An accurate assessment of deflection can only be achieved if consideration is given to the factors that affect it. The more important factors are discussed in detail below.
The tensile strength of concrete is an important property because the slab will crack when the tensile stress in the extreme fibre is exceeded. In Eurocode 2 the concrete tensile strength, /ctm, is a mean value (which is appropriate for deflection calculations) and increases as the compressive strength increases. This is an advancement when compared with BS 8110 where the tensile strength is fixed for all concrete strengths.
The degree of restraint to shrinkage movements will influence the effective tensile strength of the concrete. A layout of walls with high restraint will decrease the effective tensile strength. Typical examples of wall layouts are given in Figure 1. For a low restraint layout the following expression may be used for the concrete tensile strength:
/amji = Mean flexural tensile strength of reinforced concrete /am = Mean tensile strength of concrete
Figure 1
It is often recommended that the design value of the concrete tensile strength for a low restraint layout is taken as the average of /tm,fl and /ctm, to allow for unintentional restraint. For high restraint /am should be used.
Creep
Creep is the time-dependant increase in compressive strain in a concrete element under constant compressive stress. Creep is usually considered in the design by modifying the elastic modulus using a creep coefficient, h, which depends on the age at loading, size of the member and ambient conditions, in particular relative humidity. Eurocode 2 gives advice on the calculation of creep coefficients in detail in Annex B. It also advises on the appropriate relative humidity to use in Figure 3.1.
The cement strength class is required in the assessment of creep, however, at the design stage it is often not clear which class should be used. Generally, Class R should be assumed. Where the ground granulated blastfurnace slag (ggbs) content exceeds 35% of the cement combination or where fly ash (pfa) exceeds 20% of the cement combination, Class N may be assumed. Where ggbs exceeds 65% or where pfa exceeds 35% Class S may be assumed.
The elastic modulus of concrete is influenced by aggregate type, workmanship and curing conditions. The effective elastic modulus under sustained loading will be reduced over time due to the effect of creep. These factors mean that some judgement is required to determine an appropriate elastic modulus. Eurocode 2 gives recommended values for the 28-day secant modulus, Ecm, (in Table 3.1) and makes recommendations for adjustments to these values to account for different types of aggregate. The long-term elastic modulus should be taken as:
F"
a) Favourable layout of restraining walls (low restraint)
p □ q b □ cj r l j b) Unfavourable layout of restraining walls (high restraint)
where
Ec28 = 28-day tangent modulus = 1.05 Ecm
H = Creep factor. (Note that with Eurocode 2, q> relates to a 28-day short-term elastic modulus, whereas a 'true' creep factor would be associated with the modulus at the age of loading.)
The assessment of the long-term E-value can be carried out more accurately after the contractor has been appointed because they should be able to identify the concrete supplier (and hence the type of aggregates) and also the construction sequence (and hence the age at first loading).
The loading sequence and timing may be critical in determining the deflection of a suspended slab because it will influence the point at which the slab will crack (if at all) and is used to calculate the creep factors for the slab. A loading sequence is shown in Figure 2, which shows that in the early stages relatively high loads are imposed while casting the slab above. The loading sequence may vary, depending on the construction method.
Smaller loads are imposed when further slabs are cast above. The loads are then increased permanently by the application of the floor finishes and erection of the partitions. Finally, the variable actions are applied to the structure and, for the purpose of deflection calculation, the quasi-permanent combination should be used. (See Chapter 1, originally published as Introduction to Eurocodes5 for further information on combinations of actions.) However, it is likely that the quasi-permanent combination will be exceeded during the lifetime of the building and, for the purpose of determining whether the slab might have cracked, the frequent combination may be critical.
Commercial pressures often lead to a requirement to strike the formwork as soon as possible and move on to subsequent floors, with the minimum of propping. Tests on flat slabs have demonstrated that as much as 70% of the loads from a newly cast floor (formwork, wet concrete, construction loads) may be carried by the suspended floor below7. It can generally be assumed that early striking of formwork will not greatly affect the deflection after installing the cladding and/or partitions. This is because the deflection affecting partitions will be smaller if the slab becomes 'cracked' before, rather than after, the installation of the cladding and/or partitions.
Deflection of concrete sections is closely linked to the extent of cracking and the degree to which cracking capacity is exceeded. The point at which cracking occurs is determined by the moments induced in the slab and the tensile strength of the concrete, which increases with age. Often the critical situation is when the slab is struck, or when the load of the slab above is applied. Once the slab has cracked its stiffness is permanently reduced.
It is therefore necessary to find the critical loading stage at which cracking first occurs. This critical loading stage corresponds with the minimum value of K, where:
K= fct where
W = The serviceability loading applied up to that stage fctm = The concrete tensile strength at that stage Where the frequent combination is the critical load stage, then the degree of cracking (Z) calculated for the frequent combination should also be used for the quasi-permanent combination, but not for
Figure 2
Loading history for a slab - an example
h | |||||||||
b |
g |
n | |||||||
f | |||||||||
c |
| | ||||||||
n d |
J | ||||||||
a |
L-i |
r | |||||||
LJ bJ 1 | |||||||||
Loading sequence a Slab struck b 1st slab above cast c 2nd slab above cast d 3rd slab above cast |
e f g h |
Floor finishes applied Partitions erected Quasi-permanent variable actions Frequent variable actions | |||||||
Duration (days) 100 150 200 Duration (days) any of the earlier load stages. If, however, an earlier stage proves critical, the Z value at that stage should be carried forward to all subsequent stages. Further information can be found in the best practice guide Early striking and improved backpropping6 Shrinkage curvatureShrinkage depends on the water/cement ratio, relative humidity and the size and shape of the member. The effect of shrinkage in an asymmetrically reinforced section is to induce a curvature that can lead to significant deflection in shallow members. This effect should be considered in the deflection calculations. |
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