44

ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

  • Upload
    others

  • View
    0

  • Download
    0

Embed Size (px)

Citation preview

Page 1: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

� ��������� � �

� ����������������� ��� ���� !���" $#&%'� ()�+*�,.-/�102��3

�4�5�6��02 $�5� 7 �$8.��0:9;�� $�4�5�<�5�$���

=?>A@ B�CEDGFIHKJMLONQPRH

SUTWVYXKZGT\[�]_^ ]_V_]a`bXc` TedgfbTih jlkchIkcjlmW]akcnGXpoqhITWVYXrjlTs`pfbtvuck?` kxw2ylTWz{hIkxw|` T}mskcnbw~y~j~fbtvuck�Tih�kcj2�xX�ngyAX��qTWnbwTsmskcnb�cz{]amvXcwvo�XcwRTswAmskcjAXcwRwAuck{zMf ]_ylk��jlTsd�fbTWngylTWz�TWn�ylTMwlf ^bw~y~]_y~f �a`bXcwRhIkcjeX�nbmskcjAX��qTWnbweh jl�\��Tsw~��kcjltvXc`bXcwvowlTWVYXc`bXcw}nbk{ylTWj~jlTWnbk �

�ETswlylTOmvX�h �_y~f Vak oUX�^�kcjl`bX���wlT{TswlylTMy~]_hIk�` TTsw~y~j~f y~f jAX�` TmskcngylTWnbtvuck���mskcj~y~]_nGXcwKzMf V_y~]���X�nbmskcjAXc`bXcw��T�kxw?h jlkc^ VaTWz;XcwOdgfbT�V_�bTsw�wAuck�mvX�jAXcmWylTWj~�awly~]amskxwv���eT\��TWjlT\��wlTxo.nbk�TWngyAX�ngylk o2d�fbT{zMf ]_ylkxwM` kxwOXcwlw~f ngylkxwX�^�kcjl`bXc` kxwenbk�mvX�h �_y~f Vak;X�ngylTWj~]akcj�wAuckyAX�z�^I�Wz'jlTWVaTW�xX�ngylTswehGX�jAX�XcwRmskcj~y~]_nGXcw�X�nbmskcjAXc`bXcwv�

=?>�� ��F� 2¡�¡G¢K 2¡+JM �D� £F�FI¤R¡�CrLO¥¦¤¦§QH}F�D�¨lCO¤!¤RCO§UH}FI¤RJO¤

�Ek©mvXcwlk©`bXcwmskcj~y~]_nGXcw{TswlmskcjAXc`bXcwvo|k©Tsw~y~fb` kªT\��TsmWy~fGXc` k6X�n�ylTWj~]akcj~z�TWngylT«jlTWVYX�y~]_�qk6Xck©yAX�jl` kc¬«`bXTsw~y~j~f y~f jAX�` T�wlf h�kcj~ylT;h�TWj~z{]_y~]_f<ml�bTW�gX�jO­�mskcnbmWV_fbwAuck�` T®dgfbT{nGuck�h�k�` TWj~]YX��GXs�qTWjd�fGX�VadgfbTWj?ylTskcj~]YXhGX�jAX{XM` TWylTWj~z{]_nGXctvuck;` TryAX�]awih jlTswlwl¯�Tswvo�z;XcwRXMkc^bwATWj~�cXctvuck{` TKTsw°��kcjltskxw}TWz±TswlmskcjAXcwiy~]_n �GXOVaTW�xXc` k�­` T\²bn ]atvuck;` TKTWng�qkcV_�qTWn�ylTswr` Trh jlTswlwl¯�Tswvo dgfbTKmskcj~jlTswlh�kcnb` TWz¦XckxwR`p]YX��xjAX�z;XcwE` TK³UTWj~¬´X��x� ]UT?SQTsmlµI�

�EkMmvXcwlk?`bXcw¶mskcj~y~]_nGXcw¶X�nbmskcjAXc`bXcw´opX?dgfbTsw~yAuck�nGuck���X?` Ted�fGX�]aw·Xcw¸h jlTswlwl¯�Tsw¸d�fbTewlTe` TswlTWng�qkcV_�qTWznbk«yAX�jl` kc¬;`bX�Tsw~y~j~f y~f jAXpoUz;Xcw?w~]_z/hGX�jAX«d�fbT�xX�VakcjlTsw?`bXcwKh jlTswlwl¯�TswKwlTh jlk�msTs` T;­�TswlmskcV_�GX«` k�h jl�\�Tsw°��kcjltsk{`bXcw�X�nbmskcjAX��qTWnbwvo ]aw~ylk;�xo dgfGX�V.X{mvX�j~�gX;X{X�h V_]amvX�jenGXcweX�nbmskcjAX��qTWnbwv�

¹ kc^pº~TsmWy~]_�qk}» V_y~]_z�ke�xo�mWVYX�jlkRf z¼Xc` Tsd�fGXc` kRmskcz{hIkcj~yAX�z�TWngylk�`bX}mskcj~y~]_nGX}T|` k}ylTWj~jlTWnbkew~f h�kcj~yAXc` k omskcz½` Tsw~Vak�mvX�z�TWngylkxw{mskcz{hGX�y~�_�qTW]awmskcz½k�z�TW]ak¾TWn��qkcV_�qTWngylTx�©¿ÀmvX�j~�gX¾X¾X�h V_]amvX�jM�xo2Xcwlw~]_z�o.��f nbtvuck` TswlwlTRz�TW]ak o�z;Xcw¶hIk�` TEmskcnbmWV_f ]_j°��wlTrdgfbT�XMX�h V_]amvXctvuck` TRh jl�\��Tsw~��kcjltskOnGXcwiX�nbmskcjAX��qTWnbw}`p]aw~y~j~]_^ f �a` k` T��kcj~z;XrXETsdgf ]_V_]_^ jAX�j|kxw£`p]YX��xjAX�z;Xcw2` Ti³.TWj~¬´X��x� ]bTiSQTsmlµMmskcj~jlTswlh�kcnb` Txoxnbkcj~z;X�V_z�TWn�ylTxo�Xef zÁXc` TsdgfGXc` kmskcz{h�kcj~yAX�z�TWn�ylk®`bXTswlmvXv�cXctvuck �

ÂWÃbÂ

Page 2: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

ÂWÃgÄ Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

=?>�â ã�LOCM§Q¨lHRCO¤e¥¦ 2CED�H/JO ÀLO¥¦¤¦§QH}FGD�¨lCM¤ä¤RCM§QH}FI¤RJO¤

å£æèç2æ�é êìë£í|îGï�ðxñIò+ó¸ôöõ�÷Êø.÷�ó|îbùú�]_fp��wlT�nbk¾mvX�h �_y~f Vak¾X�n�ylTWj~]akcjd�fbT�k���f nbmW]akcnGX�z�TWn�ylk©` T;f z;X�mskcj~y~]_nGX¾TswlmskcjAXc`bX�wAT{^GXcwlTW]YXpo£wlk��

^ jlTWy~fb` k o nGXOj~]_�x]a` TW¬�X�[p]YX�Vû`bXcw}TswlmskcjAXcwRd�fbTxopwlTWnb` k{TWVaTW�cXc`bXpobh�TWj~z{]_ylTKd�fbTrkxw}` Tsw~Vak�mvX�z�TWn�ylkxwewlT�ºlX�zhITsdgfbTWnbkxwv�£�rXcw2wlkcV_fbts¯�Tsw·X�nbmskcjAXc`bXcwvo�Xcw|TswlmskcjAXcw|wAuck�w~f ^bw~y~]_y~f �a`bXcw2hIkcj¸TWVaTWz�TWngylkxw·mskczÁj~]_�x]a` TW¬�X�[p]YX�V` TMf z;X®kcjl` TWz¦` TO�xjAX�nb` TW¬´X®]_np��TWj~]akcjK­;`bXcwrTswlmskcjAXcw´���ruckàwlTWjAüpoGhIkcj~yAX�ngylk o:` TW��]a` k«X;TswlylTOXcw~hITsmWylkd�fbT?X{wlkcV_fbtvuck{` T�X�nbmskcjAX��qTWnbwe��kcj~nbTsmsTrf z�Xc` TsdgfGXc` k�mskcz{hIkcj~yAX�z�TWngylkà`bX{Tsw~y~j~f y~f jAXp�

S£X�jAXOk�mskcnp²bj~z;X�jvo mskcnbw~]a` TWjlT\��wlTrXMw~]_y~fGXctvuckMTswAdgfbTWz;X�y~]amvX�z�TWn�ylT?X�h jlTswlTWngyAXc`bXMnGXMýU]_�xf jAXOþp�  � ¹wlkcVak{�Kmskcnbw~y~]_y~f �a` k�h�kcjif z;X�X�jlTW]YXmskcz'ÿ�n �xf Vak�` T?X�y~j~]_ylk;` T������qoph�TswlkO�qkcV_» z{]amsk®` T����������� KTKkÿ�n �xf VakR` T¸X�y~j~]_ylkEwlkcVak���Tsw~y~j~f y~f jAX}�¸` T���� � �.¿<mskcj~y~]_nGXeXcwlwATWngyAXin�f z&Tsw~y~jAX�ylkRmskcz�^IkqXcwûmvX�jAXcmWylTWj~�aw~y~]amvXcwjlTsw~]aw~ylTWn�ylTsw�T�ylTWz�Xcwh jlkch j~]aTs`bXc` TswàTWVYücw~y~]amvXcw�` T�f z;X©hGX�jlTs` T«` T�^ITWyAuck X�j~z;Xc` k mskcz��p� à ��z�` TTsw~hITswlw~f jAXp�

H=10m

2m

2.5m

2.5m

3m

5m

ýQ]_�xf jAX�þp� Â���� ü�VamWf Vak  �p� Â�� �qTskcz�TWy~j~]YXp��Ef z�mvü�VamWf Vak  �p�  mskcnbw~]a` TWjlkcfp��wlTEdgfbT�Xcw·X�nbmskcjAX��qTWnbwvo�]_nbmWV_]_nGXc`bXcw}X������qo�wlTWj~]YX�zÁjlTvX�V_]_¬´Xc`bXcw¶z;Xcw

nGuck«wlTWj~]YX«X�h V_]amvXc` k�d�fGX�Vad�fbTWjKh jl�\��Tsw°��kcjltsk o.kcf wlT�º~Xpo���f nbmW]akcnGX�j~]YX�z½X�hITWnGXcw�X�y~jAXs�q�swM`bXàw~fGXàj~]_�x]a` TW¬��]_�xfGX�VUX�����������®�\�¸¿Eh jlTswlTWngyAX���wATKnGX{ýQ]_�xf jAX�þp� Ä Xz;X�V_�GX�` T?TWVaTWz�TWngylkxwe²bn ]_ylkxwemskcj~jlTsw~hIkcnb` TWngylT­» V_y~]_z;XO�ÊXcwlTxo kcf�wlT�ºlXpob­TswlmvXv�cXctvuck�` T  ��z'` Trh jlk���f nb`p]a`bXc` Tx�

0. 10. 20. 30. 40. 50. 60.

0.

5.

10.

15.

ýQ]_�xf jAX�þp� Ä���� ü�VamWf Vak  �p� Â���� X�V_�GX` T�TWVaTWz�TWngylkxwe²bn ]_ylkxwv�¹ wjlTsw~f V_yAXc` kxw;` kxw{` Tsw~Vak�mvX�z�TWn�ylkxw;`bX©mskcj~y~]_nGXpo¶` kxw�XcwlwlTWngyAX�z�TWn�ylkxw;` kªylTWj~jlTWnbk6w~f hIkcj~yAXc` k6T

Page 3: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò ÂWÃ��

`bXcw�h jlTswlwl¯�TswàwAkc^ jlTªX<mskcj~y~]_nGX�Tsw~yAuck<jlTWh jlTswlTWn�yAXc` kxw«nGX�ýQ]_�xf jAX�þp� � � ��Tsw~yAX�ýQ]_�xf jAX<]_nb`p]amvX�z��wlT]_�xfGX�V_z�TWngylT�kxwijlTswlf V_yAXc` kxwe`bXcwiz�Tsw~z;Xcw}�xjAX�nb` TW¬´XcwehGX�jAXk{mvü�VamWf Vak  �p� Ä oGX�nGü�Vakc�qk�Xck  �p�  o z;XcweTWzdgfbTRw�uckMX�h V_]amvXc`bXcw¸��kcjltvXcw¸nGXcw·X�nbmskcjAX��qTWnbwimskcj~jlTsw~hIkcnb` TWngylTsw}Xck�`p]YX��xjAX�z;X�` Te³.TWj~¬´X��x� ]ITeSQTsmlµ{hGX�jAXXcweX�jlTW]YXcwv�

−14

−12

−10

−8

−6

−4

−2

0

2

100 50 0 5 10 15 20 25

−0.06−0.05−0.04−0.03−0.02−0.01 0

150100500.02.04.06.08.10

Prof

undi

dade

(m)

Des

loca

men

to v

ertic

al (m

)

Tensão normal (kPa) Distância à parede (m)

Deslocamento horizontal (m) Tensão normal (kPa)

10.1 (Σ Fa=0)10.2 (Σ Fa=433kN/m)

K0=0.5KaH=0.279

ýU]_�xf jAX<þp� ��� � ü�VamWf Vakxw  �p�  T  �p� Ä�� ` TswlVak�mvX�z�TWn�ylkxw®�bkcj~]_¬vkcn�yAX�]aw«`bX mskcj~y~]_nGXpoeXcwAwlTWngyAX�z�TWn�ylkxw«` kylTWj~jlTWnbk�w~f hIkcj~yAXc` k�TKh jlTswlwl¯�Tsw}` TKylTWj~jAXcwv�¿"X�nGü�V_]awAT?` Tsw~yAX{ýQ]_�xf jAXhITWj~z{]_ylT?mskcnbw~yAX�yAX�jed�fbT �! kxwQ` Tsw~Vak�mvX�z�TWn�ylkxw£mskcj~jlTsw~h�kcnb` TWn�ylTsw2Xckemvü�VamWf Vak  �p�  wAuckRzMf ]_ylkETWVaTW�xXc` kxwQdgfbTWjûnbkEdgfbT¸jlTsw~hITW]_yAX­{mskcj~y~]_nGX{d�fbTWjeXck{ylTWj~jlTWnbk�wlf h�kcj~yAXc` k#"! X©k�mskcj~j%$WnbmW]YXª` T�` Tsw~Vak�mvX�z�TWngylkxw;TWVaTW�cXc` kxw���nbkªmvü�VamWf Vak  �p�  ��y~jAXc`pf ¬W��wlTxo|nGX�y~f jAX�V_z�TWn�ylTxo¶nGXz�kc^ ]_V_]_¬´Xctvuck�` T2f z&`p]YX��xjAX�z;XE` T2h jlTswlwl¯�Tsw:nbk}yAX�jl` kc¬¶`bX}mskcj~y~]_nGXRd�fbT2mskcj~jlTsw~hIkcnb` T·Xck}]_z{h f VawlkXcmWy~]_�qk#"

! kxw2` Tsw~Vak�mvX�z�TWngylkxw2kc^ y~]a` kxw|` k�mvü�VamWf Vak  �p� Ä wAuck�^GXcw~yAX�ngylT¶hITsdgfbTWnbkxw2T¶kr`p]YX��xjAX�z;Xr` T¶h jlTswlwl¯�Tswkc^ y~]a` krmskcj~jlTsw~hIkcnb` Txoxz�f ]_ylkKX�h jlks[p]_z;Xc`bX�z�TWngylTxopXck�`p]YX��xjAX�z;XejlTsmWyAX�n �xf VYX�j|d�fbT¶mskcj~jlTsw~h�kcnb` TWf­{TswlmskcV_�GX�`bXcwRmvX�j~�gXcwEX{X�h V_]amvX�jRnGXcwEX�nbmskcjAX��qTWnbwv�� kcnbmWV_f ]���wlTxo�XcwAw~]_z�oqd�fbTxoqmskcz�kKwlT}Tsw~hITWjAXs�xXpoxnGuckK�RXEj~]_�x]a` TW¬e`bXcw¸X�nbmskcjAX��qTWnbw¶XejlTswlh�kcnbwAüv�qTWVbhITWVYX

V_]_z{]_yAXctvuck;` kxwR` Tsw~Vak�mvX�z�TWngylkxw´�

å£æèç£æ'& ê)ë£í¸îGï�ðcñIò�ó¸ôö÷)(+*}ò.ïc÷-,pñ�ò ó|î�ó|îGï�.�ò0/pô1( î32Uðxò.ïSUk�` TWjAü¾h�TWnbw�X�j°��wlT;d�fbT;kxw` Tsw~Vak�mvX�z�TWngylkxwwAuck�z;X�ngy~]a` kxwjlTWVYX�y~]_�xX�z�TWngylT�^GX�]�[ kxwvoQnGXcwMmskcj~y~]_nGXcw

X�nbmskcjAXc`bXcwvo.X�y~jAXs�q�sw�` kàT\��TW]_ylk�` T�]_z{hIkxw~]atvuck«` T` Tsw~Vak�mvX�z�TWngylkxw?mvX�fbw�Xc` k®hITWVakàh jl�\��Tsw°��kcjltsk oI]aw~ylk��xoh�TWVakz�k´��]_z�TWn�ylk®`bX{mskcj~y~]_nGX�TWz'wlTWngy~]a` k;mskcngy~jAü�j~]ak®Xck;dgfbTKk�mskcj~jlTKnGXcwi�ÊXcwlTsw}` T?TswlmvXv�cXctvuck �� kxwly~jAX���wlTxobXcwlw~]_z�o�nGXOýQ]_�xf jAX{þp� à kxw¶jlTsw~f V_yAXc` kxwe` kxw}` Tsw~Vak�mvX�z�TWn�ylkxwR`bXOmskcj~y~]_nGXTr` kOwAkcVakMhGX�jAX

f zämvXcwlk �  �p� � �KX�nGü�Vakc�qk�Xck  �p� Ä z;Xcw�TWz!d�fbTnGuck���kcjAX�z!mskcn�yAX�^ ]_V_]_¬´Xc` kxwkxw?` Tsw~Vak�mvX�z�TWngylkxw?nGXcw

Page 4: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

ÂWÃxà Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

�ÊXcwlTswrmskcj~jlTsw~h�kcnb` TWn�ylTswM­�X�h V_]amvXctvuck«` TOh jl�\��Tsw°��kcjltsk oûkcf6wlT�º~Xpo�nGuckà��kc]Qmskcnbwl]a` TWjAXc` k�k�T\��TW]_ylk6��wlkc^6khIkcngylk�` TK��]aw~yAX` kxwR` TswlVak�mvX�z�TWn�ylkxw��}`bX{X�h V_]amvXctvuck®` kh jl�\��Tsw°��kcjltsk �

−14

−12

−10

−8

−6

−4

−2

0

2

100 50 0 5 10 15 20 25

−0.06−0.05−0.04−0.03−0.02−0.01 0

150100500.02.04.06.08.10

Prof

undi

dade

(m)

Des

loca

men

to v

ertic

al (m

)

Tensão normal (kPa) Distância à parede (m)

Deslocamento horizontal (m) Tensão normal (kPa)

10.1 (Σ Fa=0)10.2 (Σ Fa=433kN/m)10.3 (Σ Fa=433kN/m)

K0=0.5KaH=0.279

ýQ]_�xf jAX�þp� Ã4� � ü�VamWf Vakxw  �p�  X  �p� ��� ` Tsw~Vak�mvX�z�TWngylkxwà�bkcj~]_¬vkcngyAX�]aw«`bX�mskcj~y~]_nGXpoRXcwlwlTWn�yAX�z�TWngylkxw«` kylTWj~jlTWnbk�w~f hIkcj~yAXc` k�TKh jlTswAwl¯�Tsw}` T?ylTWj~jAXcwv�¿�X�nGü�V_]awlT«` Tsw~yAX©ýQ]_�xf jAX©h�TWj~z{]_ylT«mskcnbmWV_f ]_j;d�fbT�kxw{` Tsw~Vak�mvX�z�TWngylkxw;w�uck¾jAX�¬vkqXv�qTWV_z�TWngylT©wlTWz�T\�

V_�GX�ngylTsw�XckxwOkc^ y~]a` kxw`bX¾X�nGü�V_]awAT  �p� Ä o2wATWnb` k�hIkcj~yAX�ngylk©^GXcw~yAX�n�ylTàX��ÊXcw~yAXc` kxw` kxw` k�mvü�VamWf Vak  �p�  �� kxw~y~jAX���wlTxoqXcwlw~]_z�ogdgfbT¶nGuckr�}Xe]_z{hIkxw~]atvuckK` Ti` Tsw~Vak�mvX�z�TWngylkxw2nGXcwQ�ÊXcwlTsw2` T¶h jl�\��Tsw°��kcjltskKdgfbTUº°fbw~y~]�²GmvXXrf y~]_V_]_¬´XctvuckO` TEX�nbmskcjAX��qTWnbwvo�`bXc` k�d�fbT}ylTWz�kxw¶` kc]aw¸mvü�VamWf Vakxwr�  �p�  T  �p� � �|TWz�d�fbT}nGuck?�Gü�dgfGX�Vad�fbTWj` Tsw~Vak�mvX�z�TWngylkànGX���XcwlT�` T�h jl�\��Tsw°��kcjltskª��nbk®mvXcwlk®` k®mvü�VamWf Vak  �p�  h�kcjld�fbT?yAX�VU��XcwAT?nGuckàT\[�]aw~ylT´�}z;XcwTWz'd�fbTKkxwR` Tsw~Vak�mvX�z�TWngylkxwEwAuck�mskcnbw~]a` TWjAXv�qTWV_z�TWngylTO`p]���TWjlTWn�ylTswv�

