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,ŝƐƚŽƌŝĐĂů
^ƚƌƵĐƚƵƌĞƐ͛
ƐƐĞƐƐŵĞŶƚ ĂŶĚ
ZĞŚĂďŝůŝƚĂƚŝŽŶ
;,ŝ^ ZͿ
ĐĞ ƌĚŽŐŵƵƐ͕ WŚ͕ W
ƐƐŽĐŝĂƚĞ WƌŽĨĞƐƐŽƌ
ƵƌŚĂŵ ^ĐŚŽŽů ŽĨ ƌĐŚŝƚĞĐƚƵƌĂů ŶŐŝŶĞĞƌŝŶŐ Θ ŽŶƐƚƌƵĐƚŝŽŶ
hŶŝǀĞƌƐŝƚLJ ŽĨ EĞďƌĂƐŬĂͲŝŶĐŽůŶ ;KŵĂŚĂ ĂŵƉƵƐͿ
ZƵŵĞůŝ ,ŝƐĂƌı͕ øƐƚĂŶďƵů͕ dƺƌŬŝLJĞ
,ŝ^ Z͗ ,ŝƐƚŽƌŝĐĂů ^ƚƌƵĐƚƵƌĞƐ͛ ƐƐĞƐƐŵĞŶƚ Θ ZĞŚĂďŝůŝƚĂƚŝŽŶ
• EŽŶͲĚĞƐƚƌƵĐƚŝǀĞ ĞǀĂůƵĂƚŝŽŶ ;EͿ ŽĨ
,ŝƐƚŽƌŝĐĂů ^ƚƌƵĐƚƵƌĞƐ͗
• džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐ͕
• 'ƌŽƵŶĚ WĞŶĞƚƌĂƚŝŶŐ ZĂĚĂƌ ;'WZͿ͕
• /ŵƉĂĐƚ ĐŚŽ ;/Ϳ͕
• ŝďĞƌƐĐŽƉĞ ŽƌĞƐĐŽƉLJ͕ /ŶĨƌĂƌĞĚ͕
• hůƚƌĂƐŽŶŝĐ dĞƐƚŝŶŐ
• džƉĞƌŝŵĞŶƚĂůůLJ sĂůŝĚĂƚĞĚ ŝŶŝƚĞ ůĞŵĞŶƚ
DŽĚĞůŝŶŐ ;DͿ ŽĨ ĐŽŵƉůĞdž ŵĂƐŽŶƌLJ ƐƚƌƵĐƚƵƌĞƐ
• ŝďĞƌͲƌĞŝŶĨŽƌĐĞĚ ĐĞŵĞŶƚƐ ;ZͿ ĨŽƌ
ŵĂƐŽŶƌLJ ĂŶĚ ĐŽŶĐƌĞƚĞ ƌĞƚƌŽĨŝƚ
ĂƉƉůŝĐĂƚŝŽŶƐ
Ϯ
NC_ACol4_Heel Drop
FRF_Real Plot
0.00E+00
5.00E-07
1.00E-06
1.50E-06
2.00E-06
2.50E-06
3.00E-06
3.50E-06
4.00E-06
4.50E-06
0 5 10 15 20 25 30 35 40 45 50
Frequency (Hz)
Mag(g/N)
A1
A2
A3
A4
A5
A6
A7
ϭ
Ϯ
ϯ
,ŝ^ Z͗ ,ŝƐƚŽƌŝĐĂů ^ƚƌƵĐƚƵƌĞƐ͛ ƐƐĞƐƐŵĞŶƚ Θ ZĞŚĂďŝůŝƚĂƚŝŽŶ
• dLJƉĞƐ ŽĨ ŚŝƐƚŽƌŝĐĂů ƐƚƌƵĐƚƵƌĞƐ͗
• ƌĐŚĞŽůŽŐŝĐĂů ^ŝƚĞƐ͕ ŶĐŝĞŶƚ ZŽŵĂŶ ^ƚƌƵĐƚƵƌĞƐ ;dŚĞ
ĨĂŵŽƵƐ ͞dĞŵƉůĞ͟ WƌŽũĞĐƚͿ
• 'ŽƚŚŝĐ ĂƚŚĞĚƌĂůƐ ;EĂƚŝŽŶĂů ĂƚŚĞĚƌĂů ŝŶ ͕ /ƚĂůŝĂŶ ĂŶĚ
ƌĞŶĐŚ ĐĂƚŚĞĚƌĂůƐ͕ /ŐůĞƐŝĂ ^ĂŶ :ŽƐĞ ŝŶ WƵĞƌƚŽ ZŝĐŽͿ
• 'ƵĂƐƚĂǀŝŶŽ ŽŵĞƐ ĂŶĚ sĂƵůƚƐ ;EĞďƌĂƐŬĂ ^ƚĂƚĞ ĂƉŝƚŽůͿ
• DĂƐŽŶƌLJ ĂŶĚ ŽŶĐƌĞƚĞ ,ŝƐƚŽƌŝĐ ƌĐŚ ƌŝĚŐĞƐ ŝŶ h͘^͘
ϰ
Ed Θ Dϭ
ϱ
1) Seismic
accelerometers placed on
the structure collect data
0 2 4 6 8 10 12 14 16
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
w-Frequency (Hz)
MagH(in/k)
4) Modal analysis and determination of the
characteristics of the structure
1/c
1/k
5) FEM
updating and
verification of
mechanical
properties
2) System
excited
3) Dynamic signal analyzer processes
data
ϲ
DĞƚŚŽĚ ĂƉƉůŝĞĚ ŽŶ ǀĂƌŝŽƵƐ ŚŝƐƚŽƌŝĐĂů ƐƚƌƵĐƚƵƌĞƐ͗ 'ŽƚŚŝĐ
National Cathedral, U.S.
7
6
5
A4
3
2
1
Col
1
Col
4
Col
7
NC_ACol4_Heel Drop
FRF_Real Plot
0.00E+00
5.00E-07
1.00E-06
1.50E-06
2.00E-06
2.50E-06
3.00E-06
3.50E-06
4.00E-06
4.50E-06
0 5 10 15 20 25 30 35 40 45 50
Frequency (Hz)
Mag(g/N)
A1
A2
A3
A4
A5
A6
A7
ϳ
Cathedral in Auxerre, France Santa Maria Novella,
Florence, Italy
000000000
000000000
000000
00
0000
000000000
00000000
00
00
0000000000000000000000
000000
00000000000000
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000
0000
00
00
00000000000000
00
0000
00
0000000000000000000
00
000000
000
0000
00
000000000000
00
00
000000
000
000
000000
000
0000
00
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
AUX Hammer Impact on Nave5
FRF from sensors on Nave 4, 5  6
0.00E+00
1.00E-06
2.00E-06
3.00E-06
4.00E-06
5.00E-06
6.00E-06
0 5 10 15 20 25 30 35 40 45 50
Frequency (Hz)
Mag(g/N)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
N4
N5
N6
000000000000000000COH N5
DĞƚŚŽĚ ĂƉƉůŝĞĚ ŽŶ ǀĂƌŝŽƵƐ ŚŝƐƚŽƌŝĐĂů ƐƚƌƵĐƚƵƌĞƐ͗ 'ŽƚŚŝĐ
ϴ
• ĂƚĞ͗ ϭϵϬϬ͛Ɛ
• WůĂĐĞ͗ ŝŶĐŽůŶ͕ EĞďƌĂƐŬĂ
• DĂƐƚĞƌ͗ 'ƵĂƐƚĂǀŝŶŽ͕ :ƌ͘
DĞƚŚŽĚ ĂƉƉůŝĞĚ ŽŶ ǀĂƌŝŽƵƐ ŚŝƐƚŽƌŝĐĂů ƐƚƌƵĐƚƵƌĞƐ͗
'ƵĂƐƚĂǀŝŶŽ
ϵ
DŽĚĞů ŽŵĞ 'ŽĂůƐ͗
ϭͿhŶĚĞƌƐƚĂŶĚ ͞'ƵĂƐƚĂǀŝŶŽ͟
ŽŶƐƚƌƵĐƚŝŽŶ dĞĐŚŶŝƋƵĞ
ϮͿ/ŵƉƌŽǀĞŵĞŶƚƐ ŝŶ Ed
ŵĞƚŚŽĚ
ϭϬ
Setup #1
Sensor
ZƵŝŶŽƵƐ ĂŶĐŝĞŶƚ
ZŽŵĂŶ ĐŝƚLJ ŽĨ ŶƚŝŽĐŚ
ĂĚ ƌĂŐƵŵ ŝŶ ƉƌĞƐĞŶƚ
ĚĂLJ 'ĂnjŝƉĂƐĂ͕ dƵƌŬĞLJ
ϭϭ
/ŵƉĞƌŝĂů dĞŵƉůĞ
