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Sapienza stochino-25-06-2013

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Flexural Models of Reinforced Concrete Beams

Nowadays, the issue of structural safety under blast loading has become a dramatic problem. The tragic news of the terrorist attacks of recent years raise important, urgent questions regarding the real safety and reliability of our buildings. Extreme loads such as impacts, explosions, etc., can occur in everyday life with unexpectedly high frequency. This seminar deals with the flexural failure of Reinforced Concrete beams under blast loads. The main aim is to develop dynamic and energy models capable of evaluating the response of R.C. under explosive load. The seminar is composed of three sections. Various dynamic models are developed in Section 1, taking into account the strain-rate sensitivity of both steel and concrete, as well as other nonlinearities in structural behaviour. In Section 2, the same problem is solved in a different way: starting from the principle of energy conservation. This procedure, less accurate than the previous one, produces very good results regarding midspan displacement, especially as it requires less computation time. In order to better understand the phenomenon, with the aim of identifying the key parameters in structural response, a sensitivity analysis is developed in Section 3. In this way it is possible to attain simple predictive polynomial formulations and, finally, simple table for early structural assessment of beams under blast load during the design procedure.

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Sapienza stochino-25-06-2013

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18. 18. " 3 " "/ " ✁ ✂ " " " \$5 \$5 " : # #           ✄     ✌ ✍ ✆ ✆ ✞ ✟ ✆ ✎ ✏ ✠ ✡ ✆ ☛ ☞ ✎ ✏ ☎ ✝ ✑ ✆ ✎ ✏ ☎ ✆ ✎ ✏ ✒ ✓ ✔ ✕ ✖ " " \$5 \$5 \$5 " # # ✗ ✗ ✗ ✗ ✘ ✗ ✗ ✙ ✚ ✛ ✛ ✜ ✢ ✛ ✣ ✤ ✥ ✦ ✧ ★ ✣ ✤ ✩ ✪ ✫ ✛ ✣ ✤ ✩ ✛ ✣ ✤ ✬ ✭ ✮ ✯ ✰ ✯ ✰ ✯ ✰ " " " \$5 " : :! #           ✄     ✌ ✍ ✆ ✆ ✞ ✟ ✆ ✎ ✏ ✠ ✡ ✆ ☛ ☞ ✎ ✏ ✝ ☎ ✑ ✆ ✎ ✏ ☎ ✆ ✎ ✏ ✒ ✓ ✱ ✲ ✳ ✲ ✳ ✲ ✳ " " \$5 \$5 " :! # ✴ ✴ ✴ ✴ ✵ ✴ ✴ ✶ ✷ ✸ ✸ ✹ ✺ ✸ ✻ ✼ ✽ ✾ ✿ ❀ ✻ ✼ ❁ ❂ ❃ ✸ ✻ ✼ ❂ ✸ ✻ ✼ ❄ ❅ ❆ !" + " &3 " "/ " " " " ! " " 9 "
19. 19. !" "
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21. 21. " & & " ;< = 4 = " > \$ >   ✁ ✁ ☎ ✆ ✆ ✞ ✟ ✄ ✂ ✕ ✠ ✡ ✂ ☛ ☞ ✝ ✌ 1 \$ ✍ ✁ ✁ ✆ ✄ ✂ ✂ ✖ \$ > ✎ ✎ ✎ ✏ ✑ ✒ ✓ ✔ ✗ ✘ ✔ ✙ ✚ " \$ " > ✁ ✁ ✁ ✆ ✞ ✟ ✄ ✂ ✠ ✡ ✂ ☛ ☞ \$5 \$ \$5 \$5 > " ✛ ✛ ✜ ✜ ✢ ✣ ✤ ✥ ✦ ✧ ★ ✩ ✪ ✫ ✬ ✭ ✧ ✮ ✯ ✰ ✱ !"
22. 22. ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ 4 4 ! ! " " " " ! ! !   ✌ ✍ ✞ ✟ ✞ ✟ ✞ ✟ ✎ ✏ ✠ ✡ ✠ ✡ ✠ ✡ ✎ ✏ ☛ ☞ ☛ ☞ ☛ ☞ ✑ ✒ ✄ ✄ ✄ ✄ ✄ ✆ ☎ ☎ ✝ ✄ ✄ ✄ ✄ ✄ ! # " " 0 # 2!" ! " / " /\$ #" % ! 3 " " 2! # " ! " 0 " ? +! 3 " " " " .& 2" ! # " / " " " / / " /\$ " 00 ! ' " "# 0 " 0 2!" ! " " # " % ! " 0 ! 2" % 3 " " , !" .\$ " , " / !"
