Structural Analysis of the St. George of Greeks Cathedral
Ata
Atun
Structural analysis of the main apse vault of
St. George of Greeks Cathedral built c.1390 at Famagusta, Cyprus
Ata Atun
Faculty of
Engineering,
Abstract
Foundation date of the Cathedral Church of St. George of the Greeks[1] can
be dated with a high degree of probability to the end of the XIV century. This
magnificent building was built on the edge of the Greek quarter, which occupied
almost the whole of the southern end of the city of
The history says that this building was abandoned after 1571, as it had
suffered severely from the fire of the battery established by the Turks on the
rock to the southeast of the harbour and the marks of cannonballs can be seen
on the walls of the apse.
The building was built so strong that it could stand any kind of battering
and to earthquake to a certain extend. In detail survey was done to find out the
building technique and materials used, including the quarry where the stones
were cut, the chemical composition and the strength of the stones and mortar
used in between. A very sophisticated structural analysis[2] was carried to find
out the strength of the main vault, its behavior and reactions to external
forces, especially to earthquake and cannon balls.
Location

Figure 1: Part of the Stephan Gibellino’s gravure detailing the siege of
The Ottoman cannonballs battered the church were fired from;
a)
The cannons located on
the rock to the south east of the harbour.[3]
b)
The galleys outside the port.[3]
Mainly the cannonballs fired from the cannons positioned
on the rock to the south east of the harbour
hit and damaged the Cathedral.
Figure 2: Marks and levels of cannonballs on the
walls of the apse.
(Rear façade)
Wall details of the Cathedral
Main
building outer walls
Thickness
: 123125 cm.
Outer layer
: 37 cm. thick yellow sand stone, sized 25 (w)
x
50 (l)
x 35 (h)cm.
Middle layer
: 50 cm. (smaller size yellow sand stones embedded in plaster.)
Inner layer
: 37 cm. thick yellow sand
stone.
Apse
walls
Thickness
: 72 cm.
Outer layer
: 37 cm.
Middle layer
: 10 cm. (smaller size yellow sand stones embedded in a plaster)
Inner layer
: 25 cm.
Yellow sand stone specifications
Density
: 1.86 kg/m^{3
}[4]
Compressive strength : 62.50 kg/cm^{2 }[4]
Modulus of rupture
: 14 kg/cm^{2
}[4]
Figure 3 : Main building wall details
Cannons
Total of four cannons located
on the rock to the south east of the
harbour.
Distance from the Cathedral :
1062 m.
Height from the sea level
: 2.10 m.
Type
: Siege
Bore
: 15.60 cm
Calibre
: 49 cm.
Groove
: No grooves
Length
: 200 cm.
Max distance/impact angle : 45^{0
} [5]
Weight : 3,178 kg
(7,000 lb)
Gunpowder :
Mixture of
varying amounts
of sulfur
(11.85%),
Salt Peter –
potassium nitrate (74.64%), and
charcoal (13.51%). [6]
Cannonballs
Weight
: 17100 gr. (38 lb.)
Diameter
: 15.50 cm
Perimeter
: 48.69 cm
Impact Area
: 188.69 cm^{2}
Muzzle velocity :
100  300 m/s [7]
Ball
trajectory, velocity and angles
y = ax^{2}
+ bx + c
condition 1
: for y=0, x=0 and c=0
condition 2
: for y=(26.462.10) m., x=1062 m.
condition 3
: dy/dx=1 at y=0 and x=0
trajectory
formula : y=0.000764x^{2} + 0.834x
or : y = 
0.00092x^{2} + x ………….(1)
from the
equation y = 
[8] …….(2)
muzzle
velocity = 103.2 m/s
firing angle
: 45^{0} maximum
impact angle
: 43.51^{0}
peak point,
xcordinate : b/2a = (1/2x0.00092) = 543.48m.
peak point,
ycordinate : for x=543.48 y= 271.74
m.
range :
1086.95 m.
Impact
energy of cannonball
E_{impact }= E_{horizontal} + E_{vertical}
E_{horizontal }=_{ }½ m V_{ox}^{2 }
where
V_{o} = 103.2 m/s (cannonball’s initial [muzzle] velocity),
V_{ox}
= Horizontal component = cos 45
x
V_{o}
= 72.98 m/s
m=mass (kg) = w/g = 17.1/9.81 = 1.743
kg
E_{horizontal}= ½
x
1.743
x 72.98^{2 }= 4641.68
joule
E_{vertical
}= m
x g
x
h where m=mass (kg), g=gravity
(m/s^{2}), h=max. height (m.)
= 1.743
x 9.81
x
271.74 = 4646.44 joule
E_{impact }= 4641.68 + 4646.44 = 9288.12 joule (Newtonmeter) =
946.80 kgfm
Impact force of the cannonball
E_{impact }= ½
x F
x
e
x L
[9]
Where F = force generated by
the impact energy (kgf)
e
= strain
(0.001 for sand stone)
L= thickness of the wall. (m.)
946.80 = ½
x
F
x
0.001
x
1.23
F = 1,539,512.19 kgf (Impact force)
Effect of a cannonball to a single sand stone
A = Impact Area : 188.69 cm^{2}
Compressive force exerted by cannonball :
kg/cm^{2}
Contact area of yellow sand stone
with cannon ball : 50
x 25 = 1250 cm^{2}
Resisting area of yellow sand
stone to cannon ball : 50
x
25 = 1250 cm^{2}
Resisting force of a single sand stone (1 cm thick): 1250
x 62.50 = 78,125 kg
Resisting force of a single sand stone (35 cm thick) : 78125
x 35 = 2,734,375 kg
Resisting force (2,734,375 kgf)
Impact force
(1,539,512 kgf)
This means
that a single cannon ball can only penetrate to the wall but can not knock it
down. To knock down a part of the
wall, at least three cannon balls
should hit the same exact point with same velocity and same angle of impact.
