By Tits J.
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If one wanted to exclude tension structures, one might stipulate that shells have to work in both tension and compression, but how about masonry vaults that can only work in compression? Most people would describe masonry vaults as a type of shell structure. 1 A glasses case is a shell However, the word ‘shell’ has the implication of something relatively rigid, and this book is about such structures. We therefore need to have a separate category of tension structures to include sails and balloons as well as piano strings and fishing nets.
5 which is known as the biharmonic equation. Even though it looks complicated, it actually behaves very well and is not difficult to solve (Timoshenko & Goodier, 1970). Plate bending in the x and y directions respectively. The variables qx and qy are the loads per unit area applied to the plate, in its own plane, for example the self-weight of a wall. Thus we have three unknown stresses and only two equations of equilibrium so that plane stress is statically indeterminate. 1). Note that even if qx and qy are zero, the plate can still be loaded at its edges.
In-plane membrane stress is a central concept in shell theory and corresponds to the axial stress in an arch – as opposed to the bending stress. Membrane stress is usually quoted as a force per unit length crossing an imaginary cut, rather than force per unit area. Equilibrium of moments about the normal tells us that oxy = oyx. 4 Plane stress The shear stresses oxy and oyx are in the plane of the plate. We also get shear stress perpendicular to the plate due to plate bending. 5 because the notation for plate bending is rather confusing.