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Figure A2-2. Example of interaction curves. fck = 40, co = 0,2, çef =2. general method

- stiffness method, expressions (5.22)-(5.24)

curvature method, expressions (5.31)-(5,36) (upper curve, Ky = 1)

--------- curvature method, expressions (5.31)-(5.37) (lower curve, according to (5.43))*

^ For Ä = 105 and 140, (5.43) gi\>es K0 = 1, therefore there is only one curve in these cases.

References

[1] Westerberg, B: Design Methods for Slender Concrete Columns. Tyrens Technical Report 1997:1. Stockholm, September 1997.

[2] FIP Recommendations, Practical Design of Structural Concrete. fib (CEB-FIP), September 1999.

[3] Design Handbook for High Performance Concrete Structures. Handbook published in Sweden, 1999.

[4] Beeby, A W and Narayanan, R S: Designers' Handbook to Eurocode 2, Part 1.1. Thomas Telford, London, 1995.

[5] Bresler, B: Design Criteria for Reinforced Columns under Axial Load and Biaxial Bending. ACI Journal, November 1960.

[6] Whittle, R T and Lawson, R: Biaxial bending with axial compression. An investigation into the use of Bresler coefficients for determining the capacity of reinforced concrete sections under combined axial compression and biaxial bending. March 2000

[7] König, G and Pauli, W: Nachweis der Kippstabilität von schlanken Fertigteilträgern aus Stahlbeton und Spannbeton. Beton- und Stahlbetonbau 87 (1992)

[8] Hellesland, J: On column slenderness limits. Mechanics Division, University of Oslo, 199905-28

SECTION 6 ULTIMATE LIMIT STATES (ULS)

6.1 Bending with or without axial force

SECTION 6 ULTIMATE LIMIT STATES (ULS) C6.1 Bending with or without axial force

6.1.1 Determining the compression resultant and its position compared to the edge of maximum deformation in case of rectangular section

Two cases should be distinguished:

f) virtual neutral axis (x > h) - Real neutral axis a1) Diagram parabola - exponential - rectangle

The resultant C of the block of compressive forces related to a rectangle of width b and depth x is expressed by

C = pi ■ fcd ■ b ■ x and its position, measured starting from the edge where the strain is £cu2, is defined by p2 x. The formulae of pi and p2 , in function of strain £c , are:

The numeric values of pi and p2 are shown in function of fck in Table 6.1 . In all tables limit the number of decimals to 3 maximum e.g. 0,80952 = 0,810 etc.

Table 6.1. Values of fa and fa

fck (N/mm2)

up to 50

0 0

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