ŽůŽŶŶĂĚĞĚ
^ƚƌĞĞƚ
'ƌĞĂƚ ĂƚŚ
'LJŵŶĂƐŝƵŵͬWŽŽů
/ŶǀĞƐƚŝŐĂƚŝŽŶ ŽĨ ĂŶ ŶĐŝĞŶƚ ZŽŵĂŶ ŝƚLJ ŝŶ
dƵƌŬĞLJ
dŚĞ dĞĂŵ
• /ŶƚĞƌĚŝƐĐŝƉůŝŶĂƌLJ ƉƌŽũĞĐƚ ďĞŐĂŶ ŝŶ ϮϬϬϱ
• ƌ͘ ĐĞ ƌĚŽŐŵƵƐ͕ hE͗ ƌĐŚŝƚĞĐƚƵƌĂů
ŶŐŝŶĞĞƌŝŶŐ
• ƌ͘ DŝĐŚĂĞů ,ŽĨĨ͕ hE͗ ƌĐŚĂĞŽůŽŐLJͬ ƌƚ ,ŝƐƚŽƌLJ
• ƌ͘ ZŚLJƐ dŽǁŶƐĞŶĚ͕ ůĂƌŬ hŶŝǀĞƌƐŝƚLJ͗ 'ƌĞĞŬ
ƌĐŚŝƚĞĐƚƵƌĞ Θ ůĂƐƐŝĐƐ
• ƌ͘ ŝƌŽů ĂŶ ;ϮϬϭϭͲƉƌĞƐĞŶƚͿ͕ ƌnjƵƌƵŵ ƚĂƚƵƌŬ
hŶŝǀĞƌƐŝƚLJ͕ dƵƌŬĞLJ͗ ƌĐŚĞŽůŽŐLJ
• :ŽƐŚƵĂ ƌĞĞĚůĂŶĚ͕ t: Θ ;EĞǁ͊Ϳ ƌĂŶŬ DĂƚĞƌŽ͕
hWĞŶŶ͗ ŽŶƐĞƌǀĂƚŝŽŶ
ϭϮ
dƌƵůLJ ŝŶƚĞƌĚŝƐĐŝƉůŝŶĂƌLJ ĨƌŽŵ ƚŚĞ
ƐƚĂƌƚ ŽĨ ƚŚĞ ƉƌŽũĞĐƚ͊
ŽŶƐĞƌǀĂƚŝŽŶ
ϭϯ
dŚĞ /ŵƉĞƌŝĂů dĞŵƉůĞ
ϭϰ
dŚĞ /ŵƉĞƌŝĂů dĞŵƉůĞ
/ŵƉĞƌŝĂů dĞŵƉůĞ͗ WƌŽũĞĐƚ 'ŽĂůƐ
• dŽ ƉĂƌƚŝĂůůLJ ƌĞĐŽŶƐƚƌƵĐƚ ƚŚĞ ƚĞŵƉůĞ ƚŽ ƐŚŽǁͲ
ĐĂƐĞ ŝƚƐ ŽƌŝŐŝŶĂů ĚĞƐŝŐŶ
• dŽ ĞƐƚĂďůŝƐŚ Ă ǁĞůůͲĚŽĐƵŵĞŶƚĞĚ ƉƌŽĐĞƐƐ ĨŽƌ
ƐƵĐŚ ĂŶ ĞdžƚĞŶƐŝǀĞ Θ ƵŶŝƋƵĞůLJ
ŝŶƚĞƌĚŝƐĐŝƉůŝŶĂƌLJ ƌĞĐŽŶƐƚƌƵĐƚŝŽŶ ƉƌŽũĞĐƚ
͞ ƌĐŚĞŽůŽŐŝĐĂů ŶŐŝŶĞĞƌŝŶŐ͟
ϭϱ
ϭϲ
ϮϬϭϰϮϬϭϰ
/ŵƉĞƌŝĂů dĞŵƉůĞͲ ϮϬϭϰ ^ĞĂƐŽŶ
DĂƚĞƌŝĂů ŚĂƌĂĐƚĞƌŝƐƚŝĐƐ͗
WĞƚƌŽŐƌĂƉŚŝĐ ŶĂůLJƐĞƐ
• ϴ ƐĂŵƉůĞƐ ĂƌĞ ĂŶĂůLJnjĞĚ
• DĂƚĞƌŝĂů ŝƐ ĚĞŶƐĞ ŵĂƌďůĞ ;ŵĞƚĂŵŽƌƉŚŽƐĞĚ
ůŝŵĞƐƚŽŶĞͿ
• ϯ ǀĂƌŝĞƚŝĞƐ ĂƌĞ ŝĚĞŶƚŝĨŝĞĚ
• dƌĂĐĞ ĂŵŽƵŶƚƐ ŽĨ ƉLJƌŝƚĞ ;ŝƌŽŶ ƐƵůĨŝĚĞͿ
ĐƌLJƐƚĂůƐ ƐŝŵŝůĂƌ ŝŶ ƐŝnjĞ ƚŽ ƚŚĞ ĐĂůĐŝƚĞ ĐƌLJƐƚĂůƐ
ǁĞƌĞ ĂůƐŽ ŽďƐĞƌǀĞĚ͘
ϭϳ
dŚŝŶͲƐĞĐƚŝŽŶ
ŵŝĐƌŽŐƌĂƉŚ ƐŚŽǁŝŶŐ
ƚŚĞ ƚĞdžƚƵƌĞ ŽĨ ƚŚĞ
ŵĂƌďůĞ ƵŶĚĞƌ ĐƌŽƐƐͲ
ƉŽůĂƌŝnjĞĚ ůŝŐŚƚ͘
DĂƚĞƌŝĂů dĞƐƚŝŶŐ
• ŽŵƉƌĞƐƐŝŽŶ ƚĞƐƚŝŶŐ ŽĨ ŵĂƌďůĞ
• DĂƌďůĞ ĨƌŽŵ ƐŝƚĞ ĂŶĚ ĨƌŽŵ Ă ŶĞĂƌďLJ ƋƵĂƌƌLJ
ϭϴ
^ŽƵƌĐĞ
hůƚŝŵĂƚĞ ŽŵƉƌĞƐƐŝǀĞ ^ƚƌĞƐƐ
;ı
¡
Ϳ
DŽĚƵůƵƐ ŽĨ ůĂƐƚŝĐŝƚLJ
;Ϳ
ƉƐŝ DWĂ ƉƐŝ DWĂ
ĂŵďĂƐ ;ϭϵϵϮͿ ϭϭ͕ϮϴϬ ϳϳ͘ϴ ϯ͕ϯϯϲ͕ϬϬϬ Ϯϯ͕ϬϬϬ
ŽƵƌŬŽƵůŝƐ Θ WĂƐŝŽƵ ;ϮϬϬϵͿ ϳ͕ϵϴϬͲϭϭ͕ϲϬϬ ϱϬͲϴϬ ϳ͕ϮϱϮ͕ϬϬϬ Ͳ ϭϮ͕Ϯϱϲ͕ϬϬϬ ϱϬ͕ϬϬϬ Ͳ ϴϰ͕ϱϬϬ
ĞĞƌ Ğƚ͘Ăů͘ ;ϮϬϬϵͿ ϭϴ͕ϬϬϬ ϭϮϰ ϴ͕ϬϬϬ͕ϬϬϬ ϱϱ͕ϭϳϬ
ŽƵƌŬŽƵůŝƐ Ğƚ Ăů͘ ;ϮϬϭϬͿ Ͳ Ͳ ϭϭ͕ϲϬϯ͕ϬϬϬ ϴϬ͕ϬϬϬ
ŽƵƌŬŽƵůŝƐ ĂŶĚ WĂƐŝŽƵ ;ϮϬϭϱͿ Ͳ Ͳ ϭϬ͕ϵϮϭ͕ϬϬϬ ϳϱ͕ϯϬϬ
dĞŵƉůĞ ŽĨ ŶƚŝŽĐŚ DĂƌďůĞ ϭϮ͕ϬϴϬ ϴϯ͘ϯ ϱ͕ϮϬϯ͕ϬϬϬ ϯϱ͕ϴϳϬ
YƵĂƌƌLJ DĂƌďůĞ ϵ͕ϳϳϬ ϲϳ͘ϰ ϴ͕ϳϴϬ͕ϬϬϬ ϲϬ͕ϱϬϬ
ϭϵ
,ĂŶĚŬͲ ĂƐĞĚ ŽŶ /KDK^Ύ
Ύ/ŶƚĞƌŶĂƚŝŽŶĂů ŽƵŶĐŝů ŽŶ DŽŶƵŵĞŶƚƐ ĂŶĚ ^ŝƚĞƐ
ϮϬ
ůŽĐŬ ƐƐĞƐƐŵĞŶƚ ŽƌŵƐ
džƚĞƌŶĂů ZĂƚŝŶŐ ĨŽƌ DĂƌďůĞ ůŽĐŬƐ
• ǀĞƌĂŐĞ ĐĞůůĂ ďůŽĐŬ
ĚŝŵĞŶƐŝŽŶƐ͗ ϭ͘ϱϰ ŵ dž Ϭ͘ϱϯ
ŵ dž Ϭ͘ϱϭ ŵ
Ϯϭ
džƚĞƌŶĂů
ŽŶĚŝƚŝŽŶ
ZĂƚŝŶŐ
ĞƐĐƌŝƉƚŝŽŶ ůŽĐŬƐ
ϭ
EŽ ŵŝƐƐŝŶŐ ƉĂƌƚƐ͕ ŵŝŶŝŵĂů ĐŚŝƉƉŝŶŐ
Ăƚ ĐŽƌŶĞƌƐ͘ ŶLJ ĐƌĂĐŬƐ ĂƌĞ ƚŚŝŶ ĂŶĚ
ďĂƌĞůLJ ǀŝƐŝďůĞ͘
EĞǁ ŵĂƌďůĞ
ďůŽĐŬƐ
Ϯ
^ŽŵĞ ŵŝƐƐŝŶŐ ƉĂƌƚƐ͕ ďƵƚ ůĞƐƐ ƚŚĂŶ
ϭϬй ŽĨ ƚŚĞ ďůŽĐŬ͘ ^ŽŵĞ ƐƵƌĨĂĐĞ
ĐƌĂĐŬƐ͘
dϬϭϭ͕ dϬϲϱ͕
dϬϳϭ͕ dϱϱϵ
ϯ
WƌĞƐĞŶĐĞ ŽĨ ŵŝƐƐŝŶŐ ƉĂƌƚƐ ;ϭϬй Žƌ
ŵŽƌĞͿ ĂŶĚͬŽƌ ƐĞǀĞƌĞ͕ ĚĞĞƉ
ƐƚƌƵĐƚƵƌĂů ĐƌĂĐŬƐ͘
dϬϲϴ͕ dϬϭϰ /ŶƚĞƌŶĂů ǀŽŝĚƐ͍
/ŵƉĂĐƚͲĐŚŽ EŽŶĚĞƐƚƌƵĐƚŝǀĞ
dĞƐƚŝŶŐ
• ĂĐŬŐƌŽƵŶĚ ŽŶ DĞƚŚŽĚ
• ĞǀĞůŽƉĞĚ ŝŶ ϭϵϴϬ͛Ɛ͘
• ǀĂůƵĂƚŝŽŶ ŽĨ ŝŶƚĞƌŶĂů ĐŽŶĚŝƚŝŽŶ ŽĨ ƐƚƌƵĐƚƵƌĂů
ĐŽŵƉŽŶĞŶƚƐ
• ч ϯ͘ϭй ĞƌƌŽƌ ĨŽƌ ƚŚŝĐŬŶĞƐƐ ŵĞĂƐƵƌĞŵĞŶƚƐ ŽĨ Ϭ͘Ϯ ŵͲƚŚŝĐŬ
ƉĂǀĞŵĞŶƚ ;^ĂŶƐĂůŽŶĞ ϭϵϵϳͿ͘
• dĞŵƉůĞ WƌŽũĞĐƚ
• Ăď ǀĂůŝĚĂƚŝŽŶ Θ ŝŶ ƐŝƚƵ ƚĞƐƚŝŶŐ͗ ϮϬϭϭͲƉƌĞƐĞŶƚ
• hƐĞĚ ĨŽƌ ĂƐƐĞƐƐŵĞŶƚ ŽĨ ŝŶƚĞƌŝŽƌ ĐŽŶĚŝƚŝŽŶ ŽĨ ĞdžĐĂǀĂƚĞĚ
ƚĞŵƉůĞ ďůŽĐŬƐ
ϮϮ
/ŵƉĂĐƚͲĐŚŽ dĞƐƚŝŶŐ
Ϯϯ
sŽŝĚ ĞƚĞĐƚŝŽŶ WͲǁĂǀĞ
dĞƐƚŝŶŐ
Ăď sĂůŝĚĂƚŝŽŶ
• ĂƐƚ ŵŽƌƚĂƌ ďůŽĐŬƐ͗
Ϭ͘ϴϱ ŵ dž Ϭ͘ϯϲ ŵ dž Ϭ͘ϯϰ ŵ
Ϯϰ
Block
Block
Face
Tested
Percent
Error
Relative Amplitude
(relative to amplitude
of 3rd or 4th mode)
8.89 cm x
8.89 cm
square
void
Top
4.
6
%
5.2%
1.38
1.08
1.14
Side
5.
8
%
0.78
8.89 cm
diameter
void
Top
2.
0
%
2.2%
1.07
1.09
Side
2.
4
%
1.11
3.81 cm x
3.81 cm
square
void
Top
1.
4
%
2.3%
0.68
1.24
Side
3.
