Crack Width
Published: 28/05/26, Updated:
Version: 1.0.0
Crack width form performs crack width calculations of rectangular cross-sections currently to EN1992-1-1 and BS8110. Serviceability limit state requires cracks within reinforced concrete structural elements to be controlled down to allowable width. This form allows user to enter data promptly and perform selected code check on a described section.
Assumptions
The following assumptions are considered in analysis:
Constant elasticity of steel modulus E = 200GPa and rectangular cross-section.
Constant cover around the perimeter.
Limitations
The calculation has the following limitations:
Positive moment input only to induce cracking at the bottom face.
Section width and height limited to 1000mm.
Concrete compressive strength and resultant properties are code dependent.
| Input Variable | Description | Limits |
|---|---|---|
| Concrete strength | C12/15, C16/20, C20/25, C25/30, C28/35, C30/37, C32/40, C35/45, C40/50, C45/55, C50/60 | |
| fck | Characteristic concrete compressive cylinder strength | Derived from concrete grade — EN1992-1-1 Table 3.1 |
| fcm | Mean compressive cylinder strength | fcm = fck + 8 — EN1992-1-1 Table 3.1 |
| Es | Modulus of steel elasticity | 200 GPa — EN1992-1-1 cl.3.2.7(4) |
| fyk | Characteristic yield strength of reinforcement | 400 ≤ fyk ≤ 600 N/mm² — EN1992-1-1 cl.3.2.2 |
| b | Section width | 100 ≤ b ≤ 1000 mm |
| h | Section height | 100 ≤ h ≤ 1500 mm |
| Mqp | Quasi-permanent moment | 0 < Mqp ≤ MEd — EN1992-1-1 cl.7.3.4 |
| Med | Design bending moment | 0 < MEd ≤ 9999 kNm |
| tcr | Cracking age | 1 ≤ tcr ≤ 28 days — EN1992-1-1 cl.3.1.2 |
| cem | Cement type | S (slow), N (normal), R (rapid) — EN1992-1-1 cl.3.1.2(6) |
| tdur | Term duration | Short, Long — EN1992-1-1 Table 7.2N |
| c | Concrete cover | 15 ≤ c ≤ 75 mm — EN1992-1-1 cl.4.4.1 |
| φ | Creep ratio | 0 ≤ φ ≤ 2.0 — EN1992-1-1 cl.3.1.4 |
| lbot | Number of bottom rebar layers | 1, 2, 3, 4 |
| nbot | Number of bottom bars | 1 ≤ nbot ≤ 20 |
| Øbot | Diameter of bottom rebars | 6, 8, 10, 12, 16, 20, 25, 32, 40, 50 mm |
| ltop | Number of top rebar layers | 1, 2, 3, 4 |
| ntop | Number of top bars | 0 ≤ ntop ≤ 20 |
| Øtop | Diameter of top rebars | 6, 8, 10, 12, 16, 20, 25, 32, 40, 50 mm |
| Ølinks | Diameter of links | 6, 8, 10, 12, 16, 20, 25, 32, 40, 50 mm |
| Ølinks,r | Link inner radius | Minimum radius for scheduling — IStructE Standard method of detailing structural concrete (4th edition), Table C1 |
| svert | Vertical spacing between longitudinal bars | 20 ≤ svert ≤ 150 mm — EN1992-1-1 cl.8.2 |
| wk,limit | Crack width limit | 0.2, 0.3, 0.4 mm — EN1992-1-1 Table 7.1N |
| dagg | Maximum aggregate size | EN1992-1-1 cl.8.2(2) — minimum bar spacing depends on aggregate size |
| ρs | Steel density | 7850 kg/m³ — typical density of reinforcing steel |
| Result Variable | Description |
|---|---|
| Ecm | Modulus of elasticity of concrete |
| αe | Effective modular ratio |
| fcm(t) | Mean compressive strength of concrete at time (t) |
| fctm | Mean concrete tensile strength |
| fctm(t) | Mean tensile strength of concrete at time (t) |
| As,bot | Area of bottom reinforcement |
| Ac,top | Area of top reinforcement |
| As,min | Minimum tensile reinforcement |
| Ac,min | Minimum compression reinforcement |
| As,max | Maximum reinforcement |
| sbar,bot | Bottom reinforcement horizontal bar spacing |
| sbar,top | Top reinforcement horizontal bar spacing |
| σs,max | Maximum steel stress |
| d | Effective depth to tensile reinforcement |
| dt | Effective depth to top reinforcement |
| xu | Uncracked neutral axis position |
| Iu | Moment of inertia of the uncracked section |
| Mcr | Cracking moment |
| Cracking status | |
| xcr | Cracked neutral axis position |
| σc | Concrete stress |
| σs | Steel stress |
| Ac,eff | Effective area of concrete in tension |
| ρp,eff | Effective reinforcement ratio |
| Wtop | Weight of top reinforcement |
| Wbot | Weight of bottom reinforcement |
| Warea | Weight of reinforcement per unit area |
| sr,max | Maximum of tension steel spacing |
| εavg | Average strain between cracks |
| z | Lever arm |
| εsc | Strain in compression steel |
| εc | Strain in concrete block |
| εs | Strain in tensile reinforcement |
| Fsc | Top rebar force |
| Fc | Concrete block force |
| Fst | Bottom rebar force |
| wk | Crack width |
| Design Variable | Description |
|---|---|
| smin,bot | Minimum bottom horizontal bar spacing |
| smax,bot | Maximum bottom horizontal bar spacing |
| smin,top | Minimum top horizontal bar spacing |
| smax,top | Maximum top horizontal bar spacing |
| smin,vert | Minimum vertical bar spacing |
| σc | Stress in concrete block |
| σs | Stress in reinforcement |
| As,min,bot | Minimum area of bottom reinforcement |
| As,max,bot | Maximum area of bottom reinforcement |
| As,min,top | Minimum area of top reinforcement |
| As,max,top | Maximum area of top reinforcement |
| wcr | Crack width to limit |
Standards
EN1992-1-1
BS8110-1
BS8110-2
References
- BS EN 1992-1-1 2014
- BS 8110-1 1997
- BS 8110-2 19851
- BS 8007 19872
- Mosley, Bungey, Hulse, Reinforced Concrete Design to EC2, 6th Edition, 2007
| Release Date | Version | Description |
|---|---|---|
| January 2024 | 1.0.0 | Initial release. |