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Genk, Belgium, December 9th, 2014 
Dordrecht, Netherlands , December 10th, 2014 
Eurocode 2 Design of Composite Concrete 
...
IDEA RS - Literature 4 
Book on Prestressing by J. Navratil 
€ 100 eBTW 
http://eurocode2-naslagwerken-idea.eventbrite.com
3 
Design of composite cross-section 
Ultimate Limit States 
• Flexure, Shear, Torsion 
• Interaction of internal forces 
...
4 
Shear in composite joint 
• Standard EN approach 
• Lever arm, factor b, shortcomings 
• Alternative approach 
• Compar...
5 
Design of composite cross-section 
Serviceability Limit States 
• Stress limitation 
• Decompression condition 
• Crack...
6 
Prefabricated composite structures 
became very popular … 
• Reinforced/Prestressed beams with 
composite slab 
• Floor...
Different static systems during construction 7 
Construction stages 
p 
po 
pa 
p 
8 
pw     pA 
pr 
pe...
1 
2 
3 
5 
4 
long-term effects 
initial stresses 
ini 
p 
ini 
c 
composite section 
variable load 
Different “startin...
ULS - initial state method 9 
Unbalanced stresses 
(a) (b) (c) 
c(<0) 
ini 
c1 
c(<0) 
ini c(<0) 
c1 
unbalanced 
...
ULS - initial state method 10 
Unbalanced forces 
unbalanced 
stresses 
unbalanced forces 
unbalanced 
resultants 
n 
Mc ...
ULS - initial state method 11 
Composite prestressed section
ULS - initial state method 12
ULS shear design 13 
Equilibrium conditions of the truss model 
d z 
Asw 
bw As + Ap 
(a) 
Fs + Fp 
D V 
(b) 
0,5(Fs + F...
Design for shear 
ULS shear design 14 
• Model of cross-section is built in 
current time – according to existing 
phases ...
ULS shear design 15 
Assumptions and parameters 
• Material characteristics of concrete are 
considered as the smallest of...
16 
Strength of stirrups 
ULS shear design 
• Stirrup will be added into css 
model together with first phase, 
in which i...
17 
Torsion resistance 
Internal forces resisting torsion 
T 
x 
z 
y 
 Asw c 
s 
longitudinal r. 
stirrups 
concrete 
E
ULS design for torsion 18 
Equivalent thin-walled section 
• Program determines 
based on stirrup 
effective for torsion 
...
ULS design for torsion 19 
Equivalent section from stirrup 
Equivalent section is determined 
from stirrup and current css...
ULS design for torsion 20 
Equivalent section from stirrup 
... equivalent section is determined from stirrup and current ...
Design for torsion 
ULS design for torsion 21 
• Model of cross-section is built in current time – according to 
existing ...
22 
Ultimate Limit States 
Design of composite cross-section 
• Flexure 
• Shear 
• Torsion 
• Interaction of internal for...
Shear at the Interface According to EC 2 23 
Standard EN approach 
design value of 
v  v shear stress 
Edi Rdi design she...
Lever arm 
Shear in joint - standard EN 24 
Creep and shrinkage: 
Stress-strain 
response of the 
section is 
governed by ...
Factor b 
25 
Shear in joint - standard EN 
Ratio of the longitudinal force in new concrete 
area and the total longitudin...
26 
Shear in joint - standard EN 
Discontinuity in stresses distribution 
• consecutive construction 
• differential creep...
Double bending 
27 
Shear in joint - standard EN 
It is recommended to consider conservative value of b = 1.0 in case 
of ...
Shear in joint from difference 
of normal Forces 28 
Shear in joint – alternative approach 
dN 
Average shear stress at th...
Comparative study 
29 
Comparison of standard and 
alternative methods 
What error is introduced in vEdi by using standard...
Comparative study - results 
30 
Comparison of standard and 
alternative methods 
Conclusions 
• EN underestimates real sh...
Analysis of real-life structure 31 
length of beams - 15.8 m 
12 prefabricated pretensioned beams (C50/60) 
width of the b...
Composite concrete bridge 32 
The analyses: 
3D FEM model - equivalent portion of the load resisted by one beam 
TDA - tim...
33 
shear stresses at distance 
1.1 m from support 
1200 
1000 
800 
600 
400 
200 
0 
100 150 200 250 300 350 400 
Shear ...
