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A cooperative transportation research program between Kansas Department of Transportation, Kansas State University Transportation Center, and The University of Kansas Report No. K-TRAN: KSU-08-5 FINAL REPORT October 2011 SOFTWARE FOR AASHTO LRFD COMBINED SHEAR AND TORSION COMPUTATIONS USING MODIFIED COMPRESSION FIELD THEORY AND 3D TRUSS ANALOGY Abdul Halim Halim Hayder A. Rasheed, Ph.D., P.E. Asad Esmaeily, Ph.D., P.E. Kansas State University

Software for Simplified Modified Compression Field Theory -Shear Design

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A research and development work report on modified compression field theory in shear and torsion design in RC element.

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Page 1: Software for Simplified Modified Compression Field Theory -Shear Design

A cooperative transportation research program betweenKansas Department of Transportation,Kansas State University Transportation Center, andThe University of Kansas

Report No. K-TRAN: KSU-08-5 � FINAL REPORT � October 2011

SOFTWARE FOR AASHTO LRFD COMBINED

SHEAR AND TORSION COMPUTATIONS

USING MODIFIED COMPRESSION FIELD

THEORY AND 3D TRUSS ANALOGY

Abdul Halim HalimHayder A. Rasheed, Ph.D., P.E.Asad Esmaeily, Ph.D., P.E. Kansas State University

Page 2: Software for Simplified Modified Compression Field Theory -Shear Design

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' ( � � " � � � � � ! � u � � � � �, | } ~ | } � � � � | } ~ � � � | � � } � � � � | � � � } � � � � � � � | � � � �� � � � � � � � � �� ^ F ] ^ F W G f G D i X ] X D c ] D g C ^ F � � � V � A � k a v G X S j F a F ] X j c � f F B X g X B W C X D c ] � H � � � � _ W ] � F U U W ] C ^ F ] X Y f U X g X F S� � � V � A f G D B F S T G F g D G f G F ] C G F ] ] F S W c S c D c � f G F ] C G F ] ] F S G F X c g D G B F S B D c B G F C F Y F Y E F G ] � F G F X c i F ] C X j W C F S W c S B D Y f W G F SC D C ^ F X G F � T X i W U F c C � h � t I � � � � f G D i X ] X D c ] \ F ] f D c ] F � H � � � X ] W c W c W U [ C X B W U C D D U S F i F U D f F S g D G ] ^ F W G g D G B F � E F c S X c jY D Y F c C X c C F G W B C X D c E W ] F S D c C ^ F l D S X g X F S h D Y f G F ] ] X D c k X F U S � ^ F D G [ � l h k � � \ � ^ X ] C D D U � W ] g X G ] C i W U X S W C F S W j W X c ] CC ^ F F � X ] C X c j F � f F G X Y F c C W U S W C W W c S C ^ F c T ] F S C D j F c F G W C F G F ] T U C ] g D G B W ] F ] � ^ F G F c D F � f F G X Y F c C W U S W C W � W ] W i W X U W E U F \� F i F G W U G F X c g D G B F S W c S f G F ] C G F ] ] F S B D c B G F C F E F W Y ] _ F X C ^ F G ] X Y f U [ ] T f f D G C F S D G B D c C X c T D T ] � F G F F � W Y X c F S C D F i W U T W C FC ^ F � � � V � A W c S � h � ] ^ F W G S F ] X j c f G D i X ] X D c ] g D G ] ^ F W G � B G X C X B W U E F W Y ] \� c W S S X C X D c _ C ^ F � � � V � A � k a f G D i X ] X D c ] g D G B D Y E X c F S ] ^ F W G W c S C D G ] X D c � F G F X c i F ] C X j W C F S W c S C ^ F X G W B B T G W B [� W ] i W U X S W C F S W j W X c ] C C ^ F W i W X U W E U F F � f F G X Y F c C W U S W C W \ � ^ F ] F f G D i X ] X D c ] � F G F W U ] D B D Y f W G F S C D C ^ F X G F � T X i W U F c C � h �B D S F G F � T X G F Y F c C ] \ � ^ F U W C F ] C S F ] X j c f G D B F S T G F ] X c E D C ^ B D S F ] B W c E F F � C F c S F S C D S F G X i F F � W B C ] ^ F W G � C D G ] X D c X c C F G W B C X D cF � T W C X D c ] C ^ W C B W c S X G F B C U [ E F B D Y f W G F S C D C ^ F F � f F G X Y F c C W U G F ] T U C ] E [ B D c ] X S F G X c j W U U g W B C D G ] W ] D c F \ � c C ^ X ]B D Y f G F ^ F c ] X i F ] C T S [ _ S X g g F G F c C D i F G � G F X c g D G B F S _ Y D S F G W C F U [ � G F X c g D G B F S _ W c S T c S F G � G F X c g D G B F S ] F B C X D c ] � X C ^ ^ X j ^ �] C G F c j C ^ W c S c D G Y W U � ] C G F c j C ^ B D c B G F C F g D G E D C ^ ] D U X S W c S ^ D U U D � ] F B C X D c ] � F G F W c W U [ � F S \� ^ F Y W X c D E � F B C X i F ] D g C ^ X ] ] C T S [ � F G F C D F i W U T W C F C ^ F ] ^ F W G W c S C ^ F ] ^ F W G � C D G ] X D c f G D B F S T G F ] f G D f D ] F S E [� � � V � A � k a � H � � � � W c S � h � t I � � � � _ i W U X S W C F C ^ F B D S F f G D B F S T G F ] W j W X c ] C C ^ F F � f F G X Y F c C W U G F ] T U C ] E [ Y W f f X c jC ^ F F � f F G X Y F c C W U U X Y X C f D X c C ] D c C ^ F B D S F � E W ] F S F � W B C T U C X Y W C F X c C F G W B C X D c S X W j G W Y ] _ W c S W U ] D S F i F U D f W l W C ^ h � af G D j G W Y W ] W S F ] X j c C D D U g D G ] F B C X D c ] ] T E � F B C F S C D ] ^ F W G D G B D Y E X c F S ] ^ F W G W c S C D G ] X D c F g g F B C ] \� O   � u o � � & �h D Y f T C F G ` G D j G W Y _ � k a _ � D W S W c S F ] X ] C W c B Fk W B C D G a F ] X j c _ v G X S j F � G T ] ] � D G ] X D c � d @ � � � � � ) ( � � � � ' � ! � � � � � �� D G F ] C G X B C X D c ] \ � ^ X ] S D B T Y F c C X ]W i W X U W E U F C D C ^ F f T E U X B C ^ G D T j ^ C ^ F� W C X D c W U � F B ^ c X B W U � c g D G Y W C X D c � F G i X B F _� f G X c j g X F U S _ ¡ X G j X c X W H H I m I� e ' � � ( � � � u " ! � � � L � � ! � � � �Q � L � P � � � � � � � � R� c B U W ] ] X g X F S � n ' � � ( � � � u " ! � � � L � � ! � � � �Q � L � P � � � ! # � R� c B U W ] ] X g X F S � � � � � L � ! # � �I � � � � K � � � �¢ £ ¤ ¥ ¦ § ¨ ¢ © ª « « ¬ ª ­ ® ¯ ª ° ±

Page 3: Software for Simplified Modified Compression Field Theory -Shear Design
Page 4: Software for Simplified Modified Compression Field Theory -Shear Design

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Page 5: Software for Simplified Modified Compression Field Theory -Shear Design

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Page 6: Software for Simplified Modified Compression Field Theory -Shear Design

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Page 7: Software for Simplified Modified Compression Field Theory -Shear Design

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Page 11: Software for Simplified Modified Compression Field Theory -Shear Design

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# þ ÿ � ü ü � � þ � � þ � � � � � � � ù � þ � ü û þ ÿ ý ÿ � � � þ � � ù � � � � ý � � � � ù � þ � ü û þ ÿ ý � � þ � � ù � � � ÿ � �� � ý ü ù � � ÿ ý þ ý þ ' þ � � � � þ � � � � � þ ý þ � ù � � ý ÿ � � ù � þ � � � þ � � ù � þ ü � � þ � ý � � � � � û þ � ÿ ü þ ü � ÿ � � � � � ý � �� û þ � þ ü ù � � � ý � � þ ü ü � û ù � þ � û þ � � û þ ý þ þ � � ù ü � � � ü ù � þ ý þ � ü þ � � � � ÿ ý � � ) � � û ù ü ü � � � � ü � ý � � ý ÿ �� � � � ý þ � þ � þ ÿ � ü ü � � þ � � þ � � � ü û þ ÿ ý � ý � � � � ù � þ � ü û þ ÿ ý ÿ � � � � ý ü ù � � ÿ ý þ � � � ü ù � þ ý þ � � û ù � þ � û þ þ þ � � ü� � þ � � ù � � � � � þ � � ÿ ý þ � þ � � þ � � þ � � ú û ù ü � û ÿ � � þ ý ù ü � þ � � þ � � � � û þ ý þ ù þ � � � û þ þ � � þ ý ù � þ � � ÿ �ü � � ù þ ü ÿ � � � û þ � þ ü ù � � � ý � � þ � ý þ ü � ý � û þ ü � ý � � ý ÿ � ý þ ù � � ý � þ � � � � � ý þ � þ � þ ÿ � ü � ù � û � þ � � ù � ù � � þ� þ � � ù � � þ þ � � ü �0 þ � � û � � û � û þ � þ û ÿ ù � ý � ü � ý � � ý ÿ � � � � � ý þ � þ � þ ÿ � ü ü � � þ � � þ � � � ü û þ ÿ ý û ÿ ü � þ þ �ü � � ù þ � � ý � � ý þ � û ÿ � + % % � þ ÿ ý ü � � û þ ý þ ù ü � ; � þ � � � û ÿ � ý þ þ � þ � � ÿ � � � � ý þ ü þ ÿ ý � û þ ý ü ÿ � � � û � � � û þ� � � � ý þ � þ � � � � ý ù � � þ ü � � ü û þ ÿ ý ý þ ü ù ü � ÿ � � þ � ÿ ý þ ù � � ý � þ � � ý � ý þ ü � ý þ ü ü þ � � � � � ý þ � þ � þ ÿ � � ú û ù ü ù ü� ÿ ù � � � � þ � ÿ ü þ � � û þ � ÿ � � � ù þ ý þ � � � þ � û ÿ � ù ü � ü ù � � � þ � ù � ü û þ ÿ ý � ý ÿ � ü þ ý � ý � � þ ü ü � ü � ý � � ý ÿ �� � � � ý þ � þ � þ � � þ ý ü ü � û ÿ ü ÿ � � ý þ � ÿ � þ ù � � þ ý � � � � � ý ù � � þ ý ÿ � þ ü û þ ÿ ý � ý ÿ � ü þ ý ÿ � ý � ü ü � ý ÿ � � ü � ü û þ ÿ ý� ý ÿ � ü þ ý ù � � � � � ý þ ü ü ù � � � � � ý ÿ � � þ � � - � � þ � � � � þ � ÿ � � ù � � � ÿ � � ý þ ü ù � ÿ � � þ � ü ù � þ ü � ý þ ü ü þ ü � � ý � ÿ � � �� ý ÿ � � ü � � � � þ þ ý � � û þ ý þ ù ü ÿ � þ � þ ý ÿ � ÿ � ý þ þ � þ � � ÿ � � � � ý þ ü þ ÿ ý � û þ ý ü � û ÿ � ÿ � � ý þ � ÿ � þ ù � � þ ý � � � � ÿ � �� � � � ý þ ü ü ù � � - � � þ ÿ ý þ � û þ � þ � � � � � � � þ � � ü � � � � � ý þ � þ � � � � ý ù � � ù � � � � ü û þ ÿ ý ý þ ü ù ü � ÿ � � þ �< = > ? @ A B C D E F G H I J I K L G M N O P G F J P N J N P J Q R S T K F U K L U F P J P V P G W N C" ù � ý þ $ � + ü û � � ü � û þ � ý ÿ � ù � ù � � ÿ � ü û þ ÿ ý � þ ü � ü þ � � � � ý � � � � ý þ � þ � þ ÿ � ü � " ý � � � û þ ù � ý þ � ù � ù ü� � � � � � þ � � û ÿ � � û þ ý þ � ù � � � þ � � þ þ � � û þ � � � � þ � � ý ÿ � þ � � � ÿ � ü ÿ � � � ù þ � ÿ � � û þ � � � � � û þ � þ ÿ � ù üü � � þ � � þ � � � � ý þ � þ � ý þ � û þ ý þ ÿ ü � û þ ü û þ ÿ ý ü � ÿ � ü ÿ ý þ ü � � þ � � þ � � � � � � ü � ÿ � � ü û þ ÿ ý ÿ � � � ù � þ ÿ ý � �

