Issue 51

E. Mousavian et alii, Frattura ed Integrità Strutturale, 51 (2020) 336-355; DOI: 10.3221/IGF-ESIS.51.25 347 which can be rewritten as: 1 1 1 θ θ θ θ 1 1 1 θ θ θ θ x 2sin 2sin 2 2 b b i i i i i i b b i i i i i i z z z z x x x x x x x                            (23) Eqn. (23) for two control points A and #1 is 1 1 θ θ θ 1 1 θ  θ 2sin 2 b b b A A x x x x x x           , since both x A   and x A b are zero. Substituting x 1 b with [  /(2 sin (  /2))] x 1  in Eqn. (23) for control points 1 and 2 and then continuing it for every control points i and i +1, the following equation is obtained: θ θ  θ 2sin 2 b i i x x        (24) Figure 10 : Graphic presentation of the relation between H j  and H j b . C ONVEX CONTACT MODEL FOR INTERLOCKING INTERFACES n this section, an algorithm referred to a single interface with given orientation and number of locks is developed to demonstrate the sliding behaviour of the interlocking interfaces within a hemispherical dome. A numerical strategy is also proposed to idealize the stress state on this interface as a set of internal forces at one point on the interface, according to the convex contact formulation. Modelling of an interlocking interface in a hemispherical dome The hemispherical dome is composed of horizontal rows of blocks, which produce curved interfaces between blocks stacked over each other. The curved interface is a section of a cone, whose vertex is the hemisphere centre and whose base is a horizontal circle, as depicted in Fig. 11. If these interfaces, here called hoop interfaces, are designed to be interlocking, they can represent the curved surfaces where the locks are attached to the main bodies of the interlocked blocks. If the lock height is zero, each curved surface represents a row. As a simple approximation, the hoop interface of each block is assumed to be flat and to be abstracted to a trapezoid shape, as depicted in Fig. 12a. Modelling an interface as a trapezoid enables us to develop numerical formulations to calculate the value of width g and length b of the locks affecting the sliding resistance (Fig. 12b). Finding the value of the geometric parameters through the numeric formulations reduces the computation time considerably. The formulas are presented later in this section. Given the number m and orientation  of locks, these can be modelled on a trapezoid face (Fig. 13), following the proposed steps: first, line L is considered as the projection of the diameter d or the longer base of the trapezoid p , I