34 
1200 
1000 
800 
600 
400 
200 
0 
β-2 dx-2 
β-1-1 dx-1-1 
β = 1,0 
EN 1992-1-1 
100 150 200 250 300 350 400 
Shear st...
35 
1200 
1000 
800 
600 
400 
200 
0 
dx-1-1 dx-2 
β-1-1 β-2 
dx no cr-2 dx lin-2 
dx lin-1-1 
shear stresses at distance...
36 
30 
25 
20 
15 
10 
5 
0 
0 
-1 
-2 
-3 
σc,b-2 
σc,b-1-1 
σs,t-2 
σs,t-1-1 
normal stresses at distance 
1.1 m from s...
Casting of composite slab after 20 years 37 
60 
50 
40 
30 
20 
10 
0 
0 
-0.5 
-1 
-1.5 
-2 
1 10 100 1000 10000 100000 ...
Casting of composite slab after 20 years 38 
1200 
1000 
800 
600 
400 
200 
0 
dx-1-1 dx-2 
β-1-1 β-2 
dx lin-1-1 dx lin-...
39 
Comparison composite slab after 
60 days/20 years 
1200 
1000 
800 
600 
400 
200 
0 
dx 60 days-2 
dx 60 days-1-1 
dx...
Shear in construction joint 40 
Conclusions for shear in composite joint 
• Eurocode 2 method 
• does not reflect stress r...
SLS crack width 41 
Crack width according to EN 
  k r sm cm w  s    ,max 
  
   
s 
  
, ,  
  0.6 
sm c...
SLS crack width 42 
Tension stiffening 
Effective embedment zone Zones of tension in concrete
SLS crack width 43 
Depth of effective embedment zone 
hc,ef is influenced by 
• total depth of css 
• effective depth of ...
SLS crack width 44
45 
• Model of cross-section is built in current time – according to 
existing phases of cross-section, and with respect t...
SLS crack width 
Crack width in composite sections 
46 
RC composite T-section 
Construction stages 
• (1) prefabricated w...
Crack width in composite sections 
47 
Casting of slab 7 days after casting of web 
SLS crack width
SLS crack width 48 
Crack width in composite sections 
Casting of slab 365 days after casting of web
SLS crack width 49 
Crack width in composite sections 
Casting of slab 10 years after casting of web
SLS crack width 50 
Crack width in composite sections 
Casting of slab 30 years after casting of web
SLS crack width 
Crack width in composite sections 
51 
RC composite T-section (after 100 years) 
Casting of composite sla...
IDEA StatiCa Composite Beam 52 
Repeated requirement from practice: a tool for design of 
composite concrete structures id...
IDEA RS - Literature 4 
Book on Prestressing by J. Navratil 
€ 100 eBTW 
http://eurocode2-naslagwerken-idea.eventbrite.com
Thank you for your attention 
www.ideastatica.com www.idea-rs.com
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Eurocode 2 design of composite concrete

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Abstract (Dutch)

Samengestelde betonnen liggers vervaardigd van prefab voorgespannen- en/of gewapende elementen zijn zeer populair in de huidige praktijk van de civiele techniek. Twee betonnen, samengestelde delen van de ligger worden gestort op verschillende tijdstippen. Verschillende elasticiteitsmoduli, opeenvolgende belastingaanbrenging, en verschillend krimp en kruip veroorzaken een herverdeling van de normaalspanning en ongelijke rekken en spanningen in twee aansluitende vezels in het aansluitvlak.
Dit seminar richt zich op de berekening volgens de EN 1992-1-1 en EN 1992-2. De aannames met betrekking tot de berekening en de controle van de gewapende en/of voorgespannen samengestelde liggers en doorsnedes zal worden toegelicht.
Ook wordt er ingegaan op:
• De spanning/rek respons van de doorsnede belast door normaalkracht en buigende momenten,
• De principes van het gebruik van de “initiële toestand” in berekeningen van de uiterste grenstoestand en de bruikbaarheidsgrenstoestand,
• De controle van dwarskracht en wringing,
• De interactie tussen alle snedekrachten,
• De principes van de controles van de spanningbeperking,
• De achtergrond van de scheurwijdtecontrole
Speciale aandacht zal er worden gegeven aan de berekening van de schuifspanning in het aansluitvlak, en de beschouwing van de invloed van de verschillende leeftijd van de betonnen delen met betrekking tot de schuifspanningen. Een alternatieve berekeningsmethode ten opzichte van de Eurocode 2 zal worden voorgesteld en worden getest.
