3.1 DDA analysis

Most of studies dealing with the bearing capacity of masonry structures are based on stresses computed by continuum mechanics. This scheme may be taken granted for a bonded masonry, since it implies that generation of a crack in a block or at an interface limits the bearing capacity. On the other hand, dry-masonry has its initial cracked state, so that the application of this scheme is questionable.

We have been studying the applicability of the Discontinuous Deformation Analysis (DDA) (Shi 1993) to dry-masonry structures. DDA is formulated as incremental dynamic equilibrium for blocks based on the theory of the least total potential energy with iteration scheme for preventing intrusion and tensile stress at interfaces of blocks. DDA can guarantee existence and uniqueness of the solution and can be practical on usual PC platforms.

We are interested in the response of masonry structures to wind load exerted horizontally on the structures. Equilibrium under the gravitational load was first achieved, and then horizontal load was applied gradually to let sliding occur between blocks. Figure 8

Figure 8. Response of series of blocks to horizontal loads simulated by DDA.

Figure 8. Response of series of blocks to horizontal loads simulated by DDA.

shows the responses of a series of square blocks lined in vertical, which is subjected to horizontal load either at upper portion (upper panel) or at all of the blocks (lower panel). The different collapse modes can be simulated by DDA, i.e. sliding at the interface right below the loaded portion for partial loading and uplift of whole blocks for whole loading.

3.2 Response of the northern library to horizontal load by DDA

The north-south section of the northern library including columns and walls is simplified by plane strain model with consideration on symmetry shown in Figures 9-10. Friction angle is set to 30 degrees, mass density 2.52 g/cm3, Poisson's ratio 0.11; no cohesion and no dynamic friction are considered. Uniformly distributed horizontal load along the wall height is replaced by nodal forces exerted gradually at the rate of 7,937 N/m2/s after the settlement under gravitational load. Figure 11 shows development of deformation and variation of principal stress with increase of horizontal load. The principal axes for the initial gravitational load in vertical (a) are firstly inclined by combination of axial force and shear force due to friction at interfaces (b), and back to vertical again due to the occurrence of slide (c). The first sliding occurs at 20,117 N/m2 of uniform load, which can be viewed as a bearing capacity of the model.

3.3 Bearing capacity of the library to the wind load The wind load density can be evaluated by (1).

where D: horizontal force [N], S: area [m2], C: resistance factor, p: density [kg/m3], V: wind velocity [m/s]. For wind velocity of 40m/s, (1) gives about 10,000 N/m2, which is less than a half of the evaluated bearing capacity of the first slide at 20,117 N/m2. Then the safety margin for the wind load corresponding to wind velocity of 40 m/s is more than twice.

(d> Gravitational load and horizontal load of 20,720 N/m2 where the remarkable sliding at the wall base is. observed.

Figure 11. Deformation and principal stress in the northern library DDA model for horizontal load.

(d> Gravitational load and horizontal load of 20,720 N/m2 where the remarkable sliding at the wall base is. observed.

Figure 11. Deformation and principal stress in the northern library DDA model for horizontal load.

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