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Erdogmus sapienza-may2015
29 May 2015 - Rome Research Meeting with University of Brasilia–Brazil University of Nebraska-Lincoln (Omaha Campus) University of Rome La Sapienza StroNGER
Erdogmus sapienza-may2015
- 1. ,ŝƐƚŽƌŝĐĂů ^ƚƌƵĐƚƵƌĞƐ͛ ƐƐĞƐƐŵĞŶƚ ĂŶĚ ZĞŚĂďŝůŝƚĂƚŝŽŶ ;,ŝ^ ZͿ ĐĞƌĚŽŐŵƵƐ͕ 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^͘
- 4.
- 5. ϱ 1) Seismic accelerometers placedon 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 ŽŶǀĂƌŝŽƵƐ 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 ϭͿhŶĚĞƌƐƚĂŶĚ͞'ƵĂƐƚĂǀŝŶŽ͟ ŽŶƐƚƌƵĐƚŝŽŶ dĞĐŚŶŝƋƵĞ ϮͿ/ŵƉƌŽǀĞŵĞŶƚƐ ŝŶ Ed ŵĞƚŚŽĚ
- 10.
- 11. ZƵŝŶŽƵƐ ĂŶĐŝĞŶƚ ZŽŵĂŶ ĐŝƚLJŽĨ 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 • /ŶƚĞƌĚŝƐĐŝƉůŝŶĂƌLJƉƌŽũĞĐƚ 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
- 13.
- 14.
- 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
- 16.
- 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 • ŽŵƉƌĞƐƐŝŽŶƚĞƐƚŝŶŐ 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
- 20.
- 21. džƚĞƌŶĂů ZĂƚŝŶŐ ĨŽƌDĂƌďůĞ 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 • ĂĐŬŐƌŽƵŶĚŽŶ 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
- 23. /ŵƉĂĐƚͲĐŚŽ dĞƐƚŝŶŐ Ϯϯ sŽŝĚ ĞƚĞĐƚŝŽŶWͲǁĂǀĞ dĞƐƚŝŶŐ
- 24. Ăď sĂůŝĚĂƚŝŽŶ • ĂƐƚŵŽƌƚĂƌ 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 DĂƌďůĞůŽĐŬ 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 ŽůƵŵŶZĂŝƐŝŶŐ ƌ͘ ŝƌŽů ĂŶ Θ ƌ͘ ĐĞ ƌĚŽŒŵƵƔ ϯϬ
- 31. KŶĞ ůĂƐƚ ůŽŽŬĂƚ 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 ĂŶĚĐŽŵƉůĞdž ƐƚƌƵĐƚƵƌĞ ϯϰ EĞǁ͗ ^ĂŶ :ŽƐĞ /ŐůĞƐŝĂ͕ WƵĞƌƚŽ ZŝĐŽ
- 35. džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐΘ D • ZĞƐĞĂƌĐŚ ŝŶ ƉƌŽŐƌĞƐƐ͗ ϭͿ /ŶͲƐŝƚƵ ĂƐƐĞƐƐŵĞŶƚ ĚŽŶ Ăƚ ϯ ůŽĐĂƚŝŽŶƐ͘ ϮͿ DͬD ŝŶ ƉƌŽŐƌĞƐƐ͘ ϯͿ WƌĞůŝŵŝŶĂƌLJ ƌĞƉŽƌƚ ƐƵďŵŝƚƚĞĚ ϯϱ
- 36. džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐΘ D • ZĞƐĞĂƌĐŚ ŝŶ ƉƌŽŐƌĞƐƐ͗ ϭͿ /ŶͲƐŝƚƵ ĂƐƐĞƐƐŵĞŶƚ ĚŽŶ Ăƚ ϯ ůŽĐĂƚŝŽŶƐ͘ ϮͿ DͬD ŝŶ ƉƌŽŐƌĞƐƐ͘ ϯͿ WƌĞůŝŵŝŶĂƌLJ ƌĞƉŽƌƚ ƐƵďŵŝƚƚĞĚ ϯϲ
