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DNV-OS-C502 Offshore Concrete Structures

App.F: Crackwidth Calculation (Guidelines)

A: General

App.F
A. General

App.F
A 100   Introduction

App.F
A 200   Stabilized crackpattern

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:

sro	=	20 mm (a constant length with presumed loss of bond)
ftk /tbk	=	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.
Acef	=	b·hcef, 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).
hcef	=	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, hcef = 2.5 (c + f / 2). hcef 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, hcef is calculated for each side, hcef shall in this case never be larger then h/2.
kc	=	a coefficient which accounts for the strain distribution within the cross-section. kc = (1 + eII/eI)/2 where eII/eI 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, kc =1.0.
kb	=	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
sb	=	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.

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.

App.F
A 300   Distance between cracks with deviations between the principle strain directions and the direction of the reinforcement

s_m = 1/{(sin n /s_mx ) + (cos n /s_my)}

where:

n	=	the angle between the principle strain and the y-direction (x-direction) when the reinforcement is presumed to be position in the x-direction (y-direction).
smx	=	the predicted distance between the cracks in the x-direction.
smy	=	the predicted distance between the cracks in the y-direction.

App.F
A 400   General Method

The mean tensile strain, e_sm , may be calculated using the principles outlined in Sec.6 H 'General Design Method for Structural Members subjected to In-Plane Forces'. The mean strain may be calculated based on the assumption that the concrete contribute between the cracks with an average tensile stress, s_s f_tk , and a corresponding strain,e_cm = b_s f_tk / E_ck, where

b_s is the ratio between the mean tensile stress and the tensile strength of the concrete in the influence area of the characteristic crack.

bs	=	0.6 for short duration one time loadings
	=	0.4 for long duration or repeated loads at actual load level.
Eck	=	9500 (fcck)0.3

App.F
A 500   Simplified Approach

The crackwidth may be calculated by the following simplified equation:

Where:

ss2	=	the stress in the reinforcement in the crack for the actual cross-sectional forces
ssr2	=	the reinforcement stress at the crack location for those cross-sectional forces which give maximum tensile stress in the reinforcement at cracking of the concrete (max tensile stress in concrete equal to tensile strength). The calculation of reinforcement stress is based on cracked concrete.
srk	=	See A200 above.

s_sr2 is calculated based on the same ratio between the cross-sectional forces (the same location of the neutral axis) as used in the calculation of, s_s2 , and shall not be larger than s_s2.

For structures exposed to water pressure, the reinforcement stress, s_s2, shall include the effect of full water pressure, p_w, on the crack surface.

Additional simplification may be made by presuming b_s = 0, thus neglecting the shrinkage strain.