strength by splitting test
(Essai brésilien)
 Design of ri...
14
fctk : Characteristic axial tensile strength of concrete
fctk 0,05  fctm  fctk 0,95
1. Concrete 2. Steel  Annexes
15
 Behaviour of Concrete – Stress-Strain Diagram
1. Structural Analysis
2. Sections Design
1. Concrete 2. Steel  Annexes
16
1. Structural Analysis/ Second order effect
1. Concrete 2. Steel  Annexes
17
Modulus of Elasticity
Secant modulus Ecm (@ 0.4 fcm), for short term loading
Effective modulus of elasticity of concr...
18
2. Section Design
a) Parabola-rectangle
diagram
b) Bi-linear stress-strain relation
1. Concrete 2. Steel  Annexes
19
c) Rectangular stress distribution
Note : In the present lecture, the design of section at ULS is conducted using the
...
20
 Other aspects – Creep (EC2, 3.1.4)
1. Concrete 2. Steel  Annexes
21
At t =  , under a constant compression stress
 Ec : Tangent modulus of elasticity (may be taken as 1,05 Ecm)
 t0 : ...
22
Creep Coefficient
where Ac is the concrete cross-sectional area and u is
the perimeter of that part which is exposed to...
23
Creep Coefficient
1. Concrete 2. Steel  Annexes
24
M. SADEK
Poisson ratio
 = 0 - Calculation of internal forces
 = 0.2 - strain Calculation
1. Concrete 2. Steel  Annex...
25
M. SADEK
Steel
1. Concrete 2. Steel  Annexes
26
M. SADEK
 High bond (twisted):
 bars
 welded wire mesh
 Round or plain bars : rarely used in Europe (only if foldin...
27
M. SADEK
Steel used in R.C
1. Concrete 2. Steel  Annexes
28
M. SADEK


Tension Test
1. Concrete 2. Steel  Annexes
29
M. SADEK
The ductility of Steel of the reinforced concrete is characterized by :
εuk Characteristic strain of reinforc...
30
M. SADEK
 A : Normal ductility B500A (welded wire mesh in general, and bars with
low diameter)
 B : high ductility B5...
31
M. SADEK
The application rules for design and detailing in this Eurocode are valid for
a specified yield strength range...
32
M. SADEK
Idealised / Design stress-strain diagrams
for reinforcing steel (ULS)
s = 1.15 (persistent)
1.0 (accidentel)...
33
M. SADEK
 Design stress-strain diagrams:
 a horizontal top branch without the need to check the strain limit
 an inc...
34
M. SADEK
 Note : the calculation of the slope using the diagram A gives different value from that of
diagram B, due to...
35
M. SADEK
Elastic modulus Es = 200 000 MPa
Density = 7.85 T/m3
 Thermal expansion coefficient= 1.10-5
 Diameters:
6,...
36
M. SADEK
Annexes
1. Concrete 2. Steel  Annexes
37
M. SADEK
1. Concrete 2. Steel  Annexes
38
 6 8 10 12 14 16 20 25 32 40
1 0.28 0.50 0.79 1.13 1.54 2.01 3.14 4.91 8.04 12.57
2 0.57 1.01 1.57 2.26 3.08 4.02 6.2...
39
Welded wire mesh (anti cracking)
1. Concrete 2. Steel  Annexes
40
Welded wire mesh (France)
1. Concrete 2. Steel  Annexes
41
M. SADEK
42
M. SADEK
43
 Determination of the slope of the diagram (/) for steel A & B
 Deduce the equation of s for both Steel classes.
...
