RAM Concept Help

Section 8.6.3/9.5.2.3 Crack Control with Direct Crack Width Calculation

When crack widths are assessed by direct calculation, cracked equilibrium strains are calculated using the equations in 8.6.2.3 assuming that concrete has no tensile strength. The characteristic maximum crack width can be input directly or using the selected "Environment" as noted in section 65.6.11. No limits are imposed on the input crack widths.

This criterion is applied to two-way slabs and other wide cross sections, but will not provide accurate crack width predictions for these wide cross sections when reinforcement is not spaced according to the varying stress patterns across the section. For narrower cross sections with a uniform stress pattern, the bonded reinforcement should be spaced uniformly. For this reason, it may not be appropriate to do a "crack width" onlydesign on full panel strip widths.

The crack-limiting capabilities of appropriately placed bonded tendons are considered, and the balance loading will be considered if included in the load combinations.

w = sr,maxsm- εcm) ≤ w’max

εsm - εcm = σscr/Es – 0.6(fct/(Espeff ))(1 + ne peff ) + εcs ≥ 0.6 σscr / Es

where
σscr
=
tension stress in un-tensioned reinforcement from a cracked section analysis, or maximum differential bonded tendon stress from tendon stress level at zero strain in the concrete at the same level
εcs
=
input ultimate shrinkage strain (Criteria > Calc Options > Load History/ECR tab)
ne
=
effective module ratio = (1+ σcc) Es / Ec
σcc
=
creep coefficient (since RAM Concept does not know at what time cracking occurred, this value is conservatively taken as zero)
fct
=
mean value of the axial tensile strength of concrete
peff
=
Ast/ Ac,eff
Ast
=
area of un-tensioned reinforcement or bonded tendons within area hc,ef
Ac,eff
=
area of concrete within depth hc,ef
hc,ef
=
minimum of 2.5(D-d), (D-kd)/3, or D/2
D
=
overall depth of the cross-section
d
=
effective depth of the tension steel, taken as the resultant tension force depth
kd
=
depth of the neutral axis of the cracked section
sr,max
=
3.4c + 0.3k1k2db / peff = maximum crack spacing (eq. 8.6.2.3(3))
c
=
average cover to reinforcement, weighted by bar/tendon units
k1
=
coefficient accounting for bond properties of reinforcement
  • 0.8 for un-tensioned reinforcement or 1.6 for bonded tendons
  • averaged for cross sections containing both tendons and un-tensioned reinforcement, weighted by bar/tendon units

k2
=
coefficient accounting for longitudinal strain distribution
  • 0.5 for bending
  • (ε1 + ε2) / 2ε1 for combined tension and bending