Limit analysis of structures formed from rigid blocks

Abstract

In this paper a technique previously developed for the analysis of rigid-plastic structural frames is adapted to provide a formal procedure for finding the limit load of any structure formed from rigid blocks. In this procedure the load factor is maximized subject to the equilibrium equations of the structure and linear constraints imposed by criteria of failure at the block interfaces.In part I of the paper it is assumed that the limiting shear force associated with sliding at a block interface is independent of the normal component of force across the interface. This assumption means that the normality rule is satisfied, so that the upper-and lower-bound theorems of classical limit analysis apply. This part includes a description of a computer program for the collapse analysis of masonry arches with joints incapable of carrying tension.In part I1 the limit on the shear force at a block interface is assumed to be that associated with Coulomb friction. It is not difficult to extend the computational algorithm described in part I to deal with this situation. However, the failure mechanism computed by the algorithm will not necessarily satisfy the normality rule. The corresponding limit load may therefore be an over-estimate of the true failure load, even though it is computed by a lower-bound (equilibrium) approach. A criterion is established for testing the validity of a failure load computed in these circumstances. 1853 w + p = Hr , provided that the quantities w, p, H and r are appropriately re-defined. The dead-weight and live-load limit analysis problems now have exactly the same algebraic form as before.t The three linearly independent variables q, s and f still detine the state of stress at an interface. The variables 14 and I J iire introduccd simply for computational convenience.

Mesoscale partitioned analysis of brick-masonry arches

“…Thus, over the past few decades a growing interest has developed in studying their behaviour up to collapse and assessing their ultimate load capacity. Significant laboratory and in-situ tests were carried out [3][4][5][6][7][8][9] and different analytical and numerical descriptions were proposed [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Current modelling strategies for arches in masonry bridges are mainly based upon the use of limit analysis concepts [20][21][22], the finite element method (FEM) [13,24,25,26,27], the discrete element method [23] or discontinuous modelling techniques [19].…”

Experimental Validation of in-Plane Frictional Resistances in Dry Block Masonry Walls

“…In particular, the macro-block modelling approach has demonstrated to be useful for masonry buildings without a box-type behaviour, where frictional resistances might play a predominant role at the onset of in-plane and out-of-plane failure mechanisms [2][3][4][5][6][7][8][9][10][11][12][13][14]. According to it, each block represents a portion of masonry which remains undamaged and is separated from others by a number of localized cracking where the frictional resistances can take place.…”

An Automatic Method for Geometric Segmentation of Masonry Arch Bridges for Structural Engineering Purposes

“…The effect of different loading (static, dynamic, cyclic) together with accumulative effects, provokes gradual changes of geometry along time. It is well known that the geometry of this typology of bridge is a key factor in terms of they load carrying capacity (Heyman, 1969;Livesley, 1978;Gilvert, 2007). The change of use, incorrect conservation policies and the increase of the loadings along their life has probably provoked changes in geometry, and so, changes in the shape of the arches may be comprising the stability and load capacity.…”