44
fck(t)=fcm(t) – 8
fcm(t) = cc x fcm
cc= 1 (FNA)
C = 1.5 (persistent) ; 1.2 (accidental)
Reminder of main formulas
45
s = 1.2 (persistent)
1.0 (accidental)
or
Reminder of main formulas
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Rcs1-chapter3-constitutive-law

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- Mechanical Characteristics of Materials
Behaviour
- Constitutive Law
- Compressive strength of concrete
- Concrete Constitutive law - Diagrams (parabola rectangle , bilinear, rectangular)
- Steel constitutive law - horizontal top branch / inclined top branch diagrams
- classes of ductility

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Rcs1-chapter3-constitutive-law

  1. 1. 1 Reinforced Concrete Structures 1 - Eurocodes RCS 1 Professor Marwan SADEK https://www.researchgate.net/profile/Marwan_Sadek https://fr.slideshare.net/marwansadek00 Email : marwansadek00@gmail.com If you detect any mistakes, please let me know at : marwansadek00@gmail.com
  2. 2. 2 RCS1 M. SADEK Ch 1 : Generalities – Reinforced concrete in practice Ch 2 : Evolution of the standards – Limit states Ch 3 : Mechanical Characteristics of materials – Constitutive relations Ch 4 : Durability and Cover Ch 5 : Beam under simple bending – Ultimate limit state ULS Ch 6 : Beam under simple bending – serviceability limit state SLS Ch 7 : Section subjected to pure tension
  3. 3. 3 Selected References French BAEL Code (91, 99)  Règles BAEL 91 modifiées 99, Règles techniques de conception et de calcul des ouvrages et constructions en béton armé, Eyrolles, 2000.  J. Perchat (2000), Maîtrise du BAEL 91 et des DTU associés, Eyrolles, 2000.  J.P. Mougin (2000), BAEL 91 modifié 99 et DTU associés, Eyrolles, 2000.  …. EUROCODES  H. Thonier (2013), Le projet de béton armé, 7ème édition, SEBTP, 2013.  Jean-Armand Calgaro, Paolo Formichi ( 2013) Calcul des actions sur les bâtiments selon l'Eurocode 1 , Le moniteur, 2013.  J. M. Paillé (2009), Calcul des structures en béton, Eyrolles- AFNOR, 2009.  Jean Perchat (2013), Traité de béton armé Selon l'Eurocode 2, Le moniteur, 2013 (2ème édition)  Manual for the design of concrete building structures to Eurocode 2, The Institution of Structural Engineers, BCA, 2006.  A. J. Bond (2006), How to Design Concrete Structures using Eurocode 2, The concrete centre, BCA, 2006. https://usingeurocodes.com/ M. SADEK
  4. 4. 4 In addition to Eurocodes, the references that are mainly used to prepare this course material are :  Thonier 2013  Perchat 2013  Paillé 2009 Some figures and formulas are taken from  Cours de S. Multon - BETON ARME Eurocode 2 (available on internet)  Cours béton armé de Christian Albouy M. SADEK
  5. 5. 5 CHAPTER III Mechanical Characteristics of Materials Behaviour Constitutive Law M. SADEK 1. Concrete 2. Steel Annexes
  6. 6. 6 Concrete compressive strength - Test M. SADEK  France : Cylindrical Concrete specimen, H/D = 2 (diameter16 cm, height 32 cm) 1. Concrete 2. Steel  Annexes
  7. 7. 7 M. SADEK Concrete compressive strength - Test 1. Concrete 2. Steel  Annexes
  8. 8. 8 M. SADEK  fcm : Mean value of concrete cylinder compressive strength  fck : Characteristic compressive cylinder strength of concrete at 28 days (fck  90 MPa) Characteristic value & 5% Fractile % specimen fck(t)=fcm(t) – 8 (in MPa) Concrete compressive strength - Standard 1. Concrete 2. Steel  Annexes
  9. 9. 9 Concrete compressive strength 1. Concrete 2. Steel  Annexes
  10. 10. 10 > 200 MPa  Ultra high performance concrete Fiber Reinforced Concrete 1. Concrete 2. Steel  Annexes