2
%
1.80
džĂŵƉůĞƐ ŽĨ DĂƌďůĞ ůŽĐŬ ZĞƐƵůƚƐ
Ϯϱ
Block AT068, External
Condition Rating = 3
Block AT071, External
Condition Rating = 2
New marble block,
External Condition
Rating = 1
AT014, External
Condition Rating = 3
WƌĞƐĞƌǀĂƚŝŽŶ ŽĨ ůŽĐŬƐ
• ůŽĐŬ ĐůĞĂŶŝŶŐ ƉƌŽĐĞƐƐ
• dŚƌŽƵŐŚ ĐŽŶĚŝƚŝŽŶ ĂƐƐĞƐƐŵĞŶƚ͕ ůŝĐŚĞŶ ĂŶĚ ĂůŐĂĞ ĂƌĞ ŵŽƐƚ ĐŽŵŵŽŶ ĨŽƌŵƐ
ŽĨ ĚĞƚĞƌŝŽƌĂƚŝŽŶ ŽŶ ƐŝƚĞ
• ůŽĐŬƐ ǁĞƌĞ ƐƵďũĞĐƚ ƚŽ ǀĂƌŝŽƵƐ ƉĂƚƚĞƌŶƐ ŽĨ ŚĞĂƚ ƚƌĞĂƚŵĞŶƚ ĂŶĚ ĐůĞĂŶŝŶŐ
Ϯϲ
^ƵĐĐĞƐƐĨƵů ĐůĞĂŶŝŶŐ ƚƌĞĂƚŵĞŶƚ hŶƐƵĐĐĞƐƐĨƵů ĐůĞĂŶŝŶŐ ƚƌĞĂƚŵĞŶƚ
^ƵĐĐĞƐƐĨƵů ƚƌĞĂƚŵĞŶƚ ƉƌŽĐĞƐƐ
ƉŚĂƐĞƐ
• WƌĞͲǁĞƚ ǁŝƚŚ ůŽǁ ĐŽŶĐĞŶƚƌĂƚŝŽŶ
ƐŽůƵƚŝŽŶ
• ĞĞƉ ǁĞƚ ƵƐŝŶŐ ĚĂŵƉ ĐůŽƚŚ
• ŽǀĞƌ ǁŝƚŚ ƚĂƌƉ ƵŶĚĞƌ ĂŵďŝĞŶƚ ŚĞĂƚ
• ƌƵƐŚ ůŝŐŚƚůLJ ĂĨƚĞƌ ƚĂƌƉ ƌĞŵŽǀĂů
Ϯϳ
ϯ ůŽĐŬ DŽĚĞůŝŶŐ
• sŝƐƵĂůŝnjĂƚŝŽŶ ƚŽŽů ĂŶĚ ĂƐƐŝƐƚ ƚŽ D ƐƚƌƵĐƚƵƌĂů ĂŶĂůLJƐŝƐ
Ϯϴ
Ϯϵ
KƚŚĞƌ EŽŶͲĞƐƚƌƵĐƚŝǀĞ dĞƐƚŝŶŐ
• 'ƌŽƵŶĚ ƉĞŶĞƚƌĂƚŝŶŐ ƌĂĚĂƌ ;'WZͿ
• ŝďĞƌƐĐŽƉĞ ƌĞŵŽƚĞ ŝŶƐƉĞĐƚŝŽŶ
^ƵŵŵĞƌ ϮϬϭϰ͗ ŽůƵŵŶ ZĂŝƐŝŶŐ
ƌ͘ ŝƌŽů ĂŶ Θ ƌ͘ ĐĞ ƌĚŽŒŵƵƔ
ϯϬ
KŶĞ ůĂƐƚ ůŽŽŬ Ăƚ ŽƵƌ ƐŝƚĞ ŝŶ ϮϬϭϰ
ϯϭ
ZĞƐĞĂƌĐŚ ŝŶ WƌŽŐƌĞƐƐͬ^ĞĞŬŝŶŐ
/ŶƉƵƚ͙
• ZŽŵĂŶ ŽƌƵŵ ĂŶĂƐƚLJůŽƐŝƐ ŝŶĨŽƌŵĂƚŝŽŶ͗
• dŚĞ ƚĞĂŵ͍
• tŚĞƌĞ ŝƐ ƚŚĞ ŝŶĨŽƌŵĂƚŝŽŶ ƉƵďůŝƐŚĞĚ͍
• dĞĐŚŶŝƋƵĞƐ ƵƐĞĚ
ϯϮ
EĞǁ͗ /ŐůĞƐŝĂ ^ĂŶ :ŽƐĞ ;/^:Ϳ͕ WƵĞƌƚŽ
ZŝĐŽ
• ϭϲƚŚͲĐĞŶƚƵƌLJ ^ƉĂŶŝƐŚ 'ŽƚŚŝĐ ĂƌĐŚŝƚĞĐƚƵƌĞ
• ŽŶƐƚƌƵĐƚŝŽŶ͗ ϭϱϯϮ ƚŽ ϭϳϯϱ ďLJ ƚŚĞ ŽŵŝŶŝĐĂŶ KƌĚĞƌ
ϯϯ
WůĂŶŶĞĚ ƐƐĞƐƐŵĞŶƚ͗
•džƉĞƌŝŵĞŶƚĂů DŽĚĂů
ŶĂůLJƐŝƐ ;D Ϳ
•ŝŶŝƚĞ ůĞŵĞŶƚ
DŽĚĞůŝŶŐ ;DͿ
• hŶŝƋƵĞ ĂŶĚ ĐŽŵƉůĞdž ƐƚƌƵĐƚƵƌĞ
ϯϰ
EĞǁ͗ ^ĂŶ :ŽƐĞ /ŐůĞƐŝĂ͕ WƵĞƌƚŽ ZŝĐŽ
džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐ Θ
D
• ZĞƐĞĂƌĐŚ ŝŶ ƉƌŽŐƌĞƐƐ͗ ϭͿ /ŶͲƐŝƚƵ ĂƐƐĞƐƐŵĞŶƚ ĚŽŶ Ăƚ
ϯ ůŽĐĂƚŝŽŶƐ͘ ϮͿ DͬD ŝŶ ƉƌŽŐƌĞƐƐ͘ ϯͿ WƌĞůŝŵŝŶĂƌLJ
ƌĞƉŽƌƚ ƐƵďŵŝƚƚĞĚ
ϯϱ
džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐ Θ
D
• ZĞƐĞĂƌĐŚ ŝŶ ƉƌŽŐƌĞƐƐ͗ ϭͿ /ŶͲƐŝƚƵ ĂƐƐĞƐƐŵĞŶƚ ĚŽŶ Ăƚ
ϯ ůŽĐĂƚŝŽŶƐ͘ ϮͿ DͬD ŝŶ ƉƌŽŐƌĞƐƐ͘ ϯͿ WƌĞůŝŵŝŶĂƌLJ
ƌĞƉŽƌƚ ƐƵďŵŝƚƚĞĚ
ϯϲ
džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐ Θ
D
• ZĞƐĞĂƌĐŚ ŝŶ ƉƌŽŐƌĞƐƐ͗ ϭͿ /ŶͲƐŝƚƵ ĂƐƐĞƐƐŵĞŶƚ ĚŽŶ Ăƚ
ϯ ůŽĐĂƚŝŽŶƐ͘ ϮͿ DͬD ŝŶ ƉƌŽŐƌĞƐƐ͘ ϯͿ WƌĞůŝŵŝŶĂƌLJ
ƌĞƉŽƌƚ ƐƵďŵŝƚƚĞĚ
ϯϳ
džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐ Θ
D
• DĂŝŶ ǀĂƵůƚ͗ ƵŶĚĂŵĞŶƚĂů ĨƌĞƋƵĞŶĐLJ ŵĂƚĐŚ Ăƚ Ϯϴ ,nj
ďĞƚǁĞĞŶ D ĂŶĚ D͕ ƵƐŝŶŐ ǀĂůŝĚĂƚĞĚ /ŶĚŝĂŶĂ
ŝŵĞƐƚŽŶĞ ƉƌŽƉĞƌƚŝĞƐ
ϯϴ
ϯϵ
D Θ D͗ DĂŝŶ sĂƵůƚ
EŽƌƚŚ ,ĂůĨ ;ůĞĨƚͿ ĂŶĚ ^ŽƵƚŚ ŚĂůĨ ;ƌŝŐŚƚͿ ƉƌĞƐĞŶƚ ĚŝĨĨĞƌĞŶĐĞƐ ĚƵĞ ƚŽ ǀĂƌLJŝŶŐ
ĐŽŶĚŝƚŝŽŶ ĂŶĚ ŝŶƐƵůĂƚŝŽŶ͘ ƵƌƚŚĞƌ ƌĞĨŝŶĞŵĞŶƚƐ ŶĞĞĚĞĚ͘
ϰϬ
^ƚƌƵĐƚƵƌĂů
ZĞŚĂďŝůŝƚĂƚŝŽŶ ŽĨ
DĂƐŽŶƌLJ
Ϯ
ϰϭ
ŝďĞƌ ZĞŝŶĨŽƌĐĞĚ
DŽƌƚĂƌ ;ZDͿ
ϮͲĂ
ϰϮ
ZĞŚĂďŝůŝƚĂƚŝŽŶ͗ ŝďĞƌ ZĞŝŶĨŽƌĐĞĚ DŽƌƚĂƌ
^ƵĐĐĞƐƐĨƵů ƌĞŚĂďŝůŝƚĂƚŝŽŶ
DĂƚĞƌŝĂů ĐŽŵƉĂƚŝďŝůŝƚLJ
ZĞƉĂŝƌ ĚƵƌĂďŝůŝƚLJ
ŽŶŐͲƚĞƌŵ ŵĂŝŶƚĞŶĂŶĐĞ
ŝďĞƌ dLJƉĞƐ
^ƚĞĞů
'ůĂƐƐ
^LJŶƚŚĞƚŝĐ
KƌŐĂŶŝĐ
ϰϯ
DĂĐƌŽ ĨŝďĞƌƐ
Ϭ͘ϱ ƚŽ Ϯ͘ϱ ŝŶĐŚĞƐ
DŝĐƌŽ ĨŝďĞƌƐ
ĞƐƐ ƚŚĂŶ Ϭ͘ϱ ŝŶĐŚĞƐ
ŝĂŵĞƚĞƌ ǀĂƌŝĞƐ
ZĞŚĂďŝůŝƚĂƚŝŽŶ͗ ŝďĞƌ ZĞŝŶĨŽƌĐĞĚ DŽƌƚĂƌ
ŝďĞƌͲƌĞŝŶĨŽƌĐĞĚ ŵŽƌƚĂƌ͗ WŝůŽƚ
