Annex F (Clauses 35.3.2 and 43.1) calculation of crack width

Provided that the strain in the tension reinforcement is limited to $0.8 F_{y} / E_{s}$, the design surface crack width, which should not exceed the appropriate value given in 35.3.2 may be calculated from the following equation:

Design surface crack width

$W_{\mathrm{cr}}=\frac{3 a_{\mathrm{cr}} \quad \epsilon_{\mathrm{m}}}{1+\frac{2\left(a_{\mathrm{cr}}-C_{\mathrm{mle}}\right)}{h-x}}$

where

• $a_{c r}=$ distance from the point considered to the surface of the nearest longitudinal bar,

$C_{\min }=$ minimum cover to the longitudinal bar;

$\boldsymbol{\epsilon}_{\mathrm{m}}=$ average steel strain at the level considered,

$h \quad=$ overall depth of the member, and

x = depth of the neutral axis.

The average steel strain $\varepsilon_{\mathrm{m}}$ may be calculated on the basis of the following assumption:

The concrete and the steel are both considered to be fully elastic in tension and in compression. The elastic modulus of the steel may be taken as 200 kN/mm² and the elastic modulus of the concrete is as derived from the equation given in 6.2.3.1 both in compression and in tension.

These assumptions are illustrated in Fig. 28, where

$h=$ the overall depth of the section,

• $x$ = the depth from the compression face to the neutral axis.
• $f_{\mathrm{c}}=$ the maximum compressive stress in the concrete,
• $f_{\mathrm{t}}=$ the tensile stress in the reinforcement, and

$E_{\mathrm{r}}=$ the modulus of elasticity of the reinforcement.

Alternatively, as an approximation, it will normally be satisfactory to calculate the steel stress on the basis of a cracked section and then reduce this by an amount equal to the tensile force generated by the triangular distributions, having a value of zero at the neutral axis and a value at the centroid of the tension steel of 1N/mm² instantaneously, reducing to 0.55 N/mm² in the long-term, acting over the tension zone divided by the steel area. For a rectangular tension zone, this gives

$\varepsilon_{\mathrm{m}}=\varepsilon_{1}-\frac{b(h-x)(a-x)}{3 E_{\mathrm{s}} A_{\mathrm{s}}(d-x)}$

where

• = area of tension reinforcement,
• $b \quad=$ width of the section at the centroid of the tension steel,
• $\boldsymbol{\epsilon}_{\mathrm{i}}=$ strain at the level considered, calculated ignoring the stiffening of the concrete in the tension zone,

a

• = distance from the compression face to the point at which the crack width is being calculated, and
• $d=$ effective depth.

SECTION CRACKED, STRAIN, and STRESS Diagrams

Annotations

• Neutral Axis (horizontal_line - position: at depth x)
• STRESS IN CONCRETE 1 N/mm² IN SHORT TERM 0.55 N/mm² IN LONG TERM (text_label - position: Right of STRESS diagram, pointing to tension zone)

Fig. 28