å£æèç2æèç ê)ô1.�ðxîbõqô1,pñIò4ó|ò îGï�ðcô:ó¸ò+ó¸î<ðcî52¸ï�ñIò� kcnbmWV_f ]���wlTxo�` kxwEh�kcn�ylkxw�X�n�ylTWj~]akcjlTswvo�d�fbT�XcwrX�nbmskcjAX��qTWnbwenGuck���f nbmW]akcnGX�z�hITWVYX{w~fGX{j~]_�x]a` TW¬MnbTWz

hITWVYX�]_z{hIkxw~]atvuck` Tr` Tsw~Vak�mvX�z�TWngylkxwv�·¿ehITswAX�ji` Tsw~ylTswRXcw~hITsmWylkxw·hIk�` TWjlTWz yAX�zM^��Wz mskcn�y~j~]_^ f ]_jRhGX�jAXk��f nbmW]akcnGX�z�TWngylk�`bXcw·X�nbmskcjAX��qTWnbw2nGXcw|Tsw~y~j~f y~f jAXcw|` T}mskcn�ylTWnbtvuckKZGT\[p�_�qTW]awvogXcw|X�nbmskcjAX��qTWnbw¸y~jAX�^GX�V_�GX�z�owlkc^ jlTWy~fb` k o hITWVYX�X�V_ylTWjAXctvuck®` k{Tsw~yAXc` k�` TrylTWnbwAuck�d�fbTKmvX�fbwAX�z nbk;wlkcVak{w~f hIkcj~yAXc` k �6rT¶f z;XE��kcj~z;Xrwl]_z{h V_]�²GmvXc`bXpoqhIk�` TiX�nGX�V_]awAX�j°��wlT}k�h jlkc^ VaTWz;X?X�y~jAXv�q�sw|` kKdgfbTiwlT¶]_nb`p]amvX�nGX�ýQ]_�xf jAX

þp�87p� � kcnbw~]a` TWjlT\��wlTxopXcwlw~]_z�ogf z�TWVaTWz�TWn�ylkO` k�wlkcVak?nbk�yAX�jl` kc¬E` TRf z;X�mskcj~y~]_nGXMX�nbmskcjAXc`bXp� � kcnbw~]a` TWjlT\�wlTKX�]_nb`bX{d�fbTxo ` TW��]a` k�­TswAmvXs�xXctvuck��è��XcwAT  `bXýQ]_�xf jAXq�\oGXMylTWnbwAuck��qTWj~y~]amvX�VÊo491:vopnbTsw~ylTKTWVaTWz�TWn�ylk{nGuckwlT?X�V_ylTWjAX;T?dgfbTMXOylTWnbwAuck��bkcj~]_¬vkcn�yAX�V;9 wAk���jlTKf z5` TsmWjl�swlmW]_z�k �·¿�w}ylTWnbwl¯�Tsw<9=:eT�9 wAuck�h j~]_nbmW]_hGX�]awT?Xc`pz{]_yAX���wlTMdgfbTKwlTrz;X�n�y%$Wz'h j~]_nbmW]_hGX�]awE`pf jAX�ngylTMX�TswlmvXs�xXctvuck�TKkh jl�\��Tsw°��kcjltsk �

ú|TWj~]�²GmvX���wlTxo�Xcwlw~]_z�opdgfbTr` TW��]a` k{­MTswAmvXs�xXctvuck{wlT��qTWj~]�²GmvXOf z±]_nbmWjlTWz�TWngylk�`bXMylTWnbwAuck{` TW��]YX�yl�cj~]amvX9 :?> 9 o|k6d�fbTàylTWz mskcz�k6mskcnbwlTsd�f4$WnbmW]YX6XªTW�qkcV_fbtvuckªylTWnbwAuck���` T\��kcj~z;Xctvuck yAX�z�^I�Wz ]_nb`p]amvXc`bXªnGXýQ]_�xf jAXp� �eTvX�V_]_¬´X�nb` k���wAT kÑh jl�\��Tsw°��kcjltsk&�è�ÊXcwlT Ä �\ormskcnbw~]a` TWjlT\��wlTxoryAX�z�^I�Wz�o?d�fbT X�h�TWnGXcw¾X<ylTWnbwAuck�bkcj~]_¬vkcngyAX�VIwlk���jlTRX�V_ylTWjAXctvuck o�k�dgfbTiylTWz mskcz�k�mskcnbwlTsdgf4$WnbmW]YX?f z ` TsmWjl�swlmW]_z�kM`bX�ylTWnbwAuck?` TW��]YX�yl�cj~]amvXp�¿'T\[ TsmWfbtvuck ` T�nbk´�cX6TswAmvXs�xXctvuck mvX�fbwAX©nbkªz�Tsw~z�kªhIkcngylk6f z�XcmWjl�swAmW]_z�k ` T�ylTWnbwAuck ` TW��]YX�yl�cj~]amvX

Page 5: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò ÂWà 7

13

3Aδ3

δ3Α

δ

δ1 1

2

3

3σ −σ1

2

ýU]_�xf jAX;þp�87 � �eTWh jlTswlTWn�yAXctvuck;Tswld�fbTWz;ü�y~]amvX{`bXTW�qkcV_fbtvuck®` k{Tsw~yAXc` k�` TrylTWnbwAuck�TWz TWVaTWz�TWn�ylk;` T?wAkcVakw~f h�kcj~yAXc` k�h�kcjRmskcj~y~]_nGX®X�nbmskcjAXc`bXp��è��XcwlT � �\oGk{dgfbTrjlTsw~f V_yAX�TWz nbkv�xX{TW�qkcV_fbtvuck{nGX{mWf j~�xXOylTWnbwAuck�` T\��kcj~z;Xctvuck�]_nb`p]amvXc`bX{nGX{ýQ]_�xf jAXp�¿�mskcnbwlTsd�f4$WnbmW]YXO` Tsw~yAXOwlTsdgf4$WnbmW]YXO` T�TswlmvXs�xXctvuck oph jl�\��Tsw°��kcjltskTETswlmvXv�cXctvuck�xo Xcwlw~]_z�o XM` T\��kcj~z;X��

tvuck�@A��dgfbT?wATE]_nb`p]amvX�nGXýQ]_�xf jAXp�� kcnbw~]a` TWjlT\��wlTxo�X��qkcjAXpoed�fbT�nGuck�wlTWj~]YX�jlTvX�V_]_¬´Xc` k<h jl�\��Tsw°��kcjltsk �1¿!wATW�xf nb`bX6�ÊXcwlT©` T¾TswlmvXv�cXctvuck

mvX�fbwAX�j~]YX k�z�Tsw~z�k ]_nbmWjlTWz�TWn�ylk<` T�ylTWnbwAuck oiz;Xcw;k�h�kcn�ylk�`bX�mWf j~�cX ylTWnbwAuck���` T\��kcj~z;Xctvuck<wlTWj~]YX�kh�kcn�ylkCB ÂED oUh�TWVak¾dgfbT;X�` T\��kcj~z;Xctvuck�²bnGX�V·wlTWj~]YXF@A��G TWzäV_f �gX�jM` TH@��po£kcf�wlT�ºlXpoUwlf ^bw~yAX�nbmW]YX�V_z�TWngylTz;X�]akcjeTKz;X�]aw}h jl�v[�]_z�k®`bXOjlkcy~f jAXp�

³.TWz��wlTxo Xcwlwl]_z�ogd�fbT}f z;X�mskcj~y~]_nGXMX�nbmskcjAXc`bX?y~jAX�^GX�V_�GXpopwlkc^ jlTWy~fb` k o�hITWVYX�X�V_ylTWjAXctvuckO` k�Tsw~yAXc` kM` TylTWnbwAuck�mvX�fbwAXc`bXhITWVYXcweX�nbmskcjAX��qTWnbwvo�mskcz�k{h jlTWhGX�jAXctvuck;`bXcw}��XcwlTsw}wATW�xf ]_ngylTswv�

=?>JI KMLONR QP�JM MRMFTS;Ug 2¡3VsH}FINQH

� kcnbw~]a` TWjlT\��wlTO` kc]awEmvü�VamWf VakxwKXc`p]amW]akcnGX�]awvo  �p� à T  �p�87po�X�nGü�Vakc�qkxwKXck®mvü�VamWf Vak  �p� Ä o�mskcz�T\[ msTWhItvuck` kMn �_�qTWV:` TEh jl�\��Tsw°��kcjltskX�h V_]amvXc` k �·�EkOmvü�VamWf Vak  �p� à o mskcnbw~]a` TWjlkcfp��wlTrd�fbTEkOh jl�\��Tsw°��kcjltsk{X�h V_]amvXc` k{TWjAXz�TWyAXc` T;` k���kcj~nbTsmW]a` k�hITWVakxw�`p]YX��xjAX�z;XcwO` T�³.TWj~¬´X��x� ]iT�SQTsmlµT"£nbk�mvü�VamWf Vak  �p�87poQXc`pz{]_y~]_fp��wlT®dgfbT;kh jl�\��Tsw°��kcjltsk®X�h V_]amvXc` k;wlTWj~]YXk�` kc^ jlk;` kO��kcj~nbTsmW]a` k{hIkcjEXcd�fbTWVaTswR`p]YX��xjAX�z;Xcwv�

¹ w2jlTsw~f V_yAXc` kxw|kc^ y~]a` kxw´oqnbkKd�fbTijlTsw~h�TW]_yAXKXr` TswlVak�mvX�z�TWn�ylkxw¸�bkcj~]_¬vkcn�yAX�]aw¸`bX�hGX�jlTs` TxopXcwlwlTWngyAX�z�TWnp�ylkxw�` k®ylTWj~jlTWnbk�w~f hIkcj~yAXc` k®TMh jlTswlwl¯�Tsw�nGX�]_n�ylTWj°��XcmsTwlkcVak���mskcj~y~]_nGXpo:TWnbmskcn�y~jAX�z��wlTjlTWh jlTswlTWngyAXc` kxw?nGXýU]_�xf jAX;þp� þp�

¿"X�nGü�V_]awAT?` Tsw~yAX{ýQ]_�xf jAXhITWj~z{]_ylT?mskcnbw~yAX�yAX�jed�fbT �

! k?mvü�VamWf Vak  �p� à ��kcj~nbTsmsTxo�mskcz�k?wlTWj~]YX?` TRTsw~hITWjAX�jvog` Tsw~Vak�mvX�z�TWngylkxw¶w~f hITWj~]akcjlTsw·Xckxw¸d�fbTRwlT}kc^ y%$Wz`bX©X�nGü�V_]awlT  �p� Ä "|k¾`p]YX��xjAX�z;X©` T�h jlTswlwl¯�Tsw?nGX�]_ngylTWj°�ÊXcmsT�wlkcVak���mskcj~y~]_nGX��;nbk¾mvXcwAk�` k�mvü�VamWf Vak �p� à o|^GXcwlyAX�ngylT«h jl�v[�]_z�k6` k6`p]YX��xjAX�z;Xª` T�]_z{h f Vawlkxw�XcmWy~]_�qkxw¾��nbkcylT\��wlT«dgfbTxo|hGX�jAXªk©mvü�VamWf Vak �p� Ä o:X{jlTsw~f V_yAX�n�ylT` k;`p]YX��xjAX�z;Xà` T�³UTWj~¬´X��x� ]£TMSUTsmAµ¾� � �XW w~f hITWj~]akcj�Xck®]_z{h f Vawlk�XcmWy~]_�qk#":Xmskcnbw~]a` TWjAXctvuck©` Tf zä`p]YX��xjAX�z;X�` T�h jlTswlwl¯�TswK]_�xfGX�V·X�z�TWyAXc` T®` Tsw~ylT{jlTsw~f V_yAXpo.nGX�y~f jAX�V_z�TWngylTxongf z;X<jlTswlf V_yAX�ngylT6]_np��TWj~]akcj�Xck<`p]YX��xjAX�z;X ` T¾h jlTswAwl¯�Tsw�mskcj~jlTsw~hIkcnb` TWngylT Xck<]_z{h f Vawlk XcmWy~]_�qk#"�qTWj~]�²GmvX���wlTxoGh�kcj~yAX�n�ylk obf z;X�X�V_ylTWjAXctvuck�` T�mvX�j~�gX{`bXcweX�nbmskcjAX��qTWnbw�` TryAX�Vûz�k�` k{d�fbT�XOh jlTswlw�ucknGX]_n�ylTWj°��XcmsT?²GdgfbT?X�h jlkv[�]_z;Xc`bX�z�TWn�ylTM]_�xfGX�VQXck{`p]YX��xjAX�z;X�` TK]_z{h f VawlkxwEXcmWy~]_�qkxw��E"

Page 6: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

ÂWà þ Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

−14

−12

−10

−8

−6

−4

−2

0

2

100 50 0 5 10 15 20 25

−0.06−0.05−0.04−0.03−0.02−0.01 0

150100500.02.04.06.08.10

Prof

undi

dade

(m)

Des

loca

men

to v

ertic

al (m

)

Tensão normal (kPa) Distância à parede (m)

Deslocamento horizontal (m) Tensão normal (kPa)

10.1 (Σ Fa=0)10.2 (Σ Fa=433kN/m)10.4 (Σ Fa=216kN/m)10.5 (Σ Fa=866kN/m)

K0=0.5KaH=0.279

ýQ]_�xf jAX¾þp� þ ��� ü�VamWf Vakxw  �p�  o  �p� Ä o  �p� à T  �p�87 � ` Tsw~Vak�mvX�z�TWngylkxw�bkcj~]_¬vkcn�yAX�]aw`bX�mskcj~y~]_nGXpo|XcwlwlTWn�yAX��z�TWngylkxwE` k{ylTWj~jlTWnbk�w~f hIkcj~yAXc` k�Trh jlTswlwA¯�TswR` T?ylTWj~jAXcwv�

! kEmvü�VamWf Vak  �p�87po�mskcj~jlTsw~hIkcnb` TWngylT}Xif z�n �_�qTWV�` T|h jl�\��Tsw°��kcjltske`pf h VakE` ki��kcj~nbTsmW]a` keh�TWVake`p]YX��xjAX�z;X` T�³.TWj~¬´X��x� ].TKSQTsmlµIoGmskcnb`pf ¬MX` TswlVak�mvX�z�TWn�ylkxweT\[ msTswlw~]_�qkxwY"bXcw}ylTWnbwA¯�Tsw}nbkcj~z;X�]awRnGXO]_ngylTWj°�ÊXcmsTw�uck o}mskcz�k�wlT«hIk�` T��qTWjvoijAX�¬vkqXs�qTWV_z�TWn�ylT6mskc]_nbmW]a` TWngylTsw�mskcz X�`p]aw~y~j~]_^ f ]atvuck<` T�h jl�\��Tsw°��kcjltskX�h V_]amvXc`bXp�

ýGX�¬W��wATenbkOTWngyAX�n�ylkMnbkcyAX�jvo X?h jlkch��xw~]_ylkO` kxw¶` Tsw~Vak�mvX�z�TWn�ylkxw}kc^ y~]a` kxw·` kOmvü�VamWf Vak  �p�87po�d�fbTek�z�k��` TWVak` TEmskcz{hIkcj~yAX�z�TWngylk®Xc` kch yAXc` khGX�jAXMkOwlkcVak��TWVYücw~y~]amsk��Êh�TWj°��TW]_yAX�z�TWngylT?h VYücw~y~]amsk opkOd�fbT�w~]_�xn ]�²GmvXd�fbT?k{z���`pf Vak{nGX�` TswlmvX�j~�gX�mskc]_nbmW]a` TMmskcz'k�z���`pf Vak;nGX{mvX�j~�gXpobylTWnb` k®mskcz�k�mskcnbwlTsd�f4$WnbmW]YX�d�fbT?kxw` Tsw~Vak�mvX�z�TWngylkxw}kc^ y~]a` kxw¶hIk�` TWjAuckMwlTWj¶wl]_�xn ]�²GmvX�y~]_�cX�z�TWn�ylTKw~f h�TWj~]akcjlTswiXckxw¶dgfbT�wlTWj~]YX�zÀkc^ y~]a` kxw·n�f z;Xw~]_y~fGXctvuck{jlTvX�V¶��kcf�wlTKwlTrf y~]_V_]_¬´XcwlwATrnbkxwemvü�VamWf VakxwRf z±z�k�` TWVak�` T?mskcz{hIkcj~yAX�z�TWngylk;z;X�]awEXc` Tsd�fGXc` kg�\�

¿1ýQ]_�xf jAX®þp�[Z{z�kxw~y~jAX;X;TW�qkcV_fbtvuck®`bXcwe�cX�j~]YXcts¯�Tsw�` T�mvX�j~�gX{nGXcwrX�nbmskcjAX��qTWnbwrmskcz5k���XcwlTvX�z�TWn�ylkmskcnbw~y~j~f y~]_�qk �{SQk�` T��qTWj~]�²GmvX���wlTxo.` Tsw~yAX®²b�xf jAXpoUdgfbTnbk«mvXcwAk«` k«mvü�VamWf Vak  �p�  Xcw?mvX�j~�gXcw�X�f z�TWn�yAX�zw~]_�xn ]�²GmvX�y~]_�xX�z�TWngylTxo�k{dgfbTKwAT¶º�fbw~y~]�²GmvX{h�TWVYXOnbTsmsTswlwl]a`bXc` T�` TKTsd�f ]_V_�_^ j~]ak�`bXcwRh jlTswlwA¯�TswRXcmWy~]_�xXcwv�

��k�mvXcwlk®` k�mvü�VamWf Vak  �p� Ä XcwemvX�j~�gXcwE�cX�j~]YX�z5h�kcfbmsk �¶�Ek;mvXcwlk;` k�mvü�VamWf Vak  �p� à oGmskcj~jlTswlh�kcnb` TWn�ylTX;z�TWyAXc` TO`bXcwrmvX�j~�gXcwKmskcj~jlTsw~hIkcnb` TWngylTsw?Xck�`p]YX��xjAX�z;Xà` T³.TWj~¬´X��x� ]|TOSUTsmAµ�oûXcw��xX�j~]YXcts¯�Tswr` TOmvX�j~�gXwAuck�z;X�]awMw~]_�xn ]�²GmvX�y~]_�xXcwvoQnbk�wATWngy~]a` k©` k¾X�f z�TWngylk �]\|w~ylTàX�f z�TWngylk©h jlTWnb` T\��wlTàmskcz X«nbTsmsTswAw~]a`bXc` TT\[p]aw~ylTWngylTxo·yAX�V}mskcz�kªnbk6mvXcwlkª` k©mvü�VamWf Vak  �p�  o¸` T�Tsdgf ]_V_]_^ jAX�jàXcwh jlTswlwl¯�TswXcmWy~]_�xXcwv� ¹ jlTsw~f V_yAXc` kkc^ y~]a` k«` kàmvü�VamWf Vak  �p�87®�kà` TOf z;X®`p]_z{]_n�f ]atvuck�`bXcwrmvX�j~�gXcwrnGXcw?X�nbmskcjAX��qTWnbwv�Kú|TWj~]�²GmvX���wlTxoUXcwlw~]_z�od�fbT�nGXcwOw~]_y~fGXcts¯�TswM^ITWz½`p]_z�TWnbw~]akcnGXc`bXcwvo|XcwM�xX�j~]YXcts¯�TswM` T;h jl�\��Tsw°��kcjltsk�w�uck�hITsdgfbTWnGXcwv���EkxwMmvXcwlkxwTWz¦dgfbTMk�h jl�\��Tsw°��kcjltsk«X�h V_]amvXc` k®�M]_np��TWj~]akcjKXck;mskcj~jlTswlh�kcnb` TWn�ylT�X{f z/Xc` TsdgfGXc` kà`p]_z�TWnbw~]akcnGX�z�TWngylk�Gü{X�f z�TWngylk;`bXMmvX�j~�gXOnGXcwEX�nbmskcjAX��qTWnbw���k{dgfbT�ylTWz'XOw~]_y~fGXctvuck{T\[py~jlTWz;XOnbk{mvXcwlk` k{mvü�VamWf Vak  �p�  �\��rXcwRw~]_y~fGXcts¯�TswR` T?X�h V_]amvXctvuck�T\[ msTswlw~]_�xX` Trh jl�\��Tsw°��kcjltsk oGmskcnbw~yAX�yAX���wlT?d�fbT?XcwRmvX�j~�gXcwRnGXcwEX�nbmskcjAX��qTWnbwylTWnb` TWz X�`p]_z{]_ngf ]_jv�^\|w~ylT;T\��TW]_ylk�` T®`p]_z{]_ngf ]atvuck©wlTWj~]YX�h jlk´�cXv�qTWV_z�TWngylTàz�TWnbkxwMmWVYX�jlk¾wlT{k«z�k�` TWVakXc` kch yAXc` k�hGX�jAX6k�mskcz{hIkcj~yAX�z�TWngylk<` k�wlkcVak�mskcnbw~]a` TWjAXcwlwlT�f z;X6mWf j~�cX ylTWnbwAuck���` Tsw~Vak�mvX�z�TWngylk�nGuckV_]_nbTvX�jvobmskcz z���`pf Vak�` T?` TswAmvX�j~�gX{w~f hITWj~]akcjeXckxw}z���`pf VakxwenGX{mvX�j~�gXp�

Page 7: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò ÂWà Z

−40

−20

0

20

40

60

80

100

0 1 2 3 4 5 6 7

Acr

ésci

mo

de fo

rça

(kN

/m)

