Pile Crack Width Design

Serviceability limit state. Combined service axial force and bending on circular reinforced concrete piles (bored, CFA and spun piles).

ACI 224R-01 · ACI 318-19 · ACI 350-06EN 1992-1-1:2004BS 8110-2:1985 · BS 8007:1987

Input Data

Circular pile section

mm
mm
mm

Longitudinal reinforcement

no.
mm

Materials

MPa
MPa
MPa
MPa

Design code (verdict basis)

ACI options
mm

EN 1992-1-1 options
mm
–
–
–
–
–
MPa
mm

BS options
mm
BS 8007 Appendix B Eq. (2)/(5) apply only to a 0.2 mm limit and Eq. (3)/(6) only to 0.1 mm. The code does not allow interpolation, so the method follows the limit selected.

Service load cases

N: + compression / − tension (kN)  ·  M: service moment (kN·m)
IDDescription (combination / depth)N (kN)M (kN·m)
Load caseN kNM kN·mACI 224R-01EN 1992-1-1BS 8110-2 / BS 8007
w mmratiowk mmratiow mmratio

Selected load case

Crack width formulas by code

as printed in each code, with SI forms

ACI

ACI 224R-01 · ACI 224.2R-92

Flexure: a compression zone exists (0 < x < D)

w = 0.076 β fs ∛(dcA) × 10⁻³ACI 224R-01 Cl. 4.2.1, Eq. (4-2a): w in in., fs in ksi, dc in in., A in in²
w = 1.102×10⁻⁵ β fs ∛(dcA)The same equation in SI: w and dc in mm, fs in MPa, A in mm² (0.076×10⁻³ / 6.895)

Direct tension: whole section in tension

w = 0.10 fs ∛(dcA) × 10⁻³ACI 224R-01 Cl. 4.8, Eq. (4-21); ACI 224.2R-92 Cl. 3.5, Eq. (3.6) (in., ksi)
w = 1.450×10⁻⁵ fs ∛(dcA)The same equation in SI (mm, MPa)

Terms for a circular pile

β = (D − x)/(d1 − x) ;  A = 2dcs ;  s = 2πRbc/n
w
most probable maximum crack width at the tension face
fs
service stress in the most highly stressed bar (cracked section under N + M)
β
ratio of the distances from the neutral axis to the tension face and to the bar
dc
extreme tension fibre to bar centre = cnom + φlink + φ/2
A
concrete area symmetric with the reinforcement, divided by the number of bars
x, d1
neutral-axis depth; depth of the most stressed bar
Rbc, n
radius of the bar circle; number of bars

Dubai requirement

Crack-width calculation checks to ACI 224RDBC 2021 Cl. F.8.4. Piles: 0.2 mm under tension load; 0.1 mm under permanent tension or groundwater uplift (DBC Table F.17; DM Res. 37/2021 Art. 57; Trakhees Grey Code Cl. 1.6.1)

Allowable

w ≤ wallowACI 224R-01 Cl. 4.4, Table 4.1 (humidity, moist air, soil: 0.30 mm; seawater, wetting and drying: 0.15 mm)

Eurocode

EN 1992-1-1:2004, Cl. 7.3.4

Crack width

wk = sr,max (εsm − εcm)Eq. (7.8)
εsm − εcm = [σs − kt(fct,eff/ρp,eff)(1 + αeρp,eff)] / Es ≥ 0.6σs/EsEq. (7.9)
ρp,eff = As/Ac,effEq. (7.10)

Maximum crack spacing

sr,max = k3c + k1k2k4φ/ρp,effEq. (7.11): where the bar spacing is ≤ 5(c + φ/2)
sr,max = 1.3(h − x)Eq. (7.14): where the bar spacing is > 5(c + φ/2)
k2 = (ε1 + ε2)/2ε1Eq. (7.13), eccentric tension; k2 = 0.5 bending, 1.0 pure tension

Effective tension area

hc,ef = min{2.5(h − d); (h − x)/3; h/2}Cl. 7.3.2(3), Fig. 7.1. For a circular pile, Ac,eff is the circular segment of depth hc,ef, or an annulus when the whole section is in tension. Fig. 7.1 is drawn for rectangles, so both readings are calculated: the segment, and a ring band of thickness hc,ef within the tension zone. The larger wk governs.
σs
stress in the most stressed bar, cracked section
c
clear cover to the longitudinal bar
φ
bar diameter
k1
0.8 high-bond bars; 1.6 plain bars
k3, k4
3.4 and 0.425, recommended values (National Annex)
kt
0.4 long-term; 0.6 short-term loading
αe
Es/Ecm; fct,eff = fctm (Cl. 7.1(2))

