DNV-OS-C502 Offshore Concrete Structures

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A300: Distance between cracks with deviations
between the principle strain directions and the direction of the reinforcement

DNV-OS-C502 Offshore Concrete Structures

App.F: Crackwidth Calculation (Guidelines)

A: General

A200: Stabilized crackpattern

App.F
A 200 Stabilized crackpattern

App.F A
201 Influence length, l_sk

For stabilized crackpattern, the influence length, l_sk, equals the characteristic distance between cracks, s_rk.

The characteristic distance between cracks for cracks normal to the reinforcement direction is predicted from the following formulae:

s_rk = 1.7 s_m = 1.7{s_ro + k_c A_cef / S [p f / (f_tk k_b /t_bk)]}

where the summation, S, covers tensile reinforcement within the concrete area influencing the transfer of tensile stresses between concrete and tensile reinforcement between cracks, A_cef.

App.F A
202 In plates and slabs with single bars or bundles of bars of equal diameter and constant spacing between the bars, the distance between the cracks may be calculated from:

s_rk = 1.7 s_m = 1.7{s_ro + (f_tk /t_bk) k_b k_c h_cef s_b /(p n f)}

where:
s_ro = 20 mm (a constant length with presumed loss of bond)
f_tk /t_bk = the effective ration between tensile strength and bond strength and is taken as 0.75 for deformed bars, 1.15 for post-tension bars and 1.50 for plain bars.
A_cef = b·h_cef, the effective concrete area in the part of the concrete tension zone which is presumed to participate in carrying tensile stresses which is transferred from the reinforcement to the concrete by bond.
b = the width of the effective concrete section considered (mm).
h_cef = the height of the effective concrete area =
2.5 (h - d), where (h - d) is the distance from the concrete surface on tension side to the centre of gravity of the reinforcement. For a tension zone with reinforcement of single tensile bars in one layer, h_cef = 2.5 (c + f / 2).
h_cef shall be less than the height of the tensile zone (h - x), where x is the distance from the concrete edge on the tensile side to the neutral axis and h is the total cross-sectional height.
For double reinforce cross-sections with through going tensile stresses, h_cef is calculated for each side, h_cefshall in this case never be larger then h/2.
k_c = a coefficient which accounts for the strain distribution within the cross-section. k_c = (1 + e_II/e_I)/2 where e_II/e_I is the ratio between minimum and maximum strain in the effective concrete area calculated for cracked cross-section. For a cross-section with through going tensile stresses, k_c =1.0.
k_b = 0.15 n + 0.85, a coefficient which accounts for reduced bond of bundled reinforcement.
c = the concrete cover for the reinforcement under investigation.
f = the diameter of the reinforcement bar
s_b = the distance between reinforcement bars or bundles of bars, maximum value in the calculation 15f (for bundles of reinforcement raster .
n = number of bars in a bundle.

App.F A
203 Characteristic distance between cracks, s_rk, shall not be larger than 2.5 (h - x) and not less than 2.5 c, where c < (h-x).

App.F A
204 Should the reinforcement be distributed unevenly between different parts of the cross-section, then the characteristic distance between the cracks, s_rk, shall be predicted individually for groups with similar intensity of reinforcement.

App.F A
205 For reinforcement with perpendicular reinforcement bars spaced at a distance, s, then the characteristic distance between the cracks can be taken as n · s, where n is a whole number, and when the predicted distance between the cracks is greater than n · s and less than (n + 0.3) s.

s_ro	=	20 mm (a constant length with presumed loss of bond)
f_tk /t_bk	=	the effective ration between tensile strength and bond strength and is taken as 0.75 for deformed bars, 1.15 for post-tension bars and 1.50 for plain bars.
A_cef	=	b·h_cef, the effective concrete area in the part of the concrete tension zone which is presumed to participate in carrying tensile stresses which is transferred from the reinforcement to the concrete by bond.
b	=	the width of the effective concrete section considered (mm).
h_cef	=	the height of the effective concrete area = 2.5 (h - d), where (h - d) is the distance from the concrete surface on tension side to the centre of gravity of the reinforcement. For a tension zone with reinforcement of single tensile bars in one layer, h_cef = 2.5 (c + f / 2). h_cef shall be less than the height of the tensile zone (h - x), where x is the distance from the concrete edge on the tensile side to the neutral axis and h is the total cross-sectional height. For double reinforce cross-sections with through going tensile stresses, h_cef is calculated for each side, h_cefshall in this case never be larger then h/2.
k_c	=	a coefficient which accounts for the strain distribution within the cross-section. k_c = (1 + e_II/e_I)/2 where e_II/e_I is the ratio between minimum and maximum strain in the effective concrete area calculated for cracked cross-section. For a cross-section with through going tensile stresses, k_c =1.0.
k_b	=	0.15 n + 0.85, a coefficient which accounts for reduced bond of bundled reinforcement.
c	=	the concrete cover for the reinforcement under investigation.
f	=	the diameter of the reinforcement bar
s_b	=	the distance between reinforcement bars or bundles of bars, maximum value in the calculation 15f (for bundles of reinforcement .
n	=	number of bars in a bundle.

DNV-OS-C502 Offshore Concrete Structures

App.FA 200 Stabilized crackpattern

App.F
A 200 Stabilized crackpattern