Figure 3.17. Calculated values for and A for a rectangular and triangular cross-section, in comparison with the design equation for the rectangular case.

3.1.8 Flexural tensile strength

3.1.9 Confined concrete

C3.1.8 Flexural tensile strength

The flexural tensile strength is larger than the concentric tensile strength. This is caused by strain softening at cracking concrete. The size effect of concrete in bending is therefore the same as for concrete subjected to shear or punching (see f.i. Walraven, 1995), so that the size factor k = 1 + may be expected to apply for the relation between flexural tensile strength and concentric tensile strength as well. However, in this case the phenomenon is more sensitive to the effect of drying shrinkage, temperature gradients and imposed deformations. Therefore the more conservative equation fctm ,fl = ^1,6 _ 10Q ^ ftm — fctm has been chosen. C3.1.9 Confined concrete

Having a uniform radial compressive stresses CT2 at the ULS as a result of confinement, the axial strength fck,c is:

fck,c = fck [1+5,000 (02 /fck)] fck,c = fck [1,125 + 2,5 (02 /fck)]

Axial strength increases by 50% if the lateral compressive stresses are 15% of fck, it doubles if compressive stresses are 35% of fck. Also the strain at failure increase up to 3-4 times. Lateral stresses may be achieved by confinement of the compressed member. Index c after fck, stands for "confined".

3.2 Reinforcing steel

3.2.1 General

3.2.2 Properties

3.2.3 Strength

3.2.4 Ductility characteristics

3.2.5 Welding

3.2.6 Fatigue

C3.2.2 Properties

Clause [3.2.2(3P)-EC2] states that the design rules of Eurocode are valid when steel having characteristic yield fyk between 400 and 600 N/mm2 is used.

3.2.7 Design assumptions

C3.2.7 Design assumptions

Safety factor ys for ultimate limit states is i,i5 according to Table [2.iN-EC2]. The design stress-strain diagram is shown in Fig. 3.i8.

3.3 Prestressing steel

3.3.1 General

3.3.2 Properties

3.3.3 Strength

3.3.4 Ductility characteristics

Figure 3.18. Idealised and design stress-strain diagrams for reinforcing steel [Fig. 3.8-EC2]

Figure 3.18. Idealised and design stress-strain diagrams for reinforcing steel [Fig. 3.8-EC2]

For normal design, either of the following assumptions may be made:

c) an inclined top branch with a strain limit of £ud and a maximum stress of k— where k =

Ys d) a horizontal top branch without the need to check the strain limit. The recommended value of £ud is 0,9 £uk.

The value of

, given in Annex C for class C steel, is between i,i5 and i,35.

The value of the elasticity modulus Es may be taken as 200000 Nmm-2 . C3.3 Prestressing steel

Data from EC2, integrated with those from EN i0i38 which is referred to in EC2, are recalled hereafter. Prestressing steel are geometrically classified as:

- wires with plain or indented surface, of diameter between 3,0 and ii,0 mm

- two-wire strands spun together over a theoretical common axis; nominal diameter of the strand between 4,5 and 5,6 mm

- three-wire strands spun together over a theoretical common axis; nominal diameter of the strand between 5,2 and 7,7 mm

- seven-wire strands of which a straight core wire around which are spun six wires in one layer; nominal diameter of the strand between 6,4 and i8,0 mm

- ribbed bars; nominal diameter between i5,0 and 50,0 mm.

Within each type, reinforcing steel is classified according to the following properties:

- Strength, denoting the value of tensile strength fp and the value of the 0,i% proof stress (fp0,ik).

- Ductility, denoting the value of the ratio of tensile strength to proof strength (fpk /fp0,ik), which should be at least i.i, and elongation at maximum load (£uk). Although it's not indicated in EC2, in accordance with ENi0i38 £uk should be at least 0,035.

- Class, indicating the relaxation behaviour. Three classes are defined in the Eurocode:

• Class i: wire or strand - ordinary relaxation

• Class 2: wire or strand - low relaxation

• Class 3: hot rolled and processed bars

The design calculations for the losses due to relaxation of the prestressing steel should be based on the value of pi000, the relaxation loss (in %) at i000 hours after tensioning and at a mean temperature of 20 °C. The value of pi000 is expressed as a percentage ratio of the initial stress and is obtained for an initial stress equal to 0,7fp, where fp is the actual tensile strength of the prestressing steel samples. pi000 values indicated in EC2 for structural design are: 8% for Class i, 2,5% for Class 2, 4% for Class 3.

Clause [3.3.2(7)-EC2] gives the formulae for calculation of relaxation at different t times for the three above-mentioned classes. Annex [D-EC2] provides the elements needed for accurate calculations.

Fatigue: prestressing tendons are liable to fatigue. Relevant criteria and methods for verification are

3.3.5 Fatigue given at clause [6.8-EC2].

On top of strength and ductility values, the Eurocode provides the following design assumptions:

3.3.6 Design assumptions

- Modulus of elasticity recommended for strands: 195000 N/mm2; for wires and bars: 205000 N/mm2

- Design stress-strain diagrams. As represented in Fig. 3.19, taken the safety factor s = 1,15, the design diagram is made of a rectilinear part up to ordinate fpd from which two ways start: a rectilinear inclined branch, with a strain limit £ud = 0,9 £uk, or 0,02; the other branch is a horizontal branch without strain limit.

3.3.7 Prestressing tendons in sheaths

3.4 Prestressing devices

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