Abstract
A limit analysis method for masonry domes composed of interlocking blocks with non-isotropic sliding resistance is under development. This paper reports the first two steps of that work. It first introduces a revision to an existing limit analysis approach using the membrane theory to find the minimum thickness of a hemispherical dome under its own weight and composed of conventional blocks with finite isotropic friction. The coordinates of an initial axisymmetric membrane surface are the optimization variables. During the optimization, the membrane satisfies the equilibrium conditions and meets the sliding constraints where intersects the block interfaces. The results of the revised procedure are compared to those obtained by other approaches finding the thinnest dome. A heuristic method using convex contact model is then introduced to find the sliding resistance of the corrugated interlocking interfaces. Sliding of such interfaces is constrained by the Coulomb’s friction law and by the shear resistance of the locks keeping the blocks together along two orthogonal directions. The role of these two different sliding resistances is discussed and the heuristic method is applied to the revised limit analysis method.
Highlights
This paper reports a part of an ongoing research on the development of limit analysis for hemispherical domes composed of interlocking blocks
A limit analysis method for masonry domes composed of interlocking blocks with non-isotropic sliding resistance is under development
A similar approach was previously applied to find the internal forces at the 2D conventional [9] and interlocking interfaces [2] of a semi-circular arch. For such a convex model specialized for the hemispherical dome, the constraints on all the six internal forces preventing the mentioned structural failures are as follows: to avoid the block separation, fn must be in compression; two tangential forces are considered along the locks ft1, and normal to the locks ft2; ft1 must satisfy the Coulomb’s friction law, otherwise the block slides along the locks; ft2 and torsion moment tr must be less than the lock shear, bending and torsional resistance, as explained later; lastly, since the flow of forces, within the dome thickness, passes through the contact points of the convex model, bn1 and bn2 are zero and ignored (Fig. 16c)
Summary
This paper reports a part of an ongoing research on the development of limit analysis for hemispherical domes composed of interlocking blocks. A limit analysis method for masonry domes composed of interlocking blocks with non-isotropic sliding resistance is under development.
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