Learn Assumptions in limit state of collapse in flexure (Bending),relationship between the stress strain distribution in concrete,*stresses in the reinforcement are taken from the stress-strain curve*

### Assumptions in limit state of collapse in flexure (Bending) (REFER CL. 38, IS 456)

The design of reinforced concrete sections for limit state of collapse in bending, is based on the following assumptions :

(a) *Plane sections normal to the axis remain plane after bending.* It means that the strain at any point in the cross-section is proportional to the distance from the neutral axis.

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

(c) *The relationship between the stress-strain distribution in concrete is assumed to be parabolic,* as shown in Fig. 4.1.

For design purpose, the compressive strength of concrete is assumed to be parabolic, as shown in Fig. 4.1. For design purpose, the compressive strength of concrete is assumed to be 0.67 times the characteristic strength of concrete. The partial safety factor (r_{mc})=1.5 shall be applied in addition to this

Maximum compressive stress in concrete = \[\frac {0.67 f_{ck}}{1.5}\]

where f_{ck}= Characteristic strength of concrete.

(d) *The tensile strength of the concrete is ignored.*

(e) *The stresses in the reinforcement are taken from the stress-strain curve for the type of steel used* as shown in Fig. 4.2.

*For design purposes, the partial safety factor (r _{ms}) 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

\[\frac {f_{y}}{1.15E_{s}}+0.002\]

f_{y} = Characteristic strength of steel

E_{s} = Modulus of elasticity of steel.

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