Fase

10.1 (Fa=0)10.2 (Fa=433kN/m)10.4 (Fa=216kN/m)10.5 (Fa=866kN/m)

ýQ]_�xf jAX�þp�[Z ��� ü�VamWf Vakxw  �p�  o  �p� Ä o  �p� à T  �p�87 � �cX�j~]YXcts¯�TswR` T?mvX�j~�gXnGXcwEX�nbmskcjAX��qTWnbwv�=?>`_ aÁ¨A¥¦ 2CO¡G¨lHRCO¤e¥¦ 2CED�H¦ 2¡ D�F�L�D�LMF�¤<P

¹ jlTsmWf jlwlk{XckMz��Wylk�` k` kxwiTWVaTWz�TWngylkxw}²bn ]_ylkxwK��kcf�XOkcf y~jlkxwiz��Wylk�` kxw}d�fbTEh�TWj~z{]_ylTWz mskcnbw~]a` TWjAX�jk6mskcz{h�kcj~yAX�z�TWn�ylk ylTWnbwAuck���` T\��kcj~z;Xctvuck ` kªylTWj~jlTWnbkg�OylTWz `p]_�qTWjlwAXcw�xX�ngyAX��qTWnbw´o·TWn�y~jlT�Xcw{dgfGX�]aw{wAT` Tsw~yAXcmvX�X�hIkxwlw~]_^ ]_V_]a`bXc` TO` TOh jlTW��]awAuckà` TO` Tsw~Vak�mvX�z�TWn�ylkxwvo:` TMjlTvX�V_]_¬´Xctvuck«mskcz¦mWfbwlylk;jlTWVYX�y~]_�xX�z�TWngylTjlTs`pf ¬s]a` kà` TX�nGü�V_]awlTsw�` TMwATWnbw~]_^ ]_V_]a`bXc` Txo:TWylmx�eS£X�jAX�X�Va�Wz�` Tsw~yAXcw´o�k®z��Wylk�` k®hITWj~z{]_ylT�]_�xfGX�V_z�TWn�ylT{kmskcn �bTsmW]_z�TWngylk oG��XcwlT?XM�ÊXcwlTxo ` kxwETsw°��kcjltskxwR]_nbw~yAX�VYXc` kxw}nGX{Tsw~y~j~f y~f jAX�` T?w~f hIkcj~ylTx�

¿¼ýQ]_�xf jAX®þp�8b�X�h jlTswlTWngyAX;kxw}z�kcz�TWngylkxweZGTsmWylkcjlTswE]_nbw~yAX�VYXc` kxwRnGX{mskcj~y~]_nGX{hGX�jAX;XcwR`p]_�qTWjlwAXcwR��XcwATswmskcnbw~y~j~f y~]_�cXcw?hGX�jAX«k«mvXcwlk�` k«mvü�VamWf Vak  �p� Ä oûhIk�` TWnb` k�XàhGX�j~y~]_j?` Tsw~ylTsw?`p]YX��xjAX�z;Xcwvo.h jlk�msTs` TWj°��wlT®XckwlTWf�`p]_z�TWnbw~]akcnGX�z�TWngylkàTsw~y~j~f y~f jAX�VÊ�

SUk�` TWj~]YXpobnGX�y~f jAX�V_z�TWn�ylTxo�kc^ ylTWj°��wAT?`p]YX��xjAX�z;Xcwe` kz�Tsw~z�k�y~]_h�khGX�jAX{k{Tsw~��kcjltsknbkcj~z;X�V.TrhGX�jAX�kTsw°��kcjltsky~jAX�nbwl�qTWjlwlk �

=?>�= c drLM¨%PeLOfMFI¨lHgNR £FGD�¨A§U¤<P¾JM À 2¡bDGF�L�D�LMF�¤e¡�JM À§QHRCED� 2CONUPRH

å£æèå£æ�é hA2Uðxõqò2ó¸í�,pñIò¿Ew·mskcj~y~]_nGXcw·` TemskcngylTWnbtvuckMZGT\[��_�qTW]aw¶X�nbmskcjAXc`bXcw}X�h jlTswlTWngyAX�z�opmskcz�k�wAT}��]_fàX�ngylTWj~]akcj~z�TWngylTxobX�V_�xfp�

z;Xcw}w~]_�xn ]�²GmvX�y~]_�cXcwi�xX�ngyAX��qTWnbw}wAkc^ jlTrXcwimskcj~y~]_nGXcw}TswlmskcjAXc`bXcw´opjlTs`pf ¬s]_nb` k{k�ylTWz{hIkOnbTsmsTswlwAü�j~]akOhGX�jAXXT\[pTsmWfbtvuckKT·h�TWj~z{]_y~]_nb` krf z;XEz;X�]akcjQZGT\[p]_^ ]_V_]a`bXc` TinbkEh jlk�msTswlwlk�mskcnbw~y~j~f y~]_�qkK` TW��]a` kKXckEz;X�]akcj2Tsw~hGXctsk`p]aw~h�kcn �_�qTWV.nbk{]_ngylTWj~]akcj�`bXTswlmvXs�xXctvuck �

¿Ew£wlkcV_fbts¯�Tsw£` TimskcngylTWnbtvuck?d�fbT¸jlTsmskcj~jlTWz X�X�nbmskcjAX��qTWnbw|mskcz�TstvX�jAX�z X�wlTWjQf y~]_V_]_¬´Xc`bXcw¸XehGX�j~y~]_j|`bXi TW�xf nb`bXkj�fbTWj~jAX � f nb`p]YX�VgTxo�Tsw~hITsmW]YX�V_z�TWngylTxoqX¶hGX�j~y~]_jQ` kxwUX�nbkxwUþ��po��qTWj~]�²GmvX�nb` k���wlT·dgfbT|wAT£y%$Wz&��]_nb` kX}]_z{hIkcjUTWz¼` TWy~j~]_z�TWn�ylkr` kRjlTsmWf jlwlkrX}TswlmskcjAX�z�TWn�ylk�JjKkcf Va`:o ÂYl�l �q�\�Q¿�]_V_fbw~y~jAü��ÊVak o ¹nm �ekcf j~µqT¶T�oqkcnbTsw

Page 8: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

ÂWà b Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

0

2

4

6

8

10

12

14

16

−200 −150 −100 −50 0 50 100

y (m

)

Momento flector (kNm/m)

fase 0fase 1fase 2fase 3fase 4fase 5fase 6fase 7

ýQ]_�xf jAX�þp�8b �p� ü�VamWf Vak  �p� Ä�� z�kcz�TWn�ylkxwRZGTsmWylkcjlTswehGX�jAX�XcwR`p]_�qTWjlwAXcwi�ÊXcwlTswRmskcnbwly~j~f y~]_�cXcwv�

� ÂYl�l �q��Tsw~y~]_z;X�z/d�fbTqb�7XW5`bXcwKTswlmvXv�cXcts¯�TswKTWjAX�z�oû­à`bX�yAXà`bX;h f ^ V_]amvXctvuck oûjlTvX�V_]_¬´Xc`bXcw?mskcz¦jlTsmWf jlwlkX;X�nbmskcjAX��qTWnbwrh jl�\��Tsw~��kcjltvXc`bXcwv�ESQX�jlTsmsTOyAX�zM^��Wz/` TWz�kcnbw~y~jAXc`bX�X�T\²GmvücmW]YX®`bXcwrmskcj~y~]_nGXcwKX�nbmskcjAXc`bXcwv�i ml� nbkcjlT<� ÂYl�l �q�\o¶h�kcj�T\[ TWz{h Vak o¸y~jAXc`pf ¬s]_nb` k<XªT\[�hITWj~]r$WnbmW]YX6` k ��Ttsvu¸kcj~µ i yAX�ylTw6rTWhGX�j~y~z�TWngy®k��³ûjAX�nbwlh�kcj~yAX�y~]akcnûobmWVYXcwAw~]�²GmvX` TxB�^GX�]�[pk D kMj~]awAmskO` TKXcwlwATWngyAX�z�TWngylkxwEw~]_�xn ]�²GmvX�y~]_�qkxwR` kwlkcVakw~f hIkcj~yAXc` khIkcj}hGX�jlTs` TswEX�nbmskcjAXc`bXcwv�

¿�w�X�nbmskcjAX��qTWnbwvornbkÑTWn�yAX�ngylk o�X�h V_]amvX�zì­ mskcj~y~]_nGXÑw~]_�xn ]�²GmvX�y~]_�xXcw���kcjltvXcw��qTWj~y~]amvX�]aw�` T wlTWn�y~]a` k` TswlmsTWnb` TWn�ylTxobdgfbT�nGuckT\[p]aw~ylTWz�nGXcw}Tswly~j~f y~f jAXcw}TswlmskcjAXc`bXcw}TrdgfbTEylkcj~nGX�z±]_z{h�kcj~yAX�n�ylT?XM�qTWj~]�²GmvXctvuck`bX{wlTW�xf jAX�nbtvX�TWz jlTWVYXctvuck;­Tsw~yAX�^ ]_V_]a`bXc` T��qTWj~y~]amvX�V.`bXhGX�jlTs` Tx�

S£X�jAXàdgfbT��GX�º~X®Tsdgf ]_V_�_^ j~]ak®nbTsw~yAX®`p]_jlTsmstvuck®��nbTsmsTswlwAü�j~]ak o�yAX�V£mskcz�k®wlT�h jlTWylTWnb` T�jlTWh jlTswATWngyAX�jKnGXýQ]_�xf jAX�þp� l ��Xq�\oGd�fbT?XM��kcjltvX�qTWj~y~]amvX�VU` TW��]a`bX{­cwemskcz{hIkcnbTWngylTswe�qTWj~y~]amvX�]awE`bXcwi��kcjltvXcwR`bXcw�X�nbmskcjAX��qTWnbwT{Xckàh�Tswlk®h jl�ch j~]ak«`bX®hGX�jlTs` T{wlT�ºlX®mskcz{hITWnbwAXc`bX®hITWVYX���kcjltvX®�qTWj~y~]amvX�V|dgfbTwlTO` TswlTWn��qkcV_�qT{nbkàh��`bXhGX�jlTs` TàT�hITWVYX«jlTsw~f V_yAX�n�ylT®`bXcwMylTWnbwl¯�Tsw�` Tàmskcj~ylT�nGXcwM]_ngylTWj°�ÊXcmsTswOwAkcVak��ÊhGX�jlTs` T®` TW��]a` k¾­cw���kcjltvXcwO` Tmskcj~ylTxob` TKz�k�` k�X{d�fbTKwlT�ºlXO�qTWj~]�²GmvXc`bX�X{Tsd�fGXctvuck

y{zr|`zr}e~1���C��}%�O�-�e����� � }%���%�A�Y��� ���;����� �} ��� }} ��þp�  �kcnb` T�y�zr|`zr}e~��|X·��kcjltvXiylkcyAX�Vg�qTWj~y~]amvX�V�B�XcmWy~fGX�ngylT D nGX¶hGX�jlTs` TxoX�C�Y}e�O�-�%�U�2kih�TswAk}`bXihGX�jlTs` Txo���� }%���%�A�Y����eXK��kcjltvX?�qTWj~y~]amvX�VGylkcyAX�V�` TW��]a`bX�­cw¶X�nbmskcjAX��qTWnbwvo��;�¸�eXr��kcjltvXKd�fbTewlTR` TswATWng�qkcV_�qTEnGXK^GXcwlTR`bX?hGX�jlTs` Txo� �} ��X¾��kcjltvX6` T�mskcj~ylT�nGXª]_ngylTWj°�ÊXcmsT�wlkcVak��ÊhGX�jlTs` T¾` k6VYXc` k6hGXcwlwl]_�qk T^� }} �¾X©��kcjltvXª` T�mskcj~ylT�nGX]_ngylTWj°�ÊXcmsT�` kVYXc` k®XcmWy~]_�qk �

¿���kcjltvX����;` TW�qTWjAü��qTWj~]�²GmvX�j�X wlTW�xf jAX�nbtvX<TWz jlTWVYXctvuck<­�mvX�hGXcmW]a`bXc` TªjlTsw~]aw~ylTWn�ylT��qTWj~y~]amvX�VK` kylTWj~jlTWnbk�T;k�wlTWf mvü�VamWf Vak��;mskcn �bTsmW]a` k�hGX�jAX�kxw�mvXcwlkxw�` T�Tswly~j~f y~f jAXcw�` T�mskcn�ylTWnbtvuck¾mskcz�k©XcwKhGX�jlT\�

Page 9: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò ÂWÃ�l

W

�����)� � �¡ �¢��¡£¤¦¥ §[¥ ¨ª©%«p¬5­'¨¯®¯°[±ª°E²0³k´ ¨¯µ·¶ª¸º¹¼»¾½«�´E¿¾²0´ ¨¨ ²0´ ­¨

´ ¨¨

´ ­¨

´ ¿

´ ¨ªµ·¶

´ ¨ªµ·¶

½

½

ÀrÁtÂ1Ã#ÁeÄJÅOÆ�ÅQÇÉÈEÊ[Æ�Á¾Æ�Á

W

F

���r�)� � �¡ r¢��¡£¤¦¥ §[¥ ¨ª©%«p¬5­'¨¯®¯°[±ª°E²Q³x´ ¨ªµ·¶¯¸·¹r»¾½«�¤ ­'°8®ªË�Ì © ²0´ ¨

´ ¨ªµ·¶

´ ¨ªµ·¶´ ¨

½

½

À�Í�ÂTÃ#Á%ÄJÅOÆAÅ0ÎJÏ8Ð�ÈÉÑÒÅ-ÄJÊ[Ï8Ç

ýU]_�xf jAX;þp� l�� \|d�f ]_V_�_^ j~]ak��qTWj~y~]amvX�V.` TKhGX�jlTs` TswE` TKmskcngylTWnbtvuck�ZGT\[��_�qTW]awv�

` TswMz�kcVa`bXc`bXcw´o2h�k�` TWnb` k©hGX�jAX¾yAX�V¶wlTW�xf ]_j°��wATàk¾jlT\��TWj~]a` k©TWzÔÓKX�ngy~�GX�µqkxw�� ÂYl�l�à �Mkcf�z�TWylk�` kcVakc�x]YXcwwlTWz�TWV_�GX�ngylTswvoRnbkcj~z;X�V_z�TWngylTª^GXcwlTvXc` kxw®nGXcw���kcj~z�f VYXcts¯�Tswà` T¾mvX�hGXcmW]a`bXc` T©` T�mvX�j~�gX�` T«��f nb`bXcts¯�Tswh jlk���f nb`bXcwv�¸�EkOmvXcwlk` T�hGX�jlTs` Tsw}mskcz�k{mskcj~y~]_nGXcw}` T�TswlyAXcmvXcw°�Êh jAX�nbml�GXcwvobnbkOTWn�yAX�ngylk oGXMz�TWnbkxw}d�fbTKXmskcj~y~]_nGX?Tsw~ylT�ºlXKXcwlwlTWn�ylT}ngf z Tswly~jAX�ylkKz�f ]_ylk�jlTsw~]aw~ylTWngylTxognGuckK�GüKXrhIkxwlw~]_^ ]_V_]a`bXc` TR` T}` TswATWng�qkcV_��]_z�TWngylk` TKjlTvXcmstvuck{nGX^GXcwlT�Õ·����Ö×��Ø\o hIkcjeTsw~yAXOnGuck�h�kxwlwlf ]_j}VYX�j~�xf jAX{w~]_�xn ]�²GmvX�y~]_�xXp�� X�ylkxw¶ýbTWj~nGX�nb` TswK� ÂYl b � �|z�kxw~y~jlkcfàd�fbTEX?z�kc^ ]_V_]_¬´Xctvuck`bXKjlTsw~]aw~y%$WnbmW]YX�nGXK]_n�ylTWj°��XcmsTrwlkcVak��ÊhGX�jlTs` T

` k VYXc` k hGXcwAw~]_�qk oÙ� �} o¶ylTWz�f z hGX�hITWVe]_z{hIkcj~yAX�ngylT¾nbk�Tsd�f ]_V_�_^ j~]ak �qTWj~y~]amvX�VÊoRTWz Tsw~y~j~f y~f jAXcw®mskcz�kXcw�hGX�jlTs` Tswàz�kcVa`bXc`bXcw®kcf mskcj~y~]_nGXcw®` T¾Tsw~yAXcmvXcw°�Êh jAX�nbmA�GXcwvo}]_nbmWV_fbw~]_�xX�z�TWngylT©nbkxw;mvXcwAkxw®TWz dgfbT�kxwXcwlwlTWngyAX�z�TWn�ylkxwR`bXMhGX�jlTs` TrwlT�º~X�z z�f ]_ylkjlTs`pf ¬s]a` kxw´�|SUTWVak{mskcn�y~jAü�j~]ak opz�Tsw~z�kdgfbTKXMTsw~y~j~f y~f jAXOwlk���jAXXcwlwlTWngyAX�z�TWn�ylkxw}z�f ]_ylkTWVaTW�xXc` kxwvo XMjlTsw~]aw~y%$WnbmW]YX�nGX�]_n�ylTWj°��XcmsTrwlkcVak��ÊhGX�jlTs` TK` kMVYXc` k{XcmWy~]_�qk o�� }} o�nGuck�mskcz{h VaTWyAX�z�TWngylTRz�kc^ ]_V_]_¬´Xc`bX{� � X�ylkxw2ýbTWj~nGX�nb` Tswvo ÂYl b � o ÂYl b�7�"x³.j~]_�qk o ÂYl�l ��" � X�ylkxw£ýbTWj~nGX�nb` Tsw·TWy|X�VÊ�_oÂYl�l�� o ÂYl�l�à �\�ú|TWj~]�²GmvX���wlTxo¶nbk TWngyAX�n�ylk o}dgfbT�z�Tswlz�k TWz V_]_ylTWjAX�y~f jAX�XcmWy~fGX�VEwlT�Xc`pz{]_ylT�wlTWjlTWz�Xc` Tsd�fGXc`bXcw®Xcw

ylTWnbwl¯�TswQ` T¶mskcj~ylT·TWn�y~jlT¶XRhGX�jlTs` T¶T·kewlkcVak�w~f hIkcj~yAXc` kehGX�jAXR��kcj~nbTsmsTWj£XRjlTvXcmstvucke�qTWj~y~]amvX�Vp]_nb`p]aw~hITWnbwAüs�qTWVXck�Tsd�f ]_V_�_^ j~]ak<��¿ i � \Ro ÂYl�l Zx�\� ¹ � X�nGXc`p]YX�nÑýbkcf nb`bX�y~]akcnÚ\2n �x]_nbTsTWj~]_n � � X�ngfGX�VK� ÂYl Z�bq�?mskcnbw~]a` TWjAXz�Tsw~z�k?d�fbTRX�h�TWnGXcw|` TW�qTWjAü�wlTWj|mskcngyAX�^ ]_V_]_¬´Xc`bXOX�jlTsw~]aw~y%$WnbmW]YXKVYX�ylTWjAX�VG` kKVYXc` k�XcmWy~]_�qk �2¿ö]_z{h�kcj~yAÿ�nbmW]YX` Tsw~ylT©XcwAw~f ngylk�hGX�jlTsmsTxoemskcn�y~fb` k oETsw~yAX�jàmWVYX�jAX<` Tswl` T¾k�]_n �amW]ak�`bX f y~]_V_]_¬´Xctvuck�` TªX�nbmskcjAX��qTWnbw®h jl�\�Tsw°��kcjltvXc`bXcweTWzÀkc^ jAXcwe` T�mskcn�ylTWnbtvuck � � kcz T\��TW]_ylk o#Û¶jlkcz�w�� ÂYl þ�bq�·]a` TWngy~]�²GmvX�jAXKº~üXM]_z{h�kcj~yAÿ�nbmW]YX�` T� �} T{X®`p]����amW]_V£z�kc^ ]_V_]_¬´Xctvuck�` Tn� }} TqÜrX�n nGX©� ÂYl þ�bq�ejlT\��TWj~]_jAXàdgfbTOnbkxwrmvXcwlkxwr` TOjlkcy~f jAX�` T�hGX�jlTs` TswX�nbmskcjAXc`bXcw|` T}dgfbT¶y~]_n �GXrmskcn �bTsmW]_z�TWn�ylk opX�mvX�fbwAX�y~]_n �GXrwl]a` k oc]_ng�xX�j~]YXs�qTWV_z�TWngylTxo kKX�hIkc]akr]_nGXc` TsdgfGXc` k`bXr^GXcwlTe`bXKhGX�jlTs` Tx�2¿öz�Tswlz;Xr]a` TW]YX?�}y~jAX�nbwlz{]_y~]a`bX?hIkcjpjrkcVa`p^ITWj~��TWy¶X�VÊ��� ÂYl Zcþq�\o�Xck�X�²bj~z;X�jlTWzÀd�fbT

Page 10: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 7�� Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

XKz;X�]akcj·hGX�j~ylTE` kxw·h jlkc^ VaTWz;XcwidgfbTek�mskcj~jlTWz jlTWVYXcmW]akcnGXc` kxwimskcz mskcj~y~]_nGXcwiX�nbmskcjAXc`bXcwi`p]_¬vTWz�jlTsw~hITW]_ylkXckxw}z�k´��]_z�TWn�ylkxwe�qTWj~y~]amvX�]awET\[pmsTswlwl]_�qkxwv�

