Keywords: inflatable beams, limit loads, limit analysis, pneumatic hinge.

Inflatable structures made of modern textile materials with important mechanical characteristics can be inflated at high pressure which is interesting from the following points of view: deflections are inversely proportional to the constitutive law of the fabric and to the applied pressure; collapse loads are proportional to the applied pressure. The deflections have been established in some of our previous papers [1,2] for inflatable panels and tubes. The aim of the paper is to draw out the theory of the behaviour of inflatable beams made of prestressed coated fabrics when the loads are such that wrinkles and collapse appears.

Limit analysis of plastic beams is well known. When plasticity appears on the inner or outer fibers of a beam, the load, which leads to the beginning of plasticity, seems to be the wrinkling load of an inflated beam. One can define M₀, the maximum elastic moment (equivalent to the moment of an inflatable beam in which wrinkling has occurred). When the load is increased, a plastic zone grows until a plastic hinge appears and the section of the beam is entirely plastified. In the case of inflatable beams, we have the same situation: the stress falls in the fabric until the limit load is reached. The difference arises from the fact that for inflatable structures, the behaviour leads to "reversible" collapse.

The limit loads of inflatable beams are therefore given by the same formulae to those of plastic beams provided that the total or plastic bending momentum M₁ is well defined for inflatable beams. This limit momentm has been defined for inflatable panels in [1]. In the case of inflatable tubes, Comer & Levy [3] have suggested that this bending momentum is obtained when the stress is nil in the entire tube, except at a point of the envelope of the tube. Our experiments have shown that in fact, collapse appears when only half of the tube section is submitted to zero normal stress.

Experiments have been done on inflated panels and tubes for three kinds of boundary conditions (simply supported at the two ends, simply supported at one end and clamped at the other end, and finally clamped at the two end) and for various values of internal pressure. There is a good agreement between theoretical and experimental results: errors are less than 15%. In the case of the tubes, and by using Comer and Levy's definition of the bending moment, the difference between analytical and experimental results grows up to 45%. A cone has also been tested and comparisons between theoretical and experimental are in good agreement.

The analogy between limit plastic analysis of beams and the theoretical results obtained for limit loads of inflatable beams compared to experimental results prove that one can use the usual "plastic" theory to compute limit loads for inflatable beams. The two theorems of limit analysis lead to optimisation problems and may be used to compute limit loads of complex inflated structures.

1

C. Wielgosz and J.-C. Thomas, "Deflections of inflatable fabric panels at high pressure", Thin Walled Structures, 40, 523-536, 2002. doi:10.1016/S0263-8231(02)00010-1

2

J.-C. Thomas and C. Wielgosz, "Deflections of highly inflated fabric tubes", Thin Walled Structures, 42, 1049-1066, 2004. doi:10.1016/j.tws.2004.03.007

3

R.L. Comer and S. Levy, "Deflections of an inflated circular cylindrical cantilever beam", A.I.A.A. Journal, 1(7), 1652-1655, 1963. doi:10.2514/3.1873

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