De praktische voorbeelden volgens de Eurocode 2 zullen worden uitgevoerd met behulp van de IDEA StatiCa software.

Publicado en: Ingeniería
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Eurocode 2 design of composite concrete

  1. 1. Genk, Belgium, December 9th, 2014 Dordrecht, Netherlands , December 10th, 2014 Eurocode 2 Design of Composite Concrete Structures Assoc. Prof. Jaroslav Navrátil, M.Sc., Ph.D.
  2. 2. IDEA RS - Literature 4 Book on Prestressing by J. Navratil € 100 eBTW http://eurocode2-naslagwerken-idea.eventbrite.com
  3. 3. 3 Design of composite cross-section Ultimate Limit States • Flexure, Shear, Torsion • Interaction of internal forces • Fatigue • Shear in composite joint
  4. 4. 4 Shear in composite joint • Standard EN approach • Lever arm, factor b, shortcomings • Alternative approach • Comparative study Prestressed composite bridge design • Comparison and standard EN approach • Effects of creep and shrinkage • Comparison of EN 1992-1-1 and EN 1992-2 Scope
  5. 5. 5 Design of composite cross-section Serviceability Limit States • Stress limitation • Decompression condition • Crack width • Brittle failure
  6. 6. 6 Prefabricated composite structures became very popular … • Reinforced/Prestressed beams with composite slab • Floors composed of prefabricated beams made subsequently monolithic by cast-in-place concrete • Filigran type floors • Permanent shuttering floor systems • Composite bridge beams
  7. 7. Different static systems during construction 7 Construction stages p po pa p 8 pw     pA pr pe      pT pr      pc      ps peq peg1 to ta tg1 tq t 8 t • Different moduli of elasticity • Consecutive load application • Change of boundary conditions • Differential creep and shrinkage
  8. 8. 1 2 3 5 4 long-term effects initial stresses ini p ini c composite section variable load Different “starting” values of the strain and stress are used for each fibre of the cross-section effects Mq Nq ULS - initial state method 8
  9. 9. ULS - initial state method 9 Unbalanced stresses (a) (b) (c) c(<0) ini c1 c(<0) ini c(<0) c1 unbalanced c ini c(<0) c3 ini c4 unbalanced c(>0) c(>0) c Non-linear method is used to find stress–strain state with respect to “starting” values of the strain and stress
  10. 10. ULS - initial state method 10 Unbalanced forces unbalanced stresses unbalanced forces unbalanced resultants n Mc n Nc Their resultants of unbalanced forces must be added to the internal forces due to variable loads
  11. 11. ULS - initial state method 11 Composite prestressed section
  12. 12. ULS - initial state method 12
  13. 13. ULS shear design 13 Equilibrium conditions of the truss model d z Asw bw As + Ap (a) Fs + Fp D V (b) 0,5(Fs + Fp ) c VE E   s z * cos  s A s w * w s * sin  (c) c 0,5(Fs + Fp )
  14. 14. Design for shear ULS shear design 14 • Model of cross-section is built in current time – according to existing phases of cross-section, and with respect to age of concrete • „Initial effects“ of shear force in individual css phases are not considered in the calculation • It is assumed that sum of shear forces from all previous construction stages act on current configuration of css
  15. 15. ULS shear design 15 Assumptions and parameters • Material characteristics of concrete are considered as the smallest of the one, which are found in governing part of css (where bw is identified) • Dimensions for shear design bw, d, z • from distribution of total strain on current css • from code setup (one set of dimensions is valid for css with and without composite slab) • Resultant of shear forces Vy a Vz is assessed
  16. 16. 16 Strength of stirrups ULS shear design • Stirrup will be added into css model together with first phase, in which it is located • Development lengths are respected in determination of stirrup strength • Ultimate force is linearly interpolated • place, where stirrup leaves css • place, where stirrup is cut by line perpendicular to direction of shear force going through centroid
  17. 17. 17 Torsion resistance Internal forces resisting torsion T x z y  Asw c s longitudinal r. stirrups concrete E
  18. 18. ULS design for torsion 18 Equivalent thin-walled section • Program determines based on stirrup effective for torsion • Program calculates from ratio of area and perimeter of css • User defines specific values
