Unless the design code in use specifies a calculation for estimating crack widths, RAM Concept estimates crack widths based on a paper by Frosch [Frosch, R. J., "Another Look at Cracking and Crack Control in Reinforced Concrete", ACI Structural Journal, V. 96, No. 3, May-June 1999, pp. 437-442].

In cracked concrete, with the concrete assumed to carry only small tension stress, the crack width can be calculated as:

wc = εc sc

where

wc	=	crack width
ε c	=	cross section strain at crack elevation
sc	=	crack spacing

The cross section strain (ε_c ) at the crack elevation can be easily calculated in a cracked-section analysis using the "plane sections remain plane" assumption.

The crack spacing (s_c) is more difficult to predict.

For reinforcement with no bond to the concrete, the crack spacing can be shown to be:

h ≤ sc ≤ 2 h

where

h

=

height of the tension zone

For reinforcement with "no-slip" with the concrete, the crack spacing can be shown to be:

d* ≤ sc ≤ 2 d*

where

d*	=	distance from crack to centroid of nearest reinforcement $=\sqrt{c^2+{(s_b/2)}^2}$ for a single layer of reinforcement
c	=	perpendicular (shortest) distance from concrete face to reinforcement centroid
sb	=	spacing of reinforcement

For deformed bars without special coatings (such as epoxy), Frosch has shown that:

s_c = 2 d*

leads to reasonable predictions of the maximum crack width. RAM Concept uses this assumption, but limits d* to a maximum value of h (the crack height); this limiting value typically only controls in slabs without bonded reinforcement. The final equation RAM Concept uses for crack width calculation can be written as:

w_c = 2 ε_c d* (d* ≤ h)

For multiple bars and layers of reinforcement, the reinforcement can be optimally placed such that:

for all reinforcement i

w = Σs;

where

ci	=	perpendicular (shortest) distance from concrete face to reinforcement i centroid
si	=	length along on concrete tension face allocated to reinforcement i
w	=	width of concrete tension face

RAM Concept iteratively solves for d* (to within 1 mm), using all bonded reinforcement that when considered minimizes the value of d*. When using bonded post-tensioning, each duct is considered as a reinforcing bar equivalent. Unbonded and external post-tensioning are ignored. Tendons at an angle of less than 45 degrees to the cross section are ignored also.