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ÿ ý � ù � � � þ � � ù � � � � � þ � � � ) � ù ü þ ý � � � ù � ü � û ÿ � � û þ ý þ ü � � ü ý � � ü � û � þ ü � � � � � � � � � þ ü þ � � �� þ þ � � � ÿ � þ � þ ý ÿ � � û þ � ý � � ý ü û þ ÿ ý � þ û ÿ ù � ý � ! ù � � þ ù � ù ü ÿ � � � ü � ù � � � ü ü ù � � þ � � � þ ü ù � � ÿ �þ � � þ ý ù � þ � � ÿ � � ý � � ý ÿ � � û þ ý þ � û þ � þ ÿ � ù ü � � � � ü � � þ � � þ � � � � ý þ ü û þ ÿ ý � � û ù ü ù � � ý � ù ü � � þ � � û þ� ÿ ù � ý þ ÿ ü � � ü � û þ ý þ � û þ � ý þ ü û þ ÿ ý � þ û ÿ ù � ý � � þ ÿ � ü û ÿ ü � � � � þ þ � � � þ ý ü � � � � � û ý � � û � � � û þ� þ � ÿ � þ ü �� � þ ý � � � � � � ù � � � þ ü � ü � � ý þ ù � � ý � þ � � � � � ý þ � þ � ÿ � þ � ü ü � � þ � � þ � � � � ý þ ü û þ ÿ ý � � ý þ ÿ � ù ÿ �� � ÿ � � ÿ � � ÿ � � � � ù � ÿ � ù � � � ü û þ ÿ ý ÿ � � ÿ � ù ÿ � � � ÿ � � ÿ � � � � � þ � � û þ � ý � � ÿ � � þ � , � � ù ù þ � ( � � � ý þ ü ü ù � �" ù � þ � ú û þ � ý � � , ( " ú � � ÿ ü � þ þ � � � þ � ù � + 6 & % ü ý � � � û þ ( � � � ý þ ü ü ù � � " ù þ � � ú û þ � ý � � 5 þ � � û ù � ÿ � �( � � � ù � ü + 6 & 4 � � ú û þ , ( " ú � ÿ ü ÿ � � þ � � ÿ � � ý ÿ � þ � � � ý þ � ù � � � û þ ü û þ ÿ ý � þ û ÿ ù � ý � � � � � ý þ � þ � þ � � þ ý üü � � þ � � þ � � � ü û þ ÿ ý ÿ � � ÿ � ù ÿ � � � ÿ � ü � ú û ù ü � û þ � ý � � ÿ ü � ÿ ü þ � � � � û þ ÿ � � � û ÿ � ü ù � � ù ù � ÿ � � � þ � ü ù � þü � ý þ ü ü þ ü � � � � þ � ù ü � ù � � û þ � � � � ý þ � þ � þ � � þ þ � � û þ � ý ÿ � � ü þ þ � ÿ � þ ý � û ù � û ÿ � þ ü � ÿ þ ý ÿ � þ � þ � ü ù � þü � ý ÿ ù � ü � ) � ÿ � � ù � ù � � � � û þ ÿ � þ � ý ÿ � � � þ � � ù ÿ � � � ÿ � � � � � ý þ ü ü ù þ ü � ý þ ü ü þ ü � ÿ ü � � � ü ù � þ ý þ � ÿ ü ÿ ý ù ÿ � � þ � � � � ÿ ý þ � � � � û þ ù � þ � ÿ � þ � 1 3 ÿ ü ü � þ � � � � ( ) ( � � þ �ú � ü ù � � � ù � � û þ � ý � � þ ü ü � � ý þ � ù � � ù � � � û þ ü û þ ÿ ý ü � ý þ � � � û � ÿ ü þ � � ù � � ü ù � � � û þ , ( " ú � � û þü û þ ÿ ý ü � ý þ ü ü ù ü ÿ ü ü � þ � � � ý þ � ÿ ù � � � � ü � ÿ � � � þ ý � û þ � þ � � û � � û þ � ý � ü ü � ü þ � � ù � � ÿ � � � û þ ü þ � � ù � � ù ü� � � ü ù � þ ý þ � ÿ ü ÿ � ù ÿ � ù ÿ � þ � þ � þ � � ù � � ÿ ü þ ÿ � � ÿ � ù ÿ � ü � ý þ ü ü þ ü ÿ ý þ � ý þ ü þ � � � ú û ù ü ù � � ý � � ý � � � þ ü � û þ� ÿ ü ù ü � � û þ ü þ � � ù � � ÿ � � þ ü ù � � � � � þ � � ý ü û þ ÿ ý � û þ ý þ � û þ � � ! � ú � � � " � # ý ù � � þ � þ ü ù � �! � þ � ù ù � ÿ � ù � � ü û ÿ þ � þ þ � � ÿ ü þ � � � � # þ � � - þ � ÿ � � $ % % 4 � �0 þ � � û � � û � û þ þ ÿ ý � ù þ ý � � ! � ú � � � " � � ý � � þ � ý þ � � � ý þ � ù � � � û þ ü û þ ÿ ý ü � ý þ � � � û � ÿü þ � � ù � � � ÿ ü ü � ý ÿ ù � û � � ý � ÿ ý � � � û þ � � � � ý ù � � ù � � � � � � � ý þ � þ � � ü û þ ÿ ý ü � ý þ � � � û � ÿ ü þ � � ù � � � ÿ ü ÿ � � � ù � � � ÿ � � ÿ ý � ù � � ÿ � � � þ � ý � û ù � û � û þ ù ý ÿ � þ ü � þ ý þ � þ � þ ý � ù � þ � ü ù � � � û þ � ÿ � � þ ü� ý � ù � þ � � � � � ! � ú � � ú û þ ÿ � � � ý ù � � ù � ÿ � þ � � û þ ÿ � ù � ù � � � � ù ÿ � � � ÿ � � � � ý ÿ � � þ � � � � � ý þ � þ � �� ý ÿ � ü � ù � � þ � ü ù � � ÿ � � ü û þ ÿ ý � ú û þ � � � ù ù þ � � � � � ý þ ü ü ù � � ù þ � � � û þ � ý � ù ü � � � þ þ � � � ý þ ü ù � � � ù ù þ �� û þ � ü ù � � � þ þ ' ÿ � ù � � ü � þ ý þ � þ þ � � � þ � � ý ÿ � � � ú û þ ü þ þ ' ÿ � ù � � ü � þ ý þ � û þ � ü þ � � � � ý þ � ù � �� û þ ü û þ ÿ ý ü � ý þ � � � û ü � � ù þ ý þ � � � � � � ý þ � þ ü þ � � ù � � ü ÿ � � � û þ ý þ ü � � ü � � � � ÿ ý þ � � � � û ÿ � � � � ÿ ù � þ � ý � �, ( " ú � ( � � ü þ ' þ � � � � � û þ ü û þ ÿ ý ü � ý þ � � � û ü � ý þ � ù � � þ � � � � û þ ü ù � � � ù ù þ � � � � ù ù þ � � � � � ý þ ü ü ù � � ù þ � �� û þ � ý � ÿ � � , ( " ú � þ ý þ � � � � ÿ ý þ � � ù � û þ � � þ ý ù � þ � � ÿ � ý þ ü � � ü �ú � � ÿ � þ ü ý þ � û ÿ � � û þ ü û þ ÿ ý ü � ý þ � � � û ü � ý þ � ù � � þ � � � � û þ ü ù � � � ù ù þ � � � � ù ù þ � � � � � ý þ ü ü ù � � ù þ � � � û þ � ý � ÿ ý þ � � � ü ù ü � þ � � � ù � û þ � � þ ý ù � þ � � ÿ � ý þ ü � � ü � ÿ � ù � þ ý ÿ � � þ � � � � � ý þ � þ � ÿ � þ � ü � ù � û ÿ � �

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� ù � û � � � ý ÿ � ü þ ý ü þ ý þ ù � � ý � þ � þ � � � þ ý þ � þ ü � þ � ù � � ý þ ü û þ ÿ ý � ý ÿ � � � � ù � ÿ � ù � � � ü û þ ÿ ý ÿ � � ÿ � ù ÿ �� � ÿ � � # þ � � - þ � ÿ � � $ % % 4 � � ú û þ ü þ � ÿ � þ � ü � þ ý þ � ÿ � þ � � � � � ý þ � þ � ù � û ÿ ý ù � ü � � � � ý þ � þ � � � � ý þ ü ü ù þü � ý þ � � � û ü � � � ù þ ý þ � � � � � � ù � � ù � ÿ � ý þ ù � � ý � þ � þ � � ý ÿ � ù � ü � � ÿ � � ÿ ý ù þ � � � ÿ � � ý þ � ÿ � þ ü ù - þ ü �) � � ÿ ü � � � � û ÿ � � û þ ý þ ü � � ü � ý � � � û ü ù � � � ù ù þ � � � � ù ù þ � � � � � ý þ ü ü ù � � ù þ � � � û þ � ý � ÿ � �, ( " ú � þ ý þ ÿ � � � ü � þ � ÿ � � � � ü ù � ù � ÿ ý ÿ � � � � � û � ÿ � � û þ � � ý � � þ ý � � � � � û þ þ � � þ ý ù � þ � � ÿ � ý þ ü � � ü � ) �ÿ � � ù � ù � � � � û þ ý þ ü � � ü � þ ý þ ÿ � ü � � � � � ÿ ý þ � � ù � û � û þ � ( ) ( � � þ � û þ ý þ ù � � ÿ ü � ý þ � � � � � ûù � � � � ü ù ü � þ � � ù � � ÿ ý � ù � � ÿ ý � ý � ÿ � þ � ü � ù � û � � � ý ÿ � ü þ ý ü þ ý þ ù � � ý � þ � þ � � �

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Page 18: Software for Simplified Modified Compression Field Theory -Shear Design

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� ÿ ü þ ü ü � � ù þ � ù � � � � þ � � � þ ý � ý þ ù � � ý � þ � � � � � þ ý ÿ � þ � � � ý þ ù � � ý � þ � � ÿ � � � þ ý � ý þ ù � � ý � þ � ü þ � � ù � � ü �� � � � � � û þ � � � ÿ � * % ü � þ � ù � þ � ü ü � � ù þ � � $ $ � þ ý þ � ÿ � þ � � � ý � ÿ � ü � ý þ � � � û � � � � ý þ � þ � û ù � þ � û þý þ � ÿ ù � ù � � þ ù � û � � þ ý þ ü � þ � ù � þ � ü � ù � û û ù � û � ü � ý þ � � � û � � � � ý þ � þ � ú � � û � � � � � � � þ ý � ý þ ù � � ý � þ �ü � þ � ù � þ � ü � � � þ � ÿ � þ � û ù � û � ü � ý þ � � � û ÿ � � � û þ � � û þ ý � ÿ � þ � � � ý � ÿ � ü � ý þ � � � û � � � � ý þ � þ � þ ý þ� � � ü ù � þ ý þ � ÿ ü � þ � � � ú û þ � ý � � þ � ý þ � ý � ý ÿ � ù � � � û þ þ � ÿ � � ù � � þ ý ÿ � � ù � � � ù ÿ � ý ÿ � ü ÿ ý þ � þ ü � ý ù � þ � ù �� þ � ÿ ù � ù � ( û ÿ � � þ ý * � � û ù ü ý þ � � ý � �" ù � ý þ ü � ù þ � � þ � � � ü û � � ü � � þ � � û þ � ý � ü ü � ü þ � � ù � � ü � ý � û þ ü � þ � ù � þ � ü � � � ü ù � þ ý þ � �

