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Appendix 1 Additional provisions for the determination of the effects of time-dependent deformation of concrete 159

Appendix 2 Non-linear analysis 162

Appendix 3 Supplementary information on the ultimate limit states induced by structural deformations 167

Appendix 4 Checking deflections by calculation 174

Figure 2.1 — Application of the effective geometrical imperfections 31

Figure 2.2 — Definition of dimensions 33

Figure 2.3 — Approximate effective spans for calculation of effective breadth ratios 34

Figure 2.4 — Determination of effective span (leff) according to Equation (2.15)

for different support conditions 35

Figure 2.5 — Example of a corbel, with a strut and tie model 41

Figure 3.1 — Stress-strain diagram for uniaxial compression 48

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Figure 3.2 — Typical stress-strain diagram of reinforcing steel 52

Figure 3.3 — Typical stress-strain diagram of prestressing steel 54

Figure 4.1 — Schematic stress-strain diagram for structural analysis (4.2.1.3.3(5)-(7)] 63

Figure 4.2 — Parabolic — rectangular stress-strain diagram for concrete in compression 64

Figure 4.3 — Bi-linear stress-strain diagram for concrete 65

Figure 4.4 — Rectangular diagram 65

Figure 4.5 — Design stress-strain diagram for reinforcing steel 67

Figure 4.6 — Design stress-strain diagram for prestressing steel 69

Figure 4.8 — Relaxation losses after 1 000 h at 20 °C 71

Figure 4.9 a) and b) — Transfer of prestress in pretensioned elements 75

Figure 4.10 — Dispersion of prestress 77

Figure 4.11 — Strain diagrams in the ultimate limit state 79

Figure 4.12 — Definition of As for use in

Equation (4.18) 83

Figure 4.13 — Notation for members subjected to shear 84

Figure 4.14 — Notation for the connection between flange and web 88

Figure 4.15 — Notation used in

Section 4.3.3.1 89

Figure 4.16 — Design model for punching shear at the ultimate limit state 93

Figure 4.17 — Application of punching provisions in non-standard cases 94

Figure 4.18 — Critical perimeter round loaded areas located away from an unsupported edge 94

Figure 4.19 — Critical perimeter near an opening 95

Figure 4.20 — Critical sections near unsupported edges 95

Figure 4.21 — Approximate values for " 96

Figure 4.22 — Slab with column heads where lH < 1.5 hH 97

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Figure 4.23 — Slab with enlarged column head Where lH > 1.5 (d + hH) 98

Figure 4.24 — Bending moments mSdx and mSdy in slab-column joints subjected to eccentric loading, and effective width for resisting these moments 100

Figure 4.25 — Detailing of reinforcement over edge and corner columns 100

Figure 4.26 — Types of isolated columns 103

Figure 4.27 — Nomograms for the calculation of the effective length 104

Figure 4.28 — Slenderness limits for isolated members with rigidly or elastically restrained ends in non-sway structures 106

Figure 4.29 — Design model for the calculation of the total eccentricity 107

Figure 4.30 — Model column (notation) 108

Figure 4.31 — Assumption for separate checks in the two principal planes 110

Figure 4.32 — Separate check in the y-direction if ez > 0.2 h 111

Figure 4.33 — Effective area (typical cases) 121

Figure 5.1 — Definition of bond conditions 126

Figure 5.2 — Required anchorage length 127 Figure 5.3 — Transverse reinforcement in the region of anchored bars 128

Figure 5.4 — Adjacent laps 129

Figure 5.5 — Transverse reinforcement for lapped splices 130

Figure 5.6 — Evaluation of a1 131

Figure 5.7 — Anchorage of links 132

Figure 5.8 — Additional reinforcement in an anchorage zone where the bar diameter is greater than | 32 mm | and there is no transverse compression 133

Figure 5.9 — Minimum clear spacing for pretensioned tendons 135

Figure 5.10 — Internal and external parts of a T-beam 137

Figure 5.11 — Envelop line for the design of flexural members Anchorage lengths 138

Figure 5.12 — Anchorages of bottom reinforcement at end supports 139

Figure 5.13 — Anchorage at intermediate supports 139

Figure 5.14 — Examples for combinations of links and shear reinforcement 140

Figure 5.15 — Surface reinforcement 142

Figure 5.16 — Edge reinforcement for a slab

Figure 5.17 — Shear reinforcement near to a support

Figure 5.18a — Reinforcement of corbel with horizontal stirrups

Figure 5.18b — Reinforcement of corbel with inclined stirrups

Figure 5.19 — Definition of the areas to be introduced in Equation (5.22) Figure 5.20 — Extent of the intersection zone for the connection of secondary beams Figure A2.1 — Range of validity of Equation (A2.2)

Figure A2.2 — Allowable plastic rotation of reinforced concrete sections

Figure A3.1 — Flow Chart 1: General guide to application of section 4.3.5

Figure A3.2 — Flow Chart 2: Application of provisions of 4.3.5 and A3 to ultimate limit states due to deformation of the structure as a whole

Figure A3.3 — Flow Chart: 3 Design procedures for isolated columns Figure A3.4 — Slenderness limits in frames (A3.2)

Table 1.1 — List of equivalent terms in Community languages (to be completed for other community languages)

Table 2.1 — Design values for actions for use in the combination of actions

Table 2.2 — Partial safety factors for actions in building structures for persistent and transient design situations Table 2.3 — Partial safety factors for material properties Table 3.1 — Concrete strength classes, characteristic compressive strengths fck (cylinders) mean tensile strength fctm, and characteristic tensile strengths fctk of the concrete (in N/mm2). (The classification of concrete eg, C20/25 refers to cylinder/cube strength as defined in Section 7.3.1.1 of ENV 206)

Table 3.2 — Values of the secant modulus of elasticity Ecm (in kN/mm2)

Table 3.3 — Final creep coefficient 0(z,to) of normal weight concrete

Table 3.4 — Final shrinkage strains (cs Z (in o/oo) of normal weight concrete Table 4.1 — Exposure classes related to environmental conditions

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