¿5`p]����amW]_VRz�kc^ ]_V_]_¬´Xctvuck�`bX©jlTsw~]aw~y%$WnbmW]YXªnGX©]_n�ylTWj°��XcmsT�` kªVYXc` k XcmWy~]_�qk o·yAX�VRmskcz�k�X�hIkcngyAXc` k6hIkcjÜrX�n nGX � ÂYl þ�bq�\o � X�ylkxw�ýGTWj~nGX�nb` Tswà� ÂYl b�7q�rT � X�ylkxw?ýGTWj~nGX�nb` TswMTWyMX�VÊ�·� ÂYl�l�� o ÂYl�l�à �\oû�ÊX�¬;mskczäd�fbTXª�qTWj~]�²GmvXctvuck�` k Tsdgf ]_V_�_^ j~]ak��qTWj~y~]amvX�VETWz hGX�jlTs` Tswà` T�mskcn�ylTWnbtvuck�y~]_hIkÝÛiTWj~V_]_z wlT�ºlX©f z;X d�fbTsw~yAuck` TO�xjAX�nb` T]_z{h�kcj~yAÿ�nbmW]YXp� � kcz/T\��TW]_ylk oInbTsw~ylTOy~]_hIk�` TMhGX�jlTs` T` TmskcngylTWnbtvuck�wAuck�T\[pTsmWf yAXc` kxw���f jlkxw�qTWj~y~]amvX�]awMXck�Vakcn �qk�` k«hITWj~�_z�TWy~jlk�`bX«TswlmvXv�cXctvuck�X«jlTvX�V_]_¬´X�jvo.nbk�]_n�ylTWj~]akcjM` kxw�d�fGX�]aw?wAuck�]_nbwlyAX�VYXc` kxwhITWj°²GwUz�TWyAü�V_]amskxw£�qTWj~y~]amvX�]aw´��Þ z�Ts`p]a`bXEd�fbTiXeTswlmvXv�cXctvuck�h jlkc�xj~]a` Txox�xX�]pwlTWnb` krT\[pTsmWf yAXc`bXEf z;XEhGX�jlTs` T` T¾^�TWyAuck�X�j~z;Xc` k oR^ITWylkcnGXc`bX<`p]_jlTsmWyAX�z�TWngylT6mskcngy~jAX<k�ylTWj~jlTWnbk oeTWn��qkcV_�qTWnb` kÑkxw;hITWj°²Gwàz�TWyAü�V_]amskxw�qTWj~y~]amvX�]awv�ß\|w~ylT«h jlk�msTs`p]_z�TWngylk�]_z{h V_]amvX d�fbT«nGuck T\[p]aw~yAX©VYXc` k6hGXcwlw~]_�qk�`bX©hGX�jlTs` T�` T�mskcn�ylTWnbtvuck of z;X�qTW¬�d�fbT�X�^GX�]�[ k�` k{n �_�qTWVQ` T?TswlmvXs�xXctvuck oGTWz5mvXc`bXO��XcwATxo nGuck{�GühGX�jlTs` T�z;XcwEX�hITWnGXcwekxw}hITWj°²Gw�qTWj~y~]amvX�]awv�

¹ wàhITWj°²Gw��qTWj~y~]amvX�]aw«TxoeTW�qTWngy~fGX�V_z�TWn�ylTxoKk<VYXc` k�XcmWy~]_�qk�`bX�hGX�jlTs` Txo�` TW�qTWz$XcwAw~]_z��gX�jAX�ngy~]_j�kTsd�f ]_V_�_^ j~]ak�`bXcw}��kcjltvXcw}�qTWj~y~]amvX�]awvobk{d�fbT?w~]_�xn ]�²GmvXpoGmskcnp��kcj~z�T�X�h jlTswATWngyAXc` k�nGX�ýU]_�xf jAX;þp� l ��^��\obdgfbT

y{zr|`zr}¾~Ò���C��}%�O�-�e����� � }%���e������� �×yk���)�%àtá�~���� } ��þp� Ä �kcnb` TÉ�C�Y}%�O�`�%�QTp��� }e��� ������� y%$Wz"kew~]_�xn ]�²GmvXc` k·ºlüijlT\��TWj~]a` k o�y?�Y�-�%àtá�~g�·X}��kcjltvXRy~jAX�nbw~z{]_y~]a`bX�Xckxw.hITWj°²Gwz�TWyAü�V_]amskxwM�qTWj~y~]amvX�]aw�T�� } ��X���kcjltvX«` T;mskcj~ylTxo.z�kc^ ]_V_]_¬´Xc`bX�h�kcjMXc` Tsw�uck�T���kcf��KX�y~j~]_ylk�nGXà]_ngylTWj°�ÊXcmsTwlkcVak��ÊhGX�jlTs` Tx�\|wAmWVYX�jlTsmsTWjTWz dgfbT;z�Ts`p]a`bX�wAT�hIk�` TWjAü�z�kc^ ]_V_]_¬´X�j{X«��kcjltvX¾` T;mskcj~ylTà` k�VYXc` kªXcmWy~]_�qk©mskcnbw~y~]_y~f ]

f z;X�dgfbTswlyAuckE]_z{hIkcj~yAX�ngylTRhGX�jAXrkETsd�f ]_V_�_^ j~]akKT\[�h jlTswAwlk�h�TWVYX�Tsd�fGXctvuck?þp� Ä T¶hGX�jAX�kr`p]_z�TWnbw~]akcnGX�z�TWngylk` Tsw~ylTKy~]_hIk{` TKTsw~y~j~f y~f jAX;` TKmskcngylTWnbtvuckª�Jj�fbTWj~jAXpo ÂYl�l�l �\�â�z{h�kcj~yAXehIkc]awUmskcn �bTsmsTWj2kemskcz{hIkcj~yAX�z�TWngylkK`bXcwQmskcj~y~]_nGXcw£` T·mskcn�ylTWnbtvuck�ZGT\[��_�qTW]awUnbk�dgfbT·wlT¸jlT\��TWjlT

­cwRmvX�j~�gXcw}�qTWj~y~]amvX�]aw´obnbkcz�TvXc`bX�z�TWngylTMnbk{d�fbTrjlTsw~h�TW]_yAX{XmvXcwAkxwRTWz'd�fbTKk{Tsdgf ]_V_�_^ j~]ak{nbTswlyAX{`p]_jlTsmstvuckylTWn �GX�wl]a` k�` T\²GmW]aTWngylTx�Cã¼X�]_nb`bX�]_z{h�kcj~yAX�n�ylT;Tsw~y~fb`bX�jXcwKhGX�jlmsTWVYXcwOdgfbT�mskcz{hI¯�TWz½X«Tsd�fGXctvuck�þp� Ä od�fbTWj?nbk�d�fbT{jlTsw~hITW]_yAX�Xckxw�wlTWfbw?�cX�VakcjlTsw�V_]_z{]_ylTswMT{` T®`p]_z�TWnbw~]akcnGX�z�TWngylk o2d�fbTWj?nbk�d�fbT{jlTsw~hITW]_yAX�­w~fGX` TWylTWj~z{]_nGXctvuckàTWz mvXcwlkxwR` T?kc^ jAXp�

å£æèå2æ'& äàò�(+*}òûõxðxô1(öî52.ðxò î#å|÷�ó¸î32�/ ÷�ôIó¸òß*}ò.õæ( ò2ó|î3.�ò.ï^çOè�ïc÷-/pò.ïÜrX�n nGX�T � X�yAX�V_VYX�nGX�� ÂYl Z��q�EjlTvX�V_]_¬´X�jAX�zäf z!mskcncº°f ngylk�` T{TWnbwAX�]akxwK` TVYX�^IkcjAX�yl�cj~]ak�TWz/z�k�` TWVak

jlTs`pf ¬s]a` k«` Tsw~y~]_nGXc` kxw�Xàmskcz{hGX�jAX�j?k�mskcz{hIkcj~yAX�z�TWngylk�` TTsw~y~j~f y~f jAXcw?` Tmskcn�ylTWnbtvuck�X�nbmskcjAXc`bXcw?TWz��f nbtvuck�` T?`p]���TWjlTWngylTswe`p]YX��xjAX�z;Xcw�` Trh jl�\��Tsw°��kcjltsk;`bXcweX�nbmskcjAX��qTWnbw´�¸�Ef z;X{wl�Wj~]aTK` T?TWnbwAX�]akxwejlTvX�V_]_¬´X��` kxw?hIkcj�Tsw~ylTswMX�f ylkcjlTsw?��kcjAX�zämskcnbw~]a` TWjAXc` kxw � n �_�qTW]aw�` T®X�nbmskcjAX��qTWnbwM�bkcj~]_¬vkcn�yAX�]awY"£nGX«kcf y~jAX�Tsw~yAXcwX�nbmskcjAX��qTWnbw;TWjAX�z ]_nbmWV_]_nGXc`bXcw®Xæ������mskcz�X¾�bkcj~]_¬vkcn�yAX�VÊ�Ú\2z�X�z�^Ikxw�kxw{mvXcwlkxwO��kc]}mskcnbw~]a` TWjAXc`bX XwlTsd�f4$WnbmW]YX{mskcnbw~y~j~f y~]_�xX{w~f �qTWj~]a`bXhITWVYXýQ]_�xf jAX�þp�  �p�� kcz{hGX�jAX�nb` kMkxw2jlTsw~f V_yAXc` kxw|` TR` kc]aw¸TWnbwAX�]akxw|mskczÁkrz�Tsw~z�k?`p]YX��xjAX�z;X?` Tih jl�\��Tsw°��kcjltsk�`bXcw¸X�nbmsk��

jAX��qTWnbwRz;XcwEmskcz'`p]���TWjlTWngylTswR]_nbmWV_]_nGXcts¯�TswM�é��T{�������ikxw}jlT\��TWj~]a` kxwEX�f ylkcjlTswe�qTWj~]�²GmvX�jAX�z'nbkcj~z;X�V_z�TWngylThITsdgfbTWnGXcw£�xX�j~]YXcts¯�Tsw2` TimvX�j~�gX�nGXcw2X�nbmskcjAX��qTWnbw¸mskcz�T\[ msTWh�tvuckr` kKTWnbwAX�]akrTWz�d�fbTiXrX�V_y~f jAXrTWn�ylTWj~jAXc`bX`bX®mskcj~y~]_nGX;wlTOX�ngf Vakcf6T?hGX�jAXàX{]_nbmWV_]_nGXctvuck�` Tq�����q�eS£X�jAX;TswlyAX;w~]_y~fGXctvuck;��kc]U` TWylTsmWyAXc`bX®f z;X�hITWjl`bX

Page 11: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â 7 Â

0.50

H

0.81

H

H=0

.61m

0.23

H

0.54

H

0.85

H

0.19

H

α

α

α

ýU]_�xf jAX�þp�  � � i Tsdgf4$WnbmW]YXEmskcnbw~y~j~f y~]_�xX�Xc` kch yAXc`bXEnbkxwQz�k�` TWVakxwû���aw~]amskxwQ` T�ÜrX�n nGXeT � X�yAX�V_VYX�nGXO� ÂYl Z��q�\�

w~]_�xn ]�²GmvX�y~]_�cXr`bX�mvX�j~�gXEnbkxw2` kc]awQh j~]_z�TW]_jlkxw2n �_�qTW]aw2` T}X�nbmskcjAX��qTWnbwe��X�yl�imsTWjlmvX�` T à �XW{�UT¶f zÁX�f z�TWngylkw~f ^bw~yAX�nbmW]YX�Vûnbk{n �_�qTWV.z;X�]aw}h jlk���f nb` k¾���qTWjeýQ]_�xf jAX�þp� Âx �\�

−50

−40

−30

−20

−10

0

10

20

1 2 3 4 5 6 7 8

Var

iaçã

o de

car

ga n

as a

ncor

agen

s (%

)

Nível 1

Ancoragens 0o

Ancoragens 30o

2 3 4 5 6 7 8Fase

Nível 2

4 5 6 7 8

Nível 3

ýU]_�xf jAX«þp� ÂxÂ�� \2�qkcV_fbtvuck�`bXcwKmvX�j~�gXcwKnGXcw?X�nbmskcjAX��qTWnbw?` kxwrz�k�` TWVakxwr���awl]amskxwK` TnÜrX�n nGX�T � X�yAX�V_VYX�nGX� ÂYl Z��q�\�â�n ]amW]YX�V_z�TWn�ylTxobnGuck{�GüOh jAX�y~]amvX�z�TWn�ylT?z�k´��]_z�TWn�ylk��qTWj~y~]amvX�V.`bXhGX�jlTs` Tx��Þ�z�Ts`p]a`bX{d�fbT?X�f z�TWngyAX

X�h jlk���f nb`p]a`bXc` TETswlmvXs�xXc`bXpoq�qTWj~]�²GmvX���wlT�Xrk�mskcj~j%$WnbmW]YX�` T}` Tsw~Vak�mvX�z�TWngylkxw·VYX�ylTWjAX�]aw¸XckKn �_�qTWVG`bX�^GXcwlTe`bXhGX�jlTs` T�f V_y~jAX�hGXcwlw�X�nb` k;kxwe` TswlVak�mvX�z�TWn�ylkxw�` k;ylkch�k oGnbk�mvXcwlk®` TMXcwEX�nbmskcjAX��qTWnbw�wlTWjlTWz5�bkcj~]_¬vkcngyAX�]awv�\|w~ylTswà` Tsw~Vak�mvX�z�TWn�ylkxw�wAuck�Xcmskcz{hGX�n �GXc` kxw«` k<XcwlwlTWngyAX�z�TWn�ylk�`bX6hGX�jlTs` Tx����k�mvXcwlk�`bXcwàX�nbmskcjAX���qTWnbwi]_nbmWV_]_nGXc`bXcwvop�qTWj~]�²GmvX���wlT�f z;XMy~jAX�nbw~VYXctvuck�xVakc^GX�V:`bX�hGX�jlTs` T�nbkwlTWn�y~]a` kO`bXOTswlmvXv�cXctvuck opyAX�zM^��WzXcmskcz{hGX�n �GXc`bX�` TMXcwlwlTWn�yAX�z�TWngylkxwKd�fbT�wAuck o�hIkcjET\[ TWz{h Vak o�nGX{��XcwAT�bpo�msTWjlmvX;` T ÂY� �qTW¬vTsw�kxwEd�fbT�wAT�qTWj~]�²GmvX�z'nGXOhGX�jlTs` T�wlf h�kcj~yAXc`bXhIkcjeX�nbmskcjAX��qTWnbwR�bkcj~]_¬vkcn�yAX�]awO��ýQ]_�xf jAX®þp� ÂvÄ �\�

¿�w~f h�TWj°���amW]aT|`bXRX�jlTW]YXRw~f h�kcj~yAXc`bXEXcwlwlTWn�ylkcfMmskcnp��kcj~z�T2jlTWh jlTswlTWngyAXc` kEnGXRýQ]_�xf jAXRþp� ÂY� o�z�kxw~y~jAX�nb` k��wlTEkxw}XcwlwATWngyAX�z�TWngylkxwRhGX�j~y~]amWf VYX�j~z�TWngylT?wlTWnbwl�_�qTW]awi­�]_nbmWV_]_nGXctvuck{`bXcw}X�nbmskcjAX��qTWnbwvo wlTWnb` k o�hGX�jAXOkMmvXcwAk`bXcwRX�nbmskcjAX��qTWnbwR]_nbmWV_]_nGXc`bXcweXê�����qo��xü�j~]YXcw}�qTW¬vTsw}w~f hITWj~]akcjlTsweXckxw}dgfbTrwlT��qTWj~]�²GmvX�jAX�z nGXwl]_y~fGXctvuck{` T

Page 12: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 7 Ä Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

−0.6

−0.4

−0.2

0

Pr

ofun

dida

de (m

)

Deslocamento

5 mm

InicialAncoragens 0o

Ancoragens 30o

ë�ì�í�î#ïeð�ñ�ò�óYô�õÙöø÷�ùOúrû�üYð�ý�÷tþ�ÿ%û�ù��X÷tïOÿOìrüYð�ìrù?÷��4û�ïOì��Yû�þ�ÿeð�ìrù��4ð�3ð�ï%÷�#÷��#û�ù<ý�û��#÷túrû�ù� ��rùOìrü�û�ù��#÷��øð�þ#þ3ð�÷� ð�ÿeð�ú�ú¼ð�þ3ð�� ó��������¾ò

ð�þ4ü�û�ïeð�íX÷tþ4ù��4û�ïOì��Yû�þ�ÿeð�ìrùYò

0

0.0005

0.001

0.0015

0.002

0.0025 0 0.1 0.2 0.3 0.4 0.5 0.6

Ass

enta

men

to (m

)

Distância à parede (m)

Fase 7 (α=0)Fase 8 (α=0)

Fase 7 (α=30o)Fase 8 (α=30o)

ë�ì�í�î#ïeð�ñ�ò�ó���õ��?ù%ù%÷tþ¦ÿeð�ý�÷tþ�ÿ%û�ù �4ð�ùOî!�Ò÷tï" ��rütìr÷��#ûqÿ%÷tïOï%÷tþ4û�ùOî!�Tû�ïOÿeð#�#û$�#û�ùÉý�û��#÷túrû�ù% ��rùOìrü�û�ù%�#÷��øð�þ#þ3ð÷�� ð�ÿeð�ú�ú¼ð�þ3ð&� ó��������¾ò

' û�ý�ûxý�û�ùOÿOïeð�ý û�ù�ï%÷�ùOî#ú�ÿeð#�#û�ù(�#÷�û�î#ÿOïeð<ù*)tïOìr÷+�#÷�÷tþ4ù¾ð�ìrû�ù;ð��#ï%÷�ù%÷tþ¦ÿeð#�#û�ù,�Tû�ï,�øð�þ#þ3ð<÷+� -#î/.10�ð�úr÷2-� ó�����ô��431ð�÷65�ìrùOÿ87tþ4ütì¼ð9�#÷�î#ý ùOî!-4ùOÿOïeð�ÿ%û�ï:��í�ì;�#ûCð�ûHþ!���X÷tú(�#û<�=)>�4ð$�3ð�ï%÷�#÷�ì�ý?�Ò÷�#÷�û ð�ùeù%÷tþ�ÿeð�ý�÷tþ¦ÿ%û�#÷�ùOÿeð/3��T÷túrû�@¦î4÷xÿ%û��#û�ùÙû�ù�ý�ûA�¦ì�ý�÷tþ¦ÿ%û�ù<û¦ü�û�ïOï%÷tý þ3ð>��ì�ï%÷�üB�C�û>�4û�ïOì��Yû�þ¦ÿeð�ú=÷kû�ý�÷�üYð�þ#ìrùOý�ûêð�ù%ù%û�ütì¼ð#�#ûð�û�ý�ûA�¦ì�ý�÷tþ¦ÿ%ûD�4ð?�3ð�ï%÷�#÷�)E33þ4ûHüYð�ù%û<�#÷qð�ùkð�þ4ü�û�ïeð�íX÷tþ4ùùe÷tï%÷tý ì�þ4ütú�ì�þ3ð#�4ð�ù�3Tù%÷tý�÷tú��3ð�þ¦ÿ%÷qð�û9@�î4÷�ù%÷�X÷tïOìGF3üYðqþ4û�üYð�ùeû?�#÷�÷�ùOÿeð�ù<ù%÷tï%÷týH�4û�ïOì��Yû�þ�ÿeð�ìrùYòJI�ùOÿ%÷ü�û�ý?�Tû�ïOÿeð�ý�÷tþ�ÿ%ûHÿOïeð#��î!�2.)ù%÷E35ð�ù%ù%ì�ý�3#÷týwõ

K �#÷�ù%úrû¦üYð�ý�÷tþ¦ÿ%û�ùkü�û�þ4ùOì;�#÷tïeð��X÷tú�ý�÷tþ�ÿ%÷ný�÷tþ4û�ï%÷�ù�LK ý�ûA�¦ì�ý�÷tþ¦ÿ%û�ù9�#÷wï%û�ÿeð#B�C�ûM�4ðN�3ð�ï%÷�#÷E3pì�þ#ìrütì¼ð�ú�ý�÷tþ�ÿ%÷]÷tý ÿ%û�ïOþ4ûM�4ðN-3ð�ù%÷^÷E3POæý�÷��ì;�4ðM@¦î4÷wð

Page 13: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â 7 �

h jlk���f nb`p]a`bXc` T�` T?TswlmvXv�cXctvuck®X�f z�TWngyAXpoGTWz'ylkcj~nbk�` TKf z±hIkcngylk{Vak�mvX�V_]_¬´Xc` k®XOz�TW]YX�X�V_y~f jAX�"! Xr]_nbmWV_]_nGXctvuck?`bXcw·X�nbmskcjAX��qTWnbw·` TW]�[bXr` TiylTWj|f z;XrjlTWVaTW�xÿ�nbmW]YXKw~]_�xn ]�²GmvX�y~]_�xXrnbkKmskcz{hIkcj~yAX�z�TWngylk �S2VYX�ngy{� ÂYl Z Ä �ijlTvX�V_]_¬vkcfªTsw~y~fb` kxwEwlTWz�TWV_�GX�ngylTswvo�yAX�z�^I�Wz¦TWz z�k�` TWVak����awl]amsk obmskcz5k®kc^pº°TsmWy~]_�qk®` T