- 37. džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐΘ D • ZĞƐĞĂƌĐŚ ŝŶ ƉƌŽŐƌĞƐƐ͗ ϭͿ /ŶͲƐŝƚƵ ĂƐƐĞƐƐŵĞŶƚ ĚŽŶ Ăƚ ϯ ůŽĐĂƚŝŽŶƐ͘ ϮͿ DͬD ŝŶ ƉƌŽŐƌĞƐƐ͘ ϯͿ WƌĞůŝŵŝŶĂƌLJ ƌĞƉŽƌƚ ƐƵďŵŝƚƚĞĚ ϯϳ
- 38. džƉĞƌŝŵĞŶƚĂů DŽĚĂů ŶĂůLJƐŝƐΘ D • DĂŝŶ ǀĂƵůƚ͗ ƵŶĚĂŵĞŶƚĂů ĨƌĞƋƵĞŶĐLJ ŵĂƚĐŚ Ăƚ Ϯϴ ,nj ďĞƚǁĞĞŶ D ĂŶĚ D͕ ƵƐŝŶŐ ǀĂůŝĚĂƚĞĚ /ŶĚŝĂŶĂ ŝŵĞƐƚŽŶĞ ƉƌŽƉĞƌƚŝĞƐ ϯϴ
- 39. ϯϵ D Θ D͗DĂŝŶ sĂƵůƚ EŽƌƚŚ ,ĂůĨ ;ůĞĨƚͿ ĂŶĚ ^ŽƵƚŚ ŚĂůĨ ;ƌŝŐŚƚͿ ƉƌĞƐĞŶƚ ĚŝĨĨĞƌĞŶĐĞƐ ĚƵĞ ƚŽ ǀĂƌLJŝŶŐ ĐŽŶĚŝƚŝŽŶ ĂŶĚ ŝŶƐƵůĂƚŝŽŶ͘ ƵƌƚŚĞƌ ƌĞĨŝŶĞŵĞŶƚƐ ŶĞĞĚĞĚ͘
- 40.
- 41.
- 42. ϰϮ ZĞŚĂďŝůŝƚĂƚŝŽŶ͗ ŝďĞƌ ZĞŝŶĨŽƌĐĞĚDŽƌƚĂƌ ^ƵĐĐĞƐƐĨƵů ƌĞŚĂďŝůŝƚĂƚŝŽŶ DĂƚĞƌŝĂů ĐŽŵƉĂƚŝďŝůŝƚLJ ZĞƉĂŝƌ ĚƵƌĂďŝůŝƚLJ ŽŶŐͲƚĞƌŵ ŵĂŝŶƚĞŶĂŶĐĞ ŝďĞƌ dLJƉĞƐ ^ƚĞĞů 'ůĂƐƐ ^LJŶƚŚĞƚŝĐ KƌŐĂŶŝĐ
- 43. ϰϯ DĂĐƌŽ ĨŝďĞƌƐ Ϭ͘ϱ ƚŽϮ͘ϱ ŝŶĐŚĞƐ DŝĐƌŽ ĨŝďĞƌƐ ĞƐƐ ƚŚĂŶ Ϭ͘ϱ ŝŶĐŚĞƐ ŝĂŵĞƚĞƌ ǀĂƌŝĞƐ ZĞŚĂďŝůŝƚĂƚŝŽŶ͗ ŝďĞƌ ZĞŝŶĨŽƌĐĞĚ DŽƌƚĂƌ
- 44. ŝďĞƌͲƌĞŝŶĨŽƌĐĞĚ ŵŽƌƚĂƌ͗ WŝůŽƚ ϰϰ DŽƌƚĂƌŵŝdž 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.
- 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 ĞdžƉĞƌŝŵĞŶƚĂůƉƌŽŐƌĂŵ ;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 ĞdžƉĞƌŝŵĞŶƚĂůƉƌŽŐƌĂŵ ;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 ĞdžƉĞƌŝŵĞŶƚĂůƉƌŽŐƌĂŵ ;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 ĞdžƉĞƌŝŵĞŶƚĂůƉƌŽŐƌĂŵ ;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 dĞƐƚƉƉĂƌĂƚƵƐ 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 ƌŵǁŽŽĚ͕͕͘͘ 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.
- 54. ϱϰ hŶͲWƵďůŝƐŚĞĚ ZĞƐƵůƚƐ͗ ůĞdžƵƌĂů ĂŶĚ^ŚĞĂƌ ŽŶĚͲƐƚƌĞŶŐƚŚ
- 55. ϱϱ ŝďĞƌ ZĞŝŶĨŽƌĐĞĚ ĞŵĞŶƚ ;ZͿ ƚŽ^ƚƌĞŶŐƚŚĞŶ ŽŶĐƌĞƚĞ ^ůĂďƐ ϮͲď
- 56. Z ^ƚƌĞŶŐƚŚĞŶŝŶŐ • /ĚĞĂǁĂƐ 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 1.001.50 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 tĞĂƌĞ 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 • ^ĂƉŝĞŶnjĂhŶŝǀĞƌƐŝƚĂ 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