Safety of the strip method

Hillerborg (Hillerborg, 1996) introduced a number of approximations and simplifications to the strip method in order to make it more convenient for practical application. Although it was the intention that the modifications should be conservative, no formal guarantees exist that this is the case and it is therefore conceivable that unsafe designs might be generated, although Hillerborg contends that “the yield line theory of slabs designed according to the recommendations of the book never show that it is on the unsafe side, at least as far as I have found”. To examine the validity of this claim, the automated yield line method, employing fine meshes to establish probable mechanisms and then coarse meshes to optimise the geometry of the detected mechanism, have been undertaken (Johnson,

2001) for a range of the examples considered by Hillerborg. The results of these analyses are summarised in Table 1.

Table 1: Automated yield line analyses summary

In Table 1 the pairs of load factors (LF) given for each example relate to the initial fine mesh automated yield line solution and the subsequent coarse mesh used to optimise the detected mechanism form. In general, it is expected that the coarse mesh should produce a more critical (lower load factor) than the fine mesh. This may be seen not to be the case in all instances, presumably because in some of the examples the fine mesh allows the generation of a somewhat more complex variation of the mechanism taken as the basis for the coarse analysis. The load factors are based on the reinforcement design generated by the strip method and, taking the yield line results as essentially exact, a value above unity therefore represents a conservative strip design and a below unity represents an unsafe design. On this basis, Table 1 supports Hillerborg’s contention that the strip method does not generate unsafe designs for the examples but does indicate significant conservatism for some of the more complex examples, where 20-30% overdesigns are encountered on occasion.