Tsw~y~fb`bX�j¸X�]_npZbf4$WnbmW]YXr`bX�]_nbmWV_]_nGXctvuck?`bXcw|X�nbmskcjAX��qTWnbw|nbkKmskcz{hIkcj~yAX�z�TWngylk�` T}mskcj~y~]_nGXcw|` T}mskcngylTWnbtvuck oylTWnb` kà` TWylTsmWyAXc` k«`p]_z{]_n�f ]ats¯�TswK` TOmvX�j~�gX®nGXcwKX�nbmskcjAX��qTWnbwKdgfbTOml�bTW�gX�jAX�zäX�X�y~]_n �x]_j�7��XW±nbkxwrmvXcwlkxw`bXcw£z;X�]akcjlTsw|]_nbmWV_]_nGXcts¯�Tswvoc�ÊXcmsTiXckrz;ü�[p]_z�kK` T ÂvÄ W"` TWylTsmWyAXc` kKnbkKmvXcwlkr`bXcw|X�nbmskcjAX��qTWnbw¸�bkcj~]_¬vkcngyAX�]awv�¹ wiXcwAwlTWngyAX�z�TWn�ylkxw}` k�ylTWj~jlTWnbkw~f hIkcj~yAXc` k opk?z�kv��]_z�TWngylk{`bX�hGX�jlTs` TrTEXcw¶�xX�j~]YXcts¯�Tsw¶`bXcwimvX�j~�gXcw·nGXcwX�nbmskcjAX��qTWnbwey~]_�qTWjAX�z'mskcz{hIkcj~yAX�z�TWngylkà` ky~]_hIk�` k{kc^ y~]a` k�hIkcj<Ü�X�n nGX�T � X�yAX�V_VYX�nGX�� ÂYl Z��q�\�

¹ jlT\��TWj~]a` k6X�f ylkcj�` TWylTsmWylkcf X�]_nb`bXªÿ�n �xf Vakxw�` T«X�y~j~]_ylk©z�kc^ ]_V_]_¬´Xc` kxw�TWngy~jlT«kªwlkcVakªw~f hIkcj~yAXc` kªTXàhGX�jlTs` T���` T;X�V_f z{�_n ]akg�Kmskcz!k��cX�VakcjKz;ü�[p]_z�k�` TDQEQ � o.k«d�fbT{k�mskcj~jlTWf hGX�jAX�f z;Xà]_nbmWV_]_nGXctvuck�`bXcwX�nbmskcjAX��qTWnbw;` Tw�����q��¿ef z�TWn�yAX�nb` k�X©]_nbmWV_]_nGXctvuck6hGX�jAXSR�T���o·X�hITswAX�j�` T«k6XcwlwlTWngyAX�z�TWn�ylk�wlTWj{y~j%$sw�qTW¬vTswMw~f hITWj~]akcjvoQk�ÿ�n �xf Vak¾` T®X�y~j~]_ylk�z�kc^ ]_V_]_¬´Xc` k©�;X�hITWnGXcw�`bX�kcjl` TWz ` T9T � �®ú|TWj°��wlT\��üpo£mskcnp��kcj~z�Tkc^bwlTWj~�cXc` k h�kcj � X�ylkxw�ýbTWj~nGX�nb` TswàTWy;X�VÊ�R� ÂYl�l�� �\o·d�fbT«Tsw~ylT«mskcz{hIkcj~yAX�z�TWngylk<�«mskcnp²bj~z;Xc` k6h�TWVakxwjlTsw~f V_yAXc` kxwRn�f z��Wj~]amskxwEkc^ y~]a` kxweh�kcjRTsw~ylTswEX�f ylkcjlTswv�

¹ f y~jlkxw£Tsw~y~fb` kxw£TWz&z�k�` TWVakR���aw~]amsk�` kRz�Tsw~z�kEy~]_h�kR��kcjAX�z"jlTvX�V_]_¬´Xc` kxw£hIkcjU¿Enb` TWjlwlkcnOTWy£X�VÊ��� ÂYl Z�7poÂYl b Ä �\o ylTWnb` k�w~]a` k�kc^ y~]a`bXcwEmskcnbmWV_fbwl¯�TsweX�nGü�Vakc�gXcwv�

å£æèå£æèç ä®ò�(+*}òûõqðcô1( î32Uðxòöî4å2÷�ó|î32�/ ÷Êô:ó|ò+*}òûõ ( ò£ó¸î3.ÊòUïw2£í�(VUbõg÷-/pò.ï¹ jlTsmWf jlwlk X¾z�k�` TWVakxwn�f z��Wj~]amskxw�hITWj~z{]_ylTxo|yAX�VRmskcz�k6kxwz�k�` TWVakxw���aw~]amskxwvo2y~]_jAX�j{]_z{hIkcj~yAX�ngylTsw

mskcnbmWV_fbwl¯�Tswwlkc^ jlT®k¾mskcz{hIkcj~yAX�z�TWngylk6` T®mskcj~y~]_nGXcw{` T;mskcn�ylTWnbtvuck6dgfGX�nb` k©wAuck�` T\²GmW]aTWn�ylTsw�XcwMmskcnp�`p]ats¯�TswO` T;Tsd�f ]_V_�_^ j~]ak��qTWj~y~]amvX�VÊ�w6�]_�qTWjlwlkxwMy~jAX�^GX�V_�bkxw{X�^�kcjl`bX�z Tsw~ylT®XcwAw~f ngylk o£` Tsw~yAXcmvX�nb` k���wlTàkxwO` T� X�ylkxwRýGTWj~nGX�nb` TswO� ÂYl b � o ÂYl b�7q�\oG³ûj~]_�qk¾� ÂYl�l �q�}T � X�ylkxwEýbTWj~nGX�nb` TsweTWyEX�VÊ�û� ÂYl�l�� o ÂYl�l�à �\�� X�ylkxwrýbTWj~nGX�nb` TswKTWyKX�VÊ�£� ÂYl�l�� �}]a` TWn�y~]�²GmvX�jAX�zäkxweh j~]_nbmW]_hGX�]aw?Xcwlh�TsmWylkxwr` k;mskcz{hIkcj~yAX�z�TWngylk�` T

mskcj~y~]_nGXcwOZGT\[��_�qTW]awTWz jlTWVYXctvuckª­cwOmvX�j~�gXcwO�qTWj~y~]amvX�]awvo¸X�y~jAXv�q�sw{` TàX�nGü�V_]awlT®hIkcjOTWVaTWz�TWn�ylkxwO²bn ]_ylkxw{` kmvXcwlk�` T{Tsw~y~fb` k�mWfcº~Xcwrh j~]_nbmW]_hGX�]aw?mvX�jAXcmWylTWj~�awly~]amvXcw�wlTO]_nb`p]amvX�z/nGXàýQ]_�xf jAX«þp� ÂWà �M¿�wKX�nGü�V_]awlTswr��kcjAX�zjlTvX�V_]_¬´Xc`bXcwUTWz l ��XcwATsw � TswlmvXs�xXctvuckRnGXcwû��XcwATsw  o � o�7po�ZiT l T¸X�h V_]amvXctvucke` keh jl�\��Tsw°��kcjltskE`bXcwUX�nbmskcjAX��qTWnbw��w~f h�kxwlyAXcwemskcz¦wlTWVYX��qTWz ² [bX{nGX{��jlkcn�ylTW]_jAX�]_np��TWj~]akcj�`bX�z;X�V_�GXpo�mskc]_nbmW]a` TWn�ylTmskcz�k{ylTsmWylkà` k{²bj~z�T´�nGXcwe�ÊXcwlTsw Ä o à o:þ®T�bp� ¹ w à mvü�VamWf Vakxw�jlTvX�V_]_¬´Xc` kxwvo:mskcnp��kcj~z�TO]_nb`p]amvXc` k®nGX®ýQ]_�xf jAX®þp� ÂWà oI`p]���TWjlTWz¦nbk�cX�Vakcje`bX{X�V_y~f jAX�TWngylTWj~jAXc`bX®`bXmskcj~y~]_nGXp�

¿'ýQ]_�xf jAX6þp�  7©z�kxw~y~jAXªkxw{` Tsw~Vak�mvX�z�TWngylkxw®`bX©hGX�jlTs` T«kc^ y~]a` kxw�`bXcw;X�nGü�V_]awlTsw{¿�X 6oUhGX�jAX6Xcw» V_y~]_z;Xcw à �ÊXcwlTswOmskcnbw~y~j~f y~]_�cXcw´�¾SQk�` Tà�qTWj~]�²GmvX�j°��wlT�d�fbTà­�z�Ts`p]a`bX©dgfbT�X¾mskcnbw~y~j~fbtvuckªwlTàX�h jlkv[�]_z;X`bX�» V_y~]_z;Xà�ÊXcwlT{k«mskcz{h�kcj~yAX�z�TWn�ylk¾`bX«hGX�jlTs` T����kcj~ylTWz�TWngylT�]_npZbfbTWnbmW]YXc` k�h�TWVYX�X�V_y~f jAX«TWngylTWj~jAXc`bXp�� kcz T\��TW]_ylk o�nGXcwiX�nGü�V_]awATsw·¿�TkÛro�TWzÀdgfbTrX�X�V_y~f jAXOTWn�ylTWj~jAXc`bX�hIk�` TEwlTWj¶mskcnbw~]a` TWjAXc`bXOwAX�y~]aw°�ÊX�yl�cj~]YXpopkz�kv��]_z�TWngylk?`bXehGX�jlTs` Ti�xoxwlkc^ jlTWy~fb` k ox�bkcj~]_¬vkcngyAX�VÊo�X�f z�TWngyAX�nb` kKw~fGXv�qTWz�TWngylTRmskcz�kEh jlkc�xjlTs`p]_j|`bXeTsw~�mvXs�xXctvuck �|�Ekxw·mvXcwlkxw¶TWz d�fbTEXMX�V_y~f jAX�TWn�ylTWj~jAXc`bXM�E]_nbw~fp²GmW]aTWn�ylT��X�nGü�V_]awATsw � Tk6?�2kxw¶` Tsw~Vak�mvX�z�TWngylkxw�qTWj~y~]amvX�]aw�T��bkcj~]_¬vkcngyAX�]awrylkcj~nGX�z��wlTxo�nGXcwE» V_y~]_z;XcwR�ÊXcwlTsw�mskcnbw~y~j~f y~]_�cXcw´o�w~fbmsTswAw~]_�cX�z�TWn�ylT?z;X�]awE]_z{h�kcj°�yAX�ngylTswvopmskcngy~j~]_^ f ]_nb` k�Xcw·h jl�ch j~]YXcw·��XcwATsw¸` TEh jl�\��Tsw°��kcjltskMhGX�jAXOX�f z�TWngyAX�jRX�z�^GXcw}Xcw¶mskcz{h�kcnbTWn�ylTsw}` k` Tsw~Vak�mvX�z�TWn�ylk �

Page 14: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 7 à Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

γ =20kN/mσv’c =20+0.30u (kPa)

WWWWWWWWWWWW

XXXXXXXXXXXX

YZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZYYZYZYZY

[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[[Z[Z[Z[

10m

8m

45o

6m 0.6m

0.4 Hγ

3

K =0.50

E =300cu uν =0.49

c =70 kPau

d

variávelABCD

8.05.02.80.0

c =ca u

τ

2mm δ

Interfacesolo−parede

Análise d(m)

ýQ]_�xf jAXªþp� ÂWÃ4�H� X�jAXcmWylTWj~�aw~y~]amvXcw{` k©mvXcwlk¾` TàTsw~y~fb` k¾ngf z��Wj~]amsk X�h jlTswlTWn�yAXc` kªh�kcj � X�ylkxwOýGTWj~nGX�nb` TswTWyeX�VÊ�.� ÂYl�l�� �\�

ýQ]_�xf jAX®þp�  7 � 6rTsw~Vak�mvX�z�TWngylkxwr`bX{hGX�jlTs` TMnGXcwe��XcwlTsw�þ;X l oGnGXcwrX�nGü�V_]awlTsw�¿ÁX�6'� � X�ylkxwEýGTWj~nGX�nb` TswTWyeX�VÊ�_o ÂYl�l�� �\��rXàýU]_�xf jAX�þp�  þ�kxwKX�f ylkcjlTswKjlTWh jlTswlTWn�yAX�z!kxwK` Tsw~Vak�mvX�z�TWngylkxwr²bnGX�]awK`bX®hGX�jlTs` T{T`bXàw~f h�TWj°���amW]aT

` k�ylTWj~jlTWnbk®hGX�jAX;Xcw�X�nGü�V_]awlTsw�¿Mo � T{6�G¿�X�nGü�V_]awlTM¿�TW��]a` TWnbmW]YX®XcwlwlTWn�yAX�z�TWngylkà�qTWj~y~]amvX�VQ`bX�hGX�jlTs` Th jAX�y~]amvX�z�TWngylTin�f Vak o�h�TWVakEdgfbT·Tsw~yAXeX�h V_]amvXR��kcjltvXcwQ` T¸mskcj~ylT¶` T¸wATWngy~]a` krXcwlmsTWnb` TWngylT}XckewAkcVakew~f hIkcj~yAXc` k o

Page 15: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â 7�7

mvX�fbwAX�nb` kÑf z;X<jlTs`pfbtvuckÑ` k XcwlwlTWn�yAX�z�TWngylk nGXcw�h jlks[p]_z{]a`bXc` Tsw�`bX�TswlmvXv�cXctvuck T©]_nb`pf ¬s]_nb` kÑf z;XmWf j~�cX�y~f jAX;m\cnbmvXs�xX{nGX{w~f hITWj°���amW]aT?` k{ylTWj~jlTWnbk �·ú|TWj~]�²GmvX���wlTMX�]_nb`bX®Xmskcng�qT\[p]a`bXc` TM`bXO�ÊXcmsT?`bXO��jlTWngylT`bXhGX�jlTs` Tx�\|w~ylTMmskcz{h�kcj~yAX�z�TWn�ylk;nGuck®wlT?TW��]a` TWnbmW]YX{nbkxwemvXcwAkxwR`bXcwEX�nGü�V_]awlTsw � T�6obmskcz'��jAXcmvXcwemskcnb`p]ats¯�Tsw

` T©X�hIkc]ak<�qTWj~y~]amvX�V � X�hGX�jlTs` T¾nGuck�X�h jlTswlTWn�yAX�dgfGX�Vad�fbTWjàmskcn��qT\[�]a`bXc` T6TªX�w~f h�TWj°���amW]aTª` k�ylTWj~jlTWnbkw~f h�kcj~yAXc` krylkcj~nGX���wATRmskcng�qT\[bXpog` TW��]a` k?­KX�h V_]amvXctvuck�­cd�fbTWVaTiylTWj~jlTWnbk?` T·��kcjltvXcw|` T}mskcj~ylT}` TswAmsTWnb` TWngylTswv�â��xfGX�Vpmskcz{h�kcj~yAX�z�TWn�ylkrh�k�` T¸wATWjQkc^bwlTWj~�xXc` kEnbkxwUjlTswlf V_yAXc` kxwQkc^ y~]a` kxwQhIkcj�ÜrX�n nGXET � X�yAX�V_VYX�nGXO� ÂYl Z��q�dgfbTKwlT?X�h jlTswATWngyAX�jAX�z�nGXýU]_�xf jAX;þp� ÂY� �

ýU]_�xf jAX®þp�  þ � 6rTsw~Vak�mvX�z�TWngylkxwe²bnGX�]awe`bXhGX�jlTs` TMTK`bX{w~f hITWj°���amW]aT?` k�ylTWj~jlTWnbk�nGXcweX�nGü�V_]awlTswE¿Mo � T�6� � X�ylkxwRýGTWj~nGX�nb` TswETWyEX�VÊ�_o ÂYl�l�� �\���XrýQ]_�xf jAXKþp�  Z�hIk�` T¶kc^bwATWj~�cX�j°��wlTRXcw|�cX�j~]YXcts¯�Tsw|`bXcw2mvX�j~�gXcw|nGXcw|X�nbmskcjAX��qTWnbw���T\[�h jlTswAwAXcw|TWz�hITWj°�

msTWngyAX��qTWzÁ` k�jlTsw~hITsmWy~]_�qkEh jl�\��Tsw~��kcjltskg�Q` kxwQn �_�qTW]aw  T � Xck�Vakcn �qkr`bXEmskcnbwly~j~fbtvuck �Q��k�mvXcwlkr`bXEX�nGü�V_]awlT¿Mo��qTWj~]�²GmvX���wlTRX�TW�qkcV_fbtvuckry~�_h ]amvXr` TiTswlmvXs�xXcts¯�Tsw2mskcz�Xc` Tsd�fGXc` kKmskcz{hIkcj~yAX�z�TWngylk®� � X�ylkxw2ýbTWj~nGX�nb` TswTWyEX�VÊ�_o ÂYl�l�� � �! Xcw�mvX�j~�gXcwM`bXcwMX�nbmskcjAX��qTWnbwO` T�`bXc` k«n �_�qTWViX�f z�TWngyAX�z nGXcwr��XcwATsw?` T�TswlmvXv�cXctvuck¾T�`p]_z{]_ngfbTWzd�fGX�nb` k�dgfGX�Vad�fbTWjekcf y~jlk{n �_�qTWVU�rh jl�\��Tsw°��kcjltvXc` k#"

! X®mvX�j~�gX;z;ü�[p]_z;X®TWz�mvXc`bX;n �_�qTWV2�MX�y~]_n �x]a`bX®nGX{�ÊXcwlTM` TMTswlmvXv�cXctvuckà]_z�Ts`p]YX�yAX�z�TWn�ylT�wlTW�xf ]_ngylT­{` k{wlTWf«h jl�\��Tsw~��kcjltsk#"

! Xcw}�xX�j~]YXcts¯�TswE` TKmvX�j~�gX{wAuckhITsdgfbTWnGXcw´���X«X�nGü�V_]awAT�6 �qTWj~]�²GmvX���wAT{f zämskcz{hIkcj~yAX�z�TWngylk�mskcnbwl]a` TWjAXs�qTWV_z�TWngylT�`p]���TWjlTWngylTxoUk�mskcj~jlTWnb` k«f z;X

jlTs`pfbtvuck©wlf ^bw~yAX�nbmW]YX�V¶`bX�mvX�j~�gX�nGXcw{X�nbmskcjAX��qTWnbwvo2k¾dgfbTà�;mskcz{hGX�y~�_�qTWV}mskcz kxwM` TswlVak�mvX�z�TWn�ylkxw{`bXhGX�jlTs` TRTW��]a` TWnbmW]YXc` kxw¸nGXcw|ýQ]_�xf jAXcw¸þp�  7rTRþp�  þpog`bXc` kKd�fbT}d�fGX�nb` k?XrTsw~yAX�^ ]_V_]a`bXc` TRwlTiylkcj~nGXrh jlTsmvü�j~]YXpoXehGX�jlTs` Tiz�k´�qT\��wlTihGX�jAXEf z;X�h�kxwl]atvuck�d�fbT¶h�TWj~z{]_yAXrXEjlTs`pfbtvuckK`bXcw2mvX�j~�gXcw£�qTWj~y~]amvX�]aw|`bXcw|X�nbmskcjAX��qTWnbwv�� X�ylkxweýbTWj~nGX�nb` TswRTWyeX�VÊ�û� ÂYl�l�� �iX�h jlTswlTWn�yAX�z5X�]_nb`bX«��ýQ]_�xf jAX�þp�  bq�iXOTW�qkcV_fbtvuck�`pf jAX�ngylT�Xmskcnbw~�

y~j~fbtvuck�`bXrz�kc^ ]_V_]_¬´XctvuckM`bXrjlTsw~]aw~y%$WnbmW]YXrVYX�ylTWjAX�V�nGXcw£�ÊXcmsTsw¸`bXE��jlTWngylTeT}` TRy~jAücw¸`bXrhGX�jlTs` Tx�2�rXE��XcmsTe`bX��jlTWn�ylTxoI�qTWj~]�²GmvX���wlTxoûmskcz/T\[pmsTWhItvuck�`bX®X�nGü�V_]awATO¿OoIX®mskcz{h VaTWyAXàz�kc^ ]_V_]_¬´Xctvuck«`bX®jlTsw~]awly%$WnbmW]YX;VYX�ylTWjAX�VÊoz�Tsw~z�k{hGX�jAX�XcwlwATWngyAX�z�TWngylkxw�`bXhGX�jlTs` TKh jAX�y~]amvX�z�TWn�ylT�n�f Vakxwvobk�d�fbTKwlTK` TW�qT�XckO�ÊXcmWylk�` TKhGX�jlTs` T�TylTWj~jlTWnbkàwAk���jlTWjlTWz¦z�kv��]_z�TWngylkxw?�qTWj~y~]amvX�]awK` TMwlTWn�y~]a` kxwKkch�kxwlylkxwv�^]EfGX�n�ylk�­{�ÊXcmsTO` T�y~jAücwvoId�fGX�nb` k«X

Page 16: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 7xþ Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

−50

−40

−30

−20

−10

0

10

1 2 3 4 5 6 7 8 9

Var

iaçã

o de

car

ga n

as a

ncor

agen

s (%

)

