was completed in 1593
A little background
• Who designed st. peters’ dome?
• Michelangelo Buonarotti in 1557
• however..
• Michelangelo had passed away in 1564…
• Before the dome was completed in 1593
First signs of trouble
• early 18th century
• gradual propagation of cracks up the side
of the dome
• in 1748 Polemi, an engineer, was brought
in to analyse the dome and decide on
what action should be taken
Where Michelangelo
Went wrong
• Difficult task to achieve
• No sophisticated methods of analysis
• Engineers relied largely on Trial and error
• Michelangelo’s design drew from the 46
meter span dome of the Florence
cathedral, by Brunelleschi in 1420
• Michelangelo had 1:15 scale models
built, one of clay and the other of wood
Finished product
• a double dome in brick, 42.3 metres in
diameter
• highest point is 120 metres above the floor
• dome was parabolic
• This exerted a smaller outward thrust
Iron tension rings were built into the masonry to
ensure no spreading at the base of the dome.
However these precautions were insufficient
• Polemi noticed that meridional cracks
were appearing below 25 degrees on the
dome
• Indicative of minor failure due to
inappropriate buttressing
• The patterns created a series of masonry
arches in a circular pattern all sharing the
same central keystone
Idea!
•
Polemi analysed the dome as a series
of 50 masonry arches
• He used Hooke’s principals to establish
that the dome was still safe :1. He hung a chain down to form an
inverted arch
2. This determined whether the hypothetical
arches lay within the line of thrust
3. He computed the weight of the sliced arch
4. Each half arch was divided into 16
sections
5. Then loaded a flexible string with 32
unequal weights, each weight in
proportion to the corresponding section
of the arch
As can be seen from the diagram below when it is
inverted the shape of the chain does lie within the
inner and outer surfaces of the arc
Solution
• To prevent any further propagation
of the cracks he added a further
four chains to the dome
• These act like the hoops on a
barrel preventing the structure from
thrusting out any more
Interesting fact!
• increasing the thickness of the dome may
actually diminish the structures efficiency
• derived from statics,
H = (1 – π/4)W
=0.215W
W is the weight of the segment being analysed
H is the uniformly distributed horizontal outward
force
The greater the load the greater amount of support
will be needed to prevent the outward thrust
Bibliography
• J.Heyman, The Stone Skeleton: Structural
Engineering of Masonry Architecture
• Howard Hibbard, Michelangelo
• McPhee, Bernini and the Bell Tower
• Giulio Carlo Argan, Bruno Contardi,
Michelangelo Architect
• Donna Walsh
• Diarmuid Kehoe
• Killian Courtney
• Paul O’ Brien