ϰϰ
DŽƌƚĂƌ ŵŝdž
WƌĞͲďůĞŶĚĞĚ WŽƌƚůĂŶĚ ĐĞŵĞŶƚ͕ ůŝŵĞ͕ ĂŶĚ ƐĂŶĚ
^dD  ϮϳϬ W dLJƉĞ E ŵŽƌƚĂƌ
ZĞŝŶĨŽƌĐŝŶŐ ĨŝďĞƌƐ
WŽůLJǀŝŶLJů ĂůĐŽŚŽů ;Ws Ϳ
,ŝŐŚ ͕ ƚĞŶƐŝůĞ ƐƚƌĞŶŐƚŚ͕ ďŽŶĚ ƐƚƌĞŶŐƚŚ
ůŬĂůŝ ƌĞƐŝƐƚĂŶƚ
ϰϱ
ϰϲ
WƵďůŝƐŚĞĚΎ ZĞƐƵůƚƐ
Ύ^ŬŽƵƌƵƉ͕ ͘ E͕͘ ĂŶĚ ƌĚŽŐŵƵƐ͕ ͘ ;ϮϬϭϬͿ͘ ͞DĞĐŚĂŶŝĐĂů ŚĂƌĂĐƚĞƌŝƐƚŝĐƐ ŽĨ Ws ŝďĞƌͲ
ZĞŝŶĨŽƌĐĞĚ W DŽƌƚĂƌƐ ĨŽƌ DĂƐŽŶƌLJ ƉƉůŝĐĂƚŝŽŶƐ͟ / DĂƚĞƌŝĂůƐ :ŽƵƌŶĂů͕ sŽů͘ ϭϬϳ͕
:ĂŶƵĂƌLJͲ ĞďƌƵĂƌLJ ϮϬϭϬ͕ EŽ͘ϭ͕͘ ƉƉ ϭͲ ϵ͕ / ƉƵďůŝĐĂƚŝŽŶƐ͘
ϰϳ
ŝďĞƌͲƌĞŝŶĨŽƌĐĞĚ ŵŽƌƚĂƌ͗ ĂƌŐĞƌ
ĞdžƉĞƌŝŵĞŶƚĂů ƉƌŽŐƌĂŵ ;EWdd ĨƵŶĚĞĚͿ
ƌŝĐŬ dLJƉĞƐ͗
•^ƚĂŶĚĂƌĚ ůĂLJ ƌŝĐŬƐ
•^ƚĂŶĚĂƌĚ ŽŶĐƌĞƚĞ ƌŝĐŬƐ
ŝŶĚĞƌ dLJƉĞƐ͗
•dLJƉĞ E WŽƌƚůĂŶĚ ŝŵĞ ĂŶĚ ^ĂŶĚ WͲ
Ϭϭ
•EĂƚƵƌĂů ,LJĚƌĂƚĞĚ ŝŵĞ ;E,Ϳ ϯ͘ϱt
;ƌĂƚŝŽƐ͗ ϭ͗Ϯ͘ϱ Θ ϭ͗ϯͿ
•EĂƚƵƌĂů ,LJĚƌĂƚĞĚ ŝŵĞ ;E,Ϳ ϱt
;ƌĂƚŝŽƐ͗ ϭ͗Ϯ͘ϱ Θ ϭ͗ϯͿ
;^ĂŶĚ ƵƐĞĚ ǁŝƚŚ ƚŚĞ E, ŝƐ ĂƉƉƌŽǀĞĚ
ĂĐĐŽƌĚŝŶŐ ƚŽ ^dD ϭϰϰͲϬϯͿ
ϰϴ
ŝďĞƌͲƌĞŝŶĨŽƌĐĞĚ ŵŽƌƚĂƌ͗ ĂƌŐĞƌ
ĞdžƉĞƌŝŵĞŶƚĂů ƉƌŽŐƌĂŵ ;EWdd ĨƵŶĚĞĚͿ
ŝďĞƌ dLJƉĞƐ͗
;EŽƚĞͲ ůů ĨŝďĞƌƐ ƚĞƐƚĞĚ Ăƚ ͘Ϯϱй ĂŶĚ ͘ϱϬй ďLJ
ǀŽůƵŵĞ ŽĨ ŵŽƌƚĂƌͿ
•ΎELJĐŽŶ'Ͳ EĂŶŽ ;ƌĞĐLJĐůĞĚ ĐĂƌƉĞƚ ĨŝďĞƌƐͿ
•WŽůLJ ǀŝŶLJů ůĐŽŚŽů ŝďĞƌƐ ;Ws Ϳ
o Z^ϳͲ ϲŵŵ
o Z^ϭϱͲ ϴŵŵ
o Z^ϭϱͲ ϴŵŵ
•ŽŶƚƌŽů ϮϬϬϬͲ ϲŵŵ; ϭϬϬй DƵůƚŝĨŝůĂŵĞŶƚ
ELJůŽŶͿ
•ΎΏ'ŽĂƚ ,ĂŝƌͲ ǀĂƌLJ ůĞŶŐƚŚ
•ΎΏ,ŽƌƐĞ ,ĂŝƌͲ ǀĂƌLJ ůĞŶŐƚŚ
•ΎΏŽƌŶƐŝůŬ ŝďĞƌƐͲǀĂƌLJ ůĞŶŐƚŚ
Ύ^ƵƐƚĂŝŶĂďůĞ ĨŝďĞƌƐ͕ ΏKƌŐĂŶŝĐ ŝďĞƌƐ
ϰϵ
ŝďĞƌͲƌĞŝŶĨŽƌĐĞĚ ŵŽƌƚĂƌ͗ ĂƌŐĞƌ
ĞdžƉĞƌŝŵĞŶƚĂů ƉƌŽŐƌĂŵ ;EWdd ĨƵŶĚĞĚͿ
ELJĐŽŶ' EĂŶŽ Z^ϳͲ Ϭ͘Ϯϱ ŝŶ Z^ϭϱͲ Ϭ͘ϯϭ ŝŶ ŽŶƚƌŽůϮϬϬϬͲ Ϭ͘Ϯϱ ŝŶ
'ŽĂƚ ,Ăŝƌ ΕϮ͘ϰϱ ŝŶ ,ŽƌƐĞ ,Ăŝƌ Εϯ͘Ϯϰ ŝŶ ŽƌŶ ƐŝůŬ
ŝďĞƌͲƌĞŝŶĨŽƌĐĞĚ ŵŽƌƚĂƌ͗ ĂƌŐĞƌ
ĞdžƉĞƌŝŵĞŶƚĂů ƉƌŽŐƌĂŵ ;EWdd ĨƵŶĚĞĚͿ
• ϴϬ ŵŝdžƚƵƌĞƐ
• ϳ ƚLJƉĞƐ ŽĨ ƚĞƐƚƐ
• tŽƌŬĂďŝůŝƚLJ ;ĨůŽǁ ƌĂƚĞͿ
• tĂƚĞƌ ƉĞƌŵĞĂďŝůŝƚLJ
• ŽŵƉƌĞƐƐŝǀĞ ^ƚƌĞŶŐƚŚ ŽĨ DŽƌƚĂƌ
• ŽŵƉƌĞƐƐŝǀĞ ƐƚƌĞŶŐƚŚ ŽĨ DĂƐŽŶƌLJ WƌŝƐŵƐ
• ůĞdžƵƌĂů ^ƚƌĞŶŐƚŚ ŽĨ DŽƌƚĂƌ ;ƐŵĂůů ƐƉĞĐŝŵĞŶ ƚĞƐƚŝŶŐͿ
• ŽŶĚ ^ƚƌĞŶŐƚŚ ŽĨ ϱͲƵŶŝƚͲƐƚĂĐŬ DĂƐŽŶƌLJ WƌŝƐŵƐ
• ^ŚĞĂƌ ŽŶĚ ^ƚƌĞŶŐƚŚ dĞƐƚ
сϮϰϬϬ ƐƉĞĐŝŵĞŶƐ
ϱϬ
ϱϭ
ůĞdžƵƌĂů DŽƌƚĂƌ dĞƐƚ ƉƉĂƌĂƚƵƐ ĂŶĚ ^ƉĞĐŝŵĞŶ
;^ŽƵƌĐĞ͗ ƌĚĂĐŬLJ ϮϬϬϴͿ
dĞƐƚ ^Ğƚ ƵƉ ĨŽƌ ĚĞƚĞƌŵŝŶĂƚŝŽŶ ŽĨ ƐŚĞĂƌ
ďŽŶĚ ƐƚƌĞŶŐƚŚ IJϬ
;^ŽƵƌĐĞ͗ ƵƌŽƉĞĂŶ ^ƚĂŶĚĂƌĚ WZE
ϮϬϱϮͲϯ WĂƌƚ ϯ ;ϭϵϵϲͿͿ
/ŶĐůŝŶĞĚ ƉůĂŶĞ ĂƉƉĂƌĂƚƵƐ ĨŽƌ ƚŚĞ ĚĞƚĞƌŵŝŶĂƚŝŽŶ ŽĨ
ƚŚĞ ĐŽĞĨĨŝĐŝĞŶƚ ŽĨ ŝŶƚĞƌŶĂů ĨƌŝĐƚŝŽŶ ;ȝͿ
WƵďůŝƐŚĞĚΎ ZĞƐƵůƚƐ
Ύ ƌŵǁŽŽĚ͕ ͕͘͘ ƌĚŽŐŵƵƐ͕ ͘ ĂŶĚ ,ĂŝĚĞƌ͕ ,͘ ;ϮϬϭϭͿ͘ ͞ĨĨĞĐƚ ŽĨ ŝďĞƌƐ ŽŶ ƚŚĞ
ůĞdžƵƌĂů ^ƚƌĞŶŐƚŚ ŽĨ DĂƐŽŶƌLJ DŽƌƚĂƌƐ͕͟ dŚĞ DĂƐŽŶƌLJ ^ŽĐŝĞƚLJ :ŽƵƌŶĂů͕ sŽů͘ Ϯϵ͕ EŽ͘
ϭ͕ ĞĐ͘ ϮϬϭϭ͕ ƉƉ͘ ϭϵͲϯϮ͘
ϱϮ
ϱϯ
ϱϰ
hŶͲWƵďůŝƐŚĞĚ ZĞƐƵůƚƐ͗ ůĞdžƵƌĂů
ĂŶĚ ^ŚĞĂƌ ŽŶĚͲƐƚƌĞŶŐƚŚ
ϱϱ
ŝďĞƌ ZĞŝŶĨŽƌĐĞĚ
ĞŵĞŶƚ ;ZͿ
ƚŽ ^ƚƌĞŶŐƚŚĞŶ
ŽŶĐƌĞƚĞ ^ůĂďƐ
ϮͲď
Z ^ƚƌĞŶŐƚŚĞŶŝŶŐ
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*Radik, M. and Erdogmus, E., Schafer, T. (2011). “Strengthening of Two-way reinforced concrete floor
slabs using polypropylene fiber reinforcement,” ASCE Journal of Materials in Civil Engineering,
Volume 23, Number 5, pp. 562-571, May 2011.