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Page 28: Software for Simplified Modified Compression Field Theory -Shear Design

+ 2ú û þ � � ! � ú � � � " � # ý ù � � þ � þ ü ù � � ! � þ � ù ù � ÿ � ù � � ü � $ % % & � � ý � � � ü þ ü � û ý þ þ � þ � û � � ü � �� þ ü ù � � ÿ � ý þ ü � ý þ ü ü þ � � ý � � � � � ý þ ü � ý þ ü ü þ � � � � � ý þ � þ ü þ � � ù � � � ý ü û þ ÿ ý � ) � ù ü ù � � � ý � ÿ � � � � � � þ ý ü � ÿ � �� û ÿ � ÿ � � ý þ ' ù ý þ � þ � � ü ü þ � � � � � ! � ú � � � ' ÿ � ù � ÿ � ÿ ý � ù � � ÿ ý � þ � û � � û ÿ þ � � � þ � þ � � ý ù � ý � � � û þÿ � � � ù � ÿ � ù � � � � û ÿ � � þ � û � � � ) � � û ù ü ý þ � � ý � � � � � � � � � þ � û � � ü � � � þ ü ù � � ÿ ü þ � � ù � � � ý ü û þ ÿ ý ù � þ � � � û þ� þ � þ ý ÿ � � ý � � þ � ý þ ÿ � � � û þ ü ù � � � ù ù þ � � ý � � þ � ý þ � ý � ý þ ü � ý þ ü ü þ � ÿ � � � � � � � ý þ ü � ý þ ü ü þ � � þ � � þ ý ü ÿ ý þ� ù ü � ü ü þ � ù � � þ � ÿ ù � � ) � ÿ � � ù � ù � � � � û þ � ý ý þ � � � ( ) � ý � ù ü ù � � ü � ý ü û þ ÿ ý � þ ü ù � � � ÿ � � � � ý þ � þ ü þ � � ù � �ÿ ý þ � ý ù þ � � � þ ü � ý ù � þ � �

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Page 29: Software for Simplified Modified Compression Field Theory -Shear Design

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Æ Ç È Ç É Ê Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ô Ö × Ø Ù Ö Ú Û Ô Ü Ý Ö Ô Þ Ú Ö Ë ß Ô × Ö Ò Ô à á â Õú û þ � � ! � ú � � � " � � þ � þ ý ÿ � � ý � � þ � ý þ � � � þ ü ù � � � ý � þ � þ ý � ù � þ � û þ ü û þ ÿ ý ü � ý þ � � � û � ÿü þ � � ù � � ù ü � ÿ ü þ � � � � û þ , � � ù ù þ � ( � � � ý þ ü ü ù � � " ù þ � � ú û þ � ý � � , ( " ú � � � ü ü � ÿ � þ � þ ÿ ý � ù þ ý � � û ù ü� û þ � ý � û ÿ ü � ý � þ � � � � þ þ ý � ÿ � � ý ÿ � þ ù � � ý þ � ù � � ù � � � û þ ü û þ ÿ ý � ÿ � ÿ � ù � � � ÿ � ý þ ü � ý þ ü ü þ � � ý � � � �� ý þ ü � ý þ ü ü þ � � � � � ý þ � þ ü þ � � ù � � � ) � ù ü ù � � � ý � ÿ � � � � � � � þ � û ÿ � � û þ � ý ý þ � � � � ! ú � � � � " � � ý � ù ü ù � � ü � ý � û þ � þ � þ ý ÿ � � þ � û � � ÿ ý þ � ÿ ü þ � � � � û þ ü ù � � � ù ù þ � , ( " ú �ú û þ � � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û � ÿ ü þ � � ù � � � ý ÿ � � � û ý þ þ � þ � û � � ü ù ü þ ' ÿ � � �A ã R G J I K L B C ÿ C D� û þ ý þ . � � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û� � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û � ý � ù � þ � � � � � � � ý þ � þ� � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û � ý � ù � þ � � � ü û þ ÿ ý ý þ ù � � ý � þ � þ � �� � � � � � þ � � ù � � û þ � ù ý þ � � ù � � � � û þ ÿ � � � ù þ � ü û þ ÿ ý � � û þ þ þ � � ù þ � ý þ ü � ý þ ü ü ù � � � ý � þù ü ÿ � � � ù � � � ÿ ÿ � � � ý � û ù � û ü û � � ü � û þ ÿ � ù � ù � � � � ù ÿ � � � ÿ � � � � ý ÿ � � þ � � � � � ý þ � þ � �� ý ÿ � ü � ù � � þ � ü ù � � ÿ � � ü û þ ÿ ý � ú û þ ÿ � � � ý ù ü ù � þ ý ü þ � � � ý � � � ý � ù � � ÿ � � � � û þ ü � ý ÿ ù � ù � � � � � ù � � ù � ÿ �� þ � ü ù � � ý þ ù � � ý � þ � þ � � � � � � û þ ü þ � � ù � � � " � ý ü þ � � ù � � ü � � � � ÿ ù � ù � � ÿ � � þ ÿ ü � � û þ � ù � ù � � ÿ � � � � � � ý ÿ � ü þ ý ü þ ý þ ù � � ý � þ � þ � � � � û þ ÿ � þ � ù ü � þ � þ ý � ù � þ � ÿ ü A ã R G J I K L B C ÿ C Bä û þ � ü þ � � ù � � ü � � � � � � � � � ÿ ù � ÿ � � þ ÿ ü � � û þ � ù � ù � � ÿ � � � � � ü û þ ÿ ý ý þ ù � � ý � þ � þ � � � � û þ ÿ � þ � ù ü � þ � þ ý � ù � þ � ÿ ü � � � � � A ã R G J I K L B C ÿ C Ó

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ú û þ ÿ � � þ þ ' ÿ � ù � � ü ÿ ý þ ÿ � ù � � � � � ù � û þ � � � � ý þ � þ ü � ý þ � � � û ù ü ù � � ü ù ÿ � � ù � ù � � û þ ü �) � û þ � � � � ý þ � þ ü � ý þ � � � û ù ü ù � , � ÿ ÿ � � ù � � � � � û þ � 1 � & ù � 0 ' ÿ � ù � � $ � 1 � $ ÿ � � $ � 1 � * � *� þ � � � þ ü % � 1 � û ù � þ 3 + ÿ � � * 6 ù � 0 ' ÿ � ù � � $ � 1 � * � þ � � � þ + * % % ÿ � � + % % % ý þ ü � þ � � ù þ � � �ù ü � ÿ � � þ � � û þ � ý ÿ � � ü � ÿ � ù � � � ÿ ý ÿ � þ � þ ý � û ù � û � ÿ � � þ þ ü � ù � ÿ � þ � ÿ üA ã R G J I K L B C ÿ C ÿù ü � û þ þ ý � ù � ÿ � � ù ü � ÿ � � þ � þ � � þ þ � û � ý ù - � � � ÿ � � ÿ � þ ý ü � � � � � ù � � ù � ÿ � � ý ÿ � � � � � � ý � � � ü � ù � �ý þ ù � � ý � þ � þ � � � ÿ � � ù ü � û þ � ÿ � ù � � ÿ � � ý þ � ÿ � þ ü ù - þ ù � ù � � û þ ü ÿ � � û ÿ ü � � þ ' ÿ � - þ ý � � û þ �� ü ù � � � � þ � û ÿ � ù � û þ � � � � ý þ � þ ü � ý þ � � � û ù ü ù � , � ÿ ÿ � � ù � � � � � û þ + � * & ÿ � � % � 4 * ù �0 ' ÿ � ù � � $ � 1 � 1 ü û � � � � þ ý þ � � ÿ � þ � � � * 3 ÿ � � + 4 � ý þ ü � þ � � ù þ � � �ú û þ � � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û � ý � ù � þ � � � � û þ � � � � ý þ � þ � ý � û þ � þ � þ ý ÿ � � ý � � þ � ý þ ù ü þ ' ÿ �� � � û þ � � û þ � � � � ý þ � þ ü � ý þ � � � û ù ü ù � , � ÿ � � � � þ þ ý � ù � � ÿ ü þù ü ù � � ü ù � ú û þ � � þ ù � ù þ � � % � % * + 4 ù ü ÿ � � ù ü ü þ � � � � � � þ ý � � û þ ý � � � ü ù � � � ü ù �ú û þ � � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û � ý � ù � þ � � � � û þ ü û þ ÿ ý ý þ ù � � ý � þ � þ � � � ÿ � � þ þ ü � ù � ÿ � þ � ÿ üA ã R G J I K L B C ÿ C �� û þ ý þ . ÿ ý þ ÿ � ü û þ ÿ ý ý þ ù � � ý � þ � þ � � � ù � û ù � ÿ � ù ü � ÿ � � þ � ù � � û þ ü å �� ù þ � � ü � ý þ ü ü � � û þ ü û þ ÿ ý � � ý ÿ � ü þ ý ü þ � ý þ ù � � ý � þ � þ � � ù � � ü ù � ý � ü ù � þ � þ � � ù � � � � � û þ� ÿ ü þ �þ þ � � ù þ ü û þ ÿ ý � þ � � û � ù � � û þ ü � ÿ � � ù ü þ ' ÿ � � � æ ç è � � � þ � û ÿ �þ þ � � ù þ � þ � � ù � � û � ù � � û þ ü �ü � ÿ � ù � � � ü � ù ý ý � ü � ù � � û þ ü �ÿ � � � þ � ù � � � ù � ÿ � ù � � � � ù ÿ � � � ÿ � � � � � ý þ ü ü ù þ ü � ý þ ü ü þ ü � ÿ ü � þ � þ ý � ù � þ � � þ � � �A ã R G J I K L B C ÿ C '

