New Deformation-Based Rule Lets Masonry Buildings Share Seismic Loads Safely

For decades, engineers designing masonry buildings in earthquake-prone regions have faced an awkward contradiction. The linear elastic analyses they rely on in daily practice paint a picture of structural behaviour that everyone knows is wrong: real masonry walls crack, yield and shuffle their loads among neighbours long before a building reaches its ultimate capacity. Codes have long permitted a partial fix, allowing designers to redistribute seismic forces among walls after a linear analysis, but the limits on how much redistribution is safe have rested on heuristic rules inherited from reinforced concrete practice rather than on any systematic study of masonry behaviour. A new study by Nicolò Damiani and Guido Magenes of the University of Pavia, together with Carlo Filippo Manzini of the EUCENTRE Foundation, published in the Bulletin of Earthquake Engineering, now supplies what has been missing: a physically grounded, deformation-based criterion that defines exactly how much force can be shifted from one wall to another without pushing the building past its true limits.

The problem begins with the behaviour factor, the famous q-factor of Eurocode 8, which scales down the elastic seismic demand to account for a structure’s capacity to deform inelastically and dissipate energy. In the newest generation of the code, q is decomposed into three contributions: one for generalized ductility, one for overstrength arising from the redistribution of forces in redundant structures, and one for other sources of reserve strength. It is the second term, often called the system overstrength ratio or OSR, that has proved so troublesome for masonry. When a masonry building is pushed laterally, the first wall to reach its strength does not usually signal the end of the road. If that wall retains deformation capacity, the surplus load flows to its stiffer or stronger companions, and the building keeps picking up lateral resistance until several walls have exhausted both their strength and their displacement capacity. The ratio between this ultimate base shear and the shear at first yield can range widely, from a theoretical minimum of 1.0 in structures with no redundancy to values between roughly 1.4 and 2.5 for most unreinforced masonry configurations, and occasionally beyond 3.0.

That variability is the crux of the difficulty. The overstrength ratio depends on the wall layout, the pattern of openings, the number of storeys, the presence of reinforced concrete ring beams or masonry spandrels, the stiffness of the floor diaphragms, and the connection details, all of which vary enormously with regional building traditions. It also depends on modelling choices: whether walls are discretised as continuum finite elements, equivalent frames or macro-elements, what constitutive laws are adopted, and how coupling between intersecting walls is treated. Previous studies have shown that calculated overstrength ratios do not even depend strongly on the assumed deformation capacity of individual walls, which makes the task of tabulating representative values for design codes nearly hopeless. A single conservative default value, derived from statistics across many configurations, could impose seismic demands far higher than any specific building actually needs, forcing designs to fail strength checks that nonlinear analysis would comfortably pass.

The Pavia team’s answer is elegant in its simplicity: set the overstrength contribution to unity, and instead of encoding redundancy in a code-specified factor, let the designer exploit it explicitly through force redistribution, bounded by the physics of wall deformation. The logic rests on a simple observation about walls acting in parallel within a storey. All walls connected to a rigid floor diaphragm share the same top displacement, so the system’s ultimate state is reached when the wall with the lowest displacement capacity gives out, regardless of how much reserve the others still hold. Wall displacement is expressed through the chord rotation at the wall base, multiplied by the wall’s effective height and a kinematic conversion factor close to unity for typical single-storey boundary conditions. The ultimate displacement of each wall follows from its ultimate chord rotation capacity, which is governed by its failure mechanism, whether shear, flexural or a hybrid of the two.

This kinematic picture immediately reveals why redistribution cannot be unlimited. Consider a storey containing a very short, stiff squat wall alongside taller, more flexible companions, a scenario common in practice wherever foundations step or openings vary in height. The squat wall attracts a disproportionate share of the elastic shear and is also the first to hit its displacement limit. Once it reaches its ultimate chord rotation, the whole system has exhausted its capacity, and the taller walls may never have developed their full strength. The maximum shear that can be transferred to any of those taller walls is therefore capped by a simple similarity-of-triangles argument: the increment is proportional to the difference between the limiting system displacement, set by the weakest wall’s ultimate capacity, and the displacement computed in the linear elastic analysis. A deliberately conservative simplification assumes the governing wall is the shortest one in the storey, failing in pure shear in double bending at the minimum possible ultimate chord rotation, a value for which reference figures are provided by the new Eurocode 8 Part 1-2.

