l Structural analysis of the equestrian monument to Marcus Aurelius in Rome G. Accardo, A. Bennici and M. Torre Centra! Institute for Restoration, Rome, Italy D. Amodio, P. Cappa and G. Santucci Department of Mechanics and Aeronautics, 'La Sapienza' University, Rome, Italy The Marcus Aurelius equestrian monument has been analyzed by the finite element method. The stress an d strain fields, relevant to the rider load an d thermal effects ha ve been calculated. The finite element mode! has been used to evaluate the best constraint conditions between tbe monument and its pedestal and to design an internai stiffening frame. Tbe numerica! results have been validated by experimentally evaluating strains and displacements in tbe horse occurring due to loading by the rider. INTRODUCTION Acting on behalf of the 'Comune di Roma', the Centrai Institute for Restoration of the 'Ministero per i Beni Culturali ed Ambientali' is taking care of the restoration work of the equestrian monument to Marcus Aurelius. The bronze was hand-manufactured in the second century BC and placed, during the sixteenth century, on the Capitoline Hill in Rome 1 • 2 • The monument, standing on a sto ne base, is constructed of two different parts: the borse, with a raised front right leg, anci the effigy ofthe emperor, rested on the edge of a large hole localized in the upper part of the animai. The restoration work necessitated the disassembly of the statue into the two constituent pieces, the disconnection of the horse from its ancient pedestal and the transfer ofthe group to the Physics Laboratory of the Institute. The horse is now resting on a steel frame which was previously used to protect it during transportation (Fig. l). Before doing any work on the monument, the Centrai Institute for Restoration performed a long series of historical and experimental investigations. Amongst these, we will mention here those aiming to obtain a deeper knowledge about the techniques used for casting and assembling the statue 3 ; we should also mention tbe investigations on the chemical composition and on the chemical-physical properties of the alloys used 4 • Photogrammetry and non-destructive (ultrasonic) tech- niques have also been used to obtain information on the monument's geometry (shape, dimensions and thickness distribution) 5 • 6 and on the structural integrity (presence of holes, inclusions, weldings an d cracks f. At the same time the nature and extent of previous restoration work has been carefully evaluated 8 . Finally, the temperature field in the monument has been carefully analyzed throughout the day and in different seasons 9 • 10 . During such preliminary investigations, the Pbysics and Environmental Contro! Laboratory of the Centrai Paper accepted November 1989. Discussion closes October 1990. © Computational Mechanics Publications 1990 Institutc for Rcstoration, and tbc Dcpartmcnt of Mechanics and Aeronautics of Rome, University 'La Sapienza', have carried out a study on tbe structural stability of t be monument 11 · 12 . The verification of t be stress distribution in the horse, due to thc ridcr's weigbt, has been the main aim ofthis study. The tbermal stresses due to the non uniform environment temperature distribution have tben been evaluated. Looking toward the future, and thc replacing of the monument onto its base, the best restraining conditions bave been studied in order to reduce the stress leve! in the borse. At the same time, investigations have been carried out on the possibility of creating an internai stiffcning frame to partially release the weigbt of tbe rider on tbe horse. The study has been carried out using finite element models validated by measuring horse displacements during loading and unloading. FINITE ELEMENT MODEL Three hundred and sixty-five shell elements and 406 nodes bave been used to mode! the horse's body: the tail and tbe head were not introduced in tbe mode!. The lower part of the threc load-bearing legs ha ve bcen modelled by bcams of circular section. A seri es of radially placed high stiffness beams link each lower part ofthe legs to the shell elements belonging to the upper part of the legs. Square section beams have also been used to mode! the stiffening cross introduced in previous centuries to consolidate the edges of the ho les o n which the rider is resting. T be thickness of each shell element has been obtained by ultrasonic investigations. The materia! forming the elements has been assumed to be isotropic and homogeneous. Mechanical tests were carried out on specimens whose chemical properties were very cio se to the rea! ones. Those tests suggested that one should assume the value of 85 G P a as the Young modulus, 0.3 as Poisson coefficient, 0.000018oC - 1 as thermal expansion coefficient an d 80 kN/m 3 as weight density. 58 Software for Engineering Workstations, 1990, Volume 6, Aprii