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Pw

is the shear reinforcement ratio

Asw

is the area of shear reinforcement within a length s

s

is the spacing of the shear reinforcement

bw

is the breadth of the web or minimum width of the member over the effective depth

a

is the angle between the shear reinforcement and the main steel (i.e. for vertical stirrups a = 90° and sin a = 1)

(6) It should be noted that there are particular risks of large cracks occurring at sections where there are sudden changes of stress, e.g.

— at changes of section

— near concentrated loads

— sections where bars are curtailed

— areas of high bond stress, particularly at the ends of laps

Care should be taken at such sections to minimise the stress changes wherever possible. However, the rules for crack control given above will normally ensure adequate control at these points provided the rules for detailing reinforcement given in chapter 5 are complied with.

4.4.2.4 Calculation of crack widths

P(1) The design crack width may be obtained from the relation:

where wk is the design crack width srm is the average final crack spacing

(sm is the mean strain allowing under the relevant combination of loads for the effects of tension stiffening, shrinkage, etc.

" is a coefficient relating the average crack width to the design value

(2) The values of " in Equation (4.80) may be taken as:

" =1.7 for load induced cracking and for restraint cracking in sections with a minimum dimension in excess of 800 mm.

= 1.3 for restraint cracking in sections with a minimum dimension depth, breadth or thickness, whichever is the lesser) of 300 mm or less.

values for intermediate section sizes may be interpolated.

(sm may be calculated from the relation:

where:

Bs is the stress in the tension reinforcement calculated on the basis of a cracked section

Bsr is the stress in the tension reinforcement calculated on the basis of a cracked section under the loading conditions causing first cracking.

"1 is a coefficient which takes account of the bond properties of the bars

= 1.0 for high bond bars

= 0.5 for plain bars

"2 is a coefficient which takes account of the duration of the loading or of repeated loading = 1.0 for a single, short term loading

= 0.5 for a sustained load or for many cycles of repeated loading. For members subjected only to intrinsic imposed deformations, Bs may be taken as equal to Bsr

(3) The average final crack spacing for members subjected dominantly to flexure or tension can be calculated from the equation:

where 0

ki is the bar size in mm. Where a mixture of bar sizes is used in a section, an average bar size may be used.

is a coefficient which takes account of the bond properties of the bars; k1 = 0.8 for high bond bars and 1.6 for plain bars. In the case of imposed deformations, k1 should be replaced by k1 • k, with k being in accordance with 4.4.2.2(3). k2 is a coefficient which takes account of the form of the strain distribution = 0.5 for bending and 1.0 for pure tension

For cases of eccentric tension or for local areas, intermediate values of k2 should be used which can be calculated from the relation:

where (1 is the greater and (2 the lesser tensile strain at the boundaries of the section considered, assessed on the basis of a cracked section.

pr is the effective reinforcement ratio, As/Aceff, where As is the area of reinforcement contained within the effective tension area, Ac.eff.

The effective tension area is generally the area of concrete surrounding the tension reinforcement of depth equal to 2.5 times the distance from the tension face of the section to the centroid of the reinforcement. (See Figure 4.33). For slabs or for prestressed members where the depth of the tension zone may be small, the height of the effective area should not be taken as greater than (h - x)/3.

The resulting value of srm will be in mm.

(4) Prestressing tendons may be taken into account in the calculation of crack spacings within a 300 mm square area surrounding the tendon provided allowance is made for bond behaviour of the tendons. Appropriate values for k1 for particular tendons should be obtained from tests but, in the absence of better information, a value of 2.0 may be taken. Where a mixture of tendons and ordinary reinforcement are present, k^ in Equation (4.82) may be replaced by C k^/n where C k^ is the sum of the diameter of all bars and tendons within the area considered, each multiplied by its appropriate bond coefficient, and n is the total number of bars and tendons.

(5) Where cracks form at a significant angle (> 15°) to the direction of the reinforcement in members reinforced in two orthogonal directions then the crack spacing may be calculated from Equation (4.83) below.

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