G/E ratio of in-plane loaded masonry

In the design of unreinforced masonry structures, accurately determining the stiffness of walls is crucial, which depends on the masonry’s elastic (E) and shear (G) moduli. Present building codes offer empirical methods to estimate the elastic modulus of masonry and suggest a G/E ratio, typically assumed to be 0.4. However, this ratio lacks solid scientific backing, leading to potential inaccuracies in representing masonry’s shear deformation in current standards. We developed precise formulas for the G/E ratio in running-bond masonry, considering factors like the thickness of joints and walls, and the orthotropic nature of blocks. These formulas, grounded in the geometry and elastic properties of blocks and joints, have been validated through comprehensive 3D finite element analysis, demonstrating reliable results. The study finds that for contemporary masonry using hollow clay bricks, the G/E ratio ranges from 0.20 to 0.25. In contrast, for historical masonry types like dry stacked or mortared stone, as well as solid clay brick masonry, the ratios are calculated to be between 0.30 and 0.40.

Recommendations for the G/E ratio according to Part 1 of Eurocode 6, the Swiss standard SIA 266, FEMA 356, the American masonry code TMS 402, the New Zealand guidelines NZSEE, the Italian technical standard NTC 08, Wilding and Beyer (WB18), and Tomasevic (T09). Image taken from Wilding et al. (2020).
Proposed values for the G/E ratio for different masonry typologies by Wilding et al. (2020).