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ú û þ ÿ � � þ þ ' ÿ � ù � � ù ü ù � � þ � þ � � þ � � � � û ù � û � ù � ü ÿ ý þ ü þ � � ý � ý �ú û þ ü � ý ÿ ù � ù � � � � � ù � � ù � ÿ � � þ � ü ù � � ý þ ù � � ý � þ � þ � � ù ü � ÿ � � � ÿ � þ � ü ù � � � û þ � � � � � ù � �þ ' ÿ � ù � � A ã R G J I K L B C ÿ C (ü ÿ � � � ý þ � � � � þ � � � � � � � � � þ � ÿ � þ � � þ ü ü � û ÿ � � � ù � � ù � � û þ ü � ÿ � � � ý þ � ÿ � ù ÿ � � ý � þ � � ÿ � þ � ÿ ü � � ü ù � ù þ ù � þ � ü ù � þ ÿ � � � þ � ÿ � ù þ ù � � � � ý þ ü ü ù þ � � ù � � ÿ � � � ý þ � ü û þ ÿ ý � ý � þ � � ù � �ÿ ý þ ÿ � � ý þ ü � ý þ ü ü ù � � ü � þ þ � � � � û þ � þ � ý ÿ � � þ � ü ù � � ü ù � þ � � û þ � þ � � þ ý � ù � � û þ ü å �% � 2 � ù � þ ü � û þ ü � þ � ù ù þ � � þ � ü ù � þ ü � ý þ � � � û � � ý þ ü � ý þ ü ü ù � � ü � þ þ � � � � ü ù �� � � � ü � þ � ÿ ü � ù � ù � � � � û þ � � � � ý þ ü � ý þ ü ü þ � ü � þ þ � � � � û þ � þ � ý ÿ � � þ � ü ù � � ü ù � þ � � û þü þ � � ù � �� � � � ü � þ � ÿ ü � ù � ù � � � � û þ � ý þ ü � ý þ ü ü ù � � ü � þ þ � � � � û þ � þ � ý ÿ � � þ � ü ù � � ü ù � þ � � û þü þ � � ù � �ÿ ý þ ÿ � � � � � � ý þ ü � ý þ ü ü þ � ü � þ þ � � � � û þ � þ � ý ÿ � � þ � ü ù � � ü ù � þ � � û þ ü þ � � ù � � � ù � � û þ ü å �ú � � ÿ � þ ü ý þ � û ÿ � � û þ � � � � ý þ � þ ü þ � � ù � � ù ü � ÿ ý � þ þ � � � û � � ü � � � ý � � û þ ÿ � � � ù þ � ü û þ ÿ ý � ù � ù üý þ ' ù ý þ � � û ÿ � ü û � � � � � � þ � � þ þ � � � � û þ ý � ù ü þ � þ � � ÿ ý � þ � û þ ü þ � � ù � � �é è ê è ë è ë ì í î í ï ð ï ñ ò ó î ô õ ö ò ô ö ÷ ö í î ø ù ò ú ö ï ö î û) � û þ ÿ � � � ù þ � ÿ � � � ý þ � ü û þ ÿ ý ù ü � ý þ ÿ � þ ý � û ÿ � � û þ ÿ � þ � 9 ü û þ ÿ ýý þ ù � � ý � þ � þ � � ù ü ý þ ' ù ý þ � � ú û þ ÿ � � � � � � ù � ù � � � ý ÿ � ü þ ý ü þ ý þ ù � � ý � þ � þ � � � ÿ � � þ þ ü � ù � ÿ � þ � ÿ üA ã R G J I K L B C ÿ C �é è ê è ë è é ì ó ü í ï ð ï ý þ ó ú í î ÿ ù ø ñ ò ó î ô õ ö ò ô ö ÷ ö í î ø ù ò ú ö ï ö î û� � � � ý � ù � � � � � û þ � � ! � ú � � � " � # ý ù � � þ � þ ü ù � � ! � þ � ù ù � ÿ � ù � � ü � � û þ ü � ÿ � ù � � � � û þ� ý ÿ � ü þ ý ü þ ý þ ù � � ý � þ � þ � � ü û ÿ � � � � � þ � � þ þ � � û þ � ÿ � ù � � � þ ý � ù � � þ � ü � ÿ � ù � � � � þ � þ ý � ù � þ � ÿ ü

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) � û þ � ù � � û þ ü) � û þ � ù � � û þ ü èä û þ ý þ ù ü � ÿ � � � ÿ � þ � ÿ ü A ã R G J I K L B C ÿ C µÆ Ç È Ç Æ Ë á � � Ø á Þ á Ô Ü Ù Ö Ú Û Ô Ü Ý Ö Ô Þ Ú Ö Ë ß Ô × Ö Ò Ô à á â Õ Ú Þ Ù Ö Ô à � Ö Ô à à Ô Ü × Õ Ü � Ú Õ �� Ö Ô à � Ö Ô à à Ô Ü � Ú Õ Û Ö Ô � Ô � Ô × � àú û þ � � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û � ý � ù � þ � � � � û þ � � � � ý þ � þ � ý � þ ý ü � ý þ ü ü þ � ÿ � � � � � �� ý þ ü � ý þ ü ü þ � � þ ÿ � ü � � � ü � � þ � � � � ü ù � � ù ù � ÿ � � ÿ � ù ÿ � � þ � ü ù � � ÿ � � � � � � ÿ ù � ù � � ÿ � � þ ÿ ü � � û þ � ù � ù � �ÿ � � � � � � ý ÿ � ü þ ý ü þ ý þ ù � � ý � þ � þ � � � ü � þ � ù ù þ � ù � ! þ � � ù � � $ � 1 � + � + � � û ù ü ý þ � � ý � � � ÿ � � þ� þ � þ ý � ù � þ � ÿ ü � û þ � ù � ù � � � � ý A ã R G J I K L B C ÿ C D ´� û þ ý þ . � � � ù � ÿ � ü û þ ÿ ý ý þ ü ù ü � ÿ � � þ � ý � ù � þ � � � � � � � ý þ � þ � û þ � ù � � � ù � þ � � ý ÿ � � ù � � ý þ ü � � ü ý � �� � � � ù � þ � ü û þ ÿ ý ÿ � � � � � þ � � � � ù � �ü û þ ÿ ý � ý � þ ÿ � ü þ � � ù � � � þ � � � ÿ � � � ý þ � � þ ÿ � � � ÿ � ÿ � � ù � � � � þ � � � û � � � � þ � � ý ÿ � þ �ÿ � � � ù ü � ý ù � � þ � � þ ÿ � � � ÿ � ü ÿ � � � ý þ � ü û þ ÿ ý � ý � þ ÿ � ü þ � � ù � � � þ � � þ � � þ ý � ÿ � � � ÿ � � � ù þ � � � ÿ � ü � � � ý ý ù � �ü ù � � � ÿ � þ � ü � � � ù � û � � ù � �� � � þ � � � ÿ ü ù � � � þ � ý ÿ � � ý ÿ � � ù � � ÿ � ü þ � � ù � � � þ � � þ � � þ ý � ÿ � � � ÿ � � � ù þ � � � ÿ � ü � � ù � �ù � � û þ ü �� ÿ � ù � � ÿ � � � ý þ � � � � þ � � ÿ � ü þ � � ù � � � þ � � þ � � þ ý � ÿ � � � ÿ � � � ù þ � � � ÿ � ü � � ù � � ù � �

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A ã R G J I K L B C ÿ C D D� û þ ý þ . ü þ � � ù � � � � � � ü � ý � û þ þ � � ý þ � þ ù � þ ý � � û þ � � � � � ü ù � þ ü þ � � ù � � � û þ ý þ � þ � ü ù � þ ü � ý þ ü üù ü � ÿ ü þ � � � þ � � þ ý � ÿ � � � ÿ � � � ù þ � � � ÿ � ü � ù � � û þ ü � �ý � � ý þ � � � � ü � � ü ù �� � � � ý þ ü ü ù þ ü � ý þ ü ü ù � � � � � ý þ � þ � þ � � þ þ � � ù þ � ý þ ü � ý þ ü ü � ý � þ ü � � � � � ÿ � þ ýÿ � � � � ÿ � � þ � ý ÿ � � � ý þ ü � ý þ ü ü � � ü ü þ ü � ÿ � þ � � ý þ � þ ù � þ ý � ü þ � � ù � � � û þ ý þ � þ � ü ù � þ ü � ý þ ü üù ü � ÿ ü þ � � � þ � � þ ý � ÿ � � � ÿ � � � ù þ � � � ÿ � ü � � ü ù �� � � ÿ � � ÿ � � � ý þ � � þ ÿ � � � ÿ � � � � þ � � ÿ � � ù � � � � � û þ � � � � � ù � û ù � � ý � � � � � � � � ü ù � þü þ � � ù � � � � ù � � ù � � û þ ü � �ú û þ � þ � ü û þ ÿ ý � ý ÿ � � ù � � � ÿ � ÿ � ù � � � � û þ ü þ � � ù � � � ÿ � � þ þ ü � ù � ÿ � þ � ÿ üA ã R G J I K L B C ÿ C D B� û þ ý þ . � � ù � ÿ � ü û þ ÿ ý ý þ ü ù ü � ÿ � � þ � ý � ù � þ � � � � � � � ý þ � þ � û þ � ù � � � ù � þ � � ý ÿ � � ù � � ý þ ü � � ü ý � � þ � � þ ü ü ù þ � ý ù � � ù � ÿ � � þ � ü ù � � ü ù � � þ � � � ù � �� � � � ý þ ü ü ù þ ü � ý þ ü ü ù � � � � � ý þ � þ � ÿ � þ ý ÿ � � � � ÿ � � þ � ý ÿ � � � ý þ ü � ý þ ü ü � � ü ü þ ü � ÿ � � þ � � ý � ù �� � ý � ü ü � ü þ � � ù � � ý þ ü ù ü � ù � � þ � � þ ý � ÿ � � � ÿ � � � ù þ � � � ÿ � ü � ý ÿ � � � � � ù � � � � þ � ÿ � � � ÿ � � þ� û þ � � û þ � þ � � ý � ù � � ù þ ü � ù � û ù � � û þ � ÿ � � þ � � ü ù � � ) � ÿ � � � � � ü ù � þ � þ � � þ ý � ù ü � û þý þ ü � � ÿ � � � � � � ý þ ü ü ù þ ü � ý þ ü ü ÿ � � û þ � þ � � ý � ù � � � û þ � � � � � ü ù � þ ü þ � � ù � � � � ý ÿ � � � � � ù � �� � þ � ÿ � � � ÿ � � þ � � þ � � � � � û � ý þ ü � ý þ ü ü ÿ � � � � � þ � � ü ý þ ü ù ü � þ � � � � ý þ � ÿ ü � � þ � � þ ýÿ � � ù � � ÿ � � � þ �� � þ ý � ÿ � � � ÿ � ù � � � û þ � þ � ý ÿ � ü û þ ÿ ý � ý ÿ � � ù � � ÿ � � � þ � ü û þ ÿ ý � ý ÿ � � ù � � � ÿ � ÿ � ù � ù þ ü � � û þü þ � � ù � � � ù � þ � � ÿ � � 9 � û þ � ù � ù � � � � û þ � � � ÿ � þ ü ù ü ü þ � þ � � þ � ÿ ü � û þ � � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û� ý � ù � þ � � � � � � � ý þ � þ �

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ú û þ � � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û � ý � ù � þ � � � � û þ ü û þ ÿ ý ý þ ù � � ý � þ � þ � � ù ü � ÿ � � � ÿ � þ � þ � ÿ � � � � � û þü ÿ � þ ÿ ü ù � 0 ' ÿ � ù � � $ � * � 3 � ù � û � û þ � � � � � ù þ ý þ � � þ � û ÿ � ù ü � ÿ � � � ÿ � þ � ÿ ü � � � � � ù � �) � ) A ã R G J I K L B C ÿ C D Óú � � ÿ � þ ü ý þ � û ÿ � � û þ � � � � ý þ � þ ü þ � � ù � � ù ü � ÿ ý � þ þ � � � û � � ü � � � ý � � û þ ÿ � � � ù þ � ü û þ ÿ ý � ù � ù üý þ ' ù ý þ � � û ÿ � ü û � � � � � � þ � � þ þ � � � � û þ ý � ù ü þ � þ � � ÿ ý � þ � û þ ü þ � � ù � � � ú û ù ü ù ü� � � � ù � ù � � ù ü þ � ÿ � � � � ü ù � ù � ÿ ý � � � û þ � � ! � ú � � þ � þ ý ÿ � � ý � � þ � ý þ þ � � � ÿ ù � þ � ÿ � � þ � � � � þ � û ÿ � � û þÿ � � � � � � ù � ù � � � ý ÿ � ü þ ý ü þ ý þ ù � � ý � þ � þ � � ÿ � � � û þ � ÿ � ù � � ü � ÿ � ù � � � ý ü � ù ý ý � ü ù ü� ÿ � � � ÿ � þ � � û þ ü ÿ � þ ÿ ü ù � ! þ � � ù � � ü $ � 1 � + � + ÿ � � $ � 1 � + � $ � � û ù ü ý þ � � ý � �, � ý þ ù � � � ý � ÿ � � � � � � û þ ÿ � � � � � � � � � ù � � ù � ÿ � ý þ ù � � ý � þ � þ � � ü û � � � ÿ � ü � � þ � û þ � � þ � ÿ � ÿ � �ü þ � � ù � � ü � � � ü ù � þ ý þ � � ú û ù ü ù ü � ý þ � ý � � � û � þ � þ ý ÿ � ÿ � � ü ù � � � ù ù þ � � ý � � þ � ý þ ü � þ ü � ý ù � þ � ÿ � � þ �� � ! � ú � � � " � � $ % % & � � ý � � � ü þ ü � û þ � � � � � ù � � þ ' ÿ � ù � � � � � û þ � � � û þ � ÿ � ÿ � ù � � � � � � � ù � � ù � ÿ � ý þ ù � � ý � þ � þ � � . A ã R G J I K L B C ÿ C D ÿ� û þ ý þ . ý þ ü ù ü � ÿ � � þ ÿ � � � ý ü � ÿ � þ � ý � � � ý � ù � � þ 3 � 3 � 1 � $ � � � ! � ú � � � " � � $ % % & � ÿ üÿ � � ý � � ý ù ÿ � þ � ý � � � þ � � � ü û þ ÿ ý ÿ � � ÿ � ù ÿ � ý þ ü ù ü � ÿ � � þ �" � ý � û þ � þ � þ ý ÿ � � ý � � þ � ý þ � � û þ ÿ � þ � ý ù � � þ � ý þ þ ù ü � ÿ � � � ÿ � þ � ü ù � � 0 ' ÿ � ù � � $ � 1 � 1 �� � � þ þ ý � � û þ ÿ � þ � ý ù ü � ù ý þ � � � � � ÿ � � � ÿ � þ � ý � � 0 ' ÿ � ù � � $ � 1 � + * � ý � û þ ü ù � � � ù ù þ �� ý � � þ � ý þ � ý � ý þ ü � ý þ ü ü þ � ÿ � � � � � � � ý þ ü � ý þ ü ü þ � � þ ÿ � ü �

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Æ Ç È Ç Ê � � Ú Ü Ô Ù Ö Ú Û Ô Ü Ý Ö Ô Þ Ú Ö Ë ß Ô × Ö Ò Ô à á â Õ Ú Þ Ù Ö Ô à � Ö Ô à à Ô Ü × Õ Ü � Ú Õ �� Ö Ô à � Ö Ô à à Ô Ü Ð Ô á Õ Þ Ú Ö Û Ô Ü � Ú Õ Û Ö Ô � Ô � Ô × � à� ( ) ( � � þ * + & � % & � ý þ ü þ � � ü ÿ ü þ � � þ ' ÿ � ù � � ü � � � ý þ � ù � � � û þ � � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û � ÿý þ ù � � ý � þ � � � � � ý þ � þ ü þ � � ù � � � 0 � � þ ý ù � þ � � ü û ÿ þ ü û � � � � û ÿ � � û þ � ( ) � ý � ù ü ù � � ü � ý ü û þ ÿ ý � � þ ý þ ü � ù � ÿ � þ � û þ ü û þ ÿ ý � ÿ � ÿ � ù � � � ÿ � ù þ � ü þ � � ù � � ÿ � � ÿ ý þ � þ � � � � � ù � ÿ � � � � � þ þ ý � ù � � ÿ üý þ � � � � ù - þ � � û ÿ � � ( ) þ ' ÿ � ù � � ü � ý ü û þ ÿ ý � þ ý � þ ü � ù � ÿ � þ ü � û þ ü û þ ÿ ý � ÿ � ÿ � ù � � � ý � ÿ ý � þ � ù � û � � �ý þ ù � � ý � þ � � � � � ý þ � þ � þ ÿ � ü � ù � û � � � ý ÿ � ü þ ý ü þ ý þ ù � � ý � þ � þ � � ! û ù � � ÿ þ � ÿ � � � + 6 & 6 � �� ü ü � ÿ � þ � þ ÿ ý � ù þ ý � � û þ � � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û � ÿ � � � � ý þ � þ ü þ � � ù � � ù ü � û þ ü � � ÿ � ù � � � � û þ� � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û ü � ý � ù � þ � � � � û þ � � � � ý þ � þ ÿ � � � û þ � ý ÿ � ü þ ý ü þ ý þ ù � � ý � þ � þ � � � ú û þ ÿ � þ � � ý ÿ � � � � � ý þ ü � ý þ ü ü þ � � � � � ý þ � þ ü þ � � ù � � ü � � þ � � þ � � � � � � � ü û þ ÿ ý ÿ � � � þ � ý þ � ÿ � � þþ ü � ù � ÿ � þ � ÿ ü A ã R G J I K L B C ÿ C D �ä û þ ý þ ÿ ü � û þ ü û þ ÿ ý ü � ý þ � � � û � ý � ù � þ � � � � û þ � � � � ý þ � þ � ý � ý þ ü � ý þ ü ü þ � � þ � � þ ý ü � ÿ � � þþ ü � ù � ÿ � þ � ü ù � � � û þ � � � � � ù � � þ ' ÿ � ù � � ü A ã R G J I K L B C ÿ C D '� ý A ã R G J I K L B C ÿ C D (� û þ ý þ � þ þ � � � � � þ � ÿ � þ � � þ ü ü � û ÿ � � ý � � � û þ ' ÿ � ù � � ü � ú û þ ÿ � þ � � � � þ � � � ÿ ü ù � � � þ � ý ÿ � � ý ÿ � � ù � � � þ � � þ � � þ ý � ÿ � � � ÿ � � � ù þ � � � ÿ � ü � ÿ � ÿ � þ ý � ÿ ù � ü þ � � ù � � ù � � � � � ù � � ù üA ã R G J I K L B C ÿ C D �

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� û þ ý þ . � � � � ý þ ü ü ù þ ü � ý þ ü ü ù � � � � � ý þ � þ � þ � � þ þ � � ù þ � ý þ ü � ý þ ü ü � ý � þ ü � � � � � ÿ � þ ýÿ � � � � ÿ � � þ � ý ÿ � � � ý þ ü � ý þ ü ü � � ü ü þ ü � ÿ � þ � � ý þ � þ ù � þ ý � ü þ � � ù � � � û þ ý þ � þ � ü ù � þ ü � ý þ ü üù ü � ÿ ü þ � � � þ � � þ ý � ÿ � � � ÿ � � � ù þ � � � ÿ � ü � � ü ù � �� � þ ý � ÿ � � � ÿ � ù � � � û þ ÿ � þ ü � ý ÿ � � � � û þ � � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û � ý � ù � þ � � � � û þ� � � � ý þ � þ ù ü ÿ ü ü � þ � ÿ ü � û þ � ù � ù � � � � ý �) � ù ü ù � � � ý � ÿ � � � � � � � þ � û ÿ � � û þ ù � � � ù � ÿ � ù � � ÿ � � � þ � ý � û þ � ù ÿ � � � ÿ � � � � � ý þ ü ü ù þ ü � ý þ ü ü ù üÿ ü ü � þ � ÿ ü 1 3 ù � � û þ ü û þ ÿ ý � ý � ù ü ù � � ü � � û þ � ( ) ( � � þ � � þ � � þ � � � þ � þ ý � ù � þ � û ù � û ù ü � û þ� � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û � ý � ù � þ � � � � û þ ü û þ ÿ ý ý þ ù � � ý � þ � þ � � � 0 ' ÿ � ù � � $ � 1 � 3 ù ü � � � ù ù þ � � �A ã R G J I K L B C ÿ C D µé è ê è � è ë ì í î í ï ð ï ñ ò ó î ô õ ö ò ô ö ÷ ö í î ø ù ò ú ö ï ö î û� � � � ý � ù � � � � ü þ � � ù � � + + � 1 � 4 � + � � û þ � ( ) ( � � þ � ÿ � ù � ù � � ÿ ý þ ÿ � ü û þ ÿ ý ý þ ù � � ý � þ � þ � �ü û ÿ � � � þ � ý � ù � þ � ù � ÿ � � ý þ ù � � ý � þ � � � � � ý þ � þ � þ � ý ÿ � � þ � � þ ý ü � � ý þ ü � ý þ ü ü þ � ÿ � � � � � �� ý þ ü � ý þ ü ü þ � � � û þ ý þ þ � � þ þ � ü � þ � � þ � � ù � � þ � � þ ý ü ü ÿ � ù ü � ù � � � û þ � ÿ ü þ ü ü � þ � ù ù þ � � � � û þ� � � þ � A ã R G J I K L B C ÿ C B ´# � ü û ÿ � � � � � � þ � þ ü ü � û ÿ � � � � ü � � û þ � � � � ý þ � þ ü � ý þ � � � û ü û � � � � þ ù � � ü ù �� � � � ý � ù � � � � ü þ � � ù � � + + � 1 � 4 � 1 � � ( ) ( � � þ � � ý � ý þ ü � ý þ ü ü þ � � þ � � þ ý ü � ù � û ÿ � þ þ � � ù þ� ý þ ü � ý þ ü ü � ý � þ � � � � þ ü ü � û ÿ � 1 % � þ ý � þ � � � � û þ � þ � ü ù � þ ü � ý þ � � � û � � û þ � þ � ý ÿ � ý þ ù � � ý � þ � þ � � �ü û ÿ � � � � � � þ � þ ü ü � û ÿ � � û þ ü � ÿ � � þ ý ÿ � þ � � 0 ' ÿ � ù � � $ � 1 � $ % � ÿ � � � 0 ' ÿ � ù � � $ � 1 � $ + � �A ã R G J I K L B C ÿ C B Dú û þ ÿ � � þ þ � � � ÿ � ÿ � ù � � � ÿ � � þ � ý ù � � þ � þ � � � ù � ù � � � ÿ ü

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A ã R G J I K L B C ÿ C B Bé è ê è � è é ì ó ü í ï ð ï ý þ ó ú í î ÿ ù ø ñ ò ó î ô õ ö ò ô ö ÷ ö í î ø ù ò ú ö ï ö î û� � � � ý � ù � � � � ü þ � � ù � � + + � 1 � 3 � + � � û þ � ( ) ( � � þ � ü � ÿ � ù � � � ü û þ ÿ ý ý þ ù � � ý � þ � þ � � � � ÿ � þ �� þ ý � þ � � ù � � ÿ ý � � ÿ � ù ü � � þ � � þ ý ü û ÿ � � � � � þ � � þ þ � � ý � � � � � ý þ ü � ý þ ü ü þ � � þ � � þ ý ü � ý � ý� ý þ ü � ý þ ü ü þ � � þ � � þ ý ü � � � ý $ 1 ù � � û þ ü �ú û þ � ÿ � ù � � ü � ÿ � ù � � ü û ÿ � � � þ ý þ � � þ � � � � � þ � û ÿ � ù þ � � þ þ � ü �" ý � û þ ý � � ý þ � ù � û þ ÿ � þ � ý þ � � þ þ � � � û þ � � � � ý þ � þ ÿ � � û þ ü þ � � ù � � � ÿ � � ý ü û � ú �ÿ � ù � � ý ü û ù � � � � û þ � � � � ý þ � þ � ÿ � ÿ ý � þ ý ü þ � � ù � � ü û � � � � þ ü þ � þ � � þ � �! þ � � ù � � 3 � & � * � 4 � � û þ � � ! ú � � � � " � # ý ù � � þ � þ ü ù � � ! � þ � ù ù � ÿ � ù � � ü � $ % % & � � ý � ù � þ ü� þ ý � ù � þ � � þ ' ÿ � ù � � ü � � � þ ü ù � � ÿ � � � � ý þ � þ ü þ � � ù � � � � þ ý � � � � ù � þ � ü û þ ÿ ý ÿ � � � � ý ü ù � � � ú û þ� ý � � þ � ý þ ù ü � ÿ ù � � � � ÿ ü þ � � � � û þ � þ � þ ý ÿ � � þ � û � � � ý ü û þ ÿ ý � ù ü � ü ü þ � þ ÿ ý � ù þ ý �� � � þ � ÿ ù � ü û ÿ þ � þ þ � � ý � ù � þ � ù � � û þ � � � þ ÿ � � � û � � � � � þ ü ù � � ÿ ü þ � � ù � � � ý � � � � ù � þ �ü û þ ÿ ý ÿ � � � � ý ü ù � � ù � û þ ü ù � � � ù ù þ � ÿ � � ý � ÿ � û ù ü ü þ � � ý � û þ ü û þ ÿ ý � ÿ ý � � � þ � � þ � � � � � � û þ � þ ü ù � �� ý � � þ � ý þ � û ù � û ù ü ù � � û þ � � � þ ù ü � ù ü � ü ü þ � û þ ý þ � � � � û þ þ � � � � û þ � ( ) � ý � � þ � ý þ � � � þ ü ù � � ÿü þ � � ù � � � � þ ý � � � � ù � þ � ü û þ ÿ ý ÿ � � � � ý ü ù � � ù ü þ � � � ÿ ù � þ � �Æ Ç � Ç É Ê Ê Ë Ì Í Î Ï Ð Ñ Ò Ò Ô à á â Õ Ù Ö Ú Û Ô Ü Ý Ö Ô Þ Ú Ö Ë Ô Û � á Ú Õ à Ë Ý � Ô Û � Ô Ü � Ú � Ú � á Õ Ô ÜË ß Ô × Ö × Õ Ü Í Ú Ö à á Ú Õ� ü ü � ÿ � þ � þ ÿ ý � ù þ ý � � û þ � � ! � ú � � � " � � þ � þ ý ÿ � � ý � � þ � ý þ ù ü ü þ � � � � þ ü ù � � ÿ ü þ � � ù � � � � þ ý� � � � ù � þ � ü û þ ÿ ý ÿ � � � � ý ü ù � � � ú û þ ü þ � � ù � � ù ü � ý ù � ÿ ý ù � � � þ ü ù � � þ � � ý � þ � � ù � � � ú û þ � þ � � þ � ý � ÿ � � � û þþ � � þ ý � ÿ � � � ÿ � ü ÿ � � � ù þ � � � � û þ ü þ � � ù � � ÿ ý þ � û þ � ü þ � � � � û þ � � � û þ ü û þ ÿ ý � � � ý ü ù � � ü � ý þ � � � û � � û þü þ � � ù � � � ! ù � � þ � þ ü ù � � ù ü ÿ � ù � þ ý ÿ � ù þ � ý � � þ ü ü � � û þ � ý � ü ü � ü þ � � ù � � ÿ � � ý � � þ ý � ù þ ü ÿ � � � û þ ý þ ù � � ý � þ � þ � �� � � û � � � � ù � � ù � ÿ � ÿ � � � ý ÿ � ü þ ý ü þ ÿ ý þ � ý � ù � þ � � ù þ ý þ � � ÿ � þ ü � � ù � � û þ � þ ü ù ý þ � ü û þ ÿ ý � � � ý ü ù � �ü � ý þ � � � û ù ü ÿ � û ù þ þ � �# þ � � � ÿ ý þ � û þ � þ � þ ü ü ÿ ý � ü � þ � ü � � � þ ü ù � � ÿ ü þ � � ù � � � ý ü û þ ÿ ý ÿ � � � � ý ü ù � � .