23. 23. ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ 4 4 ! ! " " " " ! ! !   ✌ ✍ ✞ ✟ ✞ ✟ ✞ ✟ ✎ ✏ ✠ ✡ ✠ ✡ ✠ ✡ ✎ ✏ ☛ ☞ ☛ ☞ ☛ ☞ ✑ ✒ ✄ ✄ ✄ ✄ ✄ ✆ ☎ ☎ ✝ ✄ ✄ ✄ ✄ ✄ " " ." @ " " "A " , .\$ " , " / !" ✓ ✔ ( ) ( ) ( ) ✕ ✕ ✖ ✆ ☎ ✝ ✗ ✗ ✓ ✔ ( ) ( ) ( ) ( ) ✕ ✕ ✖ ✖ ✆ ☎ ✆ ☎ ✝ ✗ ✗ ✓ ✔ ( ) ( ) ( ) ( ) ( ) 4 4 4 4 > 4 ✕ ✕ ✖ ✖ ✘ ✘ ✙ ✘ ✙ ✚ ✛ ✛ ✓ ✔ ( ) ( ) ( ) ✕ ✖ ✘ ✙ ✚ ✛ ✛
24. 24. & 0 " " @ " % " ! , .\$ " , " / !" ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ ✔ ✕ ✔ ✕ ✔ ✕ ✔ ✕ ✔ ✕ ✔ ✕ ✔ ✕ ✔ ✕ ✔ ✕ ✔ ✕ ✔ ✕ ✔ ✕ ✔ ✕ 4 4 ! ! " " " " ! ! ! ✖ ✌ ✍ ✞ ✟ ✞ ✟ ✞ ✟ ✎ ✏ ✠ ✡ ✠ ✡ ✠ ✡ ✎ ✏ ☛ ☞ ☛ ☞ ☛ ☞ ✑ ✒ ✘ ✘ ✘ ✘ ✘ ✙ ✚ ✚ ✛ ✘ ✘ ✘ ✘ ✘ & 0 " " @ " % " ! ,
25. 25. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ & 0 " " @ " % " ! , .\$ " , " / !" 0 (") +" (B) "
26. 26. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ .\$ " , " / !" " " " " 0 (") +" (B) " & 0 " " @ " % " ! ,
27. 27. .\$ " , " / !" 0 (") +" (B) " " " " C" " \$ " " C" " \$ " " & 0 " " @ " % " ! ,
28. 28. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ .\$ " , " / !" 0 (") +" (B) " " " " C" " \$ " " C" " \$ " " & 0 " " @ " % " ! ,
29. 29. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ .\$ " , " / !" 0 (") +" (B) " " " " C" " \$ " " C" " \$ " " & 0 " " @ " % " ! ,
30. 30. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ .\$ " , " / !" 0 (") +" (B) " " " " C" " \$ " " C" " \$ " " & 0 " " @ " % " ! ,
31. 31. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ .\$ " , " / !" 0 (") +" (B) " " " " C" " \$ " " C" " \$ " " & 0 " " @ " % " ! ,
32. 32. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ .\$ " , " / !" C" " \$ " " C" " \$ " " 0 (") +" (B) " " " " & 0 " " @ " % " ! ,
33. 33. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ .\$ " , " / !" C" " \$ " " C" " \$ " " 0 (") +" (B) " " " " & 0 " " @ " % " ! ,
34. 34. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ .\$ " , " / !" C" " \$ " " C" " \$ " " 0 (") +" (B) " " " " & 0 " " @ " % " ! ,
35. 35. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ .\$ " , " / !" C" " \$ " " C" " \$ " " 0 (") +" (B) " " " " & 0 " " @ " % " ! ,
