1. Material properties for serviceability analysis Sarah Kaethner 58

2. Serviceability Compression stiffness of concrete Tension stiffness of concrete Creep & long term loads Creep E=E o /(1+  ) 59

3. Compression Stress/Strain relationships Linear- elastic Useful for hand calcs… Also … Peaked curve (‘Fig 3.2’ EC2) Parabola rectangle Bi-linear Rectangular… User defined (‘Explicit’) “Schematic” 60

4. Peaked curve eg EC2 and BS8110 Pt2 1>1.4ε c1.E/fcu ε c1 61

5. Peaked curve: AdSec 62

6. Crept peaked curve E=E o /(1+  )  c1=  c1 (1+  ) 63

7. EC2 Confined Concrete Curve A is modified to produce the confined stress strain relationship. The confined maximum stress f ck,c and the strains  c2,c  cu2,c are a function of the confining stress  2 Explicit curves can also be input. 64

8. Plane sections remain plane – but the stiffness of the tension zone reduces Low strain - tension=compression Cracking starts - stiffness reduces All cracks formed - cracks open up Fully cracked - no tension stiffness Tension stiffness 65

9. Tension Stiffness in Codes BS8110 – envelope of tension stiffening gives ‘effective tensile Young’s modulus’ BS5400 allows above BUT assumes analysis with no tension ACI, AS & EC2 - interpolating between fully elastic and fully cracked condition 66

10. Tension Stiffness in AdSec EC2 Example For British codes AdSec also offers: 67

11. BS8110 Part 2 Fig. 3.1 Initial slope =E/(1+  ) 0.55MPa Section Stress ‘Stress-Strain Envelope’ 0.55MPa PD6687 for UK EC2 is similar 68

12. ‘ICE Note 372’ No Tension Ref: Concrete Society Technical Report 59 Stress-Strain Envelope Stress Section Stress 69

13. Stress-strain curves & envelopes Peaked compression curve + ICE Note 372 tension envelope Provides a fairly realistic model of the behaviour Other curves are available for ‘letter of the code’ calcs & when this approach doesn’t work. 70

14. An alternative to stress-strain envelopes A whole-section approach Interpolated methods EC2, AS & ACI 71

15. Calculated assuming concrete has no tensile strength Deflection Load Calculated assuming no cracking Actual behaviour Interpolated methods EC2, AS & ACI 72

16. S (1 -  )S SS SS Idealised steel stress EC2 interpolated model Steel stress  s2  s1 73

17. Zeta, , defines partially cracked behaviour. When  =1.0 Fully cracked behaviour When  =0.0 Un-cracked behaviour NOTE: For ACI and AS  is called the ‘interpolation factor’ EC2 interpolated model 74

18.  = 1 -  ( first crack result / un-cracked analysis result) 2  = 1 for short term, 0.5 for long term loading Partially cracked behaviour =  (cracked behaviour) + (1 -  )(uncracked behaviour) Deflection Load no cracking Actual cracked Mcr M Ed EC2 interpolated model 75

19. Deflection Load no cracking Actual cracked Mcr M Ed EC2 interpolated model  >  min if the section cracked in previous load-states Partially cracked behaviour =  (cracked behaviour) + (1 -  )(uncracked behaviour)  = 1 -  ( first crack result / un-cracked analysis result) 2 76

20. Comparison of tension stiffness Uncracked Cracked 77