Chapter 22Limit State of Collapse

22.1.1 Assumptions

Design for the limit state of collapse in flexure shall be

Table 7 Values of Partial Safety Factor $(\gamma_{i})$ For Loads

(Clause 20.4.2)

based on the assumptions given below:

a) Plane sections normal to the axis remain plane after bending.

b) The strain in the bonded reinforcement or bonded prestressing steel whether in tension or in compression is the same as that in the surrounding concrete.

c) The maximum strain in concrete at the outermost compression fibre is taken as 0.0035 in bending.

d) The relationship between the compressive stress distribution in concrete and the strain in concrete may be assumed to be rectangle, trapezoid, parabola or any other shape which results in prediction of strength in substantial agreement with the results of tests. An acceptable stress-strain curve is given in Fig. 3. For design purposes, the compressive strength of concrete in the structure shall be assumed to be 0.67 times the characteristic strength. The partial safety factor $\gamma_{\mathrm{m}} = 1.5$ shall be applied in addition to this.

NOTE — For the stress-strain curve in Fig. 3, the design stress block parameters for rectangular section are as follows (see Fig. 4):

Area of stress block = 0.36 $f_{ck}$ $x_u$ Depth of centre of compressive = 0.42 $x_u$ force from the extreme fibre in compression

where

$f_{\mathrm{ck}} =$ characteristic compressive strength of concrete, and

$x_{u}$ = depth of neutral axis.

e) The tensile strength of the concrete is ignored.

f) The stresses in bonded prestressing tendons, whether initially tensioned or untensioned, and in additional reinforcement are derived from the representative stress-strain curve for the type of steel used given by the manufacturer or typical curves given in Fig. 5 for prestressing tendons and in Part 6 'Structural Design, Section 5 Concrete, Subsection 5A Plain and Reinforced Concrete' of the Code for reinforcement. For design purposes, the partial safety factor $\gamma_{\mathrm{m}}$ equal to 1.15 shall be applied. In addition, the tendon will have an initial prestrain due to prestress after all losses. For members with permanently unbonded internal or externally prestressed tendons, the deformation of the whole member shall be taken into account for calculating strain and stress in the tendon at ultimate condition. In the absence of rigorous analysis, the strain in unbonded tendon shall be assumed not to increase above the initial value due to prestress after all losses.

FIG. 3 STRESS STRAIN CURVE FOR CONCRETE

FIG. 4 STRESS BLOCK PARAMETERS

FIG. 5 REPRESENTATIVE STRESS STRAIN CURVES FOR PRESTRESSING STEEL

PART 6 STRUCTURAL DESIGN — SECTION 5 CONCRETE: 5B PRESTRESSED CONCRETE

22.1.2 Design Formulae

In the absence of an analysis based on the assumptions given in 22.1.1, the moment of resistance of rectangular sections and flanged sections in which the neutral axis lies within the flange may be obtained by the procedure given in Annex C.

For flanged sections in which the neutral axis lies outside the flange, the moment of resistance shall be determined using assumptions given in 22.1.1.