36. 36. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ .\$ " , " / !" C" " \$ " " C" " \$ " " 0 (") +" (B) " " " " & 0 " " @ " % " ! ,
37. 37. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ .\$ " , " / !" C" " \$ " " C" " \$ " " 0 (") +" (B) " " " " & 0 " " @ " % " ! ,
38. 38. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ .\$ " , " / !" C" " \$ " " C" " \$ " " 0 (") +" (B) " " " " & 0 " " @ " % " ! ,
39. 39. " \$ " " .\$ " , " / !" C" " \$ " " C" " \$ " " 0 (") +" (B) " " " " " \$ " " & 0 " " @ " % " ! ,
40. 40. " \$ " " ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ! ! 4 > 4 " " ! ! " " ! ✆ ✂ ✆ ✂ ✆ ✆ ✂ ✂ ✆ ✆ ✂ ✂ ✞ ✟   ✁   ✗ ✠ ✡ ☛ ☞ ✞ ✟   ✁   ✁   ✁ ✞ ✟ ✗ ✁ ✠ ✡ ✠ ✡ ☛ ☞ ☛ ☞   ✁   ✁ ✁ ✄ ☎ ) 4 ( ) ( ) ( ) ✝ ✆ ✂ ✌ ✍ ✎ ✏ ✎ ✏ ✎ ✏ ✁ ✎ ✏ ✎ ✏ ✎ ✏ ✎ ✏ ✑ ✒   ✁ ✁ ✓ .\$ " , " / !" C" " \$ " " C" " \$ " " 0 (") +" (B) " " " " " \$ " " & 0 " " @ " % " ! ,
41. 41. ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ 4 4 ! ! " " " " ! ! !   ✌ ✍ ✞ ✟ ✞ ✟ ✞ ✟ ✎ ✏ ✠ ✡ ✠ ✡ ✠ ✡ ✎ ✏ ☛ ☞ ☛ ☞ ☛ ☞ ✑ ✒ ✄ ✄ ✄ ✄ ✄ ✆ ☎ ☎ ✝ ✄ ✄ ✄ ✄ ✄ ! # " " 0 # 2!" ! " / " /\$ #" % ! 3 " " 2! # " ! " 0 " ? ! # 9 D E 1E ! # E 9 1E ? +! 3 " " " " .& 2" ! # " / " " " / / " /\$ " 00 ! ' " "# 0 " 0 2!" ! " " # " % ! " 0 ! 2" % 3 " " , !" .\$ " , " / !"
42. 42. ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ 4 4 ! ! " " " " ! ! !   ✌ ✍ ✞ ✟ ✞ ✟ ✞ ✟ ✎ ✏ ✠ ✡ ✠ ✡ ✠ ✡ ✎ ✏ ☛ ☞ ☛ ☞ ☛ ☞ ✑ ✒ ✄ ✄ ✄ ✄ ✄ ✆ ☎ ☎ ✝ ✄ ✄ ✄ ✄ ✄ ! # " " 0 # 2!" ! " / " /\$ #" % ! 3 " " 2! # " ! " 0 " ? ! # 9 D E 1E ! # E 9 1E ? ! / " % 0 " % ! # 9? +! 3 " " " " .& 2" ! # " / " " " / / " /\$ " 00 ! ' " "# 0 " 0 2!" ! " " # " % ! " 0 ! 2" % 3 " " , !" .\$ " , " / !"
43. 43. ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ 4 4 ! ! " " " " ! ! !   ✌ ✍ ✞ ✟ ✞ ✟ ✞ ✟ ✎ ✏ ✠ ✡ ✠ ✡ ✠ ✡ ✎ ✏ ☛ ☞ ☛ ☞ ☛ ☞ ✑ ✒ ✄ ✄ ✄ ✄ ✄ ✆ ☎ ☎ ✝ ✄ ✄ ✄ ✄ ✄ ! # " " 0 # 2!" ! " / " /\$ #" % ! 3 " " 2! # " ! " 0 " ? ! # 9 D E 1E ! # E 9 1E ? ! / " % 0 " % ! # 9? 4 ! " 0 ! " 3 " "/ " ! " " ! 00 " / " % ? +! 3 " " " " .& 2" ! # " / " " " / / " /\$ " 00 ! ' " "# 0 " 0 2!" ! " " # " % ! " 0 ! 2" % 3 " " , !" .\$ " , " / !"
