1. 16 Material properties for ultimate analysis

2. 17 5 Minute Exercise Open Democolumn.ads Run ULS STRENGTH for analysis cases 1 2& 3 Find out where in the output to investigate the stresses and strains. Discuss the results with your neighbour

3. 18 Ultimate analysis (ULS) EC2, BS8110, BS5400 & HK similar to each other ACI and AS similar to each other Material safety factors applied separately to reinforcement and concrete Strength reduction factors applied to the results of a strength calculation

4. 19 Compression controlled: All Steel bar strains < 0.002 tension All FRP bar strains < Failure strain/1.4 All steel strain < yield strain  Transition  = 0.75 structural steel  = 0.7 spiral links & FRP bars  = 0.65 other  = 0.9 Other  =0.5 FRP bars Tension controlled: Any Steel bar strain > 0.005 tension Any FRP bar strains = Failure strain Any steel strain > 2 x yield strain  tension  =0.55 plain concrete ACI 318-02 Fig R9.3.2

5. 20 Concrete Curves for ULS EC2, BS8110, BS5400 & HK similar to each other ACI and AS similar to each other Parabola-rectangle stress strain model for concrete Simple rectangular stress strain model for concrete

6. 21 Simplified assumptions for hand (and spreadsheet ) calculation Rectangular concrete compression block No tension in concrete Steel yielded & strain <0.05. Neutral axis depth

7. 22 Ultimate ‘parabola-rectangle’ compression curve

8. 23 Modified stress block for High strength concrete Note - ultimate strain goes down as strength goes up

9. 24 Ultimate capacity: Concrete strain governs The programme iterates until: The stresses balance the applied force The moment angle is the same as the applied moment angle The maximum compressive strain matches the failure strain

10. 25

11. 26 EC2 Concrete stress blocks (3.1.5 and 3.1.7) “Parabola-rectangle” “Bi-linear” “Confined”

12. 27 EC2 Concrete properties (Table 3.1)

13. 28 Eurocode National numbers The Nationally Determined Parameters (NDP) from EC2 will affect ULS results

14. 29 Design Strength Values (3.1.6) Design compressive strength, f cd f cd =  cc f ck /  c Design tensile strength, f ctd f ctd =  ct f ctk,0.05 /  c For the UK  cc (= 0.85) and  ct (= 1,0)

15. 30 Partial factors for materials Design situation  c for concrete  s for reinforcing steel  s for prestressing steel Persistent & Transient 1.51.15 Accidental1.21.0

16. 31 Plateau of steel curve factored - not slope! Ultimate strain taken as 0.05 (used to be 0.02) REBAR

17. 32

18. 33  ud = 0.9  uk k = (f t /f y ) k Alternative design stress/strain relationships are permitted: - inclined top branch with a limit to the ultimate strain (Strain-hardening) - horizontal top branch with no strain limit (Elastic plastic) EC2 Reinforcement (5) – Design Stress/Strain Relationships (3.2.7, Figure 3.8)

19. 34 Steel stress strain curves 1770, 5400

20. 35 Ultimate capacity : steel strain governs Version 7.3 onwards –steel limiting strain is 0.05 by default This may cause convergence problems. The programme iterates until: The stresses balance the applied force The moment angle is the same as the applied moment angle The maximum tensile rebar strain matches the failure strain

21. 36 cold worked seismic hot rolled EC2 Reinforcement (2) – From Annex C

22. 37 Code issues Adsec contains libraries of default materials Changing between codes will only roughly map existing section material onto a similar material in another code. Remember to check the material modules The material data includes limiting strain. The material data includes partial safety factors for relevant codes. (UK, HK, Euro)