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Crack width of a beam (Annex F)
Elastic cracked section, steel stress, average strain with tension stiffening and the design crack width. Reference: IS 456:2000 Cl. 35.3.2 and Annex F.
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# Data
b := 300 mm
h := 600 mm
d := 540 mm
A_s := 1885 mm^2
M := 160 kN*m
f_ck := 25 MPa
E_s := 200 GPa
c_min := 40 mm
a_cr := 75 mm
# a_cr is the distance from the point considered to the surface of the nearest bar.
# Cracked section
sigma_cbc := 8.5 MPa
m_r := 280/(3*sigma_cbc/(1 MPa)) =
x := (-m_r*A_s + sqrt((m_r*A_s)^2 + 2*b*m_r*A_s*d))/b = mm
f_s := M/(A_s*(d - x/3)) = MPa
epsilon_1 := f_s*(h - x)/(E_s*(d - x)) =
epsilon_m := epsilon_1 - b*(h - x)*(h - x)/(3*E_s*A_s*(d - x))*1 MPa =
# The second term (tension stiffening) is taken with the crack width checked at the tension face, a = h.
# Crack width
w_cr := 3*a_cr*epsilon_m/(1 + 2*(a_cr - c_min)/(h - x)) = mm
w_cr <= 0.3 mm =How to use this example
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