Nível 1

ABCD

3 4 5 6 7 8 9Fase de construção

Nível 2

5 6 7 8 9

Nível 3

7 8 9

Nível 4

ýQ]_�xf jAX�þp�  Z � \2�qkcV_fbtvuckª`bXcw�mvX�j~�gXcwOnGXcwOX�nbmskcjAX��qTWnbwO` kxwMn �_�qTW]aw  T � nGXcwOX�nGü�V_]awlTswO¿±Xw6ä� � X��ylkxwRýbTWj~nGX�nb` Tsw�TWyeX�VÊ�_o ÂYl�l�� �\�X�V_y~f jAX�TWn�ylTWj~jAXc`bX;�KTWVaTW�xXc`bX;X{jlTsw~]aw~y%$WnbmW]YXz�kc^ ]_V_]_¬´Xc`bX®�rz�f ]_ylk®^GX�]�[ X�T?mskcz'wlTWn�y~]a` k;` TswlmsTWnb` TWn�ylTxow~]_�xn ]�²GmvX�nb` k«d�fbTkàwAkcVakàwlf h�kcj~yAXc` k�XcwlwATWngyAXàz;X�]awK` k�dgfbT{X®hGX�jlTs` Tx��¿ z�kc^ ]_V_]_¬´Xctvuck�w~]_�xn ]�²GmvX�y~]_�xX`bX�jlTsw~]aw~y%$WnbmW]YXMnGX?]_n�ylTWj°��XcmsTrmskcz±wlTWn�y~]a` kXcwAmsTWnb` TWngylTrwl�OwlTe�qTWj~]�²GmvXMnGXcw¸��XcwATsw¸²bnGX�]awi`bXcw}X�nGü�V_]awlTsw �T<6oxz;Xcw¸z�Tsw~z�k?nbk?mvXcwAk?`bX�X�nGü�V_]awlTx6+nGuck��eX�y~]_n �x]a`bXMXKmskcz{h VaTWyAX?z�kc^ ]_V_]_¬´XctvuckO` Tsw~yAXrjlTswl]aw~y%$WnbmW]YXpoX�hITswAX�jE` kàTWVaTW�cXc` k�XcwlwlTWn�yAX�z�TWngylk � ¹ mskcj~jlT�z�Tswlz�k;f z¦` TsmWjl�swlmW]_z�kà`bX�jlTsw~]awly%$WnbmW]YX�z�kc^ ]_V_]_¬´Xc`bX®nGX» V_y~]_z;X���XcwAT®` T�mskcnbw~y~j~fbtvuck o|kªd�fbT®wAT®` TW�qT«Xck¾z�kv��]_z�TWngylk `bX¾hGX�jlTs` Txo|d�fbT;hITWj~z{]_ylT�dgfbTàkªwlkcVakw~f hIkcj~yAXc` k�XcwlwlTWn�ylTKmskcz±XOhGX�jlTs` Txo `p]_z{]_n�f ]_nb` k;k` Tsw~Vak�mvX�z�TWngylk{jlTWVYX�y~]_�qk{`bXO]_n�ylTWj°��XcmsT�wlkcVak��ÊhGX�jlTs` TTxo¸mskcnbwATsdgfbTWn�ylTWz�TWngylTxo}X¾jlTsw~]aw~y%$WnbmW]YX©nGX©]_ngylTWj°�ÊXcmsTx� � kcnp��kcj~z�T���wAX�V_]aTWn�yAXc` k6hITWVakxw�X�f ylkcjlTsw;X�y~jAücwjlT\��TWj~]a` kxwvo.Tsw~ylT;mskcz{h�kcj~yAX�z�TWn�ylk���kcjAXà]_�xfGX�V_z�TWngylTàkc^bwlTWj~�xXc` k«h�kcjMS2VYX�ngy�� ÂYl Z Ä ��nbkxw�wlTWfbw�Tsw~y~fb` kxwmskcz z�k�` TWVak{jlTs`pf ¬s]a` k;X{d�fbTKwlT���TW¬KjlT\��TWj%$WnbmW]YX�TWz5þp� þp� Ä �� X�ylkxwKýbTWj~nGX�nb` Tsw?TWyKX�VÊ�2� ÂYl�l�à �EjlTsw~f z�TWz/k®hGXc`pjAuck�` Tmskcz{hIkcj~yAX�z�TWngylk�` Tmskcj~y~]_nGXcwK` Tmskcnp�

ylTWnbtvuck�mskcz'` T\²GmW]aTWn�ylTMX�hIkc]ak{�qTWj~y~]amvX�VÊoGmvX�jAXcmWylTWj~]_¬´X�nb` k���kà`bXwlTW�xf ]_n�ylTK��kcj~z;X �! X�hGX�jlTs` TKT\[p]_^�Te�xjAX�nb` TswRXcwlwlTWngyAX�z�TWn�ylkxwvoGXcmskcz{hGX�n �GXc` kxwR` T�` Tsw~Vak�mvX�z�TWngylkxw}�bkcj~]_¬vkcn�yAX�]awi]_z�hIkcj~yAX�ngylTswEnbk{wlTWn�y~]a` k�`bX{TswlmvXv�cXctvuck#"! kxwE` Tsw~Vak�mvX�z�TWngylkxwE�qTWj~y~]amvX�]awETK�bkcj~]_¬vkcn�yAX�]awr` k�wlkcVak�w~f hIkcj~yAXc` k;w�uck{yAX�z�^I�Wz'zMf ]_ylk;TWVaTW�xXc` kxwvoX�f z�TWn�yAX�nb` k®Tswlh�TsmW]YX�V_z�TWn�ylT?nGXcw}h jlkv[�]_z{]a`bXc` Tsw�`bX{TswlmvXv�cXctvuck#"

! XcwemvX�j~�gXcwRnGXcweX�nbmskcjAX��qTWnbwEjlTW�x]aw~yAX�z'TWz �qTWjAX�V.jlTs`pfbtvuck{z�f ]_ylk®w~]_�xn ]�²GmvX�y~]_�cXp�

å£æèå2æ;_ äàò�(+*}òûõxðxô1(öî52.ðxò î#å|÷�ó¸î32�/ ÷�ôIó¸òß*}ò.õæ/pô:ï�ò.ï�ó¸î�òa`¸õqô¿�w.Tsw~y~j~f y~f jAXcwU` T¸mskcn�ylTWnbtvuckRZGT\[p�_�qTW]aw.z;X�]aw.y~jAXc`p]amW]akcnGX�]awvoxmskcz�kEXcwUmskcj~y~]_nGXcwU` T¸Tsw~yAXcmvXcw°�Êh jAX�nbml�GXcw

kcf XcwOy~]_h�kæÛiTWj~V_]_z h jlkv��]awl�cj~]YXcwvo|TWjAX�z �GX�^ ]_y~fGX�V_z�TWngylT�f y~]_V_]_¬´Xc`bXcw�TWz mskcncº�f �gXctvuckªmskcz TswlmskcjAXcw{TX�nbmskcjAX��qTWnbw�` TOh VYXcmvX�kcf6��]_�gXpo:mskcz!mskcz{h�kcnbTWn�ylT{�qTWj~y~]amvX�V|]_nbT\[p]aw~ylTWngylT{kcf6hIkcfbmsk«w~]_�xn ]�²GmvX�y~]_�xXp�M¿Xcwlwlk�mW]YXctvuck?` TRX�nbmskcjAX��qTWnbw·h jl�\��Tsw°��kcjltvXc`bXcw|]_nbmWV_]_nGXc`bXcwiXrTsw~ylTsw2y~]_hIkxw|` TRmskcj~y~]_nGXrylTWz mskcz�k?h j~]_nbmW]_hGX�V]_nbmskcng�qTWn ]aTWn�ylTOXT\[p]aw~y%$WnbmW]YX{` T���kcjltvXcw}�qTWj~y~]amvX�]awR` T?�xjAX�nb` TW¬´X{w~f ^bw~yAX�nbmW]YX�VÊo ylkcj~nGX�nb` k;kc^ j~]_�gX�yl�cj~]YX;XX�nGü�V_]awlT?` k{Tsd�f ]_V_�_^ j~]ak�nGX`p]_jlTsmstvuck®mskcj~jlTsw~hIkcnb` TWngylTx�

Page 17: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â 7XZ

−40

−20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9

Res

istê

ncia

late

ral m

obili

zada

(%)

Fase de construção

A−passivoB−passivoC−passivoD−passivoA−activoB−activoC−activoD−activo

b,c�dEe!f*gih/j�k�l/m�nSo#p!c�q�c�rAg#s�t#o&uvg�f8wx:c;x:y8z2{v|2c}g~q}g�y8w2f*g�qJ{�g#x>g�{���q�c;x8wx>��gD����nNg�y8oEx�b�w2f:{�g�{vu!wx>w2yg�q�j��k��E�E���6j

��x:y8w%�!f8o#p!q;w2�<g��P�?c�{!c��?c�rAg#u!o>��e�g�{vu!o�����g���oEx8x:c�p!c�q�c;uvg#u!w u!w%y:f*g�{vx:�?c;x8x*t#o�uvg#x�|�g�f:d�g#x���w2f:y:c;|�g�c;xg�e!�Hwx:y:f*g�y8o$|o#��p�o�g#x�|�g�f*g#|2y8w2f:�;x:y:c;|�g#x �$w|���{!c;|�g#x�g�p�g�cG�!o$uvgwx8|�g��#g#s�t#o!j

��w6�/c;x:y8z2{v|2c}g^u!wPe!��wx8y:f*g�y8o�u!w%w2q;w2�#g#uvg#xJ|�g�f*g#|2y8w2f:�;x:y:c;|�g#x��$w|���{!c;|�g#x+{�t#o�|o#{vx:y:c�y:e!c���{vo�w2{�y*g�{�y8o!��=o#f�x:c/x8�!�#d�g�f*g�{�y:c}g�uvg c��?��oEx8x:c�p!c�q�c;uvg#u!w%u!wPo�|o#f:f8z2{v|2c}g^u!w��!f8o#p!q;w2�<g#x�u!wPwx:y*g�p!c�q�c;uvg#u!wP��w2f:y:c;|�g�q�j�b(c�{/�{vo<�"k��E�E ��(f8w6¡¢w2f8w�o�|�g#x8o�u!wPe!�<g�|o#f:y:c�{�g^y:c���o�£Pw2f:q�c��¤�!f8o���c;x8�#f:c}g���evw%x8�^¡¢o#c!��oEx8x:����w2q/¡�g�r�w2f��=w2{vw2y:f*g�f�=o#f%|2f*g�Eg#s�t#o<g�y8��e!�<g��!f8o�¡�e!{vu/c;uvg#u!w�c�{/¡�w2f:c;o#f ¥�uvg�wx8|�g��#g#s�t#o$u!w2��c;u!o?¥w6��c;x8y8z2{v|2c}g�g#|2c��<guvg�p�g#x*wu!wx:y*g~u!w�e!�¦�<g#|2c;soDf8o�|*�voEx8o!j���wx8|�g��#g#s�t#o~�!f8o#q;o#{!d�o#e/�1x8wE�(g#x8x:c����§g�p�g�cG�!oDu!o¨�=�uvg~|o#f:y:c�{�g/�§y*g�q|o#�$oDx8w�f8w2�!f8wx8w2{�y*g&wx8��evw2�<g�y:c;|�g��$w2{�y8w?{�g~b(c�dEe!f*gDh/j�k��/j��w2��c;u!o�¥¨o#f:c;w2{�y*g#s�t#oiu!wx"¡¢g���o#f*���w2q+uvg#xu!wx8|o#{�y:c�{�e!c;uvg#u!wx�u!o$�<g#|2c;so9f8o�|*�voEx8o!�©��w2f:cGª�|o#e/�1x8w�g$f8o#y:e!f*g<u!o¨g��=o#c;o<��w2f:y:c;|�g�q(uvg9|o#f:y:c�{�g/�=o<��evwx8w¨y:f*g#u/e!rc�e«w2�¬c��?��o#f:y*g�{�y8wx<u!wx:q;o�|�g��$w2{�y8oEx?��w2f:y:c;|�g�c;x$uvgi��g�f8wu!wEj­����wx*g�f�u!wDg#x|o#�?��o#{vw2{�y8wx��w2f:y:c;|�g�c;xJuvg#x�g�{v|o#f*g�d�w2{vx�x*w2f8w2�¤e!�<g�uvg#x+�!f:c�{v|2c���g�c;xJ|�g�evx*g#x�uvg^c�{vx:y*g�p!c�q�c;uvg#u!w���w2f:y:c;|�g�q©uvg#xJ|o#{�y8w2{/�s®�wx��,f8w6¡¢w2f8w6�1x8w$��evw${vwx:y8w$|�g#x*o��vo#e!��w$c�dEe�g�q��$w2{�y8wDgD|o#{�y:f:c�p!e!c;s�t#oNu!w<|�g�f:d�g#x>y:f*g�{vx:�?c�y:c;uvg#x>�=w2q}g#xx8o#p!f8w|�g�f:d�g#x u!w2��c;uvg#x�g#oy:f*�¯¡¢w2d�o!j

° g#x8oEx+x*w2�$w2q���g�{�y8wx�x*t#o^y*g���p��2��g��!f8wx8w2{�y*g#u!oEx+��o#f�±V�!c�y8w��"k���²¯³��´w%��o#f+£%g�f:q;w2µ��"k��E��²E�6j´b,c�{!{vo�"k��E�E ��^g��!f8wx8w2{�y*g~c�dEe�g�q��$w2{�y8w$e!�<g¨�$w2y8o�u!o#q;o#dEc}gDu!w|���q;|2e!q;oD��g�f*g¨y8w2f�w2�¶g�y8w2{vs�t#o�wx:y8w��$o�u!oDu!wf8o#y:e!f*g/��g�y:f*g���x�u!of8w6¡�o#f8so<u!o?�<g#|2c;so?f8o�|8�voEx8o$|o#�·g�{v|o#f*g�d�w2{vx o#e��!f8w2d�g�d�w2{vx�j

¸ x§|�g#x8oEx§u!w�f8o#y:e!f*g%�<g�c;x�¡�f8w��evw2{�y8wx(x*t#o!��{vo�w2{�y*g�{�y8o!��g#��evw2q;wx§��evw�wx:y*t#o�g#x8x*o�|2c}g#u!oEx(gP|o#{vu/c;s®�wxu!w6ª�|2c;w2{�y8wx�u!w^g���o#c;o?u!o����uvg|o#f:y:c�{�g?w2�¹�<g#|2c;soEx%y8w2f:f8oEx8oEx%p!f*g�{vu!oExA�v|o#�$o?oEx g��!f8wx8w2{�y*g#u!oEx���o#f£Jf8o#�$x(w�º�y:c�q�q;w^�"k���²#h��§w2{���o#q���w2{vu!o^|o#f:y:c�{�g#x´u!wJwx:y*g#|�g#x:���!f*g�{v|8��g#x´w���o#f´º���g�{!{vo#{?w�º�y:f*g�r�w2f%�"k���²#»��§w��c;w2y:f:c;|*��w2y´g�q�j��"k���²�kA�6�Eu!w�g�q�dEe!�<g#x,|o#f:y:c�{�g#x(y:c���o £Pw2f:q�c��¼�!f8oA��c;x8�#f:c}g#xAj(���¼y8o�u!oEx,oEx,|�g#x8oExa��w2f:cGª�|o#e/�x8w�g#x8x8w2{�y*g��$w2{�y8oEx^�>e!c�y8o9x:c�dE{!cGª�|�g�y:c���oEx^uvg?wx8y:f:e!y:e!f*g<u!w>|o#{�y8w2{vs�t#o!j�º�q}g�y8w2f?�"k��Eh�²E��g��!f8wx8w2{�y*g9e!�|�g#x8o^u!w%wx:y:evu!o�y*g���p��2��u!w�e!�<g���g�f8wu!wPy:c��=o^£Pw2f:q�c��½�!f8o���c;x8�#f:c}g�w2�½��evw+¡¢o#c!u!w2y8w|2y*g#u!o�e!�½w2q;w2�#g#u!o

Page 18: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 7�b Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

¾�¾�¾�¾�¾�¾�¾�¾�¾�¾�¾�¾¿�¿�¿�¿�¿�¿�¿�¿�¿�¿�¿�¿

Solo suportado

Maciço rochoso

Ancoragem

Escoras

Atitude das descontinuidadesdesfavorável

Plataforma para passagem de tráfego

Estrutura tipo Berlimprovisória

ýQ]_�xf jAXKþp� ÂYl�� �eTWh jlTswlTWn�yAXctvuck?Tswld�fbTWz;ü�y~]amvXK` T}mvXcwlkK` T}Tsw~y~fb` kKd�fbTijlTsw~f V_ylkcf{nGX�jlkcy~f jAXK`bXE��f nb`bXctvuck`bX�mskcj~y~]_nGXKTWz1z;XcmW]atskrjlk�mA�bkxwlk ogXcmW]_z;Xr`bX�^GXcwlTi`bX�TswlmvXv�cXctvuck?T·��kcylkc�xjAX�²�Xr` k�Vak�mvX�VÊ�}��ýQ]_n nbk o ÂYl�lxÄ �\�

z�kv��]_z�TWngylk®�bkcj~]_¬vkcngyAX�V£Xcwlwlk�mW]YXc` k�Xf z±z�kv��]_z�TWngylk®�qTWj~y~]amvX�V.d�fbT?X�y~]_n �x]_f¾msTWjlmvX{` T��p� l �{z��¿Ák�mskcj~j%$WnbmW]YX�` T` Tsw~Vak�mvX�z�TWngylkxwKw~]_�xn ]�²GmvX�y~]_�qkxwvo.TWz¦Tswlh�TsmW]YX�V2` TXcwlwlTWngyAX�z�TWn�ylkxw�`bX®mskcj~y~]_nGXpoû�

X�V_]Yücw{f z ]_z{hIkcj~yAX�ngylT�]_nb`p�amW]ak ` k6]_nGXc` Tsd�fGXc` k mskcz{hIkcj~yAX�z�TWngylk<TWz jlTWVYXctvuck�­cw�mvX�j~�gXcw;�qTWj~y~]amvX�]awv�ÀEV_j~]aml�"� ÂYl b l ��dgfbTxo·hGX�jAX6zMf ]_ylkxw®mvXcwAkxw�` T�kc^ jAXcw®` T�TswlmvXs�xXctvuck�d�fbT�kc^bwlTWj~�qkcfûo¶y~]_n �GX jlTW�x]aw~yAXc` k` Tsw~Vak�mvX�z�TWngylkxw�qTWj~y~]amvX�]awO]_np��TWj~]akcjlTswX�z�TWyAXc` T�` kxw��bkcj~]_¬vkcn�yAX�]awz;ü�[�]_z�kxw`bX�hGX�jlTs` Txo£�qTWj~]�²GmvX�nb` k]_nbmWV_fbw~]_�xX�z�TWngylTxoeX�V_�xf z;Xcw®�qTW¬vTswvoRX6k�mskcj~j%$WnbmW]YX�` T«z�kv��]_z�TWngylkÑXcwlmsTWnbw~]akcnGX�V�` Tsw~yAXpo¶z�Ts`p]_fön�f z;XhGX�jlTs` T{` TOTsw~yAXcmvXcw?XcwlwlTWn�yAX�z�TWngylkxw�X�nbkcj~z;X�V_z�TWn�ylT;TWVaTW�xXc` kxw���XcmsTXckàz�kv��]_z�TWngylk«�bkcj~]_¬vkcn�yAX�VÊoûmskcnp�mWV_f ]_nb` k�`bX6]_z{h�kcj~yAÿ�nbmW]YX�` T«jlTvX�V_]_¬´X�j®k�`p]_z�TWnbw~]akcnGX�z�TWngylk�`bX�nb` k hGX�j~y~]amWf VYX�j«X�ylTWnbtvuck�­cw;mvX�j~�gXcw�qTWj~y~]amvX�]awv�

�Ef z$mvXcwlk�` T©f z;X<mskcj~y~]_nGX<y~]_hIk ÛiTWj~V_]_z X�nbmskcjAXc`bXpo�Áö]_n�ylTWj6� ÂYl�l �q�®jlTW�x]awlyAX�` TswlVak�mvX�z�TWn�ylkxw�bkcj~]_¬vkcngyAX�]aw|h�kcfbmskrw~]_�xn ]�²GmvX�y~]_�qkxw£nbkxwQ]_nbmWV_]_nb�cz�TWy~jlkxw2z;Xcw2XcwlwlTWn�yAX�z�TWngylkxw|mskczÁX�V_�xf z;XE]_z{hIkcj~yAÿ�nbmW]YX