Effect of a cannonball hit to the apse vault
Impact angle : 43.51^{0}
Vertical component : Sin 43.51
= 0.6887 (downwards : ve)
Horizontal component : Cos 43.51 = 0.7250 (to
the right : +ve)
F (Impact force) = 1,539,512 kgf
F_{vertical}
= 1,539,512
x 0.6887 = 1,060,261.91 kgf
F_{horizontal} = 1,539,512 x
0.7250 =
1,116,146.20 kgf
Figure 4 shows the dimensions and numberings of the main apse vault
stones.

Figure 4 :
Main apse vault dimensions.
Assuming
direct hits to the stone no.s 27, 30 and 33, which are the most weakly covered
stones of the vault.
The
computer based static analysis results
Resisting
Moment of yellow sand stone : Rbd^{2}/6
Where R =
Compressive strength :
62.50 kg/cm^{2}
b = Breadth
of stone = 35 cm.
d = Depth of
stone = 25 cm.
M_{R}
= 62.50
x
35
x 25^{2}/6 = 227,864.58 kgfcm
=
2,278.64 kgfm
Hit on stone
no. 27
Maximum end
force occurs on stone 46
: 1,860,774 kgf
Maximum
moment on stone 46
: ve 105,182 kgfm
End moments
on stone 46
: 174,727 kgfm
Maximum
Moment
Resisting Moment
No failure
Hit on stone
no. 30
Maximum end
force occurs on stone 34
: 3,664,973 kgf
Maximum
moment on stone 34
: ve 114,522 kgfm
End moments
on stone 34
: 232,820 kgfm
Maximum
Moment
Resisting Moment
No failure
Hit on stone
no. 33
Maximum end
force occurs on stone 38
: 3,495,401 kgf
Maximum
moment on stone 38
: +ve 483,969 kgfm
End moments
on stone 38
: 389,880 kgfm
Maximum
Moment
Resisting Moment
Failure of
stone 33
Conclusion
It can be
seen from the results that;
a)
When the
cannonball hit the main side walls, it could not knock down the wall fully or
partially but damage it locally, penetrating inside the outer wall 2030 cm.
with an angle of 43.51^{0}.
b)
When the cannonball hit the main apse
vault stones, No.1 to 32 and No. 35 to 66, it could not knock down the stone
wholly or partially but damage the upper cover stones locally, penetrating
inside the cover 2020 cm. with an angle of
43.51^{0}.
c)
When the
cannonball hit the main apse vault stones, No.33 and 34 which are the keystones
of the vault (arch) , it damaged the upper cover stones locally where the
thickness was around 10 cm. and knocked down or moved the keystones, which lead
to the partial fall down of the roof. The fall down ended where the side covers
of the vault reached to the thickness in excess of 10 + 10 cms.
My findings
lead me to the fact that the battering of the Ottoman cannonballs managed
to knock down the
central part of the roof around the keystone and the repair of the roof
seemed very hard or impossible or was not of importance.
The cannonballs hitting the side walls managed to dig holes of 2035 cm
deep only but could not severely damage or knock down the walls. Due to the
scare look of the partially damaged vaulted roof, no body dared to stand under
it and the building was abandoned. [1]
The earth
quake which shook the whole island on 1556 [10], knock down the partially
damaged and hardly standing roof
completely. The earth quakes which
took place on 1735 [11] [12] and 1741 [13] [14]
knocked down the 80% of the already shaken walls, where most of the
stones (I believe) were loose.
During the
construction years of the Suez Canal which begun on 1859 [15] and city of Port
Said (named after Said Pasha), the stones of the medieval buildings knocked down
by the earthquakes allover in the island of Cyprus were dispatched to the area
for construction purposes. This
destruction of the antiquity lasted till 1905, completion of the
Reference
[1] Enlart C.,Gothic
art and the renaissance in
[2] Ata
Atun, Deprem ve
Rüzgar etkisindeki yapıların bilgisayar ile statik analizi esasları, KTMMOB,
Nicosia, pp 1.
[3]
Gibellino, S., Citta di
Famagosta (Map),
[4]
Çağnan, Ç., Yapı üretiminde doğal malzemenin yeri ve buna dayalı olarak
KKTC örneğinde üretilmesi ve kullanımı için model, Nicosia, pp.1, 2003
[5]
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[6]
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[7]
Information Department,
Military Museum, İstanbul
[8]
Arney D.C., Clark C., King of battle,
http://www.dean.usma.edu/math/ pubs/ mmm99/C6.HTM,
1999
[9]
Mackin, T.J., Calculating the impact force of a mass falling on an
elastic structure,
http://www.asse.org/prac_spec_calculation_wtc.pdf,
pp.13, 2002
[10]
Ata Atun.,
Mağusa Yazıları, Samtay Vakfı,
Famagusta, Cyprus: pp 103, 2002.
[11]
Ata Atun., Mağusa Yazıları,
Samtay Vakfı, Famagusta, Cyprus: pp 161 & 184, 2002.
[12]
Cobham C.D., Excerpta Cypria, Cambridge University press: UK, pp.
251270., 1908
[13]
Ata Atun., Mağusa Yazıları,
Samtay Vakfı, Famagusta, Cyprus: pp 228 & 267, 2002.
[14]
Cobham C.D., Excerpta Cypria, Cambridge University press: UK, pp.
424450, 1908.
[15]
Encyclopaedia Britannica Inc.,
Encyclopaedia Britannica, William Benton : USA, pp. 271272, 1966
[16]
Lazarides S.G., Souvenir of Famagusta, Laiki Group Cultural Centre, Nicosia, Cyprus:
pp. 222 & 252, 2001