UK National Annex

Table NA.4: wmax = 0.3 mm (X0 to XS3) ;  k3 = 3.4, k4 = 0.425NA to BS EN 1992-1-1. Members cast against the ground: wk may be checked at the durability cover, wk × (cmin,dur + Δcdev)/cnom (NA to 7.3.4(3))

Allowable

wk ≤ wmaxCl. 7.3.1(5), Table 7.1N, quasi-permanent combination (XC2 to XC4, XD, XS: 0.3 mm)

British Standards

BS 8110-2:1985 Cl. 3.8.3 · BS 8007:1987 Appendix B

Flexure, and flexure with axial force

w = 3acrεm / [1 + 2(acr − cmin)/(h − x)]BS 8110-2 Eq. 12; BS 8007 Eq. (1)
εm = ε1 − bt(h − x)(a′ − x) / [3EsAs(d − x)]BS 8110-2 Eq. 13; BS 8007 Eq. (2) for a 0.2 mm limit
ε2 = 1.5bt(h − x)(a′ − x) / [3EsAs(d − x)]BS 8007 Eq. (3), for a 0.1 mm limit
Whole section in tension: (h − x) taken between h and 2hBS 8110-2 Cl. 3.8.3

Direct tension

w = 3acrεm ;  ε2 = 2bth/(3EsAs) or bth/(EsAs)BS 8007 Eq. (4), with Eq. (5) for 0.2 mm or Eq. (6) for 0.1 mm

Concrete modulus for strains

Ec = ½(K0 + 0.2fcu), K0 = 20 kN/mm²BS 8110-2 Eq. 17 and Cl. 3.8.3 (half the instantaneous value)
acr
distance from the point considered to the surface of the nearest bar
a′
distance from the compression face to the point considered
ε1
strain at that level, ignoring concrete stiffening
bt
width at the centroid of the tension steel: 2√[R² − (d − R)²] for a circle. For a circular tension zone, the smaller of bt and beq = ∫b(y)(y − x)dy/∫(y − x)dy is used (Cl. 3.8.3); beq = b for a rectangle, and beq·h = Ag in uniform tension
cmin
minimum cover to the tension steel
d, As
effective depth (tension-steel centroid); area of tension steel
h, x
overall depth (h = D); neutral-axis depth

Allowable

w ≤ 0.3 mm (BS 8110-2 Cl. 3.2.4); 0.2 or 0.1 mm (BS 8007 Cl. 2.2.3.3)Steel strain ≤ 0.8fy/Es (BS 8110-2 Cl. 3.8.3; BS 8007 Cl. B.2, B.5)

Calculation sheet

Design notes for piles

  • Load combination. EN 1992-1-1 Table 7.1N limits apply to the quasi-permanent combination (Cl. 7.3.1(5)). The ACI 224R-01 Table 4.1 widths are for service loads. BS 8110-2 Cl. 3.8.3 and BS 8007 Cl. B.3 use characteristic (service) loads.
  • Where to check. Enter N and M from the lateral pile analysis at the pile head (fixed-head piles) and at the depth of maximum moment. Uplift piles also need the pure tension case.
  • Concrete modulus. Each code uses its own value. ACI uses Ec = 4700√f′c (Cl. 19.2.2.1(b)). EN 1992 uses Ecm/(1+φ). BS 8110-2 Cl. 3.8.3 uses half the instantaneous modulus of Eq. 17. The steel stress therefore differs slightly from code to code.
  • Dubai. DBC 2021 Cl. F.8.4 requires crack-width calculation checks to ACI 224R. Piles are limited to 0.2 mm under tension load and 0.1 mm under permanent tension or groundwater uplift (DBC Table F.17). DM Resolution 37/2021 Art. 57 and the Trakhees Grey Code Cl. 1.6.1 give the same values.
  • Large cover. ACI 224R-01 Cl. 4.2.2 notes that the earlier crack-width equations are valid only for covers up to about 63 mm. Pile covers are normally 75 mm, so a warning is shown. ACI 224R-01 Cl. 4.4 adds that a larger cover, even if it leads to a larger surface crack width, may be preferable for corrosion control. For EN 1992, the UK National Annex allows members cast against the ground to be checked at the durability cover.
  • Combined actions. BS 8007 Cl. 3.2.2(c) requires the flexural strain to be modified for direct strain. This calculator does that by solving the cracked section for N and M together, for every code.
  • Direction of bending. Enter the resultant moment M = √(Mx² + My²). A circular section has the same properties about every axis, and the cage is checked in its two critical orientations.