44. 44. ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ 4 4 ! ! " " " " ! ! !   ✌ ✍ ✞ ✟ ✞ ✟ ✞ ✟ ✎ ✏ ✠ ✡ ✠ ✡ ✠ ✡ ✎ ✏ ☛ ☞ ☛ ☞ ☛ ☞ ✑ ✒ ✄ ✄ ✄ ✄ ✄ ✆ ☎ ☎ ✝ ✄ ✄ ✄ ✄ ✄ ! # " " 0 # 2!" ! " / " /\$ #" % ! 3 " " 2! # " ! " 0 " ? ! # 9 D E 1E ! # E 9 1E ? ! / " % 0 " % ! # 9? 4 ! " 0 ! " 3 " "/ " ! " " ! 00 " / " % ? ! " " /\$ " % ! " " " % ! # # ? +! 3 " " " " .& 2" ! # " / " " " / / " /\$ " 00 ! ' " "# 0 " 0 2!" ! " " # " % ! " 0 ! 2" % 3 " " , !" .\$ " , " / !"
45. 45. ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ 4 4 ! ! " " " " ! ! !   ✌ ✍ ✞ ✟ ✞ ✟ ✞ ✟ ✎ ✏ ✠ ✡ ✠ ✡ ✠ ✡ ✎ ✏ ☛ ☞ ☛ ☞ ☛ ☞ ✑ ✒ ✄ ✄ ✄ ✄ ✄ ✆ ☎ ☎ ✝ ✄ ✄ ✄ ✄ ✄ ! # " " 0 # 2!" ! " / " /\$ #" % ! 3 " " 2! # " ! " 0 " ? ! # 9 D E 1E ! # E 9 1E ? ! / " % 0 " % ! # 9? 4 ! " 0 ! " 3 " "/ " ! " " ! 00 " / " % ? ! " " /\$ " % ! " " " % ! # # ? > ! " " ! 0 \$ " 0 0 " " ? +! 3 " " " " .& 2" ! # " / " " " / / " /\$ " 00 ! ' " "# 0 " 0 2!" ! " " # " % ! " 0 ! 2" % 3 " " , !" .\$ " , " / !"
46. 46. +! 0 " 2! ! 0 " " 2!" ! ! / " ! " ! " " ( " ) " " " ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ 4 4 ! ! " " " " ! ! !   ✌ ✍ ✞ ✟ ✞ ✟ ✞ ✟ ✎ ✏ ✠ ✡ ✠ ✡ ✠ ✡ ✎ ✏ ☛ ☞ ☛ ☞ ☛ ☞ ✑ ✒ ✄ ✄ ✄ ✄ ✄ ✆ ☎ ☎ ✝ ✄ ✄ ✄ ✄ ✄ ! # " " 0 # 2!" ! " / " /\$ #" % ! 3 " " 2! # " ! " 0 " ? ! # 9 D E 1E ! # E 9 1E ? ! / " % 0 " % ! # 9? 4 ! " 0 ! " 3 " "/ " ! " " ! 00 " / " % ? ! " " /\$ " % ! " " " % ! # # ? > ! " " ! 0 \$ " 0 0 " " ? < ! 0 # ! ! " ! " " ( \$ \$ ) /\$ 2!" ! ! # " "" ! +! 3 " " " " .& 2" ! # " / " " " / / " /\$ " 00 ! ' " "# 0 " 0 2!" ! " " # " % ! " 0 ! 2" % 3 " " , !" .\$ " , " / !"
47. 47. .- " % . % . 0" % " " % " "# \$ " % " +! " 0 5 " 0 " ! # " " !"
48. 48. \$ \$ \$ ; ! ☎ ✄ ☎ ✄ .- !"
49. 49. \$ \$ \$ ; ! ☎ ✄ ☎ ✄ 4 \$ \$ &\$ ;4 ;4 ☎ ☎ ☎ ☎ ✄ ✄ ☎ ☎ " " .- !"
50. 50. \$ & &\$ ;4 ☎ ✄ ✄ ☎ " " 4 \$ \$ &\$ ;4 ;4 ☎ ☎ ☎ ☎ ✄ ✄ ☎ ☎ " " \$ \$ \$ ; ! ☎ ✄ ☎ ✄ .- !"
51. 51. ; ! ☎ ✄ ☎ ✄ 4 \$ \$ &\$ ;4 ;4 ☎ ☎ ☎ ☎ ✄ ✄ ☎ ☎ " " \$ \$ \$ ; ! ☎ ✄ ☎ ✄ \$ & &\$ ;4 ☎ ✄ ✄ ☎ " " .- !"