Extending the criterion to buildings that twist under seismic loading required a careful treatment of torsion. When the centres of mass, stiffness and strength do not coincide, different walls experience different displacement demands, and the neat assumption of equal top displacements breaks down. The researchers distinguish torsionally restrained systems, which possess at least one adequately stiff, strong and well-spaced wall couple in the perpendicular direction capable of developing restraining torque, from torsionally unrestrained systems, where in-plan rotation runs free. For restrained systems, they propose dividing the floor plan into two zones around the critical wall. In the soft-edge zone, ultimate displacements are conservatively taken equal to the critical wall’s capacity; in the stiff-edge zone, they are assumed proportional to the elastic displacement field, which is safe because nonlinear analyses consistently show that in-plan twist diminishes as walls yield. For unrestrained systems, no general rule is offered, and the authors argue such layouts should simply be avoided in new construction.

The validation campaign is one of the most thorough aspects of the work. Two single-storey case-study buildings were deliberately configured at the borderline of plan regularity and torsional restraint, with wall heights ranging from 1.00 to 3.40 metres to generate marked eccentricities. Walls were modelled in the Ruaumoko3D program as nonlinear beam-column elements with lumped plasticity, assigned flag-shaped hysteretic rules for flexural response and modified Takeda or Schoettler-Restrepo rules for shear response, calibrated against full-scale cyclic tests of clay-unit masonry walls conducted at the EUCENTRE and University of Pavia laboratories. Incremental dynamic analyses were then run under seven bi-directional ground-motion pairs selected for two Eurocode soil classes, applied with all four sign combinations, across three period variants and three hysteretic assumptions, yielding 1,008 simulations in total. The results were strikingly consistent: once nonlinear behaviour was mobilised, the in-plan twist dropped markedly relative to the elastic case, the shortest wall always governed the attainment of ultimate conditions, and soft-edge displacements never exceeded 0.70 centimetres against the 1.02-centimetre limit, confirming a substantial margin of conservatism in the proposed redistribution bounds.

The practical payoff is demonstrated through worked examples, including a three-storey terraced house whose weak direction exhibits an overstrength ratio of 3.2. Analysed linearly with the overstrength factor set to unity and the new deformation-based redistribution applied storey by storey, with wall capacities recomputed at each step as force eccentricities changed, all walls and ring beams passed their checks up to a design base shear of 1,200 kilonewtons, roughly 2.3 times the demand at which verification would have failed without redistribution, and far beyond the maximum overstrength factor of 1.4 the new code would otherwise admit. By contrast, the older heuristic limits tied to a code-specified overstrength factor proved so restrictive in one example that a building verifiable by other means could not be checked at all, a consequence of fixed percentage thresholds being disconnected from the actual redistribution capacity of the system. The authors also discuss a cautious extension to low-rise multi-storey buildings, adding an upper bound on redistributable shear increments and capping the ultimate chord rotation at the severe-damage rather than near-collapse state to cover the additional uncertainties of multi-storey response.

The criterion now underpins the provisions of the forthcoming Eurocode 8 Part 1-2 for new masonry buildings, giving practitioners a rational alternative to both conservative default factors and full nonlinear analysis. The authors are careful to note that nonlinear static procedures, where applicable, remain more convenient, since no automated software yet exists for post-linear redistribution, and that further dynamic validation of multi-storey applications is a future task. But the significance of the work lies in closing a forty-year-old gap: since the late 1970s, when the inadequacy of linear methods for masonry was first recognised in Europe, the profession has redistributed forces on the basis of analogy and judgement. It can now do so on the basis of displacement compatibility and measured deformation capacity, bridging the persistent gap between the elastic models of everyday design and the stubbornly nonlinear reality of masonry under earthquake attack.

Subject of Research: A deformation-based criterion for limiting seismic force redistribution in masonry buildings after linear elastic analysis

Article Title: A deformation-based criterion for redistribution of seismic forces in masonry buildings after linear analysis

Article References: Damiani, N., Manzini, C. F., & Magenes, G. (2026). A deformation-based criterion for redistribution of seismic forces in masonry buildings after linear analysis. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02685-5

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02685-5

Keywords: masonry buildings, seismic design, force redistribution, linear analysis, Eurocode 8, overstrength ratio, chord rotation, torsional response, nonlinear dynamic analysis, unreinforced masonry, behaviour factor, earthquake engineering