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+ � � þ � þ ý � ù � þ � û þ þ � � þ ý � ÿ � � � ÿ � ü ÿ � � � ù þ � � � � û þ ü þ � � ù � � � � � ü ù � þ ý þ � �ú � � � � û ù ü � � û þ � þ ÿ � û ÿ ü � � � þ ÿ � ÿ � � - þ � � ý � û þ þ � � þ ý � ÿ � � � ÿ � ü ü ù � � � û þ � � ÿ � � � � � ù � ÿ � ù � � � û ÿ � � ý � ù � þ � û þ � ÿ � ù � � � � ÿ �þ þ � � ü � ú û þ ü þ � � ù � � ù ü � û þ � � þ ü ù � � þ � � ý � þ � � ù � � ÿ � � � û þ � ý � ü ü �ü þ � � ù � � ÿ � � ù � þ � ü ù � � ü ÿ � � � û þ ÿ � � � � � � � � � ù � � ù � ÿ �ý þ ù � � ý � þ � þ � � ÿ ý þ ý � � û � � � þ � þ ý � ù � þ � �$ � � ÿ ù � � � û þ þ � � þ ý � ÿ � � � ÿ � þ þ � � ü � ÿ � ù ÿ � � ý � þ � ü û þ ÿ ý � ÿ � �� þ � � ù � � � � � þ � � � ÿ � � û þ ü þ � � ù � � � � û þ ü � ý ÿ ù � ù � � û þ � � � � ù � � ù � ÿ �� þ � ü ù � � ý þ ù � � ý � þ � þ � � ù ü � ÿ � � � ÿ � þ � ü ù � � 0 ' ÿ � ù � � $ � * � 2� ý � ù � þ � ÿ � � þ � ) � ù ü ý þ ' ù ý þ � � � ü � ü � ù � � þ ù � 0 ' ÿ � ù � � $ � * � 2� ù � û � û þ þ ' ù ÿ � þ � � ü û þ ÿ ý �" � ý ü � � ù � ü þ � � ù � � ü . A ã R G J I K L B C � C D" � ý � � � ü þ � � ù � � ü . A ã R G J I K L B C � C B* � ú � � þ � þ ý � ù � þ � û þ � � � ù � ÿ � ü û þ ÿ ý ü � ý þ � � � û � ÿ ü þ � � ù � � � ý � ù � þ �� � � � � � ý þ � þ � � � û þ ÿ � þ � ý � � ü � þ � $ ù ü ü � ü � ù � � þ � ù � � �0 ' ÿ � ù � � $ � 1 � $ � � � þ � þ ý � ù � þ � û þ ÿ � þ � ý � ) � û þ � � � � ý þ � þü � ý þ � � � û ù ü � ý � ù � þ � ù � � ü ù � �� � û þ ý � ù ü þ ù ù ü � ù þ � ù � , � ÿ � ù � ü �1 � ! � ü � ù � � þ � û þ ÿ � þ � � � � ÿ ù � þ � ý � � ü � þ � $ ù � � � 0 ' ÿ � ù � �$ � 1 � 4 � � � þ � þ ý � ù � þ � û þ � � � ù ù þ � ÿ � � � þ � ù � � � ù � ÿ � ù � � � � ù ÿ � � � ÿ �� � � � ý þ ü ü ù þ ü � ý þ ü ü þ ü � ù � � þ � ý þ þ ü � �

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3 � ) ü ü û þ ÿ ý ý þ ù � � ý � þ � þ � � ý þ ' ù ý þ � � � � ü û þ ÿ ý ý þ ù � � ý � þ � þ � � ù üý þ ' ù ý þ � ù �4 � ) ü � � þ 0 ' ÿ � ù � � $ � 1 � 3 � ý ÿ � þ ýü � ü � ù � � ù � � � û þ ÿ � þ � ý � � � ÿ ù � þ � ù � ü � þ � 1 � � � � þ � û ÿ ��2 � ( ÿ � � � ÿ � þ � û þ � � ý ü ù � � ÿ � � ý ÿ � � ù � � � � � þ � � � ý � û þ ü þ � � ù � �� � � ü ù � þ ý þ � ü ù � � � û þ � ù þ � þ ' ÿ � ù � � .A ã R G J I K L B C � C Ó� û þ ý þ . ÿ � � � ý þ � � � ý ü ù � � ÿ � � � � þ � � � � ù � � ù � � û þ ü � �� � ý ü ù � � ÿ � � ý ÿ � � ù � � � � � þ � � � � ù � � ù � � û þ ü � �� � � ÿ � ÿ ý þ ÿ þ � � � � ü þ � � � � � ü ù � þ � þ ý ù � þ � þ ý � � � � � ý þ � þ� ý � ü ü � ü þ � � ù � � � ù � � û þ ü å � �� û þ � þ � � � û � � û þ � � ü ù � þ � þ ý ù � þ � þ ý � � û þ � � � � ý þ � þ ü þ � � ù � �� ù � � û þ ü � �� � � � ý þ ü ü ù þ ü � ý þ ü ü ù � � � � � ý þ � þ ÿ � þ ý � ý þ ü � ý þ ü ü � � ü ü þ ü û ÿ þ� � � ý ý þ � þ ù � û þ ý ÿ � � û þ � þ � � ý � ù � � � û þ � ý � ü ü � ü þ � � ù � �ý þ ü ù ü � ù � � � ý ÿ � ü ù þ � � � � ÿ � ü � ý ÿ � � û þ � � � � ù � � � � û þ � þ � ÿ � � � ÿ � � þ � û þ ý þ � û þ � þ � � ý � ù � � ù þ ü ù � � û þ � ÿ � � þ � � ü ù � �% � 6 � ü � þ � ù ù þ � ù � � ý � ù � � þ 3 � 3 � 1 � * � � û þ � � ! � ú � � � " �� $ % % & � �& � ! û � � � � � ý ü ù � � � þ � � � ü ù � þ ý þ � � ) � û þ þ � � þ ý � ÿ � ÿ � � � ý þ � � � ý ü ù � � ÿ �� � � þ � � ÿ � � � ù þ � � � � û þ ü þ � � ù � � ù ü ü � û � û ÿ � �� � ý ü ù � � � ü � � þ � � � ü ù � þ ý þ � � � � û þ ý � ù ü þ � ù � � � ý þ � û þ � � ý ü ù � � �

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A ã R G J I K L B C � C ÿ� û þ ý þ . ÿ ý þ ÿ þ � � � � ü þ � � � � û þ ü û þ ÿ ý � � � � ÿ � û � ù � � � � ù � � ÿ � � ÿ ý þ ÿ� û � � þ ü � û þ ý þ ù � � ù � � û þ ü å � � ) � ù ü � þ ý � ù � � þ � � � � ÿ � þ ÿ ü& 3 Ò � � û þ ÿ ý þ ÿ þ � � � � ü þ � � � � û þ � þ � � þ ý � ù � þ � ü � ù ý ý � ü �ÿ ý þ ÿ � � � þ � þ � � � � � ü þ � � ý ÿ � ü þ ý ü þ � � ý ü ù � � ý þ ù � � ý � þ � þ � �ù � ü � � ù � � þ � � þ ý ü � ù � � û þ ü å � �ÿ � � � þ � � ý ÿ � � ÿ ü � þ � þ ý � ù � þ � ù � ÿ � � � ý � ÿ � � þ � ù � û 0 ' ÿ � ù � �$ � * � 4 ü ù � � � û þ � � � ù ù þ � ü � ý ÿ ù � � ÿ � � � ÿ � þ � ù � ü � þ � $ �6 � ! � � þ 0 ' ÿ � ù � � $ � 3 � 1 � ý ÿ � � ü � ù � � ù � û � û þ � � � � � ü � þ �3 � A ã R G J I K L B C � C �+ % � ú û þ ÿ � � � � � � ý ÿ � ü þ ý ü þ ý þ ù � � ý � þ � þ � � � � � ÿ ù � þ � ý � � ü � þ � &ü û � � � � þ þ ' ÿ � � � � ý � ý þ ÿ � þ ý � û ÿ � � û þ ÿ � � � � � ù þ � � � � û þþ ' ÿ � ù � � � þ � � � A ã R G J I K L B C � C '+ + � � � � � ý � ù � � � � � û þ � � ! � ú � � � " � � � û þ ü � ÿ � ù � � � � ý ÿ � ü þ ý ü þý þ ù � � ý � þ � þ � � ü û ÿ � � � � � þ � � þ þ � � û þ � ÿ � ù � � � þ ý � ù � � þ �ü � ÿ � ù � � � � � þ � þ ý � ù � þ � ÿ ü .) � û þ � ù � � û þ ü) � û þ � ù � � û þ ü