Page 19: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â 7 l

��`bX{kcjl` TWz5` T�þ�mWz®�¶nbk�wlkcVak;X�y~jAücwE`bX{mskcj~y~]_nGXp� ¹ X�f ylkcjEX�y~j~]_^ f ]UTswlylTswR` Tsw~Vak�mvX�z�TWngylkxwr­{TW�qTWngy~fGX�Vh�TWjl`bXE` T¸wlkcVakE` TW��]a` k�­}��f jAXctvuckRhGX�jAXe]_nbw~yAX�VYXctvuck�` kxw.hITWj°²GwU�qTWj~y~]amvX�]awvocz;Xcw.f z;Xekcf y~jAXRhIkxwlw~]_^ ]_V_]a`bXc` ThGX�jlTsmsTOwATWjrX®` TTsw~ylTsw�XcwAwlTWngyAX�z�TWn�ylkxw?wlTWjlTWz º�fbwly~]�²GmvXc` kxwEhITWVakà` Tsw~Vak�mvX�z�TWn�ylk��qTWj~y~]amvX�V2`bX;h jl�ch j~]YXmskcj~y~]_nGXp�Ü�ü¾X�]_nb`bX¾X�V_�xf nbwOmvXcwlkxwOTWz½d�fbTxo2X�y~jAXs�q�sw`bX«]_nbw~y~j~f z�TWn�yAXctvuck o¸Xcw�mskcj~y~]_nGXcwTW��]a` TWnbmW]YX�z mskcz�

h�kcj~yAX�z�TWn�ylkxw�` T�`p]����amW]_V}T\[ph V_]amvXctvuck¾z;Xcw{d�fbT®h�k�` TWjAuckªTsw~yAX�j]_�xfGX�V_z�TWngylT�XcwlwAk�mW]YXc` kxw{X¾TW�qTWngy~fGX�]awXcwlwlTWngyAX�z�TWn�ylkxw`bX«mskcj~y~]_nGXpo£TW�qTWngy~fGX�V_z�TWngylTànGuck�z�Ts`p]a` kxwv� � Xcmskc]_Vak�TWyMX�VÊ�¸� ÂYl�l bq�?` TswlmWjlTW�qTWz f zmvXcwlk;` T�f z;X�TswlmvXv�cXctvuck®jlTvX�V_]_¬´Xc`bX;mskcz5f z;X�mskcj~y~]_nGX®` T�Tsw~yAXcmvXcw~�Êh jAX�nbml�GXcwrTWz5wlkcVakàX�j~�x]_Vakxwlk�z�kcVaTX?z��s`p]ak o mskcz jlTsmWf jlwlk{XMX�nbmskcjAX��qTWnbwih jl�\��Tsw~��kcjltvXc`bXcwi]_nbmWV_]_nGXc`bXcwvo X�hGX�jlTWn�ylTWz�TWngylT�wATWz�w~]_�xn ]�²GmvX�y~]_�qkX�h�kc]ak�` k�hI�{`bX«mskcj~y~]_nGXpoQTWz!dgfbTO��kcjAX�z!z�Ts`p]a` kxwMTWVaTW�cXc` kxwM` Tsw~Vak�mvX�z�TWn�ylkxw?�bkcj~]_¬vkcn�yAX�]aw�z;Xcw�nGuck��kcjAX�z jlTW�x]aw~yAXc` kxwOw~]_�xn ]�²GmvX�y~]_�cXcwO�xX�j~]YXcts¯�TswO` T;mvX�j~�gX�nGXcwX�nbmskcjAX��qTWnbwv�iÀEz;X«hIkxwlw~�_�qTWV·]_ngylTWj~h jlTWyAX��tvuck;` k��TWnb�cz�TWnbk�hIk�` TWjAü�wlTWjEX�` T�dgfbTK]_z{hIkcj~yAX�ngylTswr` Tsw~Vak�mvX�z�TWngylkxwE�qTWj~y~]amvX�]aw�`bX{hGX�jlTs` T?ylTWn �GX�z]_�xfGX�V_z�TWngylTRk�mskcj~j~]a` k oxmskcngy~jAX�^GX�VYX�nbtvX�nb` kMk�X�f z�TWn�ylkrylTWnb` TWnbmW]YX�Vb`bXcwQ��kcjltvXcw£`bXcw2X�nbmskcjAX��qTWnbw2` TW��]a` kXckxw}` Tsw~Vak�mvX�z�TWn�ylkxwi�bkcj~]_¬vkcngyAX�]awv�JÀez±mskcn�yAXcmWylk{mskczÀkxw}X�f ylkcjlTsw?� � Xcmskc]_Vak o ÂYl�l�l �·jlTW�qTWVakcf«d�fbTxo�mskczT\��TW]_ylk obwATrjlTW�x]aw~yAX�jAX�z5XcwlwlTWn�yAX�z�TWngylkxwr`bXkcjl` TWz5` T Ä 7;Xê7��z{z�obd�fbTKTsw~yAX�jAuck{yAX�z�^I�Wz jlTWVYXcmW]akcnGX��` kxwemskcz5k�z�kv��]_z�TWngylk®�xVakc^GX�VQ`bX{mWf n �GX;` T?wlkcVak®w~f h�kcj~yAXc` k � i ]_y~fGXctvuckàwlTWz�TWV_�GX�ngylTMh�k�` TrylTWjEwl]a` k�qTWj~]�²GmvXc`bX{hIkcj � XcTWj~ylTWnbwETK³i�bT2Â�w�� ÂYl�l Zx�\oGyAX�z�^I�Wz hGX�jAXf z;X{mskcj~y~]_nGX�` T?Tsw~yAXcmvXcw°�Êh jAX�nbmA�GXcwv�\2nbmskcngy~jAX���wAT�yAX�zM^��Wz�nGX^ ]_^ V_]akc�xjAX�²�X®mskcnbw~f V_yAXc`bX;X�V_�xf z;XcwEjlT\��TWj%$WnbmW]YXcwrX{mvXcwlkxwE` T?Tsw~y~fb` k®TWz

dgfbTMk{h jlkc^ VaTWz;X;`bXcw�mvX�j~�gXcwE�qTWj~y~]amvX�]awETM`bX{�gX�jAX�ngy~]YX®`bX�wlfGX�Tsw~yAX�^ ]_V_]a`bXc` TMz�TWjlTsmsTWf¾Tsw~hITsmW]YX�VQX�ylTWnp�tvuck�T�` Tsw~yAXcd�fbT;kcf ��kc]·X�mvX�fbwAX�` k«jlTsmWf jlwAk¾X«wlkcV_fbts¯�Tsw?hIkcfbmsk��GX�^ ]_y~fGX�]aw´� ã"k�mvXcwlk¾X�h jlTswlTWngyAXc` kh�kcj�ÜrX�n nGXªT i TsTWylkcn¼� ÂYl þXZx�\o·jlT\��TWjlTWn�ylT�X©f z;Xª`bXcw{h j~]_z�TW]_jAXcw;Tswly~j~f y~f jAXcw{y~]_h�kÝÛiTWj~V_]_z h jlk´��]awl���j~]YXcwMT\[ TsmWf yAXc`bXcwMmskcz k�jlTsmWf jlwlk©X�X�nbmskcjAX��qTWnbwvo£TWz dgfbTàXcw?]_nbmWV_]_nGXcts¯�TswO` TswlyAXcw�mskcz X��bkcj~]_¬vkcngyAX�VTWjAX�z5T\[py~jlTWz;X�z�TWngylTTWVaTW�cXc`bXcw´obml�bTW�gX�nb` k«X�X�y~]_n �x]_j�Ã�� � �¶SQkcjETswlylTKz�kcy~]_�qk;kxw�X�f ylkcjlTswEmskcnbmWV_f �_jAX�z`bX�nbTsmsTswlwl]a`bXc` T®` T���X�¬vTWjOh�TWnbTWy~jAX�jw~]_�xn ]�²GmvX�y~]_�xX�z�TWngylT�XcwOT\[�y~jlTWz{]a`bXc` TswO]_np��TWj~]akcjlTsw` kxwMhITWj°²GwMnbkz;XcmW]atsk�jlk�ml�bkxwlk o hIkcj}��kcj~z;X�X�gX�jAX�n�y~]_j°�ÊV_�bTswEf z;X{^�kqXO��f nb`bXctvuck�TxobmskcnbwATsdgfbTWn�ylTWz�TWngylTxo:Xc` TsdgfGXc` kmskcz{h�kcj~yAX�z�TWn�ylk®TWz jlTWVYXctvuck®­cweXcmsts¯�TswR�qTWj~y~]amvX�]awv�� X�]awrjlTsmsTWn�ylTWz�TWngylTxoUyAX�z�^I�WzäTWz/TswlmvXs�xXcts¯�Tsw?mskcz/mskcngylTWnbts¯�Tsw?y~]_hIk ÛiTWj~V_]_z/h jlk´��]awl�cj~]YXcw´o=6KXÂ

� ÂYl�l �q�EjlT\��TWjlTkàh jlkcVakcn �gX�z�TWngylk�TWz!þ®z/` kxwrh�TWj°²Gw�hGX�jAXàw~f hIkcj~ylT`bX;ylkcyAX�V_]a`bXc` T;`bXcw�mvX�j~�gXcwr�qTWj°�y~]amvX�]aw�` TW��]a`bXcwM­�Xcmstvuck�`bXcwOX�nbmskcjAX��qTWnbwOX�^GX�]�[ k�` k«n �_�qTWV¶` T{TswlmvXs�xXctvuck�T � X�V_]aTWnb` k�TWyMX�VÊ�¸� ÂYl�l �q�X�h jlTswlTWngyAX�z f z±mvXcwlk` TKTsw~y~fb` kTWz±d�fbTEhITWj°²Gwiz�TWyAü�V_]amskxw}�qTWj~y~]amvX�]awi��kcjAX�zÀ]_nbw~yAX�VYXc` kxwRTWz ��f jlkxw}` T�p� þOz'` TK`p]Yÿ�z�TWy~jlk obmskcz'wlTWVYX��qTWz5` Tr^�TWyAuck�XckVakcn �qk�` Trf z5mskcz{h j~]_z�TWngylk;` TMX�h jlks[p]_z;Xc`bX�z�TWngylTZ®z��O³QX�z�^I�Wz½�ETW]_np��f j~y?TWy�X�VÊ�|� ÂYl�l�à �Ez�kxw~y~jAX«h jlTsk�mWf hGXctvuck�mskcz!TswlylT�Xcwlw~f ngylk o.jlT\��TWj~]_nb` k¾X;f y~]��V_]_¬´Xctvuck©` Tàn �_�qTW]aw` T«X�nbmskcjAX��qTWnbw{mskcz ]_nbmWV_]_nGXctvuckªjlTWVYX�y~]_�cX�z�TWn�ylT�h�Tsd�fbTWnGXpoIº°fbw~y~]�²GmvX�nb` k6Xcwlw~]_z Xh�Tsd�fbTWnGXh jlk���f nb`p]a`bXc` T�` TKTWnbmvXcw~y~jAX�z�TWn�ylk®`bXO^GXcwlT�` kxw}h�TWj°²GwEX�^GX�]�[pk�`bXO^GXcwAT?`bXTswlmvXs�xXctvuck �� ms�Ekxw~y~]aTKTWyeX�VÊ�.� ÂYl Z Ä �i` TswlyAXcmvXpobmskcz�k�Xcw~hITsmWylk�dgfbTrylTWj~]YX{z�TWjlTsmW]a` k{z;X�]aweX�ylTWnbtvuck�` k{h jlkc�xjAX��

z;X¾` T�]_nbwly~j~f z�TWngyAXctvuck6]_z{h VaTWz�TWn�yAXc` k ngf z;XªTswAmvXs�xXctvuck6mskcz TswlyAXcmvXcw°�Êh jAX�nbml�GXcwvoiX©dgfbTswlyAuck©` kxwz�kv��]_z�TWngylkxw��qTWj~y~]amvX�]awe`bX{mskcj~y~]_nGXpo�X�h�Tsw�X�jR` T?Tsw~yAX{Tsw~yAX�j�XcwlwlTWngylT�TWz jlk�mA�GXp� � kcz�k;z�kcy~]_�qk objlT\��TWjlTk?XcwlwlTWngyAX�z�TWn�ylk?`bXrkcjl` TWzÁ` T  mWz1nbkrh�TWj~�ak�` kK` TimsTWjlmvXK` T  z�$swvox�xX�Vakcj2dgfbTiylk�`bXs��]YX�nGuck¶º�fbwly~]�²GmvXh�kcjRw~]ûwA��Xcw}h�TWjl`bXcwE` TKmvX�j~�gXz�f ]_ylk®w~]_�xn ]�²GmvX�y~]_�xXcwRjlTW�x]aw~yAXc`bXcwenGXcweX�nbmskcjAX��qTWnbwv�

ÄK�Wj~]awlTWVUTWyrX�VÊ�U� ÂYl b  �RjlT\��TWjlTWz5f z;X;TswAmvXs�xXctvuck�jlTvX�V_]_¬´Xc`bX;f y~]_V_]_¬´X�nb` kàk�z��Wylk�` k®z�kcnbTW�gXcwlmskàTWz

Page 20: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 þ�� Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

d�fbT¸wlT2�qTWj~]�²GmvX�jAX�zÁXcmWjl�swlmW]_z�kxwQ` T·XcwAwlTWngyAX�z�TWn�ylkxw2dgfGX�nb` k oxX}hGX�j~y~]_jQ` T¸` TWylTWj~z{]_nGXc`bXEh jlk���f nb`p]a`bXc` TxoXcweX�nbmskcjAX��qTWnbwEhGXcwlwAX�jAX�z'X{wATWj}z;X�]aw}]_nbmWV_]_nGXc`bXcwv�� kcnbw~yAX�yAX���wAT�Xcwlw~]_z±d�fbT?X�^ ]_^ V_]akc�xjAX�²�X;mskcnbw~f V_yAXc`bXmskcngyl�Wz'f z±ng» z�TWjlk;wl]_�xn ]�²GmvX�y~]_�qk�` TKw~]_y~fGX��

ts¯�Tsw.TWz¼d�fbT|k}h jlkc^ VaTWz;XE`bXRTswlyAX�^ ]_V_]a`bXc` T¸�qTWj~y~]amvX�V�Tsw~ylTW�qT|^ITWz&TW��]a` TWnbmW]YXc` k �Uú|TWj~]�²GmvX���wAT¸]_�xfGX�V_z�TWn�ylTd�fbT�zMf ]_yAXcwK` Tsw~yAXcwEwl]_y~fGXcts¯�TswrwlTMjlT\��TWjlTWz/X;hGX�jlTs` Tswry~]_h�k ÛiTWj~V_]_z5h jlk´��]awl�cj~]YXcw´o�Tswly~j~f y~f jAXcwKdgfbTxo�yAX�Vmskcz�k;XcwR` T\²bn ]_y~]_�xXcwvobw�uckhGX�j~y~]amWf VYX�j~z�TWngylTwlTWnbw~�_�qTW]aweXTswlylTrh jlkc^ VaTWz;Xp�

å£æèå2æÆÅ Ç /pô:ï�ò4ó¸ôIï]/pòûõxðq÷)2¸ô:ï�ðq÷J*}ò�È�îGõ�.�÷-( ó¸î!Ép2·÷�ðq÷éåIô:ïÊÌËaͧÎ�ÏÐ�Ñ!Ò­Ó(Ô!Ï$Õ�Ô!Ö�×�Ô!Ï?Ø=Î�Ö¯ÐAÙÚÕ�ÔvÙÚÏ9Û,ÒMÜ�Ö�Ò!ÝÎ�ÕEÐ�Ò

¿Eh�Tsw�X�j®` T¾Xcw®mskcj~y~]_nGXcw�` T�mskcngylTWnbtvuck<y~]_hIk�ÛiTWj~V_]_z�` T\²bn ]_y~]_�cXcwàwlTWjlTWz z�f ]_ylk���jlTsd�fbTWngylTsw�TWzSQkcj~y~f �gX�VÊoxnGucke�Güpoch jAX�y~]amvX�z�TWn�ylTxoxjlT\��TWj%$WnbmW]YXcw£nGX}^ ]_^ V_]akc�xjAX�²�XKXRTswlylT¸y~]_hIke` T¶mskcj~y~]_nGXcw£` T·mskcn�ylTWnbtvuck �¹ wrTWVaTWz�TWngylkxw?d�fbTOwlTOX�h jlTswATWngyAX�z!wlkc^ jlTTsw~ylTXcwlw~f n�ylkàTxoITWz¦hGX�j~y~]amWf VYX�jKwlkc^ jlTk®mskcz{hIkcj~yAX�z�TWngylkTWz jlTWVYXctvuck;­cwemvX�j~�gXcwR�qTWj~y~]amvX�]awvo h jlk´�X$Wz�o�Xcwlwl]_z�o ` k�dgfbT���kc]:hIkxwlw~�_�qTWV:jlTsmskcV_�bTWjehITWVak�X�f ylkcjv�Ürü«X�V_�xf nbwMX�nbkxwKhGX�jlTsmW]YX�wlTWjr��jlTsd�fbTWngylTàX«Xc` kch�tvuck�`bX�wlkcV_fbtvuck�` T{w~f hIkcj~ylT{�qTWj~y~]amvX�V¸` T��kcj~z;X

d�fGXcwlT?]_nb` TWhITWnb` TWngylT`bX{�qTskcz�TWy~j~]YX®`bX�TswAmvXs�xXctvuck®kcf©`bXcwEmvX�j~�gXcwE�qTWj~y~]amvX�]awrTWng�qkcV_��]a`bXcw � ` Tswl` T�d�fbTwlTày~jAX�yAXcwlwlT«` T�f z;XªTswAmvXs�xXctvuck6jlTvX�V_]_¬´Xc`bX6TWz ��kcj~z;Xcts¯�Tsw;X�j~�x]_Vakxw�Xcw�wlkc^ jlTsmskcnbwlkcV_]a`bXc`bXcwvoikxwhITWj°²Gwz�TWyAü�V_]amskxwf y~]_V_]_¬´Xc` kxw{TWjAX�z ` kc]awqÜk\�Û ÂvÄ �¾nbkxwOhGX�]_nb�W]awOh j~]_z;ü�j~]akxw{T;nbTWn ��f z h�TWj°²bViz�TWyAü�V_]amsk©nbkxwwlTsmWf nb`bü�j~]akxwvo.Tsw~ylTO» V_y~]_z�k�Xcw~h�TsmWylk�mskcz!X�º�fbwly~]�²GmvXctvuck«` TOd�fbTxo:wlTWnb` k�jlTvX�V_]_¬´Xc` kxwKhIkxw~ylTWj~]akcj~z�TWn�ylTxoXcwRmvX�j~�gXcwe�qTWj~y~]amvX�]awewlTWj~]YX�z y~jAX�nbwlz{]_y~]a`bXcwEXckxw}hGX�]_nb�W]aweh j~]_z;ü�j~]akxwv�

¿�T\[ph V_]amvXctvuck�hGX�jAX®Tsw~yAX�kchItvuck;TWjAX�nbTsmsTswlwAX�j~]YX�z�TWn�ylTOTWz{h �_j~]amvX®T?^GXcwATvXc`bX{nbk;mskcz{hIkcj~yAX�z�TWngylkX�hGX�jlTWngylTWz�TWn�ylTàXc` Tsd�fGXc` k«T\[p]_^ ]a` k�h�TWVYXcwKmskcj~y~]_nGXcw?` T{mskcn�ylTWnbtvuck�TWz!d�fbTOTswlyAX�wlkcV_fbtvuck«kcf6kcf y~jAXcww~]_z{]_VYX�jlTsw{TWjAX�z fbwAXc`bXcwv�6��k©TWngyAX�ngylk oiX�f y~]_V_]_¬´Xctvuck6mvXc`bX��qTW¬�z;X�]awO�qTWnbTWjAX�V_]_¬´Xc`bX6` Tàmskcj~y~]_nGXcw�` TmskcngylTWnbtvuckM` Tsw~ylTiy~]_hIk�Xcwlwlk�mW]YXc`bXcw|X��xjAX�nb` Tsw|h jlk���f nb`p]a`bXc` Tsw¸` TRTswAmvXs�xXctvuck;��ýQ]_�xf jAX?þp� Ä �q�\oqhIkcj2�qTW¬vTswTWz�z;XcmW]atskxw2` T¶��jAXcmvXcw2mvX�jAXcmWylTWj~�aw~y~]amvXcw|z�Tsmvÿ�n ]amvXcwvog` Tsw~h�TWj~ylkcf{nbkxw£h jlk�º~TsmWy~]aw~yAXcw2nbk´�cXcw£h jlTsk�mWf hGXcts¯�TswTEX?mskcnbwlmW]r$WnbmW]YX�` TEdgfbTEwlkcV_fbts¯�Tsw¸` k?y~]_hIk?`bX�` TswlmWj~]_yAX?zMf ]_ylkM`p]�²GmW]_V_z�TWn�ylT��qTWj~]�²GmvX�j~]YX�zÀX�wlTW�xf jAX�nbtvXTWz jlTWVYXctvuck o�h�kcjET\[pTWz{h Vak o�­{TWnbmWf j~�cXc`pf jAX;` kxwRhITWj°²GwRz�TWyAü�V_]amskxwE�qTWj~y~]amvX�]awvobf z;X{�qTW¬Md�fbTKnGXcw}�ÊXcwlTsw`bX�TswlmvXv�cXctvuckÑTWVaTsw«wAuckÑT\[phIkxw~ylkxw�TWz mskcz{h j~]_z�TWngylk mskcj~jlTswlh�kcnb` TWn�ylT�­<h jlk���f nb`p]a`bXc` T�TswlmvXs�xXc`bXpojlTWy~]_jAX�nb` k���wlT\�ÊV_�bTswvoEnbTsw~ylT©mskcz{h j~]_z�TWngylk o�dgfGX�Vad�fbTWj�mskcnp²bnGX�z�TWngylkÑVYX�ylTWjAX�V���ýQ]_�xf jAXcw«þp� Äp Tªþp� ÄxÄ �\�� kcz�TstskcfûogTWn�yAuck ogX�wlTWj£z;X�]awQ��jlTsd�fbTWngylT}k�jlTsmWf jlwlk?XEhITWj°²Gw£mskcz�z�TWnbkcj|Tsw~hGXctvX�z�TWngylk o�k�d�fbT¶]_z{h V_]amvXX6w~fGX6f y~]_V_]_¬´Xctvuck yAX�z�^I�Wz�nbkxw;hGX�]_nb�W]aw;wlTsmWf nb`bü�j~]akxw´�+\¸w~yAX6wlkcV_fbtvuck6hGX�jlTsmsTxoRX�V_]Yücw´o¸�ÊX�¬vTWj�ylk�` k kwlTWn�y~]a` k oE`bXc` k<dgfbTªk�fbwlk<` T�f z;X B�X�V_z�k��ÊXc`bX D ` T6X�jlTW]YX nGX�^GXcwlT©` kxwàhGX�]_nb�W]aw�hGX�jAX��gX�jAX�ngy~]_j�kXc` Tsd�fGXc` k�mskcz{h j~]_z�TWngylk` TeX�z;X�j~jAXctvuckO`bXcw·X�j~z;Xc`pf jAXcw´oghGX�jAXMXrV_]_�gXctvuckOXck?hGX�]_nbTWVG]_np��TWj~]akcj���ýQ]_�xf jAXþp� ÄxÄ �K`p]�²GmW]_V_z�TWn�ylT;hITWj~z{]_ylT�y~jAX�nbwlz{]_y~]_jOXck«ylTWj~jlTWnbk©X�y~jAXs�q�swO`bX�^GXcwlT�` kxw�hGX�]_nb�W]awMmvX�j~�gXcw��qTWj~y~]amvX�]aww~]_�xn ]�²GmvX�y~]_�xXcwv�\|wlyAX©nbTsmsTswlw~]a`bXc` T�` T�f y~]_V_]_¬´Xctvuck6` T�h�TWj°²GwnbkxwhGX�]_nb�W]aw{wATsmWf nb`bü�j~]akxw{h�k�` T�Tsw~yAX�jyAX�z�^I�Wz jlT\�

