Crack Width Predictions
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 |
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The cross section strain (εc ) at the crack elevation can be easily calculated in a cracked-section analysis using the "plane sections remain plane" assumption.
The crack spacing (sc) 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 |
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For reinforcement with "no-slip" with the concrete, the crack spacing can be shown to be:
d* ≤ sc ≤ 2 d* |
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For deformed bars without special coatings (such as epoxy), Frosch has shown that:
sc = 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:
wc = 2 εc d* (d* ≤ h)
For multiple bars and layers of reinforcement, the reinforcement can be optimally placed such that:
for all reinforcement i
w = Σs; |
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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.