ϱϳ
0
50
100
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Erdogmus sapienza-may2015

  • 1. ,ŝƐƚŽƌŝĐĂů ^ƚƌƵĐƚƵƌĞƐ͛ ƐƐĞƐƐŵĞŶƚ ĂŶĚ ZĞŚĂďŝůŝƚĂƚŝŽŶ ;,ŝ^ ZͿ ĐĞ ƌĚŽŐŵƵƐ͕ WŚ͕ W ƐƐŽĐŝĂƚĞ WƌŽĨĞƐƐŽƌ ƵƌŚĂŵ ^ĐŚŽŽů ŽĨ ƌĐŚŝƚĞĐƚƵƌĂů ŶŐŝŶĞĞƌŝŶŐ Θ ŽŶƐƚƌƵĐƚŝŽŶ hŶŝǀĞƌƐŝƚLJ ŽĨ EĞďƌĂƐŬĂͲŝŶĐŽůŶ ;KŵĂŚĂ ĂŵƉƵƐͿ ZƵŵĞůŝ ,ŝƐĂƌı͕ øƐƚĂŶďƵů͕ dƺƌŬŝLJĞ
  • 2. ,ŝ^ Z͗ ,ŝƐƚŽƌŝĐĂů ^ƚƌƵĐƚƵƌĞƐ͛ ƐƐĞƐƐŵĞŶƚ Θ ZĞŚĂďŝůŝƚĂƚŝŽŶ • EŽŶͲĚĞƐƚƌƵĐƚŝǀĞ ĞǀĂůƵĂƚŝŽŶ ;EͿ ŽĨ ,ŝƐƚŽƌŝĐĂů ^ƚƌƵĐƚƵƌĞƐ͗ • džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐ͕ • 'ƌŽƵŶĚ WĞŶĞƚƌĂƚŝŶŐ ZĂĚĂƌ ;'WZͿ͕ • /ŵƉĂĐƚ ĐŚŽ ;/Ϳ͕ • ŝďĞƌƐĐŽƉĞ ŽƌĞƐĐŽƉLJ͕ /ŶĨƌĂƌĞĚ͕ • hůƚƌĂƐŽŶŝĐ dĞƐƚŝŶŐ • džƉĞƌŝŵĞŶƚĂůůLJ sĂůŝĚĂƚĞĚ ŝŶŝƚĞ ůĞŵĞŶƚ DŽĚĞůŝŶŐ ;DͿ ŽĨ ĐŽŵƉůĞdž ŵĂƐŽŶƌLJ ƐƚƌƵĐƚƵƌĞƐ • ŝďĞƌͲƌĞŝŶĨŽƌĐĞĚ ĐĞŵĞŶƚƐ ;ZͿ ĨŽƌ ŵĂƐŽŶƌLJ ĂŶĚ ĐŽŶĐƌĞƚĞ ƌĞƚƌŽĨŝƚ ĂƉƉůŝĐĂƚŝŽŶƐ Ϯ NC_ACol4_Heel Drop FRF_Real Plot 0.00E+00 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06 3.00E-06 3.50E-06 4.00E-06 4.50E-06 0 5 10 15 20 25 30 35 40 45 50 Frequency (Hz) Mag(g/N) A1 A2 A3 A4 A5 A6 A7 ϭ Ϯ
  • 3. ϯ ,ŝ^ Z͗ ,ŝƐƚŽƌŝĐĂů ^ƚƌƵĐƚƵƌĞƐ͛ ƐƐĞƐƐŵĞŶƚ Θ ZĞŚĂďŝůŝƚĂƚŝŽŶ • dLJƉĞƐ ŽĨ ŚŝƐƚŽƌŝĐĂů ƐƚƌƵĐƚƵƌĞƐ͗ • ƌĐŚĞŽůŽŐŝĐĂů ^ŝƚĞƐ͕ ŶĐŝĞŶƚ ZŽŵĂŶ ^ƚƌƵĐƚƵƌĞƐ ;dŚĞ ĨĂŵŽƵƐ ͞dĞŵƉůĞ͟ WƌŽũĞĐƚͿ • 'ŽƚŚŝĐ ĂƚŚĞĚƌĂůƐ ;EĂƚŝŽŶĂů ĂƚŚĞĚƌĂů ŝŶ ͕ /ƚĂůŝĂŶ ĂŶĚ ƌĞŶĐŚ ĐĂƚŚĞĚƌĂůƐ͕ /ŐůĞƐŝĂ ^ĂŶ :ŽƐĞ ŝŶ WƵĞƌƚŽ ZŝĐŽͿ • 'ƵĂƐƚĂǀŝŶŽ ŽŵĞƐ ĂŶĚ sĂƵůƚƐ ;EĞďƌĂƐŬĂ ^ƚĂƚĞ ĂƉŝƚŽůͿ • DĂƐŽŶƌLJ ĂŶĚ ŽŶĐƌĞƚĞ ,ŝƐƚŽƌŝĐ ƌĐŚ ƌŝĚŐĞƐ ŝŶ h͘^͘
  • 5. ϱ 1) Seismic accelerometers placed on the structure collect data 0 2 4 6 8 10 12 14 16 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 w-Frequency (Hz) MagH(in/k) 4) Modal analysis and determination of the characteristics of the structure 1/c 1/k 5) FEM updating and verification of mechanical properties 2) System excited 3) Dynamic signal analyzer processes data
  • 6. ϲ DĞƚŚŽĚ ĂƉƉůŝĞĚ ŽŶ ǀĂƌŝŽƵƐ ŚŝƐƚŽƌŝĐĂů ƐƚƌƵĐƚƵƌĞƐ͗ 'ŽƚŚŝĐ National Cathedral, U.S. 7 6 5 A4 3 2 1 Col 1 Col 4 Col 7 NC_ACol4_Heel Drop FRF_Real Plot 0.00E+00 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06 3.00E-06 3.50E-06 4.00E-06 4.50E-06 0 5 10 15 20 25 30 35 40 45 50 Frequency (Hz) Mag(g/N) A1 A2 A3 A4 A5 A6 A7
  • 7. ϳ Cathedral in Auxerre, France Santa Maria Novella, Florence, Italy 000000000 000000000 000000 00 0000 000000000 00000000 00 00 0000000000000000000000 000000 00000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000 0000 00 00 00000000000000 00 0000 00 0000000000000000000 00 000000 000 0000 00 000000000000 00 00 000000 000 000 000000 000 0000 00 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 AUX Hammer Impact on Nave5 FRF from sensors on Nave 4, 5 6 0.00E+00 1.00E-06 2.00E-06 3.00E-06 4.00E-06 5.00E-06 6.00E-06 0 5 10 15 20 25 30 35 40 45 50 Frequency (Hz) Mag(g/N) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 N4 N5 N6 000000000000000000COH N5 DĞƚŚŽĚ ĂƉƉůŝĞĚ ŽŶ ǀĂƌŝŽƵƐ ŚŝƐƚŽƌŝĐĂů ƐƚƌƵĐƚƵƌĞƐ͗ 'ŽƚŚŝĐ
  • 8. ϴ • ĂƚĞ͗ ϭϵϬϬ͛Ɛ • WůĂĐĞ͗ ŝŶĐŽůŶ͕ EĞďƌĂƐŬĂ • DĂƐƚĞƌ͗ 'ƵĂƐƚĂǀŝŶŽ͕ :ƌ͘ DĞƚŚŽĚ ĂƉƉůŝĞĚ ŽŶ ǀĂƌŝŽƵƐ ŚŝƐƚŽƌŝĐĂů ƐƚƌƵĐƚƵƌĞƐ͗ 'ƵĂƐƚĂǀŝŶŽ
  • 9. ϵ DŽĚĞů ŽŵĞ 'ŽĂůƐ͗ ϭͿhŶĚĞƌƐƚĂŶĚ ͞'ƵĂƐƚĂǀŝŶŽ͟ ŽŶƐƚƌƵĐƚŝŽŶ dĞĐŚŶŝƋƵĞ ϮͿ/ŵƉƌŽǀĞŵĞŶƚƐ ŝŶ Ed ŵĞƚŚŽĚ
  • 11. ZƵŝŶŽƵƐ ĂŶĐŝĞŶƚ ZŽŵĂŶ ĐŝƚLJ ŽĨ ŶƚŝŽĐŚ ĂĚ ƌĂŐƵŵ ŝŶ ƉƌĞƐĞŶƚ ĚĂLJ 'ĂnjŝƉĂƐĂ͕ dƵƌŬĞLJ ϭϭ /ŵƉĞƌŝĂů dĞŵƉůĞ ŽůŽŶŶĂĚĞĚ ^ƚƌĞĞƚ 'ƌĞĂƚ ĂƚŚ 'LJŵŶĂƐŝƵŵͬWŽŽů /ŶǀĞƐƚŝŐĂƚŝŽŶ ŽĨ ĂŶ ŶĐŝĞŶƚ ZŽŵĂŶ ŝƚLJ ŝŶ dƵƌŬĞLJ