52. 52. 0 &0   ✄ ☎ ; ! ✁ ✂ ✁ ✂ 4 \$ \$ &\$ ;4 ;4 ✁ ✁ ✁ ✁ ✂ ✂ ✁ ✁ " " \$ \$ \$ ; ! ✁ ✂ ✁ ✂ \$ & &\$ ;4 ✁ ✂ ✂ ✁ " " .- !"
53. 53. ✁ ✂ & &\$ \$ 0 4     ✄ ☎ ✆ ✝ ✆ ✆ 0 &0 ✞ ✟ ✠ ; ! ✆ ✄ ✆ ✄ 4 \$ \$ &\$ ;4 ;4 ✆ ✆ ✆ ✆ ✄ ✄ ✆ ✆ " " \$ \$ \$ ; ! ✆ ✄ ✆ ✄ \$ & &\$ ;4 ✆ ✄ ✄ ✆ " " .- !"
54. 54. \$ & 0 & &\$ ✆ ✄ ✆ " ✁ ✂ & &\$ \$ 0 4     ✄ ☎ ✝ ✆ ✝ ✝ 0 &0 ✞ ✟ ✠ ; ! ✝ ✄ ✝ ✄ 4 \$ \$ &\$ ;4 ;4 ✝ ✝ ✝ ✝ ✄ ✄ ✝ ✝ " " \$ \$ \$ ; ! ✝ ✄ ✝ ✄ \$ & &\$ ;4 ✝ ✄ ✄ ✝ " " .- !"
55. 55. " & & & 4;   ☎ ✄ ☎ & & 4; ✁ ✂ ✆ ✂ & " " 0 & &\$ & \$ \$ 0 01 ✝ ✁ ✁ ✁ ✞ ✆ ✟ ✆ ✟ ✂ ✂ & & 01 ✠ ✡ ☛ ☛ ☞ ✌ ✍ ! ✎ ✏ .- !"
56. 56. + 5" % " " ! 3 " " / " " " 3 " 2" ! # " / " " , ✁ ✂ ✁ ✂ ✁ ✂ ✁ ✂ & & & & & & &\$   ✄ ✕ ✕ ! " ☎ ✆ ☎ ✆ ☎ ✆ ☎ ✆ ☎ ✆ ✝ ✞ ☎ ✆ & & 0 & 0 & & & 0 &\$ & &\$ & & ✟ ✟ ✠ ✡ ☛ ☞ ! " " " ☎ ✆ & & 0 & >> <; ! ! ! ! ✡ ✌ ✡ ✌ ✡ ✌ .- !"
57. 57. & !" " " /\$ /\$ ! " 2 " * (# ) 0 " ! "/ " 2!" ! " " "#" " % ! " ! / " "/ /
58. 58. \$ , & 0 " 0 !" # \$ F"%! 0 / /B ! 5 2 # " / 0 -' ;> & . ! & / " ! ( -') + / 2 ? !"
59. 59. \$ , & 0 " 0 !"
60. 60. % &'( ) *''+&'( , 0 % ! 6" ! " G . 0 ! " > > # + " " > > 0 "# " 0 "# % ! 4 < 1 4 / " " %" >GH H \$" % ! > 4 " * 4 * 0 " % ! 5%1 " % ! 0 "# % ! \$ " / +! / 2 2 \$ , ! " # ! " ! 0 "# A 2!" ! " "# ! " ! " A +!" # ! / 0 #" /\$ ! ! " ! / / 3 5%1 !" \$ , ! " "
61. 61. \$ , & 0 " / 4 I. & 0 " / 14 I. !"
62. 62. \$ , ' + # 4 I. + # 14 I. !"
63. 63. \$ 4 I. !"
