# Bs 8007 Crack Width Examples

Bs 8007 Crack Width Examples

## Bs 8007 Crack Width Examples

Crack width is one of the serviceability criteria for concrete structures, especially for those that are designed to retain aqueous liquids. Cracks can affect the appearance, durability, and watertightness of concrete structures. Therefore, it is important to limit the crack width to acceptable values, depending on the exposure conditions and the function of the structure.

BS 8007:1987 is a British standard that provides guidance on the design of concrete structures for retaining aqueous liquids. It extends BS 8110:1985, which is a general code of practice for the design of concrete structures, with particular emphasis on the provision of reinforcement to control crack widths. BS 8007:1987 has been replaced by Eurocode 2 Part 3, which covers the design of liquid retaining and containment structures.

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BS 8007:1987 specifies different maximum design surface crack widths for different exposure conditions, as shown in the table below.

Exposure condition

Maximum design surface crack width (mm)

Very severe

0.10

Severe

0.15

Moderate

0.20

Mild

0.30

The exposure conditions are defined in terms of the aggressiveness of the environment and the type of liquid retained. For example, very severe exposure condition applies to structures that are exposed to seawater or aggressive chemicals, or that retain liquids at temperatures above 50C. Severe exposure condition applies to structures that are exposed to de-icing salts or industrial effluents, or that retain liquids at temperatures between 20C and 50C. Moderate exposure condition applies to structures that are exposed to rain or groundwater, or that retain liquids at temperatures below 20C. Mild exposure condition applies to structures that are not exposed to any aggressive agents, or that retain potable water.

The maximum design surface crack width can be calculated by multiplying the maximum crack spacing by the mean strain of the reinforcement at the cracked section. The maximum crack spacing can be estimated by using empirical formulas given in BS 8007:1987, which depend on the cover, bar diameter, bar spacing, and bond characteristics. The mean strain of the reinforcement can be obtained by subtracting the concrete strain from the steel stress divided by the modulus of elasticity of steel.

The following are some examples of crack width calculations for different types of concrete structures designed according to BS 8007:1987.

## Example 1: Reinforced concrete wall subjected to direct tension

A reinforced concrete wall with a thickness of 300 mm is designed to retain water at a depth of 10 m. The wall is subjected to a direct tensile stress of 1.5 MPa due to hydrostatic pressure. The concrete grade is C30/37 and the reinforcement grade is B500B. The cover to the reinforcement is 40 mm and the bar diameter is 16 mm. The reinforcement ratio is 0.5% and the bars are uniformly distributed along the wall height. The bond condition is good and the exposure condition is moderate.

The maximum design surface crack width for moderate exposure condition is 0.20 mm according to BS 8007:1987.

The maximum crack spacing can be estimated by using the formula given in clause A2.4.2 of BS 8007:1987:

```html sr,max = k1c + k2k3k4φ ``` where:

```html sr,max = maximum crack spacing (mm) k1 = coefficient related to bond condition (0.8 for good bond) c = cover to longitudinal reinforcement (mm) k2 = coefficient related to bar diameter (0.5 for φ ≤ 32 mm) k3 = coefficient related to bar spacing (1.0 for φ ≤ 200 mm) k4 = coefficient related to reinforcement ratio (1.0 for ρ ≤ 0.02) φ = bar diameter (mm) ``` Substituting the given values, we get:

```html sr,max = 0.8 x 40 + 0.5 x 1.0 x 1.0 x 16 sr,max = 56 mm ``` The mean strain of the reinforcement at the cracked section can be obtained by subtracting the concrete strain from the steel stress divided by the modulus of elasticity of steel:

```html εsm = σs/Es - εc

``` where:

```html εsm = mean strain of reinforcement at cracked section σs = stress in reinforcement (MPa) Es = modulus of elasticity of steel (200 GPa) εc = strain in concrete at level of reinforcement ``` The stress in the reinforcement is equal to the direct tensile stress in the wall, which is 1.5 MPa. The strain in the concrete can be assumed to be zero, since the wall is cracked under tension. Therefore, we get:

```html εsm = 1.5 x 10 / (200 x 10) - 0 εsm = 7.5 x 10 ``` The maximum design surface crack width can be calculated by multiplying the maximum crack spacing by the mean strain of the reinforcement:

