Chapter 37Limit State of Collapse: Flexure

37.1 Assumptions

Design for the limit state of collapse in flexure shall be based on the assumptions given below:

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

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

c) 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 result in prediction of strength in substantial agreement with the results of test. An acceptable stress strain curve is given in Fig. 21. 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 $\gamma_{m}=1.5$ shall be applied in addition to this.

NOTE — For the stress-strain curve in Fig. 21 the design stress block parameters are as follows (see Fig. 22): Area of stress block = $0.36 f_{\mathrm{ck}} \cdot x_{\mathrm{u}}$ Depth of centre of compressive force = $0.42 x_{\mathrm{u}}$ from the extreme fibre in compression where

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

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

d) The tensile strength of the concrete is ignored.

e) The stresses in the reinforcement are derived from representative stress-strain curve for the type of steel used. Typical curves are given in Fig. 23. For design purposes the partial safety factor $\gamma_{\mathrm{m}}$, equal to 1.15 shall be applied.

f) The maximum strain in the tension reinforcement in the section at failure shall not be less than:

where

$f_{y} =$ characteristic strength of steel, and

NOTE — The limiting values of depth of neutral axis for different grades of steel based on the assumptions in 37.1 are as follows:

The expression for obtaining the moments of resistance for rectangular and T-Sections, based on the assumptions of 37.1, are given in Annex H.

FIG. 21 STRESS-STRAIN CURVE FOR CONCRETE

FIG. 22 STRESS BLUE PARAMETERS

38 LIMIT STATE OF COLLAPSE: COMPRESSION