Actions and partial factors
9.7 Crack width calculations
9.7.6 Crack-inducing strain due to a combination of restraint effects and loading
As discussed in Section 9.1.6, it is not generally necessary to superimpose the effects of bending and direct tension with tension from restraint. In many practical cases, particularly in basement walls, stresses and strains caused by imposed deformation (shrinkage and restraint) will be at right angles to those caused by loading and therefore they need not be combined.
However, there are cases where the effects will be additive. For instance, when there is horizontal bending in a wall due to lateral loading, the stresses and strains due to imposed (shrinkage) deformation will be in the same direction and the effects will be
additive. In basement slabs that are designed as suspended slabs but cast on ground, the stresses due to restraint effects and loading will coincide and the effects again will be additive.
Where it is necessary to combine the effects of restraint and loading, the basic formula for crack width given above may be used noting that the crack inducing strain will now be the sum of the strain caused by restraint and loading effects assuming a cracked section. This approach is largely empirical but is in accordance with DD ENV 1992-1-1[64]
4.4.2.4(6). It accommodates combinations of long and short-term shrinkage and tension stiffening and eccentricities. Adding strains may be regarded as a reasonable way of estimating crack width (but it is not a valid approach to calculate moments of
resistance). The outline for a (much) more detailed approach to fi nd neutral axis depth, stresses and strains is given in Section B3.
It will be noted that cracking relieves restraint stresses and strains in adjacent uncracked sections. Besides combining edge and end restraint, which traditionally are treated separately, recent research[61] suggests that the relief of restraint strain is related to the length of the member and spacing (and number) of cracks. The formulae for edge and end restraint strain may be thought to represent extreme cases of infi nitely long members. In members of fi nite length, it would therefore appear plausible that the relief of restraint strain limits the summation of mechanical and restraint strains. (Note that cracks do not relieve strains in uncracked sections of the same member subject to tension or constant moment.) Until this theory has been justifi ed and developed, prudence dictates that calculated restraint and mechanical strains should be simply added.
9.7.7 Examples
By way of illustration Figures 9.11 and 9.12 show the crack widths in different thickness of walls and base slabs with different reinforcement. Figure 9.11 is for the end-restraint condition and Figure 9.12 is for the edge restraint condition.
Table 9.5 shows the crack widths predicted in a 300 mm thick element for different types of restraint and reinforcement percentages.
It can be seen clearly that for the same reinforcement, the crack width predicted in each case is different and the end-restrained elements require signifi cant amount of reinforcement to achieve the same crack width.
250 270 290 310 330 350 370 390 410
0.00250 270 290 310 330 350 370 390 410
Crack width (mm)
Thickness (mm)
Wall - B16 @ 150 mm c/c Wall - B20 @ 150 mm c/c Base slab - B12 @ 150 mm c/c Base slab - B20 @ 150 mm c/c Wall B25 @ 150 mm c/c Base slab - B25 @ 150 mm c/c
Figure 9.11 End-restrained members – crack widths due to imposed deformations fck = 30 MPa.
Figure 9.12 Edge-restrained members – crack widths due to imposed deformations
fck = 30 MPa.
Reinforcement
percentage (ρ) Edge restraint Member with end
restraint thick element for different reinforcement percentages and restraint types.
BS EN 1992-3 provides charts for limiting bar sizes and bar spacing for members subject to axial tension. When cracking is dominantly caused by restraint the limiting bar sizes in chart Figure 7.103N should be used. When cracking is due to loading Figure 7.103N or 7.104N may be used.
In BS EN 1992-1-1 there are tables for the same purpose. However, it is not stated whether the tables apply to members subject to axial tension or bending. It is believed that they deal with the case of bending. The crack widths covered in the table are 0.2 mm, 0.3 mm and 0.4 mm. In the context of water excluding structures when the crack width is smaller the tables will therefore be of limited use.
In order to use either the charts or tables the stress in the reinforcement will need to be calculated. They should be based on the crack-inducing strains discussed above.
Given the above uncertainties, the calculation approach would appear to be more satisfactory.
In general defl ections are unlikely to be critical in basement structures and the procedures in BS EN 1992-1-1 including the span/depth formulae may be used. Where fi nishes are applied to the structure, manufacturers should be consulted on any limitations on the strains. Base rotation may be an issue on long cantilever walls.
BS EN 1992-3 suggests a number of strategies to minimize the risk of cracking. CIRIA C660 also provides tips for control of early thermal cracking. The following is a summary.
Materials
Use cement replacement such as ggbs or fly ash to limit the temperature rise. Avoid pure CEM I cement.
Use aggregates with high strain capacity. Generally they will be angular.
Use aggregates with a low coefficient of thermal expansion.
Use superplasticisers and water reducing agents to reduce cementitious content, but not below the level needed to achieve a good finish.
Avoid overly strong concretes.
Construction
Construct at low ambient temperatures to limit T1 and T2.
For normal section thickness (say ≤ 500 mm) use glass reinforced plastic (GRP) or steel formwork for walls.
Use sequential pours rather than alternate bay method, to limit end restraint.
Where the restraint forces act parallel to the construction joint minimise the time between pours. Similarly maximize the time when the restraint forces are at right angles to the joint.