  19. 19. ULS design for torsion 19 Equivalent section from stirrup Equivalent section is determined from stirrup and current css model Part of stirrup outside of current css • Torsional cracking moment TRd,c is calculated • Equivalent thin-walled section is calculated from ratio of area and perimeter of css
  20. 20. ULS design for torsion 20 Equivalent section from stirrup ... equivalent section is determined from stirrup and current css model … Stirrup induces the same equivalent section in 1. phase of css, and in total composite css
  21. 21. Design for torsion ULS design for torsion 21 • Model of cross-section is built in current time – according to existing phases of cross-section, and with respect to age of concrete • Sum of torsional moments from all previous construction stages act on current configuration of css • Material characteristics of concrete are considered as the smallest of the one, which are found in equivalent thin-walled section
  22. 22. 22 Ultimate Limit States Design of composite cross-section • Flexure • Shear • Torsion • Interaction of internal forces • Fatigue • Shear in composite joint unequal strains and stresses
  23. 23. Shear at the Interface According to EC 2 23 Standard EN approach design value of v  v shear stress Edi Rdi design shear resistance EN 1992-1-1, (6.24) – β factor Edi Ed i v  b V / z b Lever arm • From ultimate bending resistance • From real flexural stress distribution at loading considered
  24. 24. Lever arm Shear in joint - standard EN 24 Creep and shrinkage: Stress-strain response of the section is governed by ULS conditions • separate compression and tension zones may appear  questionable interpretation of lever arm • the use of such lever arm in EN formula would be incorrect
  25. 25. Factor b 25 Shear in joint - standard EN Ratio of the longitudinal force in new concrete area and the total longitudinal force Edi Ed i v  b V / z b Edi Ed ,max v  b v V S I b(z) y z y y I y,max S z  xz zx      Theory of elasticity - Grasshof b factor relates shear stress at the interface to the maximum shear stress b can be used if normal stresses are linear (Grasshof) or non-linear (joint lies within unbroken zone)
  26. 26. 26 Shear in joint - standard EN Discontinuity in stresses distribution • consecutive construction • differential creep and shrinkage EN formula does not reflect stress redistribution in the cross-section
  27. 27. Double bending 27 Shear in joint - standard EN It is recommended to consider conservative value of b = 1.0 in case of controversial cases
  28. 28. Shear in joint from difference of normal Forces 28 Shear in joint – alternative approach dN Average shear stress at the interface is v calculated between two neighboring sections b dx i c  Edi  The method reflects stress redistribution due to consecutive construction, differential creep and shrinkage
  29. 29. Comparative study 29 Comparison of standard and alternative methods What error is introduced in vEdi by using standard EN formula? Stress distributions considered in the study vEdi was determined using: • EN formula with b factor calculated • formula with b factor = 1.0 where necessary • alternative formula
  30. 30. Comparative study - results 30 Comparison of standard and alternative methods Conclusions • EN underestimates real shear stress in most cases with almost 60% error for stress distribution (C) • conservative application of EN overestimate shear stress by 35%
  31. 31. Analysis of real-life structure 31 length of beams - 15.8 m 12 prefabricated pretensioned beams (C50/60) width of the bridge - 12.7 m
  32. 32. Composite concrete bridge 32 The analyses: 3D FEM model - equivalent portion of the load resisted by one beam TDA - time-dependent analysis using beam model. Construction stages: • transfer of prestressing, • storage yard, • casting of composite slab, • final supports, • superimposed dead load, • service stages, • end of design working life
  33. 33. 33 shear stresses at distance 1.1 m from support 1200 1000 800 600 400 200 0 100 150 200 250 300 350 400 Shear stress [kPa] Shear force [kN] β-2 dx-2 β = 1,0 β ≤ 1,0 cracks β=0,57
  34. 34. 34 1200 1000 800 600 400 200 0 β-2 dx-2 β-1-1 dx-1-1 β = 1,0 EN 1992-1-1 100 150 200 250 300 350 400 Shear stress [kPa] Shear force [kN] β = 1,0 β ≤ 1,0 cracks cracks β=0,57 EN 1992-2 shear stresses at distance 1.1 m from support
