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Calculation of cracking w...

Calculation of cracking width

Diamonds calculates the cracking width according to EN 1992-1-1 §7.3.4:

$w_k=s_{r1.max} \cdot \left( \varepsilon_{sm}-\varepsilon_{cm} \right)$

where:

$\varepsilon_{sm}-\varepsilon_{cm}=max\left( \frac{\sigma_{s1}-k_t \cdot \frac{f_{ctm}}{\rho_{pr.eff}}\cdot \left( 1-\alpha_{cr} \cdot \rho_{pr.eff} \right)}{E_s}, 0.6 \cdot \frac{\sigma_{s1}}{E_s} \right)$

and

$s_{r1.max}=\left( d_1 - \frac{\phi_1}{2}\right) \cdot k_3 + \frac{k_1 \cdot k_2 \cdot k_4 \cdot \phi_1}{\rho_{pr.eff}}$

Here:

σ_s	the stress in the reinforcement subjected to tension in the section where a cracking occurs
k_t	coefficient which depends on the duration of load = 0.6 for a short-term load = 0.4 for a long-term load
ρ_p,eff	the effective ratio of the reinforcement = A_s/A_c,eff
A_c,eff	the cross-section effectively under tension ≤ 2.5b(h – d) ≤ b (h – x) / 3
φ	average diameter (mm)
α_e	= E_s/E_c,eff
k₁	= 0.8 (steel with good adhesion)
k₂	= 0.5 for bending = 1.0 for pure tension
k₃	= 3,4
k₄	= 0.425
c	concrete cover on the longitudinal reinforcement

Diamonds calculates the cracking width for both for bars and surfaces. For surfaces, Diamonds will first calculate the cracking width in each reinforcement direction. Based on the angle between the reinforcements directions and the direction of the principle normal forces, the maximum width of cracks will be calculated as:

$s_{r.max}=\frac{1}{\frac{cos\left( \theta \right)}{s_{r.max.y}}+\frac{sin\left( \theta \right)}{s_{r.max.z}}}$

More info

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