Influence of Nonlinear Constitutive Law on Masonry Pier Stability

The stability condition of cantilevered masonry piers subjected to their own weight and to a concentrated compressive top load is investigated, considering no-tension material with nonlinear stress-strain law in compression, of an experimental nature, and including softening behavior. The analysis is carried out by improving a numerical approach adopted in previous works where stability problems were solved assuming an infinitely elastic linear constitutive law in compression. Before the geometrical nonlinearity is considered, the limit equilibrium of a typical pier rectangular cross section is detected assuming unlimited available compressive strain. This preliminary analysis allows one to determine analytically the limit value that has to be imposed on the eccentricity of the resultant compressive force and to derive the moment-curvature relationships on which the second-order effects depend. Then the stability domains are derived in dimensionless form and their boundaries are modeled by analytical approximate expressions of practical use. Some numerical examples show that, depending on the average normal stress level, the assumption of an approximate linear constitutive law in compression, affected by the same elasticity modulus as that at the origin of the actual stress-strain law, can provide an unacceptable overestimate of the critical load.