Arch Appl Mech (2015) 85:1915–1940 DOI 10.1007/s00419-015-1027-2 ORIGINAL Nicos Makris · Haris Alexakis Limit equilibrium analysis of masonry buttresses and towers under lateral and gravity loads Received: 7 April 2015 / Accepted: 30 May 2015 / Published online: 12 June 2015 © Springer-Verlag Berlin Heidelberg 2015 Abstract This paper revisits the fracturing of masonry buttresses and towers when subjected either to a concentrated oblique force at their head or to lateral inertial loading due to ground shaking and presents the corresponding failure criteria in elongation and shear. The loading configurations examined result either from the thrust that an elevated arch exerts on its supporting buttresses or from earthquake shaking on soli- tary masonry towers. At their limit state, tall, slender masonry buttresses and towers collapse by pivoting about their base corner, whereas less slender masonry structures may collapse by developing a shear fail- ure. Because of the unilateral behavior of masonry, at the initiation of collapse of a slender buttress, the compression-free region separates from the rest of the buttress and reduces the stabilizing moment. As the ratio, base/height or the gravity load, increases, masonry buttresses and towers may fail in shear; therefore, the paper presents envelopes of their limit lateral capacity depending on the aspect ratio, the mechanical properties of masonry and the level of vertical loading. The equivalent static analysis adopted in this paper concludes that in most cases under lateral inertial loading, elongation failure is the lower failure mechanism of a tall masonry tower; nevertheless, a subsequent initiation of rocking that engages the large rotational iner- tia of the detached portion of the tower attracts additional inertia forces that may induce a follower shear failure. Keywords Stone towers · Seismic analysis · Limit state · Hinging mechanism · Shear failure · Historic structures 1 Introduction Masonry arches exert inclined thrust forces at their springings. In the event that the arch is an elevated structure supported upon buttresses, the inclined thrust force at the springing of the arch is loading the buttresses as shown in Fig. 1. Clearly, the failure of a buttress leads to a catastrophic collapse; therefore, its appropriate sizing has been a concern throughout the history of masonry structures ([1–8] among others). Figure 2 shows N. Makris (B ) Division of Structures, Department of Civil, Environmental and Construction Engineering, University of Central Florida, Orlando, FL 32816, USA E-mail: Nicos.Makris@ucf.edu N. Makris Office of Theoretical and Applied Mechanics, Academy of Athens, 10679 Athens, Greece H. Alexakis Division of Structures, Department of Civil Engineering, University of Patras, 26500 Patras, Greece E-mail: alexakis@upatras.gr