  • 12. dŚĞ dĞĂŵ • /ŶƚĞƌĚŝƐĐŝƉůŝŶĂƌLJ ƉƌŽũĞĐƚ ďĞŐĂŶ ŝŶ ϮϬϬϱ • ƌ͘ ĐĞ ƌĚŽŐŵƵƐ͕ hE͗ ƌĐŚŝƚĞĐƚƵƌĂů ŶŐŝŶĞĞƌŝŶŐ • ƌ͘ DŝĐŚĂĞů ,ŽĨĨ͕ hE͗ ƌĐŚĂĞŽůŽŐLJͬ ƌƚ ,ŝƐƚŽƌLJ • ƌ͘ ZŚLJƐ dŽǁŶƐĞŶĚ͕ ůĂƌŬ hŶŝǀĞƌƐŝƚLJ͗ 'ƌĞĞŬ ƌĐŚŝƚĞĐƚƵƌĞ Θ ůĂƐƐŝĐƐ • ƌ͘ ŝƌŽů ĂŶ ;ϮϬϭϭͲƉƌĞƐĞŶƚͿ͕ ƌnjƵƌƵŵ ƚĂƚƵƌŬ hŶŝǀĞƌƐŝƚLJ͕ dƵƌŬĞLJ͗ ƌĐŚĞŽůŽŐLJ • :ŽƐŚƵĂ ƌĞĞĚůĂŶĚ͕ t: Θ ;EĞǁ͊Ϳ ƌĂŶŬ DĂƚĞƌŽ͕ hWĞŶŶ͗ ŽŶƐĞƌǀĂƚŝŽŶ ϭϮ dƌƵůLJ ŝŶƚĞƌĚŝƐĐŝƉůŝŶĂƌLJ ĨƌŽŵ ƚŚĞ ƐƚĂƌƚ ŽĨ ƚŚĞ ƉƌŽũĞĐƚ͊ ŽŶƐĞƌǀĂƚŝŽŶ
  • 15. /ŵƉĞƌŝĂů dĞŵƉůĞ͗ WƌŽũĞĐƚ 'ŽĂůƐ • dŽ ƉĂƌƚŝĂůůLJ ƌĞĐŽŶƐƚƌƵĐƚ ƚŚĞ ƚĞŵƉůĞ ƚŽ ƐŚŽǁͲ ĐĂƐĞ ŝƚƐ ŽƌŝŐŝŶĂů ĚĞƐŝŐŶ • dŽ ĞƐƚĂďůŝƐŚ Ă ǁĞůůͲĚŽĐƵŵĞŶƚĞĚ ƉƌŽĐĞƐƐ ĨŽƌ ƐƵĐŚ ĂŶ ĞdžƚĞŶƐŝǀĞ Θ ƵŶŝƋƵĞůLJ ŝŶƚĞƌĚŝƐĐŝƉůŝŶĂƌLJ ƌĞĐŽŶƐƚƌƵĐƚŝŽŶ ƉƌŽũĞĐƚ ͞ ƌĐŚĞŽůŽŐŝĐĂů ŶŐŝŶĞĞƌŝŶŐ͟ ϭϱ
  • 17. DĂƚĞƌŝĂů ŚĂƌĂĐƚĞƌŝƐƚŝĐƐ͗ WĞƚƌŽŐƌĂƉŚŝĐ ŶĂůLJƐĞƐ • ϴ ƐĂŵƉůĞƐ ĂƌĞ ĂŶĂůLJnjĞĚ • DĂƚĞƌŝĂů ŝƐ ĚĞŶƐĞ ŵĂƌďůĞ ;ŵĞƚĂŵŽƌƉŚŽƐĞĚ ůŝŵĞƐƚŽŶĞͿ • ϯ ǀĂƌŝĞƚŝĞƐ ĂƌĞ ŝĚĞŶƚŝĨŝĞĚ • dƌĂĐĞ ĂŵŽƵŶƚƐ ŽĨ ƉLJƌŝƚĞ ;ŝƌŽŶ ƐƵůĨŝĚĞͿ ĐƌLJƐƚĂůƐ ƐŝŵŝůĂƌ ŝŶ ƐŝnjĞ ƚŽ ƚŚĞ ĐĂůĐŝƚĞ ĐƌLJƐƚĂůƐ ǁĞƌĞ ĂůƐŽ ŽďƐĞƌǀĞĚ͘ ϭϳ dŚŝŶͲƐĞĐƚŝŽŶ ŵŝĐƌŽŐƌĂƉŚ ƐŚŽǁŝŶŐ ƚŚĞ ƚĞdžƚƵƌĞ ŽĨ ƚŚĞ ŵĂƌďůĞ ƵŶĚĞƌ ĐƌŽƐƐͲ ƉŽůĂƌŝnjĞĚ ůŝŐŚƚ͘
  • 18. DĂƚĞƌŝĂů dĞƐƚŝŶŐ • ŽŵƉƌĞƐƐŝŽŶ ƚĞƐƚŝŶŐ ŽĨ ŵĂƌďůĞ • DĂƌďůĞ ĨƌŽŵ ƐŝƚĞ ĂŶĚ ĨƌŽŵ Ă ŶĞĂƌďLJ ƋƵĂƌƌLJ ϭϴ ^ŽƵƌĐĞ hůƚŝŵĂƚĞ ŽŵƉƌĞƐƐŝǀĞ ^ƚƌĞƐƐ ;ı ¡ Ϳ DŽĚƵůƵƐ ŽĨ ůĂƐƚŝĐŝƚLJ ;Ϳ ƉƐŝ DWĂ ƉƐŝ DWĂ ĂŵďĂƐ ;ϭϵϵϮͿ ϭϭ͕ϮϴϬ ϳϳ͘ϴ ϯ͕ϯϯϲ͕ϬϬϬ Ϯϯ͕ϬϬϬ ŽƵƌŬŽƵůŝƐ Θ WĂƐŝŽƵ ;ϮϬϬϵͿ ϳ͕ϵϴϬͲϭϭ͕ϲϬϬ ϱϬͲϴϬ ϳ͕ϮϱϮ͕ϬϬϬ Ͳ ϭϮ͕Ϯϱϲ͕ϬϬϬ ϱϬ͕ϬϬϬ Ͳ ϴϰ͕ϱϬϬ ĞĞƌ Ğƚ͘Ăů͘ ;ϮϬϬϵͿ ϭϴ͕ϬϬϬ ϭϮϰ ϴ͕ϬϬϬ͕ϬϬϬ ϱϱ͕ϭϳϬ ŽƵƌŬŽƵůŝƐ Ğƚ Ăů͘ ;ϮϬϭϬͿ Ͳ Ͳ ϭϭ͕ϲϬϯ͕ϬϬϬ ϴϬ͕ϬϬϬ ŽƵƌŬŽƵůŝƐ ĂŶĚ WĂƐŝŽƵ ;ϮϬϭϱͿ Ͳ Ͳ ϭϬ͕ϵϮϭ͕ϬϬϬ ϳϱ͕ϯϬϬ dĞŵƉůĞ ŽĨ ŶƚŝŽĐŚ DĂƌďůĞ ϭϮ͕ϬϴϬ ϴϯ͘ϯ ϱ͕ϮϬϯ͕ϬϬϬ ϯϱ͕ϴϳϬ YƵĂƌƌLJ DĂƌďůĞ ϵ͕ϳϳϬ ϲϳ͘ϰ ϴ͕ϳϴϬ͕ϬϬϬ ϲϬ͕ϱϬϬ
  • 19. ϭϵ ,ĂŶĚŬͲ ĂƐĞĚ ŽŶ /KDK^Ύ Ύ/ŶƚĞƌŶĂƚŝŽŶĂů ŽƵŶĐŝů ŽŶ DŽŶƵŵĞŶƚƐ ĂŶĚ ^ŝƚĞƐ
  • 21. džƚĞƌŶĂů ZĂƚŝŶŐ ĨŽƌ DĂƌďůĞ ůŽĐŬƐ • ǀĞƌĂŐĞ ĐĞůůĂ ďůŽĐŬ ĚŝŵĞŶƐŝŽŶƐ͗ ϭ͘ϱϰ ŵ dž Ϭ͘ϱϯ ŵ dž Ϭ͘ϱϭ ŵ Ϯϭ džƚĞƌŶĂů ŽŶĚŝƚŝŽŶ ZĂƚŝŶŐ ĞƐĐƌŝƉƚŝŽŶ ůŽĐŬƐ ϭ EŽ ŵŝƐƐŝŶŐ ƉĂƌƚƐ͕ ŵŝŶŝŵĂů ĐŚŝƉƉŝŶŐ Ăƚ ĐŽƌŶĞƌƐ͘ ŶLJ ĐƌĂĐŬƐ ĂƌĞ ƚŚŝŶ ĂŶĚ ďĂƌĞůLJ ǀŝƐŝďůĞ͘ EĞǁ ŵĂƌďůĞ ďůŽĐŬƐ Ϯ ^ŽŵĞ ŵŝƐƐŝŶŐ ƉĂƌƚƐ͕ ďƵƚ ůĞƐƐ ƚŚĂŶ ϭϬй ŽĨ ƚŚĞ ďůŽĐŬ͘ ^ŽŵĞ ƐƵƌĨĂĐĞ ĐƌĂĐŬƐ͘ dϬϭϭ͕ dϬϲϱ͕ dϬϳϭ͕ dϱϱϵ ϯ WƌĞƐĞŶĐĞ ŽĨ ŵŝƐƐŝŶŐ ƉĂƌƚƐ ;ϭϬй Žƌ ŵŽƌĞͿ ĂŶĚͬŽƌ ƐĞǀĞƌĞ͕ ĚĞĞƉ ƐƚƌƵĐƚƵƌĂů ĐƌĂĐŬƐ͘ dϬϲϴ͕ dϬϭϰ /ŶƚĞƌŶĂů ǀŽŝĚƐ͍
  • 22. /ŵƉĂĐƚͲĐŚŽ EŽŶĚĞƐƚƌƵĐƚŝǀĞ dĞƐƚŝŶŐ • ĂĐŬŐƌŽƵŶĚ ŽŶ DĞƚŚŽĚ • ĞǀĞůŽƉĞĚ ŝŶ ϭϵϴϬ͛Ɛ͘ • ǀĂůƵĂƚŝŽŶ ŽĨ ŝŶƚĞƌŶĂů ĐŽŶĚŝƚŝŽŶ ŽĨ ƐƚƌƵĐƚƵƌĂů ĐŽŵƉŽŶĞŶƚƐ • ч ϯ͘ϭй ĞƌƌŽƌ ĨŽƌ ƚŚŝĐŬŶĞƐƐ ŵĞĂƐƵƌĞŵĞŶƚƐ ŽĨ Ϭ͘Ϯ ŵͲƚŚŝĐŬ ƉĂǀĞŵĞŶƚ ;^ĂŶƐĂůŽŶĞ ϭϵϵϳͿ͘ • dĞŵƉůĞ WƌŽũĞĐƚ • Ăď ǀĂůŝĚĂƚŝŽŶ Θ ŝŶ ƐŝƚƵ ƚĞƐƚŝŶŐ͗ ϮϬϭϭͲƉƌĞƐĞŶƚ • hƐĞĚ ĨŽƌ ĂƐƐĞƐƐŵĞŶƚ ŽĨ ŝŶƚĞƌŝŽƌ ĐŽŶĚŝƚŝŽŶ ŽĨ ĞdžĐĂǀĂƚĞĚ ƚĞŵƉůĞ ďůŽĐŬƐ ϮϮ
  • 24. Ăď sĂůŝĚĂƚŝŽŶ • ĂƐƚ ŵŽƌƚĂƌ ďůŽĐŬƐ͗ Ϭ͘ϴϱ ŵ dž Ϭ͘ϯϲ ŵ dž Ϭ͘ϯϰ ŵ Ϯϰ Block Block Face Tested Percent Error Relative Amplitude (relative to amplitude of 3rd or 4th mode) 8.89 cm x 8.89 cm square void Top 4. 6 % 5.2% 1.38 1.08 1.14 Side 5. 8 % 0.78 8.89 cm diameter void Top 2. 0 % 2.2% 1.07 1.09 Side 2. 4 % 1.11 3.81 cm x 3.81 cm square void Top 1. 4 % 2.3% 0.68 1.24 Side 3. 2 % 1.80
  • 25. džĂŵƉůĞƐ ŽĨ DĂƌďůĞ ůŽĐŬ ZĞƐƵůƚƐ Ϯϱ Block AT068, External Condition Rating = 3 Block AT071, External Condition Rating = 2 New marble block, External Condition Rating = 1 AT014, External Condition Rating = 3
  • 26. WƌĞƐĞƌǀĂƚŝŽŶ ŽĨ ůŽĐŬƐ • ůŽĐŬ ĐůĞĂŶŝŶŐ ƉƌŽĐĞƐƐ • dŚƌŽƵŐŚ ĐŽŶĚŝƚŝŽŶ ĂƐƐĞƐƐŵĞŶƚ͕ ůŝĐŚĞŶ ĂŶĚ ĂůŐĂĞ ĂƌĞ ŵŽƐƚ ĐŽŵŵŽŶ ĨŽƌŵƐ ŽĨ ĚĞƚĞƌŝŽƌĂƚŝŽŶ ŽŶ ƐŝƚĞ • ůŽĐŬƐ ǁĞƌĞ ƐƵďũĞĐƚ ƚŽ ǀĂƌŝŽƵƐ ƉĂƚƚĞƌŶƐ ŽĨ ŚĞĂƚ ƚƌĞĂƚŵĞŶƚ ĂŶĚ ĐůĞĂŶŝŶŐ Ϯϲ ^ƵĐĐĞƐƐĨƵů ĐůĞĂŶŝŶŐ ƚƌĞĂƚŵĞŶƚ hŶƐƵĐĐĞƐƐĨƵů ĐůĞĂŶŝŶŐ ƚƌĞĂƚŵĞŶƚ
