Figure 3.5. Stress-strain relations for several time durations of axial compressive loads (Rusch, 1960)

As can be seen, the longer the loading time, the more the ultimate strength approaches the long-term value 80%. The tests carried out by Rusch were limited to concrete's with a maximum cube strength of about 60Mpa. Tests by Walraven and Han on concrete's with cube strength's up to 100 Mpa showed that the sustained loading behaviour for high strength concrete is similar to that of conventional concrete's [Han/Walraven, 1993].

However, Rusch's tests were carried out on concrete which had an age of 28 days at the time the load was applied. This condition will normally not hold for a structure in practice, which generally will be much older when subjected to a load. This means that the sustained loading effect is at least partially compensated by the increase in strength between 28 days and the age of loading. Fig. 3.6 shows the strength development in time according to eq. EC-3.3 for concrete's made with rapid hardening high strength cements RS, normal and rapid hardening cements N and R, and slowly hardening cements SL.


Figure 3.6. Compressive strength development of concrete made with various types of cement according to Eq. EC-3-3


Figure 3.6. Compressive strength development of concrete made with various types of cement according to Eq. EC-3-3

Fig 3.6 shows, that the gain in strength in 6 months ranges from 12% for rapid hardening cements to 25% for slowly hardening cements. So, a considerable part of the sustained loading effect is compensated for by the increase in strength.

Furthermore the bearing capacity as formulated in building codes is generally based on experiments in laboratories (shear, punching, torsion, capacity of columns). Normally those tests have a duration of at least 1.5 hours. In Fig. 3.5 it can be seen that in a test with a loading duration of 100 minutes, the reduction of strength with regard to 2 minutes is already about 15%.

A certain sustained loading effect is therefore already included in the results of tests. It is therefore concluded that cases in which the sustained loading effect will really influence the bearing capacity of a structure in practice are seldom and do not justify a general reduction of the design strength with a sustained loading factor of 0.8. Therefore in clause 3.1.4 it is stated that "the value of acc may be assumed to be 1, unless specified otherwise".

Such a case can for instance occur when, according to 3.1.2, the concrete strength is determined substantially after 28 days: in such a case the gain in strength may be marginal so that a value acc smaller than 1 is more appropriate.

For tension similar arguments apply.

The value of the design tensile strength fctd is defined as fctd = act fctk 0,05 /yc [(3.16)-EC2] (2.3)

where act is a safety factor, similar to acc, the value of which may be found in the National Annex;

fctk 0,05 is the characteristic axial tensile strength of concrete, fractile 5%, which can be deducted from

3.1.7 Stress-strain relations C3.1.7 Stress-strain relations for the design of cross-sections for the design of cross- Design stress-strain relations can be derived from the mean stress strain relations. This can sections principally be done using the relations given in 3.1.5, but now for the characteristic compressive strength (fck) values and subsequently reducing the stress ordinate by a factor yc = 1.5. This means that principally not only the stress values but also the Ec values are divided by yc. In order to obtain consistent and sufficiently safe design relations the ultimate strains scu have also been slightly reduced in relation to Eq. 8. By choosing the expression

for concrete strength classes C55 and higher, all curves end approximately at their top (compare Fig. 3.3). The resulting curves are shown in Fig. 3.7.

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  • bertha
    What is fctk concrete 0,005?
    8 years ago

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