  11. 11. 11 fcm(t) = cc x fcm  Normal Concrete (t < 28 jours)  fcm(t) is the mean concrete compressive strength at an age of t days 1. Concrete 2. Steel  Annexes
  12. 12. 12 M. SADEK  fcd : Design value of concrete compressive strength cc= 1 (ANF) C = 1.5 (persistent situation) ; 1.2 (accidental)  fck : Characteristic compressive cylinder strength of concrete at 28 days 1. Concrete 2. Steel  Annexes
  13. 13. 13 Another test for tensile strength of Concrete  The tensile strength by splitting test (Essai brésilien)  Design of rigid pavements Difficult  Flexure Test - 4 pts 1. Concrete 2. Steel  Annexes
  14. 14. 14 fctk : Characteristic axial tensile strength of concrete fctk 0,05  fctm  fctk 0,95 1. Concrete 2. Steel  Annexes
  15. 15. 15  Behaviour of Concrete – Stress-Strain Diagram 1. Structural Analysis 2. Sections Design 1. Concrete 2. Steel  Annexes
  16. 16. 16 1. Structural Analysis/ Second order effect 1. Concrete 2. Steel  Annexes
  17. 17. 17 Modulus of Elasticity Secant modulus Ecm (@ 0.4 fcm), for short term loading Effective modulus of elasticity of concrete Ec,eff (Creep Effect) (fcm en MPa, Ecm en GPa) 1. Structural Analysis/ Second order effect The EC2 defines a design Elastic modulus : 1. Concrete 2. Steel  Annexes
  18. 18. 18 2. Section Design a) Parabola-rectangle diagram b) Bi-linear stress-strain relation 1. Concrete 2. Steel  Annexes
  19. 19. 19 c) Rectangular stress distribution Note : In the present lecture, the design of section at ULS is conducted using the diagram c (simpler diagram) The use of diagrams a and b are authorized by the EC2. 1. Concrete 2. Steel  Annexes
  20. 20. 20  Other aspects – Creep (EC2, 3.1.4) 1. Concrete 2. Steel  Annexes
  21. 21. 21 At t =  , under a constant compression stress  Ec : Tangent modulus of elasticity (may be taken as 1,05 Ecm)  t0 : the age of concrete at the time of loading (in days) (Linear creep) (Non-Linear creep)  Other aspects – Creep (EC2, 3.1.4) 1. Concrete 2. Steel  Annexes
  22. 22. 22 Creep Coefficient where Ac is the concrete cross-sectional area and u is the perimeter of that part which is exposed to drying 1. Concrete 2. Steel  Annexes
  23. 23. 23 Creep Coefficient 1. Concrete 2. Steel  Annexes
  24. 24. 24 M. SADEK Poisson ratio  = 0 - Calculation of internal forces  = 0.2 - strain Calculation 1. Concrete 2. Steel  Annexes
  25. 25. 25 M. SADEK Steel 1. Concrete 2. Steel  Annexes
  26. 26. 26 M. SADEK  High bond (twisted):  bars  welded wire mesh  Round or plain bars : rarely used in Europe (only if folding out needed) used in Lebanon especially in villages because of the ease bending of stirrups Types of Steel 1. Concrete 2. Steel  Annexes
  27. 27. 27 M. SADEK Steel used in R.C 1. Concrete 2. Steel  Annexes
  28. 28. 28 M. SADEK   Tension Test 1. Concrete 2. Steel  Annexes
  29. 29. 29 M. SADEK The ductility of Steel of the reinforced concrete is characterized by : εuk Characteristic strain of reinforcement steel at maximum load  the Characteristic value of 3 Classes of ductility Stress/strain 1. Concrete 2. Steel  Annexes
  30. 30. 30 M. SADEK  A : Normal ductility B500A (welded wire mesh in general, and bars with low diameter)  B : high ductility B500B (in general the HB bars with a diameter > 12)  C : very high ductility C450 (generally used in seismic areas, especially in USA)  L’EN 10080 defines 3 classes of ductility : 1. Concrete 2. Steel  Annexes