  35. 35. 35 1200 1000 800 600 400 200 0 dx-1-1 dx-2 β-1-1 β-2 dx no cr-2 dx lin-2 dx lin-1-1 shear stresses at distance 100 150 200 250 300 350 400 Shear stress [kPa] Shear force [kN] cracks cracks 1.1 m from support
  36. 36. 36 30 25 20 15 10 5 0 0 -1 -2 -3 σc,b-2 σc,b-1-1 σs,t-2 σs,t-1-1 normal stresses at distance 1.1 m from support 1 10 100 1000 10000 100000 Steel stress [MPa] Concrete stress [MPa] Age of prefabricated beam [days]
  37. 37. Casting of composite slab after 20 years 37 60 50 40 30 20 10 0 0 -0.5 -1 -1.5 -2 1 10 100 1000 10000 100000 Steel stress [MPa] Concrete stress [MPa] Slab age [days] σc,b-2 σc,b-1-1 σs,t-2 σs,t-1-1
  38. 38. Casting of composite slab after 20 years 38 1200 1000 800 600 400 200 0 dx-1-1 dx-2 β-1-1 β-2 dx lin-1-1 dx lin-2 β = 1,0 cracks cracks 100 150 200 250 300 350 400 Shear stress [kPa] Shear force [kN]
  39. 39. 39 Comparison composite slab after 60 days/20 years 1200 1000 800 600 400 200 0 dx 60 days-2 dx 60 days-1-1 dx 20 years-2 dx 20 years-1-1 100 150 200 250 300 350 400 Shear stress [kPa] Shear force [kN]
  40. 40. Shear in construction joint 40 Conclusions for shear in composite joint • Eurocode 2 method • does not reflect stress redistribution caused by construction and differential creep and shrinkage • underestimates shear stresses (calculated b factor) or leads to uneconomic design (conservative b factor) • Alternative method was proposed and tested numerically • Shear in construction joint is sensitive to creep and shrinkage redistribution • Rhelological effects according to EN 1992-1-1 exhibit higher effects than according to EN 1992-2
  41. 41. SLS crack width 41 Crack width according to EN   k r sm cm w  s    ,max      s   , ,    0.6 sm cm E E r p eff s c k k ,max 1 2 ,  3.4  0.425  /   s s ct eff e p eff s p eff t s f k E   1 ,     1.3h  x for distance of reinforcement > 5 (c + Ф/2) Stress in the reinforcement is the basis for crack width calculation
  42. 42. SLS crack width 42 Tension stiffening Effective embedment zone Zones of tension in concrete
  43. 43. SLS crack width 43 Depth of effective embedment zone hc,ef is influenced by • total depth of css • effective depth of css • depth of compression zone coeficient k2 • 0.5 flexure • 1.0 pure tension • interpolation for eccentric tension
  44. 44. SLS crack width 44
  45. 45. 45 • Model of cross-section is built in current time – according to existing phases of cross-section, and with respect to age of concrete • Initial effects in individual css phases are respected • Crack width is calculated in each phase and it is assessed individually • Effective embedment tensile zone is determined from • d, k2 determined from css phases separately • x from total plane of strain of appropriate css phase • the direction of in-plane gradient of the load plane (RC) / strain plane (PC) SLS crack width Crack width in composite sections
  46. 46. SLS crack width Crack width in composite sections 46 RC composite T-section Construction stages • (1) prefabricated web • (2) slab  tref • (3) superimposed dead • (4) variable load composite section Crack width at midspan for different „initial“ stress distributions obtained for different tref
  47. 47. Crack width in composite sections 47 Casting of slab 7 days after casting of web SLS crack width
  48. 48. SLS crack width 48 Crack width in composite sections Casting of slab 365 days after casting of web
  49. 49. SLS crack width 49 Crack width in composite sections Casting of slab 10 years after casting of web
  50. 50. SLS crack width 50 Crack width in composite sections Casting of slab 30 years after casting of web
  51. 51. SLS crack width Crack width in composite sections 51 RC composite T-section (after 100 years) Casting of composite slab [days] Crack in slab [mm] Crack in web [mm]
  52. 52. IDEA StatiCa Composite Beam 52 Repeated requirement from practice: a tool for design of composite concrete structures id needed ? Fast and simple input Workflow and logic of structural engineer must not be adapted to the method of analysis Make it easy & provide correct and complete solution Focused, simple, and fast tool instead of generic and complicated program
  53. 53. IDEA RS - Literature 4 Book on Prestressing by J. Navratil € 100 eBTW http://eurocode2-naslagwerken-idea.eventbrite.com
  54. 54. Thank you for your attention www.ideastatica.com www.idea-rs.com

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