Stability of Masonry Piers under Their Own Weight and Eccentric Load

The stability of masonry piers subjected to their own weight and to eccentric compressive force at the top is analyzed. Prismatic fixed free-ended columns are examined, considering no tension material having linear behavior in compression. The column is ideally divided into a number of elements that is unknown a priori, all of the same length. Along each of them, the curvature corresponding to the equilibrium condition is assumed to be constant. For each assigned value of rotation of the free end this hypothesis makes it possible to express in recursion form the rotation of the cross sections characterizing the model, which obviously decreases with an increase in the number of elements considered starting from the upper cross section. The unknown length of the column corresponding to an assigned load condition is deduced from the number of elements needed to obtain a zero value of rotation, because the latter condition characterizes the section at the base. Applying the procedure with variation in the value of rotation of the free end, stability domains are deduced for different ratios between weight and concentrated load. The results, obtained in dimensionless form, show the optimum value of this ratio for a given eccentricity value.