  • 27. ^ƵĐĐĞƐƐĨƵů ƚƌĞĂƚŵĞŶƚ ƉƌŽĐĞƐƐ ƉŚĂƐĞƐ • WƌĞͲǁĞƚ ǁŝƚŚ ůŽǁ ĐŽŶĐĞŶƚƌĂƚŝŽŶ ƐŽůƵƚŝŽŶ • ĞĞƉ ǁĞƚ ƵƐŝŶŐ ĚĂŵƉ ĐůŽƚŚ • ŽǀĞƌ ǁŝƚŚ ƚĂƌƉ ƵŶĚĞƌ ĂŵďŝĞŶƚ ŚĞĂƚ • ƌƵƐŚ ůŝŐŚƚůLJ ĂĨƚĞƌ ƚĂƌƉ ƌĞŵŽǀĂů Ϯϳ
  • 28. ϯ ůŽĐŬ DŽĚĞůŝŶŐ • sŝƐƵĂůŝnjĂƚŝŽŶ ƚŽŽů ĂŶĚ ĂƐƐŝƐƚ ƚŽ D ƐƚƌƵĐƚƵƌĂů ĂŶĂůLJƐŝƐ Ϯϴ
  • 29. Ϯϵ KƚŚĞƌ EŽŶͲĞƐƚƌƵĐƚŝǀĞ dĞƐƚŝŶŐ • 'ƌŽƵŶĚ ƉĞŶĞƚƌĂƚŝŶŐ ƌĂĚĂƌ ;'WZͿ • ŝďĞƌƐĐŽƉĞ ƌĞŵŽƚĞ ŝŶƐƉĞĐƚŝŽŶ
  • 30. ^ƵŵŵĞƌ ϮϬϭϰ͗ ŽůƵŵŶ ZĂŝƐŝŶŐ ƌ͘ ŝƌŽů ĂŶ Θ ƌ͘ ĐĞ ƌĚŽŒŵƵƔ ϯϬ
  • 31. KŶĞ ůĂƐƚ ůŽŽŬ Ăƚ ŽƵƌ ƐŝƚĞ ŝŶ ϮϬϭϰ ϯϭ
  • 32. ZĞƐĞĂƌĐŚ ŝŶ WƌŽŐƌĞƐƐͬ^ĞĞŬŝŶŐ /ŶƉƵƚ͙ • ZŽŵĂŶ ŽƌƵŵ ĂŶĂƐƚLJůŽƐŝƐ ŝŶĨŽƌŵĂƚŝŽŶ͗ • dŚĞ ƚĞĂŵ͍ • tŚĞƌĞ ŝƐ ƚŚĞ ŝŶĨŽƌŵĂƚŝŽŶ ƉƵďůŝƐŚĞĚ͍ • dĞĐŚŶŝƋƵĞƐ ƵƐĞĚ ϯϮ
  • 33. EĞǁ͗ /ŐůĞƐŝĂ ^ĂŶ :ŽƐĞ ;/^:Ϳ͕ WƵĞƌƚŽ ZŝĐŽ • ϭϲƚŚͲĐĞŶƚƵƌLJ ^ƉĂŶŝƐŚ 'ŽƚŚŝĐ ĂƌĐŚŝƚĞĐƚƵƌĞ • ŽŶƐƚƌƵĐƚŝŽŶ͗ ϭϱϯϮ ƚŽ ϭϳϯϱ ďLJ ƚŚĞ ŽŵŝŶŝĐĂŶ KƌĚĞƌ ϯϯ WůĂŶŶĞĚ ƐƐĞƐƐŵĞŶƚ͗ •džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐ ;D Ϳ •ŝŶŝƚĞ ůĞŵĞŶƚ DŽĚĞůŝŶŐ ;DͿ
  • 34. • hŶŝƋƵĞ ĂŶĚ ĐŽŵƉůĞdž ƐƚƌƵĐƚƵƌĞ ϯϰ EĞǁ͗ ^ĂŶ :ŽƐĞ /ŐůĞƐŝĂ͕ WƵĞƌƚŽ ZŝĐŽ
  • 35. džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐ Θ D • ZĞƐĞĂƌĐŚ ŝŶ ƉƌŽŐƌĞƐƐ͗ ϭͿ /ŶͲƐŝƚƵ ĂƐƐĞƐƐŵĞŶƚ ĚŽŶ Ăƚ ϯ ůŽĐĂƚŝŽŶƐ͘ ϮͿ DͬD ŝŶ ƉƌŽŐƌĞƐƐ͘ ϯͿ WƌĞůŝŵŝŶĂƌLJ ƌĞƉŽƌƚ ƐƵďŵŝƚƚĞĚ ϯϱ
  • 36. džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐ Θ D • ZĞƐĞĂƌĐŚ ŝŶ ƉƌŽŐƌĞƐƐ͗ ϭͿ /ŶͲƐŝƚƵ ĂƐƐĞƐƐŵĞŶƚ ĚŽŶ Ăƚ ϯ ůŽĐĂƚŝŽŶƐ͘ ϮͿ DͬD ŝŶ ƉƌŽŐƌĞƐƐ͘ ϯͿ WƌĞůŝŵŝŶĂƌLJ ƌĞƉŽƌƚ ƐƵďŵŝƚƚĞĚ ϯϲ
  • 37. džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐ Θ D • ZĞƐĞĂƌĐŚ ŝŶ ƉƌŽŐƌĞƐƐ͗ ϭͿ /ŶͲƐŝƚƵ ĂƐƐĞƐƐŵĞŶƚ ĚŽŶ Ăƚ ϯ ůŽĐĂƚŝŽŶƐ͘ ϮͿ DͬD ŝŶ ƉƌŽŐƌĞƐƐ͘ ϯͿ WƌĞůŝŵŝŶĂƌLJ ƌĞƉŽƌƚ ƐƵďŵŝƚƚĞĚ ϯϳ
  • 38. džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐ Θ D • DĂŝŶ ǀĂƵůƚ͗ ƵŶĚĂŵĞŶƚĂů ĨƌĞƋƵĞŶĐLJ ŵĂƚĐŚ Ăƚ Ϯϴ ,nj ďĞƚǁĞĞŶ D ĂŶĚ D͕ ƵƐŝŶŐ ǀĂůŝĚĂƚĞĚ /ŶĚŝĂŶĂ ŝŵĞƐƚŽŶĞ ƉƌŽƉĞƌƚŝĞƐ ϯϴ
  • 39. ϯϵ D Θ D͗ DĂŝŶ sĂƵůƚ EŽƌƚŚ ,ĂůĨ ;ůĞĨƚͿ ĂŶĚ ^ŽƵƚŚ ŚĂůĨ ;ƌŝŐŚƚͿ ƉƌĞƐĞŶƚ ĚŝĨĨĞƌĞŶĐĞƐ ĚƵĞ ƚŽ ǀĂƌLJŝŶŐ ĐŽŶĚŝƚŝŽŶ ĂŶĚ ŝŶƐƵůĂƚŝŽŶ͘ ƵƌƚŚĞƌ ƌĞĨŝŶĞŵĞŶƚƐ ŶĞĞĚĞĚ͘
  • 42. ϰϮ ZĞŚĂďŝůŝƚĂƚŝŽŶ͗ ŝďĞƌ ZĞŝŶĨŽƌĐĞĚ DŽƌƚĂƌ ^ƵĐĐĞƐƐĨƵů ƌĞŚĂďŝůŝƚĂƚŝŽŶ DĂƚĞƌŝĂů ĐŽŵƉĂƚŝďŝůŝƚLJ ZĞƉĂŝƌ ĚƵƌĂďŝůŝƚLJ ŽŶŐͲƚĞƌŵ ŵĂŝŶƚĞŶĂŶĐĞ ŝďĞƌ dLJƉĞƐ ^ƚĞĞů 'ůĂƐƐ ^LJŶƚŚĞƚŝĐ KƌŐĂŶŝĐ
  • 43. ϰϯ DĂĐƌŽ ĨŝďĞƌƐ Ϭ͘ϱ ƚŽ Ϯ͘ϱ ŝŶĐŚĞƐ DŝĐƌŽ ĨŝďĞƌƐ ĞƐƐ ƚŚĂŶ Ϭ͘ϱ ŝŶĐŚĞƐ ŝĂŵĞƚĞƌ ǀĂƌŝĞƐ ZĞŚĂďŝůŝƚĂƚŝŽŶ͗ ŝďĞƌ ZĞŝŶĨŽƌĐĞĚ DŽƌƚĂƌ
  • 44. ŝďĞƌͲƌĞŝŶĨŽƌĐĞĚ ŵŽƌƚĂƌ͗ WŝůŽƚ ϰϰ DŽƌƚĂƌ ŵŝdž WƌĞͲďůĞŶĚĞĚ WŽƌƚůĂŶĚ ĐĞŵĞŶƚ͕ ůŝŵĞ͕ ĂŶĚ ƐĂŶĚ ^dD ϮϳϬ W dLJƉĞ E ŵŽƌƚĂƌ ZĞŝŶĨŽƌĐŝŶŐ ĨŝďĞƌƐ WŽůLJǀŝŶLJů ĂůĐŽŚŽů ;Ws Ϳ ,ŝŐŚ ͕ ƚĞŶƐŝůĞ ƐƚƌĞŶŐƚŚ͕ ďŽŶĚ ƐƚƌĞŶŐƚŚ ůŬĂůŝ ƌĞƐŝƐƚĂŶƚ
  • 45. ϰϱ
  • 46. ϰϲ WƵďůŝƐŚĞĚΎ ZĞƐƵůƚƐ Ύ^ŬŽƵƌƵƉ͕ ͘ E͕͘ ĂŶĚ ƌĚŽŐŵƵƐ͕ ͘ ;ϮϬϭϬͿ͘ ͞DĞĐŚĂŶŝĐĂů ŚĂƌĂĐƚĞƌŝƐƚŝĐƐ ŽĨ Ws ŝďĞƌͲ ZĞŝŶĨŽƌĐĞĚ W DŽƌƚĂƌƐ ĨŽƌ DĂƐŽŶƌLJ ƉƉůŝĐĂƚŝŽŶƐ͟ / DĂƚĞƌŝĂůƐ :ŽƵƌŶĂů͕ sŽů͘ ϭϬϳ͕ :ĂŶƵĂƌLJͲ ĞďƌƵĂƌLJ ϮϬϭϬ͕ EŽ͘ϭ͕͘ ƉƉ ϭͲ ϵ͕ / ƉƵďůŝĐĂƚŝŽŶƐ͘
  • 47. ϰϳ ŝďĞƌͲƌĞŝŶĨŽƌĐĞĚ ŵŽƌƚĂƌ͗ ĂƌŐĞƌ ĞdžƉĞƌŝŵĞŶƚĂů ƉƌŽŐƌĂŵ ;EWdd ĨƵŶĚĞĚͿ ƌŝĐŬ dLJƉĞƐ͗ •^ƚĂŶĚĂƌĚ ůĂLJ ƌŝĐŬƐ •^ƚĂŶĚĂƌĚ ŽŶĐƌĞƚĞ ƌŝĐŬƐ ŝŶĚĞƌ dLJƉĞƐ͗ •dLJƉĞ E WŽƌƚůĂŶĚ ŝŵĞ ĂŶĚ ^ĂŶĚ WͲ Ϭϭ •EĂƚƵƌĂů ,LJĚƌĂƚĞĚ ŝŵĞ ;E,Ϳ ϯ͘ϱt ;ƌĂƚŝŽƐ͗ ϭ͗Ϯ͘ϱ Θ ϭ͗ϯͿ •EĂƚƵƌĂů ,LJĚƌĂƚĞĚ ŝŵĞ ;E,Ϳ ϱt ;ƌĂƚŝŽƐ͗ ϭ͗Ϯ͘ϱ Θ ϭ͗ϯͿ ;^ĂŶĚ ƵƐĞĚ ǁŝƚŚ ƚŚĞ E, ŝƐ ĂƉƉƌŽǀĞĚ ĂĐĐŽƌĚŝŶŐ ƚŽ ^dD ϭϰϰͲϬϯͿ
  • 48. ϰϴ ŝďĞƌͲƌĞŝŶĨŽƌĐĞĚ ŵŽƌƚĂƌ͗ ĂƌŐĞƌ ĞdžƉĞƌŝŵĞŶƚĂů ƉƌŽŐƌĂŵ ;EWdd ĨƵŶĚĞĚͿ ŝďĞƌ dLJƉĞƐ͗ ;EŽƚĞͲ ůů ĨŝďĞƌƐ ƚĞƐƚĞĚ Ăƚ ͘Ϯϱй ĂŶĚ ͘ϱϬй ďLJ ǀŽůƵŵĞ ŽĨ ŵŽƌƚĂƌͿ •ΎELJĐŽŶ'Ͳ EĂŶŽ ;ƌĞĐLJĐůĞĚ ĐĂƌƉĞƚ ĨŝďĞƌƐͿ •WŽůLJ ǀŝŶLJů ůĐŽŚŽů ŝďĞƌƐ ;Ws Ϳ o Z^ϳͲ ϲŵŵ o Z^ϭϱͲ ϴŵŵ o Z^ϭϱͲ ϴŵŵ •ŽŶƚƌŽů ϮϬϬϬͲ ϲŵŵ; ϭϬϬй DƵůƚŝĨŝůĂŵĞŶƚ ELJůŽŶͿ •ΎΏ'ŽĂƚ ,ĂŝƌͲ ǀĂƌLJ ůĞŶŐƚŚ •ΎΏ,ŽƌƐĞ ,ĂŝƌͲ ǀĂƌLJ ůĞŶŐƚŚ •ΎΏŽƌŶƐŝůŬ ŝďĞƌƐͲǀĂƌLJ ůĞŶŐƚŚ Ύ^ƵƐƚĂŝŶĂďůĞ ĨŝďĞƌƐ͕ ΏKƌŐĂŶŝĐ ŝďĞƌƐ