  31. 31. 31 M. SADEK The application rules for design and detailing in this Eurocode are valid for a specified yield strength range (400 fyk600 Mpa)  Note : for bridges and for construction in seismic zones, steel B and C are authorized (The French N.A allows the use of steel A outside the critical zones)  L’EN 10080 defines 3 classes of ductility : 1. Concrete 2. Steel  Annexes
  32. 32. 32 M. SADEK Idealised / Design stress-strain diagrams for reinforcing steel (ULS) s = 1.15 (persistent) 1.0 (accidentel) 1. Concrete 2. Steel  Annexes
  33. 33. 33 M. SADEK  Design stress-strain diagrams:  a horizontal top branch without the need to check the strain limit  an inclined top branch with a strain limit (s0  s  ud = 0.9uk ) 1. Concrete 2. Steel  Annexes
  34. 34. 34 M. SADEK  Note : the calculation of the slope using the diagram A gives different value from that of diagram B, due to an error of the presentation of the diagram in EC2. It explains the difference in the expression of the stress obtained by different authors (Perchat, Paillé, Thonier, Ricotier)  In this document, we will calculate the slope on the basis of the diagram B. 1. Concrete 2. Steel  Annexes
  35. 35. 35 M. SADEK Elastic modulus Es = 200 000 MPa Density = 7.85 T/m3  Thermal expansion coefficient= 1.10-5  Diameters: 6, 8, 10, 12, 14, 16, 20, 25, 32, 40, (50 , 56)  Welded wire mesh: with lower diameter (see Annex) Other characteristics 1. Concrete 2. Steel  Annexes
  36. 36. 36 M. SADEK Annexes 1. Concrete 2. Steel  Annexes
  37. 37. 37 M. SADEK 1. Concrete 2. Steel  Annexes
  38. 38. 38  6 8 10 12 14 16 20 25 32 40 1 0.28 0.50 0.79 1.13 1.54 2.01 3.14 4.91 8.04 12.57 2 0.57 1.01 1.57 2.26 3.08 4.02 6.28 9.82 16.08 25.13 3 0.85 1.51 2.36 3.39 4.62 6.03 9.42 14.73 24.13 37.70 4 1.13 2.01 3.14 4.52 6.16 8.04 12.57 19.63 32.17 50.27 5 1.41 2.51 3.93 5.65 7.70 10.05 15.71 24.54 40.21 62.83 6 1.70 3.02 4.71 6.79 9.24 12.06 18.85 29.45 48.25 75.40 7 1.98 3.52 5.50 7.92 10.78 14.07 21.99 34.36 56.30 87.96 8 2.26 4.02 6.28 9.05 12.32 16.08 25.13 39.27 64.34 100.53 9 2.54 4.52 7.07 10.18 13.85 18.10 28.27 44.18 72.38 113.10 10 2.83 5.03 7.85 11.31 15.39 20.11 31.42 49.09 80.42 125.66 11 3.11 5.53 8.64 12.44 16.93 22.12 34.56 54.00 88.47 138.23 12 3.39 6.03 9.42 13.57 18.47 24.13 37.70 58.90 96.51 150.80 13 3.68 6.53 10.21 14.70 20.01 26.14 40.84 63.81 104.55 163.36 14 3.96 7.04 11.00 15.83 21.55 28.15 43.98 68.72 112.59 175.93 15 4.24 7.54 11.78 16.96 23.09 30.16 47.12 73.63 120.64 188.50 16 4.52 8.04 12.57 18.10 24.63 32.17 50.27 78.54 128.68 201.06 17 4.81 8.55 13.35 19.23 26.17 34.18 53.41 83.45 136.72 213.63 18 5.09 9.05 14.14 20.36 27.71 36.19 56.55 88.36 144.76 226.19 19 5.37 9.55 14.92 21.49 29.25 38.20 59.69 93.27 152.81 238.76 20 5.65 10.05 15.71 22.62 30.79 40.21 62.83 98.17 160.85 251.33 Wt kg / ml 0.222 0.395 0.617 0.888 1.208 1.578 2.466 3.853 6.313 9.865 1. Concrete 2. Steel  Annexes
  39. 39. 39 Welded wire mesh (anti cracking) 1. Concrete 2. Steel  Annexes
  40. 40. 40 Welded wire mesh (France) 1. Concrete 2. Steel  Annexes
  41. 41. 41 M. SADEK
  42. 42. 42 M. SADEK
  43. 43. 43  Determination of the slope of the diagram (/) for steel A & B  Deduce the equation of s for both Steel classes.  Practice : determination of the value of (s) for different (s)  Difference between diagrams with horizontal top branch and inclined top branch  (persistent situation / accidental)  Determine the creep coefficient for a column Exercices
  44. 44. 44 fck(t)=fcm(t) – 8 fcm(t) = cc x fcm cc= 1 (FNA) C = 1.5 (persistent) ; 1.2 (accidental) Reminder of main formulas
  45. 45. 45 s = 1.2 (persistent) 1.0 (accidental) or Reminder of main formulas

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