```html wk = sr,maxεsm

``` where:

```html wk = maximum design surface crack width (mm) ``` Substituting the values, we get:

```html wk = 56 x 7.5 x 10 wk = 0.00042 mm ``` The calculated crack width is much smaller than the allowable value of 0.20 mm, so the design is satisfactory.

## Example 2: Reinforced concrete beam subjected to bending and shear

A reinforced concrete beam with a cross-section of 300 mm x 600 mm is designed to support a uniformly distributed load of 50 kN/m over a span of 6 m. The beam is simply supported at both ends and has a clear span of 5.8 m. The concrete grade is C30/37 and the reinforcement grade is B500B. The cover to the top and bottom reinforcement is 40 mm and the cover to the side reinforcement is 30 mm. The beam has four bars of 20 mm diameter at the bottom and two bars of 16 mm diameter at the top. The shear reinforcement consists of links of 8 mm diameter spaced at 150 mm along the span. The bond condition is good and the exposure condition is mild.

The maximum design surface crack width for mild exposure condition is 0.30 mm according to BS 8007:1987.

The maximum crack spacing can be estimated by using the formula given in clause A2.4.2 of BS 8007:1987, as in Example 1. For the bottom reinforcement, we get:

```html sr,max,bottom = k1c + k2k3k4φ sr,max,bottom = 0.8 x 40 + 0.5 x (300 - 40 -20) / (4 x20) x (4 x20) / (300 -40) x20 sr,max,bottom = 72 mm ``` The mean strain of the reinforcement at the cracked section can be is 12 mm. The reinforcement ratio is 0.2% for both directions and the bars are uniformly distributed along the slab. The bond condition is good and the exposure condition is severe.

The maximum design surface crack width for severe exposure condition is 0.15 mm according to BS 8007:1987.

The maximum crack spacing can be estimated by using the formula given in clause A2.4.2 of BS 8007:1987, as in Example 1 and Example 2. For both directions of reinforcement, we get:

```html sr,max = k1c + k2k3k4φ sr,max = 0.8 x 25 + 0.5 x (150 - 25 -12) / (12 x0.002) x (12 x0.002) / (150 -25) x12 sr,max = 52 mm ``` The mean strain of the reinforcement at the cracked section can be obtained by subtracting the concrete strain from the steel stress divided by the modulus of elasticity of steel, as in Example 1 and Example 2. The stress in the reinforcement can be obtained by using the bending moment diagram and the section properties of the slab. The maximum bending moment due to the uniformly distributed load occurs at mid-span of the longer side and is equal to:

```html Mmax,load = wL/10 Mmax,load = 10 x 10 x 5/10 Mmax,load = 25 kN.m ``` where: ```html Mmax,load = maximum bending moment due to load (kN.m) w = uniformly distributed load (kN/m) L = longer side of slab (m) ``` The section modulus of the slab is equal to: ```html Z = bd/6 Z = 150 x 138/6 Z = 4.18 x 10 mm ``` where: ```html Z = section modulus (mm) b = width of slab (mm) d = effective depth of slab (mm) ``` The stress in the reinforcement due to the load is equal to: ```html σs,load = Mmax,load/Z σs,load = 25 x 10 / (4.18 x 10) σs,load = 5.98 MPa ``` where: ```html σs,load = stress in reinforcement due to load (MPa) ``` The maximum bending moment due to the restrained shrinkage and temperature effects can be estimated by using the formula given in clause A3.3.1 of BS 8007:1987: ```html Mt,s = αεt,sEc,IeffIeff/L ``` where: ```html Mt,s = maximum bending moment due to shrinkage and temperature effects (kN.m/m) α = coefficient related to restraint conditions (0.6 for four-sided restraint) εt,s = total strain due to shrinkage and temperature effects (0.0005 for severe exposure condition) Ec,Ieff = effective modulus of elasticity of concrete at transfer