  • 49. ϰϵ ŝďĞƌͲƌĞŝŶĨŽƌĐĞĚ ŵŽƌƚĂƌ͗ ĂƌŐĞƌ ĞdžƉĞƌŝŵĞŶƚĂů ƉƌŽŐƌĂŵ ;EWdd ĨƵŶĚĞĚͿ ELJĐŽŶ' EĂŶŽ Z^ϳͲ Ϭ͘Ϯϱ ŝŶ Z^ϭϱͲ Ϭ͘ϯϭ ŝŶ ŽŶƚƌŽůϮϬϬϬͲ Ϭ͘Ϯϱ ŝŶ 'ŽĂƚ ,Ăŝƌ ΕϮ͘ϰϱ ŝŶ ,ŽƌƐĞ ,Ăŝƌ Εϯ͘Ϯϰ ŝŶ ŽƌŶ ƐŝůŬ
  • 50. ŝďĞƌͲƌĞŝŶĨŽƌĐĞĚ ŵŽƌƚĂƌ͗ ĂƌŐĞƌ ĞdžƉĞƌŝŵĞŶƚĂů ƉƌŽŐƌĂŵ ;EWdd ĨƵŶĚĞĚͿ • ϴϬ ŵŝdžƚƵƌĞƐ • ϳ ƚLJƉĞƐ ŽĨ ƚĞƐƚƐ • tŽƌŬĂďŝůŝƚLJ ;ĨůŽǁ ƌĂƚĞͿ • tĂƚĞƌ ƉĞƌŵĞĂďŝůŝƚLJ • ŽŵƉƌĞƐƐŝǀĞ ^ƚƌĞŶŐƚŚ ŽĨ DŽƌƚĂƌ • ŽŵƉƌĞƐƐŝǀĞ ƐƚƌĞŶŐƚŚ ŽĨ DĂƐŽŶƌLJ WƌŝƐŵƐ • ůĞdžƵƌĂů ^ƚƌĞŶŐƚŚ ŽĨ DŽƌƚĂƌ ;ƐŵĂůů ƐƉĞĐŝŵĞŶ ƚĞƐƚŝŶŐͿ • ŽŶĚ ^ƚƌĞŶŐƚŚ ŽĨ ϱͲƵŶŝƚͲƐƚĂĐŬ DĂƐŽŶƌLJ WƌŝƐŵƐ • ^ŚĞĂƌ ŽŶĚ ^ƚƌĞŶŐƚŚ dĞƐƚ сϮϰϬϬ ƐƉĞĐŝŵĞŶƐ ϱϬ
  • 51. ϱϭ ůĞdžƵƌĂů DŽƌƚĂƌ dĞƐƚ ƉƉĂƌĂƚƵƐ ĂŶĚ ^ƉĞĐŝŵĞŶ ;^ŽƵƌĐĞ͗ ƌĚĂĐŬLJ ϮϬϬϴͿ dĞƐƚ ^Ğƚ ƵƉ ĨŽƌ ĚĞƚĞƌŵŝŶĂƚŝŽŶ ŽĨ ƐŚĞĂƌ ďŽŶĚ ƐƚƌĞŶŐƚŚ IJϬ ;^ŽƵƌĐĞ͗ ƵƌŽƉĞĂŶ ^ƚĂŶĚĂƌĚ WZE ϮϬϱϮͲϯ WĂƌƚ ϯ ;ϭϵϵϲͿͿ /ŶĐůŝŶĞĚ ƉůĂŶĞ ĂƉƉĂƌĂƚƵƐ ĨŽƌ ƚŚĞ ĚĞƚĞƌŵŝŶĂƚŝŽŶ ŽĨ ƚŚĞ ĐŽĞĨĨŝĐŝĞŶƚ ŽĨ ŝŶƚĞƌŶĂů ĨƌŝĐƚŝŽŶ ;ȝͿ
  • 52. WƵďůŝƐŚĞĚΎ ZĞƐƵůƚƐ Ύ ƌŵǁŽŽĚ͕ ͕͘͘ ƌĚŽŐŵƵƐ͕ ͘ ĂŶĚ ,ĂŝĚĞƌ͕ ,͘ ;ϮϬϭϭͿ͘ ͞ĨĨĞĐƚ ŽĨ ŝďĞƌƐ ŽŶ ƚŚĞ ůĞdžƵƌĂů ^ƚƌĞŶŐƚŚ ŽĨ DĂƐŽŶƌLJ DŽƌƚĂƌƐ͕͟ dŚĞ DĂƐŽŶƌLJ ^ŽĐŝĞƚLJ :ŽƵƌŶĂů͕ sŽů͘ Ϯϵ͕ EŽ͘ ϭ͕ ĞĐ͘ ϮϬϭϭ͕ ƉƉ͘ ϭϵͲϯϮ͘ ϱϮ
  • 53. ϱϯ
  • 55. ϱϱ ŝďĞƌ ZĞŝŶĨŽƌĐĞĚ ĞŵĞŶƚ ;ZͿ ƚŽ ^ƚƌĞŶŐƚŚĞŶ ŽŶĐƌĞƚĞ ^ůĂďƐ ϮͲď
  • 56. Z ^ƚƌĞŶŐƚŚĞŶŝŶŐ • /ĚĞĂ ǁĂƐ ƚŽ ƐƚƌĞŶŐƚŚĞŶ ϮͲǁĂLJ ƌĞŝŶĨŽƌĐĞĚ ĐŽŶĐƌĞƚĞ ƐůĂďƐ ƵƐŝŶŐ Z ;ƉƵďůŝƐŚĞĚΎͿ ϱϲ 1 in- FRC SpecimenGFRP SpecimenControl Specimen *Radik, M. and Erdogmus, E., Schafer, T. (2011). “Strengthening of Two-way reinforced concrete floor slabs using polypropylene fiber reinforcement,” ASCE Journal of Materials in Civil Engineering, Volume 23, Number 5, pp. 562-571, May 2011.
  • 57. ϱϳ 0 50 100 150 200 250 300 350 400 450 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 Load(kN) Deflection (cm) 1 FRC GFRP 0.5 FRC Control (Phase 2) 0.75 FRC (Phase 2) GFRP (Phase 2) Initial Rupture of GFRP Load vs. Deflection Plots for Rehabilitated Specimens Z ƐŚŽǁƐ ŐƌĞĂƚ ƉŽƚĞŶƚŝĂů ĂƐ Ă ƐƚƌĞŶŐƚŚĞŶŝŶŐ ŵĞƚŚŽĚ͗ •ϭͲŝŶ Z ůĂLJĞƌ ĐĂƵƐĞƐ ƐŝŐŶŝĨŝĐĂŶƚ ŝŶĐƌĞĂƐĞ ŝŶ ĐĂƉĂĐŝƚLJ •ƉŽdžLJ ĚƵƌĂďŝůŝƚLJ ŝƐ ŶŽƚ Ă ĐŽŶĐĞƌŶ •ϭ ŝŶ ůĂLJĞƌ ŽĨ Z ƉƌŽǀŝĚĞƐ ϭϭϯй ŵŽƌĞ ůŽĂĚ ĐĂƉĂĐŝƚLJ ƉĞƌ ΨΨ ƚŚĂŶ 'ZW͊ Z ^ƚƌĞŶŐƚŚĞŶŝŶŐ
  • 58. ŽůůĂďŽƌĂƚŝŽŶ /ŶǀŝƚĂƚŝŽŶƐ ϱϴ ĞĞƌĚŽŐŵƵƐϮΛƵŶů͘ĞĚƵ ϭ͘ ,ŝ^ Z ǁŽƌŬƐŚŽƉ ŝŶ EĞďƌĂƐŬĂ ŝŶ Ăůů ϮϬϭϱ ;KĐƚŽďĞƌ Žƌ EŽǀĞŵďĞƌͿ͘ DĂũŽƌ tŽƌŬƐŚŽƉ 'ŽĂůƐ͗ Ă͘ƐƚĂďůŝƐŚ Ă ƌĞƐĞĂƌĐŚ ĐŽŶƐŽƌƚŝƵŵ ď͘ŽƵŶĚ ĂŶ ŝŶƚĞƌŶĂƚŝŽŶĂů D͘^͘ ĚĞŐƌĞĞ ŽŶ ͞ŽŶƐĞƌǀĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ͗͟ Ϯ ŶŐŝŶĞĞƌŝŶŐ ĂŶĚ Ϯ ĐŽŶƐĞƌǀĂƚŝŽŶ ĚĞƉĂƌƚŵĞŶƚƐ͗ hE͕ ^ĂƉŝĞŶnjĂ͕ hƉĞŶŶ͕ /njŵŝƌ dĞĐŚŶŽůŽŐLJ /ŶƐƚ͘
  • 59. ŽůůĂďŽƌĂƚŝŽŶ /ŶǀŝƚĂƚŝŽŶƐ ϱϵ ĞĞƌĚŽŐŵƵƐϮΛƵŶů͘ĞĚƵ Ϯ͘ ^ƉĞĐŝĂů ^ĞƐƐŝŽŶ Ăƚ ƚŚĞ ^D ϮϬϭϲ͕ ^ŽƵƚŚ ĨƌŝĐĂ ^^ϭϰ͗ ƐƐĞƐƐŵĞŶƚ ĂŶĚ ZĞŚĂďŝůŝƚĂƚŝŽŶ ŽĨ ,ŝƐƚŽƌŝĐĂů DĂƐŽŶƌLJ ^ƚƌƵĐƚƵƌĞƐ
  • 60. ŽůůĂďŽƌĂƚŝŽŶ /ŶǀŝƚĂƚŝŽŶƐ ϲϬ ĞĞƌĚŽŐŵƵƐϮΛƵŶů͘ĞĚƵ ϯ͘ tĞ ĂƌĞ ĨŽƌŵŝŶŐ ĂŶ /ŶƚĞƌŶĂƚŝŽŶĂů ŽŶƐŽƌƚŝƵŵ ŽŶ DĂƐŽŶƌLJ ƌĐŚ ƌŝĚŐĞƐ͘ ϭƐƚ ǁŽƌŬƐŚŽƉ ǁĂƐ ŚĞůĚ ĂƐ ƉĂƌƚ ŽĨ ƚŚĞ ϭϮE D ŝŶ ĞŶǀĞƌ ŝŶ DĂLJ͘ zŽƵ ĂƌĞ ŝŶǀŝƚĞĚ͊ DĂũŽƌ 'ŽĂůƐ͗ ͲŽƌŵ Ă ƚĞĐŚŶŝĐĂů ĐŽŵŵŝƚƚĞĞ ĂƐ ƉĂƌƚ ŽĨ dD^ Ͳ WƵďůŝƐŚ ĂƐƐĞƐƐŵĞŶƚ ĂŶĚ ŶĞǁ ĚĞƐŝŐŶ ŐƵŝĚĞůŝŶĞƐ Ͳ ĚƵĐĂƚĞ ĞŶŐŝŶĞĞƌƐ ŽŶ ĚĞƐŝŐŶ ĂŶĚ ĂŶĂůLJƐŝƐ ŽĨ ĂƌĐŚĞƐ Θ ĂƌĐŚ ďƌŝĚŐĞƐ
  • 61. 'ƌĂnjŝĞ DŝůůĞ͊ • ^ĂƉŝĞŶnjĂ hŶŝǀĞƌƐŝƚĂ Ěŝ ZŽŵĂ͊ • DĂƚĞƌŝĂů ĂŶĚ ƚŝŵĞͬƐŬŝůů ĚŽŶĂƚŝŽŶƐ ĨƌŽŵ ƚŚĞ EĞďƌĂƐŬĂ DĂƐŽŶƌLJ /ŶĚƵƐƚƌLJ ĂŶĚ ĨƌŝĞŶĚƐ͊ • EĂƚŝŽŶĂů ^ĐŝĞŶĐĞ ŽƵŶĚĂƚŝŽŶ͕ hE͕ EWdd͕ ,ĂƌǀĂƌĚ ŽĞď ŽƵŶĚĂƚŝŽŶ ŐƌĂŶƚƐ • DĂŶLJ͕ ŵĂŶLJ ƐƚƵĚĞŶƚƐ͙ • ĨĞǁ͗ ĂƚŚĞƌŝŶĞ ƌŵǁŽŽĚ͕ ŽĚLJ ƵĐŬůĞLJ͕ ƌŝĐ 'ĂƌĐŝĂ͕ ƌŝĞů ŽƵƐŐĂĂƌĚ͕ ůĞdž :ŽƌĚŝŶŐ͕ ĂƚĞ ŝĐŬůĞ • DĂŶLJ͕ ŵĂŶLJ ĐŽůůĂďŽƌĂƚŽƌƐ͙ • ĨĞǁ͗ DŝĐŚĂĞů ,ŽĨĨ͕ ZŚLJƐ dŽǁŶƐĞŶĚ͕ ŝƌŽů ĂŶ͕ :ŽƐŚƵĂ ƌĞĞĚůĂŶĚ͕ DŝŬĞ ^ĐŚƵůůĞƌ ϲϭ ĞĞƌĚŽŐŵƵƐϮΛƵŶů͘ĞĚƵ