This paper deploys an existing method for the simple rigid-plastic hand calculation of slab yield-line mechanisms to address the wider problem of disproportionate collapse at lost columns in multi-storey buildings. Floor systems will be treated as grillages combining torsion-free (Hillerborg) slabs and torsion-free beams. The aim is to achieve an understanding that transcends reliance on non-linear finite element software but does not compete with it. This paper deals with lost corner columns, which are the columns most at risk; the approach can be extended to other columns.