Modified Janssen Theory for Flexible Circular Bins

The classic Janssen theory takes no consideration of the interaction between the stored material pressure and the wall deformation, and thus may give poor prediction of pressures in flexible bins. Based on the following two assumptions: (1) The vertical pressure in the stored material is uniformly distributed at the same depth; and (2) the stresses in bin walls can be modelled by the membrane theory, a modified Janssen theory has been developed, which can not only take account of the wall flexibility, but also preserve the simplicity of the original theory. It is shown that the wall flexibility can be represented by a nondimensional parameter α=E _s R/E _w t. In addition, the lateral pressure ratio, κ, may be computed based on Poisson's ratio of stored material, ν_s. It is also illustrated that the modified Janssen formula could give a very close estimation with the finite-element method for different levels of α. Therefore, the present theory may at least provide a reference for the more rational determination of some critical parameters which affect the wall pressure in future designs of flexible wall bins.