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� � � þ � û ÿ � � ù þ � ù � 0 ' ÿ � ù � � $ � * � 6 ù ü � � � ù ù þ � � ý � � ý ü ù � � ü ù � � � ý � ù � þ � � � 0 ' ÿ � ù � � ü $ � 3 � + ÿ � � $ � 3 � $ �+ $ � ) ü � û þ � ý � ü ü � ü þ � � ù � � � ÿ ý � þ þ � � � û � ) �� û þ ü þ � � ù � � ù ü � ÿ ý � þ þ � � � û � � � û þ ý � ù ü þ þ � � ÿ ý � þ � û þ ü þ � � ù � � �+ * � � ü ÿ � ÿ ü � ü � þ � � � û þ � � � � ù � � ù � ÿ � ý þ ù � � ý � þ � þ � � ù � ü � � ù � ü þ � � ù � � üü û ÿ � � � þ � ý � � � ý � ù � � þ � � � ü ÿ � ù ü �A ã R G J I K L B C � C (� û ù � þ � ý � � � ü þ � � ù � � ü � û þ � � � � ù � � ù � ÿ � ý þ ù � � ý � þ � þ � � � ý� � ý ü ù � � � ù � ÿ � � ù � ù � � � � � û ÿ � ý þ ' ù ý þ � � ý � þ � ý þ � ü û ÿ � � � � � � þ � þ ü ü� û ÿ � A ã R G J I K L B C � C �Æ Ç � Ç Æ Ê � É � � � � Ò Ô à á â Õ Ù Ö Ú Û Ô Ü Ý Ö Ô Þ Ú Ö Ë Ô Û � á Ú Õ à Ë Ý � Ô Û � Ô Ü � Ú � Ú � á Õ Ô Ü Ë ß Ô × Ö× Õ Ü Í Ú Ö à á Ú Õú � � þ ü ù � � ÿ � ý þ ü � ý þ ü ü þ � � ý � � � � � ý þ ü � ý þ ü ü þ � � þ � � þ ý � � þ ý � � � � ù � þ � ü û þ ÿ ý ÿ � � � � ý ü ù � �� � ÿ � ù � � ü ù � � � û þ � ( ) * + & � % & � ý � ù ü ù � � ü � � û þ � � � � � ù � � ü � þ � ü � ÿ � � þ � � � � � þ � .+ � ! û � � � � � ý ü ù � � � þ � � � ü ù � þ ý þ � � ) � û þ ÿ � � � ù þ � � � ý ü ù � � � � ÿü þ � � ù � � � � ý þ ü � ý þ ü ü þ � � ý � � � � � ý þ ü � ý þ ü ü þ � � ù ü � ý þ ÿ � þ ý � û ÿ � � û þ� � ý ý þ ü � � � � ù � � ÿ � þ � ù þ � � � 0 ' ÿ � ù � � $ � 3 � 6 � � û þ ü þ � � ù � � û ÿ ü � �� þ � þ ü ù � � þ � ÿ � � � ý � ù � � � � � � � û þ ý � ù ü þ � � � ý ü ù � � ù ü � � � ÿ � � � � þ ý �ÿ � � � � � � � þ ù � � � ý þ � �" � ý � � � � � ý þ ü � ý þ ü ü þ � � þ � � þ ý ü .

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A ã R G J I K L B C � C µ G" � ý � ý þ ü � ý þ ü ü þ � � þ � � þ ý ü . A ã R G J I K L B C � C µ Vù ü � û þ � � ü ù � þ � þ ý ù � þ � þ ý � � � � � ý þ � þ � ý � ü ü � ü þ � � ù � � ÿ � � ù üþ ' ÿ � � � � þ ù � þ � þ ÿ ý � ù þ ý � ù ü � û þ ý þ ü ù ü � ÿ � � þ ÿ � � � ý � û ù � û ù üþ ' ÿ � � � % � 2 3 � � � � þ � û ÿ � ù ü � û þ � û ý þ ü û � � � � � ý ü ù � � �$ � 0 ' ù � ù � ý ù � � ý � � � � ÿ � ù � ù � ù � � � � ý ü ù � � � � � � � ý � ù � � � � ü þ � � ù � �+ + � 3 � $ � + � � ( ) ( � � þ � ù � û þ ÿ � � � ù þ � ÿ � � � ý þ � � � ý ü ù � � � ù � ÿ� þ � � þ ý ù ü ý þ ' ù ý þ � � � � ÿ ù � � ÿ ù � þ ' ù � ù � ý ù � ÿ � � ù ü � ý þ ÿ � þ ý � û ÿ �� û þ ÿ � þ � ù þ � � � 0 ' ÿ � ù � � $ � 3 � 6 � þ � þ � � ù � � � � � û þ � û þ ý � û þ� þ � � þ ý ù ü � ý þ ü � ý þ ü ü þ � � ý � � � � � ý þ ü � ý þ ü ü þ � � � û þ � þ � � þ ý ü û ÿ � � � þ� þ ü ù � � þ � � � � ÿ ý ý � � � � � þ þ ý � ù � ÿ ü � ÿ � ù � ÿ � � � ù � � þ � þ ý � ù � ÿ � þü � ý � � ý þ � û þ ý þ ü ù � � ù ù � ÿ � � ý þ � � � ù � � ù � � ÿ � � � � ý � � �� ý ÿ � � ù � � � � û þ � ÿ � ù � � ù ü � þ ý � ù � � þ � � � � þ ý þ � � þ � � � � û þ ÿ � þ ü � ù þ � � � 0 ' ÿ � ù � � $ � 3 � + % �* � " � ý � � � � � ý þ ü � ý þ ü ü þ � � þ � � þ ý ü . A ã R G J I K L B C � C D ´ G" � ý � ý þ ü � ý þ ü ü þ � � þ � � þ ý ü . A ã R G J I K L B C � C D ´ V

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1 � ) ü � û þ ü þ � � ù � � � ÿ ý � þ þ � � � û � � ý þ ü ù ü � � û þ ÿ � � � ù þ � � � ý ü ù � � � ú �ÿ � ù � � ý ü û ù � � � � û þ ü ý ÿ � þ � � � � ý þ � þ � þ � � ù � � � ù � þ �� � � � ý þ ü ü ù þ ü � ý þ ü ü þ ü � � û þ ü þ � � ù � � ü û ÿ � � û ÿ þ þ � � � û � ý � ü ü �ü þ � � ù � � ÿ � ÿ ý þ ÿ � ú û þ ü ý ÿ � þ � � � � ý þ � þ ù � û � � � � � � þ � � þ ý ü � ÿ �� ý ü û ü � � � � � � û þ ü ù � þ � û þ ý þ � û þ � þ � ý ÿ � ü û þ ÿ ý ÿ � � � � ý ü ù � � ÿ �ü û þ ÿ ý ü � ý þ ü ü þ ü ÿ ý þ ÿ � � þ � �" � ý ü � � ù � ü þ � � ù � � ü . A ã R G J I K L B C � C D D G" � ý û � � � � � ü þ � � ù � � ü . A ã R G J I K L B C � C D D V� � � þ � û ÿ � � û þ ÿ � � þ þ ' ÿ � ù � � ü � ÿ � � þ ü þ � � � � û � ý � ý þ ü � ý þ ü ü þ �ÿ � � � � � � � ý þ ü � ý þ ü ü þ � � þ � � þ ý ü � " � ý � ý þ ü � ý þ ü ü þ � � þ � � þ ý ü � � û þ� þ � � û ù � � û þ ÿ � � þ þ ' ÿ � ù � � ü ù ü � ÿ � þ � ÿ ü � û þ � ù ü � ÿ � � þ ý � �þ � � ý þ � þ � � � � ý þ ü ü ù � � ù � þ ý � � � þ � � ý � ù � � � û þ � ý þ ü � ý þ ü ü þ ü ÿ � �� � � � � ý þ ü � ý þ ü ü þ � � � � � ù � � ù � ÿ � � þ � ü ù � � ý þ ù � � ý � þ � þ � � � � � þ þ �� � � � þ � ÿ � þ � � þ ü ü � û ÿ �3 � ú û þ ü � ù ý ý � ü ÿ ý þ ÿ ý þ ' ù ý þ � � ý � û þ � � ý ü ù � � ù ü � ÿ � � � ÿ � þ � ü ù � �0 ' ÿ � ù � � $ � 3 � 1 � ú û ù ü ÿ ý þ ÿ ù ü � û þ � ÿ � � þ � � � � û þ ü � ù ý ý � ü ÿ ý þ ÿý þ ' ù ý þ � � � ü û þ ÿ ý � ÿ � � � ÿ � þ � � ÿ ü þ � � � 0 ' ÿ � ù � � $ � 1 � + 6 � ú û þÿ � � � þ ù � 0 ' ÿ � ù � � $ � 3 � 1 ù ü ÿ ü ü � þ � ÿ ü 1 3 � � ý þ ü � ý þ ü ü þ �ÿ � � * 2 � 34 � ú û þ � ù � ù � � ÿ ý þ ÿ � � ý ÿ � ü þ ý ü þ ý þ ù � � ý � þ � þ � � ý þ ' ù ý þ � � ý� � � û � � ý ü ù � � ÿ � � ü û þ ÿ ý ü û ÿ � � � � � � þ � þ ü ü � û ÿ �

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A ã R G J I K L B C � C D B� � � þ � û ÿ � � û þ ü � ÿ � ù � � � ý � ý ÿ � ü þ ý ü þ � � ý ü ù � � ý þ ù � � ý � þ � þ � � ü û ÿ � �� � � þ � � þ þ � � û þ ü � ÿ � � þ ý � � ý + $ ù � � û þ ü �2 � ú û þ � � � � ù � � ù � ÿ � ý þ ù � � ý � þ � þ � � ý þ ' ù ý þ � � ý � � ý ü ù � � � ÿ � � þ� ÿ � � � ÿ � þ � ü ù � � � û þ � � � � � ù � � þ ' ÿ � ù � � A ã R G J I K L B C � C D Óú û þ ý þ ' ù ý þ � � � � � ù � � ù � ÿ � ý þ ù � � ý � þ � þ � � � ý � � ý ü ù � � ü û � � � � � �� þ � þ ü ü � û ÿ � � û þ � ù � ù � � ý þ ù � � ý � þ � þ � � � ý � � � ü þ � � � � ( ) ÿ � �� ù þ � � þ � � � A ã R G J I K L B C � C D ÿ

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ú û þ � ý � � ü þ � � û ù ü � û ÿ � � þ ý ù ü � � þ ÿ � ÿ � þ � û þ ÿ � ÿ � � � ù � ÿ � � � � � ü þ � � � � þ � þ ý � ù � þ � û þ ü û þ ÿ ý� ÿ � ÿ � ù � � � ÿ � � � � ý þ � þ ü þ � � ù � � ÿ � � � þ þ � � � þ � ÿ � � ù � � þ ý ÿ � � ù � � � ù ÿ � ý ÿ � ü � ý � � � � ý þ � þ � þ � � þ ý üü � � þ � � þ � � � � � � � ù � þ � ü û þ ÿ ý ÿ � � � � ý ü ù � � � ) � ( û ÿ � � þ ý $ � � û ù ü ý þ � � ý � � þ � þ ü ü ÿ ý � ù � � ý � ÿ � ù � � ÿ � � �, � � ù ù þ � ( � � � ý þ ü ü ù � � " ù þ � � ú û þ � ý � � , ( " ú � ÿ � � ù � ü ÿ � � � ù � ÿ � ù � � � � � þ � þ ý � ù � þ � û þ ü û þ ÿ ý � ý� � � � ù � þ � ü û þ ÿ ý ÿ � � � � ý ü ù � � � ÿ � ÿ � ù � � � ÿ ü þ � � ù � � � þ ý þ � ý � ù � þ � � � þ ü þ ÿ ý � û � þ ý � ý � þ � � � # þ � � - þ �ÿ � � � $ % % 4 � ü û � � � û ÿ � � û þ , ( " ú ÿ � � ù � ü ü ù � � � ù ù þ � þ ý ü ù � � � ù þ ÿ � � � ü � þ � ÿ � � � � � û þ ü ÿ � þ ý þ ü � � ü ÿ � �� � � � ý � ü � þ � � � � � û þ þ � � þ ý ù � þ � � ÿ � ý þ ü � � ü � ) � � û ù ü � û ÿ � � þ ý � � � � � ý � � ÿ � ÿ � ÿ � � � ù � ÿ � � � � � � ÿ � � þ �� þ ü � � � ü þ � $ % % % � û ù � û ù ü � ÿ ü þ � � � � � � ù ù þ � � � � � ý þ ü ü ù � � ù þ � � � û þ � ý � ù ü þ ÿ � ÿ � þ � � ) � ÿ � � ù � ù � � �þ � ÿ � � ù � � þ ý ÿ � � ù � � � ù ÿ � ý ÿ � � ý � û þ � þ � þ ý ÿ � � ý � � þ � ý þ � � � ! � � � � " � ÿ ý þ � ý ÿ � � �� þ ü � � � ü þ � $ % % % � ÿ ü � þ þ � � � þ � � � # þ � � - ÿ � � ( � � � ù � ü � $ % % % � � ú û ù ü ä ù � � � � ü � ý � � ý ÿ � ù ü� ÿ ü þ � � � , ( " ú � û ù � û � ÿ � ÿ � ÿ � � - þ � � � þ � � � ü û þ ÿ ý � ü û þ ÿ ý � ÿ � ù ÿ � � � ÿ � � ÿ � � � � � þ � � � ÿ � ù ÿ � � � ÿ �ý þ ü � � � ü þ ü � ÿ � � � � ý þ � þ ü þ � � ù � � � � þ ü � � � ü þ � $ % % % ù ü � þ ü ù � � þ � � � � � � ÿ ù � � û þ ý þ ü � � � ü þ � ÿ ü þ � � ù � � ü ù � � � û þ ù � ù � ù ÿ � ù � � � � ÿ � ÿ � ú û þ ù � � � � ÿ � ÿ � þ � þ � � ü � � � û þ � þ ü ù ý þ � ý þ ü � � � ü þ � ÿ ü þ � � ù � � ù � þ � �� � � þ � � � ü û þ ÿ ý � ü û þ ÿ ý � ÿ � ù ÿ � � � ÿ � � � � � þ � � � ÿ � ù ÿ � � � ÿ � � � � � þ þ ý � � � � � ù � þ � ü û þ ÿ ý ÿ � � � � ý ü ù � � ù ü � � �� � þ ý þ � � � � û ù ü ü � � � ÿ ý þ � � � � ù � � � û þ ÿ � � � û ÿ � � þ ü � � � ü þ � $ % % % ù ü � ÿ ü þ � � � , ( " ú � � û þ � � � � ÿ � þ ü � ÿ � ü û ù �ü � ù � û � � � � � � � ÿ ý þ � � � � � ! � ú � � � " � � $ % % & � � þ � þ ý ÿ � � ý � � þ � ý þ � ý ü û þ ÿ ý � û ù � û ù ü � ÿ ü þ � � �ü ù � � � ù ù þ � , ( " ú �

