Issue 50

A. Kakaliagos et alii, Frattura ed Integrità Strutturale, 50 (2019) 481-496; DOI: 10.3221/IGF-ESIS.50.40 486 Historical records report that Orban’s gun could fire only three up to a maximum of seven shots per day (Chalkokondyles [2], Iskanter [5]). This situation reflects the effort of the gun crew to identify the appropriate gun elevation. Finally, at 4.62 0 gun elevation the projectile hit the target after 2.47 sec with an impact velocity at 191 m/sec (Fig.1). For the successful shot the maximum range was at 680m and the corresponding impact velocity on ground 183m/sec. At target impact, the projectile delivered a total kinetic energy at 11,163 KNm, value which is comparable to modern artillery shell ammunition. Figure 1: Bombardment of Constantinople inner walls. Lateral resistance and force capacity of inner wall masonry The projectile upon reaching the target can either open a breach in the wall and/or impose a global wall overturning mechanism. Considering the large size of the wall it was assumed that the delivered projectile kinetic energy would actually impose a punching shear mechanism on the Wall solid (Fig.2a). It was realized that the Inner Wall would have a block masonry outer skin at both exterior wall faces and an inner masonry core. This inner core would consist of natural stone masonry with compacted soil fill. The quality and strength of the outer skin would define the overall wall load capacity and strength. In general, Inner Wall material properties were addressed deploying Eurocode 6 (Design of Masonry Structures) considering a wall structure at Category 1. Using an average compressive strength for the masonry f b =20 MPa and mortar compressive strength f m =1.0 MPa, the characteristic masonry compressive strength f wk equals 3.5 MPa. The overall wall density was set at 20 KN/m 3 approximately. The characteristic masonry shear strength was estimated at f s =0.12 MPa with Eq.(4), whereby, σ d =0.12 MPa was considered as the mean axial wall compressive stress acting over the total wall thickness. This axial wall stress reflected the dead load effect of the wall solid above cannonball impact area. ௦ ൌ 0.075 ൅ 0.4 ௗ (4) The constant factor in Eq.(4) is taken as the average of the code provisions for masonry shear strength evaluation con- sidering vertical joints with and without mortar. This provision reflects reports, where the strength of the Wall fortifications was deteriorating and urgent wall repair and strengthening was required – Phrantzes [6]. Assuming an impact stress distribution under 45 0 into the wall solid, the punching shear capacity V m of the Inner Wall is computed with Eq.(5) (Fig.2b). Setting t w =5 m, d=0.752 m and f s =0.12 MPa the corresponding punching shear capacity yields V m =10,837 KN. ௠ ൌ ሺ ௪ ൅ ሻ ௪ ௦ (5) The wall structure would resist the implied force of projectile impact by providing adequate punching shear resistance. In case of overstress, the punching shear cylinder may slide by a certain displacement s towards the wall’s outer surface (Fig. 2a). This procedure reflects wall stiffness deterioration due to cannonball impact. During this action, energy would be absorbed due to mobilization of shear sliding mechanisms in the wall between the stone blocks at the contact interface area of punching shear cylinder area to surrounding wall solid. After sliding, the punching shear cylinder may establish a new equilibrium, whereby a reduced punching shear cylinder area shall resist the implied impact force. The reduced punching shear resistance V red was computed with Eq.(6). Considering energy equilibrium during cannonball impact on the wall together with cannonball mass m and associated impact velocity v yields the required setback s (Eq.(7)):