J. Walraven · fib Model Code for Concrete Structures 2010: mastering challenges and encountering new ones
Fig. 5. Principle of compressive membrane action [11]
160 mm thick deck was supported by prestressed beams spaced at 1500 mm c/c. Depending on the position of the concentrated load, the measured loadbearing capacity was a factor 1.6–5.2 times larger than the load predicted on the basis of the unconfined situation. The increase in the load due to compressive membrane action depends on the confining action of the adjacent part of the structure. At this moment, tests are being carried out at TU Delft on a 1:2 size model of a bridge deck in order to verify the effect of compressive membrane action on the loadbearing capacity. This bridge deck consists of prestressed beams with thin concrete slabs cast in between and connected by transverse prestressing. The concentrated load will be applied at various positions of the deck in order to quantify the effect of compressive membrane action on the capacity of this bridge prototype, representing 69 bridges in The Netherlands. The tests are being carried out in order to verify whether those decks should be strengthened or have a sufficient loadbearing capacity. General rules with regard to this phenomenon are of great importance for decision-making when it comes to strengthening existing structures.
3.6
Further development of the design recommendations for fibre-reinforced concrete
The provisions for the design of fibre-reinforced structures given in fib MC 2010 are a step forward in various respects. The recommendations are valid for the whole range between conventional fibre-reinforced concrete (FRC), with moderate strength and relatively low volumes of coarse fibres, to ultra-high-performance FRC, with a very high strength (180–200 N/mm2) and high volumes of fine steel fibres. Moreover, a classification of FRC has been introduced with regard to its mechanical properties. This means that design relationships can be assumed in advance for carrying out the design, which are verified later by tests on control specimens. Through this arrangement, the design of FRC basically follows the same pattern as the design of reinforced concrete, where the concrete strength class is chosen in advance and verified by cylinder or cube tests at a later stage. An objection that is sometimes raised against such a harmonized approach – valid for all types of FRC – is that it may be too conservative for
special FRC mixtures such as ultra-high-strength FRC. It might therefore be worthwhile comparing the results of the harmonized approach according to fib MC 2010 with those of tailor-made approaches in order to see if it makes sense to distinguish different levels of approximation, as introduced elsewhere in fib MC 2010. Another aspect that should be considered is the way in which the properties of FRC are tested. In order to determine the mechanical properties of FRC, in most cases a series of small control beams is subjected to a load at mid-span (RILEM test). The stress-crack opening relationship is then derived from this series by inverse analysis. The tests show mostly a considerable scatter in load-deflection relations. This scatter, which is reflected as well by the stress-crack opening relationship and as a consequence affects the design stress-strain relation derived afterwards, is rather a property of the test series than it is representative of the behaviour of FRC in a structure. This should be given serious consideration. One possibility is to determine as accurately as possible the mean stress-crack opening relationship from tests with low variability, such as a bending test on a circular panel on three point supports (Fig. 6), where the scatter is small because of the compensating effect of the three yield lines, and combine the stress-crack opening or stress-strain relations obtained in this way with the scatter to be expected in the real structure. In a structure the scatter decreases as the cracked area involved in the loadbearing mechanism increases. General rules could be derived here.
3.7
Reliability of non-linear finite element calculations
As mentioned before, fib MC 2010 offers various strategies for introducing reliability into numerical calculations. Three principles are given. The most practical strategy lies between the extremes of the “probabilistic method” and the “partial factor method” and is known as the “global resistance method”, and under this heading the “method of estimation of a coefficient of variation of resistance”. This method can be seen as a compromise between accuracy and practical applicability. Further case studies to optimize this method would be worthwhile. It is a step in the direction of tailor-made NLFEM analyses with the highest possible reliability.
Structural Concrete 14 (2013), No. 1
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