CRACK WIDTH CHECK FOR BASE SLAB
The crack width of the base slab is checked under service-load conditions in accordance with ACI 224R-01,
Control of Cracking in Concrete Structures. The maximum crack width is estimated using the following
expression:
w = k β fₛ √I
where the grid index is given by:
I = dᵦ₁ s₂ / (ρₜ ₁ t₁)
The parameters adopted for the crack-width calculation are summarized below.
Parameter
Fracture coefficient
Coefficient
Reinforcement yield strength
Service-load steel stress
Reinforcement diameter, Direction
1
Concrete cover
Reinforcement area provided
Reinforcement spacing, Direction 2
Active steel ratio
Grid index
Symbol
k
β
fᵧ
fₛ
Adopted Value
2.8 × 10⁻⁵
1.25
500 MPa
200 MPa = 29.0 ksi
dᵦ₁
16 mm = 0.64 in
C₁
Aₛ
s₂
ρₜ₁
I
50 mm = 2.0 in
1340.41 mm²/m = 0.633 in²/ft
150 mm = 6.0 in
0.054
71.11
1. Service-Load Stress in Reinforcement
The average service-load stress in the reinforcement is taken as 40% of the reinforcement yield strength.
fₛ = 0.40 fᵧ
fₛ = 0.40(500) = 200 MPa
fₛ = 200(0.145038) = 29.0 ksi
2. Reinforcement Diameter
The diameter of the reinforcement provided in Direction 1 (Vertical Direction) is:
dᵦ₁ = 16 mm
dᵦ₁ = 16 / 25.4 = 0.63 in ≈ 0.64 in
3. Concrete Cover
The nominal concrete cover is:
C₁ = 50 mm
C₁ = 50 / 25.4 = 1.97 in ≈ 2.0 in
4. Reinforcement Area Provided
The reinforcement area provided in the critical direction is:
Aₛ = 1340.41 mm²/m = 0.633 in²/ft
5. Reinforcement Spacing
The reinforcement spacing perpendicular to Direction 1, i.e. in Direction 2 (Horizontal Direction), is:
s₂ = 150 mm = 6.0 in
6. Active Steel Ratio
The active steel ratio is calculated as:
ρₜ ₁ = Aₛ / [12dᵦ₁ + 2C₁]
ρₜ ₁ = 0.633 / [12(0.64) + 2(2.0)]
ρₜ ₁ = 0.633 / 11.68
ρₜ ₁ = 0.054
7. Grid Index
Using the adopted parameters, the grid index is:
I = 71.11
8. Maximum Crack Width
The maximum crack width is calculated using:
w = k β fₛ √I
w = (2.8 × 10⁻⁵)(1.25)(29.0)√71.11
w = 0.0086 in
w = 0.0086 × 25.4 = 0.218 mm
wₘ ₐₓ ≈ 0.22 mm
9. Crack Width Acceptance Criteria
The calculated crack width is compared with the adopted maximum permissible crack-width limit of 0.30 mm for
the considered serviceability condition.
wₘ ₐₓ = 0.22 mm < w_allow = 0.30 mm
Conclusion
The calculated maximum crack width of the base slab is approximately 0.22 mm, which is within the adopted
permissible crack-width limit of 0.30 mm. Therefore, the base slab satisfies the crack-width/serviceability
requirement under the considered service-load condition.
∴ wₘₐₓ = 0.22 mm < 0.30 mm → OK
Design Note: The value of the grid index I = 71.11 should be verified against the actual base slab thickness t₁ and
the exact ACI 224R-01 formulation used in the original design calculation. All quantities within each equation
should be expressed in consistent units.