64. 64. 14 I. !" \$
65. 65. ." 0 % %" " " / 4 I. # % %" " " / 4 I. !" \$
66. 66. " '" ! , !" - " " , .\$ " " , & %\$ " , " "#" \$ ' \$ "
67. 67. & %\$ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ! ( ) \$ ! " ! !   ✁ ✂ ✂ ✄ ✄ ☎ ☎ ☎ ☎ ✌ ✍ ✆ ✝ ✝ ✞ ✎ ✏ ☎ ☎ ☎ ☎ ✑ ✒ ✟ ✠ ☎ ✟ ✠ ✞ ✆ ✝ ✡ ☛ ✡ ☛ ☎ ☞ ✓ ☞ ✓ ✘ ✘ ✔ ✔ ✔ ✔ ✔ ✔ ✔ ( ) ( )" ( )% !" ( ) ( )" % ✕ ( )
68. 68. 4 I. !" \$ ,
69. 69. 4 I. !" \$ ,
70. 70. 4 I. &'( ) - . " J 4 44 < " + " " J > > " 0 " J !" \$ ,
71. 71. " '" ! , !" - " " , .\$ " " , & %\$ " , " "#" \$ ' \$ "
72. 72. " "#" \$ ' \$ " F"%! 2 && >' ; 4 < & &( ) !&( ) &( ) "&( ) 0 % ! > !1 1G 1 6" ! !1 % ! 4 4 % % #   ✄ ☎ % # % # # ✁ ✂ !"
73. 73. " "#" \$ ' \$ " !" 4 " " % , K " " F"%! % ! K " " 2 2 !
74. 74. F"%! " "#" \$ ' \$ " / 0 0 , * 1 2 /3 / 1 2 4 " G ; ;G ;;4 < L " G <> ;G; ;; < /" G <4 G ;<< ; 4 ! % G >G G ;< G !"
75. 75. / 4 " "#" \$ ' \$ " ✁ ✂ %% ✄   ✆ ✘ 3 . & %()# %% %%* ☎ ✝ 3 , " / 2 ! 3 % " % ! % " ! 3 % " % ! ! 0 # ✞ ✟ ✞ ✟ %()# %% %%* ✠ ☎ ✡ ✝ ✡ ' B 3 , " " 0 " " " " # " " \$ 2! " " \$ 0 " 2" ! " / " " %% !% ✠ ✝ 3 & !"
76. 76. 2 " "#" \$ ' \$ " / 0 0 , * 1 2 /3 / 1 2 4 " ; ; ; < L " ; >4 > 4G> /" ;4 >G > 4G> 4 ! % <G ; >; 4G !"
77. 77. 2 , " "#" \$ ' \$ " ( ) ✄ ✂ ✂ 0 / 0 0 , & 3 ' 3 , & < > < ; < ; < - / 0 0 , & 1 3 ' 3 , & 1 G G > ; !"
78. 78. 2 " " "#" \$ ' \$ " 4 4 4 4 4 4 4 4 ( ) ✄ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ / 0 0 , & ;4< 3 <G< ' B 3 , <G4; & <<< !"
79. 79. 2 " " "#" \$ ' \$ " 4 4 4 4 4 4 4 4 ( ) ✄ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ / 0 0 , & ;4< 3 <G< ' B 3 , <G4; & <<< !"
80. 80. " +! / 2 / " % # \$" " 3 " " 3 " \$ " % " / " 0 / 2" " % ! " 0 # ! 2 /\$ 0 " 2" ! 0 " + 5" % " " 3 " % 0 " / " " 0 # ! ! " / ! #" / " # " ! ! " / 0 " 0 " #" 2 / " " 0 " % " 0 " / " 0 # " % ! " 0 " % ! ! 0 +! " "#" \$ \$ " ! # ! 2 ! ! "% " " 0 " ! 0 ! ! : " " % ! 2 " 0 % 0 \$ " ! # / " 2 3 ( & D ) " " % ! "% " " ! 0 " " ! \$ " / /" " " . # 0 !"
81. 81. " / 56 7 / &89') )89') :89') ;89') <89') G 44 > <G G< 4 <G G> 4 4G 4 4G >> ;4 4G >> ;4 G ;4 G > 4 4 ; > 4 < ;G < ;; > 4 / 56 7 / 989') 9\$)89') *89') ,89') &89') G @ M < 4 >> > > ; 4 4 <G 4 4; > < G; >< ; G < 4 4 ;> G; > < G 4 <G F"%! " 2 " !"
82. 82. 7 - 0 - 7 / ==7 - 0 - 7 / == !" - 0 > -?- 0 > -? - 0 > -?- 0 > -? 0 @ \$0 @ \$ "" 0 @ \$0 @ \$ ';':;))&9'+,&')&';*;*';':;))&9'+,&')&';*;* 7- 40 (7- 40 ( 4++ \$ / \$ / +4++ \$ / \$ / +
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