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f f g h i j k l m n o p q q r s g f t u k v w f k w x k f i y j z g m j l g h v f l n v g y { z| } ~ � � � � t � � � � � � � w � � � � � ~ ~ � � � m � � � � i � � � � � o t w m i s } � � g � � � � � � � � � u � � � � ~ � � � ~ � � � u � g} � � z � � � u � g w � � � � � � � | � } � ~� � � � � � � � � � � � � � � � � �� �   ¡ ¢ £ ¤¥ ¦ ¤ § ¨ � ©� �   ¡ ¥ ¦ ª « ¬ ­ ® ¯ ¯ £ ° ¢ ± ¨ � ©� ² ³ ´ � � � � µ µ � � © ´ ¶ · ¸ § ¹ ºª ® ° ª ¤¦ ­ ¦ · ¸ » ¹ ¨ � � ¼ µ � � ´ � � � � � © � � ½ © � � © � � ¾ ´ � ½ � µ � © � � � � � � ´¿ ª À Á ÂÃ Ä À ­ ® ¯ ¯ £ ° ¢ Å Æ Å ± ¸ Ç ¹ Å ¹ » Å ¨ � © È É Ê Ë Ì Í Î Ï Í Ð Ë Í Ñ Ò Ó¿ ª À Ä ¦ Ã Ô ¹ · § Ç ¸ Ç ± · º Ç Õ ¨ � ©¼ ¯ Á · ¸ » ¹ Å © � Ö� ¯ × Ç § · ¨ � ©� ¯ Ø Ç ± Å ¨ � ©� ¯ ® » Æ Õ ¨ � ©� Á ¦ » ¹ Ç ¸ Õ ¨ � ©¿ ¯ Ç Æ ¹ · · ¨ � ©¼ � » ¹ ¸ ¹ Å © � Ö� Ø º · ¨ � ©¿ Ç Õ ¹ · · ¨ � ©

Ù Ú Û Ü Ý Þ ß à á ß â á à ã ä å à ã ã æ ä Þ ä ß ã Ý ç è à è åà á á é ä Ý è ê ç é ß ä ë ä è ã Þ æ ç â á å ì ä ç è ã æ äã ä è Þ Ý ç è Þ Ý å ä à ã ã æ à ã í à é ã Ý ß â á à é Þ ä ß ã Ý ç è Ûî Ú Û ï ð ñ ò Ú Û ó ð ôê ç é ß ç ë í ç Þ Ý ã ä Þ ä ß ã Ý ç è õ æ ä é ä ã æ äë ç ë ä è ã Ý Þ è ä ö à ã Ý ÷ ä ä ø â à á Þ ù ä é ç Ûú Ú Û ê ç é ß à á ß â á à ã Ý è ö û ß é Ý è è ä ö à ã Ý ÷ äë ç ë ä è ã é ä ö Ý ç è ü ê ý ß ê ç é ã ç í í Ý è ö Þ æ ç â á åì ä ß ç è Þ Ý å ä é ä å Û þ á Þ ç ë ç é ä Ý ë í ç é ã à è ã á ÿ ü Ý êã æ ä à í í á Ý ä å ë ç ë ä è ã Ý Þ í ç Þ Ý ã Ý ÷ ä üÞ â ì Þ ã Ý ã â ã ä ã æ ä ß ç é é ä ß ã ÷ à á â ä Þ ê ç é � � ç é � �Ý è ê á ä � â é ä ê ç é ë â á à Û� Ú Û � æ ä ä ß ß ä è ã é Ý ß Ý ã ÿ ü � ü â Þ ä å ã ç ß à á ß â á à ã äê í ß Ý Þ ã æ ä å Ý Þ ã à è ß ä ì ä ã õ ä ä è ã æ ä ß ä è ã é ç Ý åç ê � � à è å ß ä è ã é ç Ý å ç ê � ß ç ë í ç Þ Ý ã äÞ ä ß ã Ý ç è Û� Ý è à á þ è Þ õ ä é Þ ê ç éÝ ë í ç é ã à è ã í à é à ë ä ã ä é Þ µ � � � � � ¡ � ½ µ � � � � � � � © µ � � µ � © � ½ � © � � µ © � � � � � � ´ � � �� ´ � � © � � � � � ´ µ � � µ µ © � µ ¡ � � � � µ � � � � µ © � � � � µ � � � � ¡ � � � � © � � � ´ � �� © ³ � � � � � � � ´ µ � � � � ´ µ � � � ³ � � � � � � � � � � � � ´ � � �

² · ¸ ¹ © � ¸ � © � ¸ ¡ � � � � � � © µ � ¡ � ´ � µ � � � � � � © ´ � ¶� Ë Ï � Ì Ñ Í Ñ � Ì Ë Ê Ñ Ì Í � Ñ Ò Ó

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- . / 0 12 . 3 4 56 3 4 52 6 2 3 4 78 9 8 : ; 9 3 4 <= 6 5 6 3 4 5= 8 5 9 3 4 5- 9 ; - 8 3 4 >- 8 9 . - 3 4 >/ 5 2 ; ; ? @ 0 1: / 3 4 5: 3 4 5- 9 - . 3 4 7- / ; 2 . 8 . 3 4 <9 96 5 2 = . 3 4 7/ ? 3 A B

C D E 1 F G H 0 I E J K L K B E 0 M L N B 1 3 O 3 1 P 0 E Q 1 E A A 3 4 R S B L N T S 3 B J 3 0 0 F Q F 4 1 1 U N 4 I E J K L K B E 0F L N B 1 3 O 3 1 P 0 E Q R 3 Q J F Q S J F 1 F Q I 3 4 V W X Y Z [ \ ] ^ _ X Y Z ^ ` ] a O N L L F J I E J K L N Q Q N 1 3 E N 4 JI K L 1 3 A L P 3 1 T P 1 U F N Q F N E 0 B L N T b T c d d e B L N T 1 U 3 O ? 4 F B B f 5 g J J 1 U F R 3 h F 4 h N L K F 1 Eg Q F N E 0 i 3 Q J F Q 0 E Q 1 E 1 N L N Q F N E 0 O E I A E B 3 1 F B F O 1 3 E 4 5j k l m n o p m qr s 3 4 >

t L N T 1 U 3 O ? 4 F B B S u [v w x y z { | } y ~ x | y � � � w | � } � � w � � w � � w � � x } � } � x � � j Y� E I F 4 1 E 0 H 4 F Q 1 3 N E 0 1 U F O E I A E B 3 1 F B F O 5 � Y6 = = - 8 5 - : 3 4 >8 2 = / 9 5 2

- 2 5 = = 3 4 5g Q F N E 0 � @ t 1 F 4 B 3 E 4 Q F 3 4 0 E Q O F I F 4 1

� 3 J 1 U E 0 � F T S T �g Q F N E 0 � Q E B B t F O 1 3 E 4 E 0 i 3 Q J F Q S j �

� � � m � � p � � � � � � � o � o � o �� � � u l p V m n � p � � � � m u � � � l � V � � � u l p V� E I A E B 3 1 F B F O 1 3 E 4 I E J K L K B 0 E Q 1 U F F e 1 Q F I F 1 E A 0 3 T F Q E 0 T F N I S � � �� p   ¡ p � l u � � � � u l p V¢ £ } | y z z � } � x ¤ w � x ¤ } � w � � w � � x } � } � x � w � � � Y

¥ 3 B 5 ¦ Q E I O F 4 1 Q E 3 J E 0 O E I A E B 3 1 F B F O 1 3 E 4 1 E F e 1 Q F I F 1 E A 0 3 T F Q E 0 B L N T S § � Y¨ E 1 N L © E 0 � @ t B 1 Q N 4 J B� E I A E B 3 1 F B F O 1 3 E 4 I E J K L K B 0 E Q 1 U F F e 1 Q F I F T E 1 1 E I 0 3 T F Q E 0 T F N I S � ^ Y¥ 3 B 5 ¦ Q E I O F 4 1 Q E 3 J E 0 O E I A E B 3 1 F B F O 1 3 E 4 1 E F e 1 Q F I F T E 1 1 E I 0 3 T F Q S § ^ Y� E I A E B 3 1 F B F O 1 3 E 4 I E J K L K B 0 E Q 1 U F F e 1 Q F I F 1 E A 0 3 T F Q E 0 B L N T S ª « ¬ ­® ¯ ° ± ² ³ ¬ ¯ ´ « ¬ µ ¶ · ¸ ¹ ¸ º » ¼ ¸ ½ º » ¾ ¿ ½ À Á . / / 2 / 5 9 6 3 4 >

 � � � à | w � � } � x | w � � x w } Ä x � Å w x x w � � � Å } | � ´ Æ � � � à | w � � } � x | w � � x w } Ä x � x w � � � Å } | � ´ «Ç È � � j n n É � p   � u � § m V q � � � u l p V m n Ê � p ¡ � � u l � � Ër p V � p   ¡ p � l u � � � � u l p V

� F 3 R U E 0 Ì F N I 8 9 5 6 2 3 4 5¥ 3 B 5 ¦ Q E I O F 4 1 Q E 3 J E 0 O E I A E B 3 1 F B F O 1 3 E 4 1 E F e 1 Q F I F 1 E A 0 3 T F Q E 0 T F N I S § � �

t A N 4 Í F 4 R 1 U S oÎ h F Q g L L ¥ F A 1 U E 0 i 3 Q J F Q S �t F O 5 I E J K L K B S F e 1 5 T E 1 1 E I 0 3 T F Q S � ^t F O 5 I E J K L K B S F e 1 5 1 E A 0 3 T F Q S � �� E I F 4 1 E 0 H 4 F Q 1 3 N S � �. 8 5 = = 3 4 5

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