VYXcmW]akcnGXc`bX mskcz kªh jlkc�xjlTswlw~]_�qk�X�^GX�nb` kcnbk�`bXªf y~]_V_]_¬´Xctvuck ` T�Xctsk6z;XcmW]ak nGXªmskcnbw~y~j~fbtvuck�` k6^ITWyAuckX�j~z;Xc` k©` Tsw~yAXcw?hGX�jlTs` Tswvo£d�fbT{hITWj~z{]_y~]YX�mskcz X�V_�xf z;X��ÊXcmW]_V_]a`bXc` TàX«wlfGX�mskcVak�mvXctvuck�` kc^ jAXc` kªX&Þ����nGX{T\[pylTWnbwAuck;` k;mskcz{h j~]_z�TWngylkà` TMX�z;X�j~jAXctvuck;TMX{mskcnbwlTsd�fbTWngylTMh�kxwlwl]_^ ]_V_]a`bXc` T?` T�TW��]_yAX�jEXjlT\��TWj~]a`bXB�X�V_z�k��ÊXc`bX D ` T?X�jlTW]YXp�Q\|wlylTrh jlk�msTs`p]_z�TWn�ylk{ylkcj~nGXs�xXhIkxwlw~�_�qTWVûXM^�TWylkcnGX��qTWz'` kOhGX�]_nbTWV:�gX�jAX�n�y~]_nb` k;k

Page 21: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â þ Â

0

20

40

60

80

100

1988 1990 1992 1994 1996 1998 2000

Núm

ero

de p

roje

ctos

de

esca

vaçã

o

Ano

Total3 caves ou +4 caves ou +5 caves ou +6 caves ou +

0

20

40

60

80

100

1988 1990 1992 1994 1996 1998 2000

Perc

enta

gem

dos

pro

ject

os d

e es

cava

ção

Ano

3 caves ou +4 caves ou +5 caves ou +6 caves ou +

ýU]_�xf jAX{þp� Ä � � �E» z�TWjlk{` TrmvXs�qTswR` kxwih jlk�º~TsmWylkxw}` TrTswlmvXs�xXctvuck�X�h jlTswlTWn�yAXc` kxwRnGX � ÿ�z;X�jAX � f n ]amW]_hGX�V` T�ß:]aw~^IkqXTWngy~jlT ÂYl b l T ÂYl�l�l ��¿EV_z�TW]a`bXpo ÂYl�l�l �\�

à!à!àà!à!àà!à!àá!áá!áá!á â!â!ââ!â!ââ!â!âã!ãã!ãã!ã ä!ää!ää!äå!åå!åå!å æ!æ!ææ!æ!ææ!æ!æç!ç!çç!ç!çç!ç!ç è!è!èè!è!èè!è!èé!é!éé!é!éé!é!éê!êê!êê!êë!ëë!ëë!ëì!ì!ìì!ì!ìì!ì!ìí!íí!íí!í

î!î!îî!î!îî!î!îî!î!îî!î!îî!î!îî!î!îî!î!î

ï!ïï!ïï!ïï!ïï!ïï!ïï!ïï!ï

ð!ð!ðð!ð!ðð!ð!ðð!ð!ðð!ð!ðð!ð!ðð!ð!ðð!ð!ð

ñ!ññ!ññ!ññ!ññ!ññ!ññ!ññ!ñ

ò!òò!òò!òò!òò!òò!òò!òò!ò

ó!óó!óó!óó!óó!óó!óó!óó!ó

ô!ôô!ôô!ôô!ôô!ôô!ôô!ôô!ôô!ôô!ô

õ!õõ!õõ!õõ!õõ!õõ!õõ!õõ!õõ!õõ!õ ö!ö!öö!ö!öö!ö!ö

ö!ö!öö!ö!öö!ö!öö!ö!öö!ö!ö

÷!÷!÷÷!÷!÷÷!÷!÷÷!÷!÷÷!÷!÷÷!÷!÷÷!÷!÷÷!÷!÷

ø!ø!øø!ø!øø!ø!øø!ø!øø!ø!øø!ø!øø!ø!øø!ø!øø!ø!øø!ø!ø

ù!ù!ùù!ù!ùù!ù!ùù!ù!ùù!ù!ùù!ù!ùù!ù!ùù!ù!ùù!ù!ùù!ù!ù ú!ú!úú!ú!úú!ú!ú

ú!ú!úú!ú!úú!ú!úú!ú!úú!ú!ú

û!û!ûû!û!ûû!û!ûû!û!ûû!û!ûû!û!ûû!û!ûû!û!û

ü!ü!üü!ü!üü!ü!üü!ü!üü!ü!üü!ü!üü!ü!üü!ü!üü!ü!üü!ü!ü

ý!ý!ýý!ý!ýý!ý!ýý!ý!ýý!ý!ýý!ý!ýý!ý!ýý!ý!ýý!ý!ýý!ý!ý

þ!þ!þ!þþ!þ!þ!þþ!þ!þ!þþ!þ!þ!þþ!þ!þ!þþ!þ!þ!þþ!þ!þ!þþ!þ!þ!þþ!þ!þ!þþ!þ!þ!þþ!þ!þ!þ

ÿ!ÿ!ÿ!ÿÿ!ÿ!ÿ!ÿÿ!ÿ!ÿ!ÿÿ!ÿ!ÿ!ÿÿ!ÿ!ÿ!ÿÿ!ÿ!ÿ!ÿÿ!ÿ!ÿ!ÿÿ!ÿ!ÿ!ÿÿ!ÿ!ÿ!ÿÿ!ÿ!ÿ!ÿÿ!ÿ!ÿ!ÿ

1 2 3 4 5 6 7 8

� Á��éÅ �0Å����-ÄJÏ���¾È � � Ä)Á���eÈ���Ï����·Î)Á¾Ê[Á���¾ÈxÆAÈ���Ð�Å-Ä����=Å��éÅ Ê[Á��¾Å Ç� Å���Å�� � ��¾ÈÙÆ�Á��YÏ��tÁÙÆ�Å�� ÈeÄJÈtÁ¾ÇÉÅ��YÎJÈ� Å����OÁ��¾Á���eÈ<ÆAÈ��� ��"!��tÅ Ê#�AÐ�ȾÄ�Ð�ÁeÏ��"$ Ï���Á¾Ê¡ÎJÅ`Ä%��ÁEÆAÈ��& Å���Å�� � ��¾È'��Ð�ÈeÄ=Ð�Á¾Ï���$ Ï���ÁeÊ8ÎJÅ-Ä%��ÁEÆ�È(����ÆAÈ(�=Ð�Á¾Ï��"$ Ï���ÆAÈ)� �"!��tÅ`Ê+*{ÄJÅOÁeÊ[Ï�,OÁ���¾È<ÅQÐ�Ä%$�-¼Å�� � ÈeÄ%� È<Æ�Á��;Á��"� ÈeÄ)Á��¾Å��"�. Å����OÁ��¾Á���eÈ<ÆAÈ0/ �"!��tÅ Ê#�AÐ�ȾÄ�Ð�ÁeÏ��"$ Ï���Á¾Ê¡ÎJÅ`Ä%��ÁEÆAÈ���*1 Å���Å�� � ��¾È'��Ð�ÈeÄ=Ð�Á¾Ï���$ Ï���ÁeÊ8ÎJÅ-Ä%��ÁEÆ�È(����ÆAÈ(�=Ð�Á¾Ï��"$ Ï���ÆAÈ2/ �"!��tÅ`Ê+*�ÄJÅOÁeÊ[Ï�,OÁ���¾È<ÅQÐ�Ä%$�-¼Å�� � ÈeÄ%� ÈÉÆ�Á���Á��"�`ȾÄ)Á��¾Å��"�3 Å����OÁ��¾Á���eÈ<ÆAÈ24� ��"!��tÅ Ê#�AÐ�ȾÄ�Ð�ÁeÏ��"$ Ï���Á¾Ê¡ÎJÅ`Ä%��ÁEÆAÈ���*5 Å���Å�� � ��¾È'��Ð�ÈeÄ=Ð�Á¾Ï���$ Ï���ÁeÊ8ÎJÅ-Ä%��ÁEÆ�È(����ÆAÈ(�=Ð�Á¾Ï��"$ Ï���ÆAÈ64 �"!��tÅ`Ê+7

ýU]_�xf jAX®þp� ÄpÂ�� 6rTswlmWj~]atvuck®Tswld�fbTWz;ü�y~]amvX�` k{h jlk�msTswlwlk�mskcnbwly~j~f y~]_�qk;`bXcw�Tsw~y~j~f y~f jAXcwe` TMmskcngylTWnbtvuck98;:�<>=?)@(A(BC:EDGFH@JILKM:;8;:JN�O"P\�mskcngyAXcmWylk`p]_jlTsmWylk` k?^ITWyAuck�nGX�^GXcwlTe` TswlylTEmskczÀk?ylTWj~jlTWnbk opkOdgfbT�XcwlwlTW�xf jAXs�xX�f z;X?y~jAX�nbw~z{]awAwAuckM`bXcwmvX�j~�gXcw��qTWj~y~]amvX�]awMz;X�]aw�T\²GmvX�¬q��¿ �qTWnbTWjAX�V_]_¬´Xctvuck©nGXcw�mskcj~y~]_nGXcwO` T�mskcngylTWnbtvuckª` kxwMXctskxwM¿ à ���c��� T�k\RocTWnb`pf jlTsmW]a` kxwvog` TW]�[pkcf{` T¶h�TWj~z{]_y~]_j|kEh jlk�msTs`p]_z�TWngylk?` TswlmWj~]_ylkrT¶hGXcwlwlkcf�XEkc^ j~]_�gX�j¸­Ef y~]_V_]_¬´XctvuckK`bX

Page 22: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 þ Ä Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

QRQQRQQRQSRSSRSSRS

TRTTRTTRTURUURUURU

VRVRVVRVRVVRVRVWRWRWWRWRWWRWRW

XRXXRXXRXXRXYRYYRYYRYYRY

ZRZRZZRZRZZRZRZZRZRZ[R[R[[R[R[[R[R[[R[R[

\R\R\\R\R\\R\R\\R\R\]R]R]]R]R]]R]R]]R]R]

^R^^R^^R^^R^^R^^R^^R^^R^

_R__R__R__R__R__R__R__R_

`R``R``R``R``R``R``R``R`

aRaaRaaRaaRaaRaaRaaRaaRa

bRbRbbRbRbbRbRbbRbRbbRbRbbRbRbbRbRbbRbRb

cRcRccRcRccRcRccRcRccRcRccRcRccRcRccRcRc

dRddRddRddRddRddRddRd

eReeReeReeReeReeReeRe

fRfRffRfRffRfRffRfRffRfRffRfRffRfRf

gRgRggRgRggRgRggRgRggRgRggRgRggRgRg

hRhRhhRhRhhRhRhhRhRhhRhRhhRhRhhRhRhhRhRhhRhRhhRhRh

iRiRiiRiRiiRiRiiRiRiiRiRiiRiRiiRiRiiRiRiiRiRiiRiRi

jRjRjjRjRjjRjRjjRjRjjRjRjjRjRjkRkRkkRkRkkRkRkkRkRkkRkRkkRkRk

lRlRllRlRllRlRllRlRllRlRlmRmRmmRmRmmRmRmmRmRmmRmRm

nRnRnnRnRnnRnRnnRnRnnRnRnnRnRnnRnRn

oRoRooRoRooRoRooRoRooRoRooRoRooRoRo

pRpRppRpRppRpRppRpRppRpRppRpRppRpRppRpRppRpRppRpRp

qRqRqqRqRqqRqRqqRqRqqRqRqqRqRqqRqRqqRqRqqRqRqqRqRq

rRrRrrRrRrrRrRrrRrRrrRrRrrRrRrsRsRssRsRssRsRssRsRssRsRssRsRs

tRttRttRttRttRttRtuRuuRuuRuuRuuRuuRu

areia

5 5A 5B

betão

5C 5D 6

� Á��éÅ �0Å����`ÄJÏ���eÈ. Å����OÁ��EÁ���¾È<Æ�È0/� ���!��tÅ Ê#��Ð�ÈeÄ�Ð�Á¾Ï���$ Ï��;ÁeÊ¡ÎJÅ`Ä%��Á¾ÆAÈ(��*.�v ÇÉÈ(��Î)Á��¾Å ÇÚÆ�ÁpÁeÄJÇ<ÁEÆ � Ä)Áw*. Ñ � ÈEÊ8Èx�OÁ���¾ÈêÆ�Å?ÁeÊ8ÇÉÈ � Á¾Æ�Á{ÆAÅkÁeÄJÅ Ï[Áy��ÁÍ�Á��éÅøÆ�È{Ð�Á¾Ï���Å`Ê+�5Ð�Á%Ä)Á{Ê8Ï��tÁ���¾ÈCÆ�Á�ÁeÄJÇ<Á¾Æ � Ä)Á�ÁeÈ�Ð�Á¾Ï���Å ÊTÆAÈy�"!��tÅ Ê

�éÅ�� � Ï���ÎJÅ(*.(z Ï����·Î)Á¾Ê[Á���¾ÈxÆ�Á{� È � Ä)Á��EÅ`ÇßÅQÍ�Å`ÎJÈ���Á��EÅ Ç|*. � ÄJÅ`ÎJÏ¡Ä)ÁEÆ�Á{Æ�Á}� È � Ä)Á��EÅ Ç ÁeÐ�~(�ÉÁÐAÄJÅ��JÁ�Æ�È{Í�Å-Î�¾È�*TÅ���Å�� � ��¾È�ÆAÈ � � ÄJÈ�Ð�ÁeÄ)Á{Á�Á��"� ÈeÄ)Á��EÅ`ÇvÅ��éÅ Ê[Á��EÅ Ç Æ�È(�

�OÁ¾Í�È���*1 Å���Å�� � ��¾È��AÐ�ȾÄ�Ð�Á¾Ï��"$ Ï��;Á¾Ê¡ÎJÅ`Ä%��ÁEÆAÈ�����Æ�È(�=Ð�ÁeÏ���$ Ï���ÆAÈ0/ �"!��tÅ Ê#*�ÄJÅOÁ¾Ê8Ï�,OÁ���¾È<Å0ÐAÄ%$�-'Å�� � ȾÄ%�`È<Æ�Á���Á��"� ÈeÄ)Á��EÅ��"��7

ýQ]_�xf jAXeþp� ÄxÄ�� 6rTWyAX�V_�bT¶` ki�ÊXcwlTvX�z�TWngylk�mskcnbw~y~j~f y~]_�qkeTWn�y~jlT¶Xcwû��XcwATsw�7}T·þ}jlT\��TWj~]a`bXcwUnGX}ýQ]_�xf jAXeX�n�ylTWj~]akcjv�

Page 23: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â þ �

jlT\��TWj~]a`bXøB�X�V_z�k���Xc`bX D ` T�X�jlTW]YXpo�mWj~]YX�nb` kOXKnbTsmsTswlw~]a`bXc` TE` TRy~jAX�nbw~z{]awAwAuck�`bXcw·mvX�j~�gXcw¸�qTWj~y~]amvX�]awiX�y~jAXs�q�sw` T?kcf y~jlkxwRTWVaTWz�TWngylkxw´�

¿�h jl�ch j~]YX®f y~]_V_]_¬´Xctvuck�` T�hITWj°²Gwez�TWyAü�V_]amskxwÜ?\�Û ÂvÄ �®hGX�jlTsmsTMwATWjEz;X�]aw·º°fbw~y~]�²GmvXc`bX�hIkcjKXcw~h�TsmWylkxwh jAü�y~]amskxwQ` k�d�fbT¸yl�smWn ]amskxwvoxTswlyAX�nb` kejlTWVYXcmW]akcnGXc` krmskcz�X}�ÊXcmW]_V_]a`bXc` T·` TiXcwlwlk�mW]YXctvuck�` Tsw~ylT|y~]_hIkE` T·hITWj°²bVz�TWyAü�V_]amskàX{��f jlkxw�` T�b�h�kcVaTW�gXc`bXcw{��X�h jlks[:�T�p� Ä z®�\o�k;d�fbT�wlT�X�h jlTswATWngyAXàmskcz'z;X�]akcjr`p]�²GmWf Va`bXc` TOnbkmvXcwlk�` TrhITWj°²Gwe` TKz;X�]akcje`p]_z�TWnbw�uck � � X�]aw}jlTsmsTWngylTWz�TWn�ylTxo�nbk;TWngyAX�ngylk o�Trh jlkv�xXs�qTWV_z�TWn�ylT{Xcwlwlk�mW]YXc` k­��qTWnbTWjAX�V_]_¬´Xctvuck{` TrTsd�f ]_hGX�z�TWngylkxw}z;X�]awihIkcylTWngylTsw´o dgfbTEh�TWj~z{]_ylTWz XOT\[ TsmWfbtvuckO` TE��f jlkxw¶nbkMylTWj~jlTWnbk` T¾z;X�]akcj«`p]Yÿ�z�TWy~jlk o�T©­�z;X�]akcj«mskcnbwlmW]r$WnbmW]YX<hGX�jAX<X�]_z{hIkcj~yAÿ�nbmW]YX<` Tsw~ylTsw�h jlkc^ VaTWz;Xcwvoey%$Wz�wl]a` kf y~]_V_]_¬´Xc` kxwvo hIkcj}�qTW¬vTswvo hITWj°²Gw}z�TWyAü�V_]amskxwxÜ?\�Û ÂWà �T�Ü?\�Û Â þ��p� � f ]_ylkjAX�jAX�z�TWn�ylT�wAuckfbw�Xc` kxw}h�TWj°²Gwy~f ^ f VYX�jlTswvopTWz�h j~]_nbmW�_h ]akOz�f ]_ylkOz;X�]awiXc` TsdgfGXc` kxw¶hGX�jAXMTsw~ylTe²bz�ogylTWnb` kOTWz mskcn�yAXOdgfbT�X�wlkcV_]amW]_yAXctvuckh jlTs` kcz{]_nGX�ngylTR�¶kETsw~��kcjltskEnbkcj~z;X�VÊ�£¿ Xc` kch�tvuckr` T·h�TWj°²GwQy~f ^ f VYX�jlTsw£kcf{` T¸y~]_hIkEwATWz�TWV_�GX�ngylT¶h�TWj~z{]_ylTX�V_]Yücw�k�wlTWf�h jlTsTWnbml� ]_z�TWngylk©]_n�ylTWj~]akcjOmskczämvX�Va`bX�` T�mW]_z�TWngylk©kcf ^ITWyAuck oUk«d�fbT�mskcn�y~j~]_^ f ]¶mskcz½f zXcmWjl�swlmW]_z�k�` TKjlTsw~]awly%$WnbmW]YXp�

SQX�jAX;X�Va�Wz'`bXdgfbTswlyAuck{` ky~]_h�k{` TrhITWj°²bV.XMf y~]_V_]_¬´X�jvo �Gükh jlkc^ VaTWz;X{`bXwlTWVYX��qTWz5Xckz;XcmW]atsk;`bXw~fGXhGX�j~ylT?]_np��TWj~]akcjv� i kc^�Tsw~ylTKhIkcngylk®` TK��]awlyAXpo yAX�ngylk®dgfGX�n�ylk;�?` k�mskcn �bTsmW]_z�TWn�ylk�` k;X�f ylkcjvobnGuck�wATylTWz jlTW�x]aw~yAXc` k{�xjAX�nb` T?TW�qkcV_fbtvuck�nGXcwewlkcV_fbts¯�TswRXc` kch yAXc`bXcwvoGwATWnb` kz�f ]_ylk{��jlTsd�fbTWngylT�XOf y~]_V_]_¬´Xctvuck®` T¬vkcnGXcw|` T}wlTWVYX��qTWzÁ` kxw2hITWj°²Gw£�qTWj~y~]amvX�]aw¸mskczÁmskcz{h j~]_z�TWn�ylk�` T  �87�zÁkcf{z�f ]_ylk?h jl�s[p]_z�k?` Tsw~ylTi�xX�Vakcjv�6rXc` kMkr�ÊXcmWylk�` TRTsw~yAX�wlTWVYX��qTWz�wAT}jlTvX�V_]_¬´X�j¸hIkcj|�xjAXs��]a`bXc` Txo�]aw~ylk?�xo�wlTWz d�fGX�VadgfbTWj·h jlTswlwAuck o��}ylk�`bXv��]YXdgfbTsw~y~]akcnGüv�qTWV:wlTEmskcz{h j~]_z�TWn�ylkxwR` Tsw~yAXMkcjl` TWz±` Te�xjAX�nb` TW¬´XMhIk�` TWzÀw~f hIkcj~yAX�j¶mvX�j~jlTW�gX�z�TWn�ylkxwRz�f ]_ylkw~]_�xn ]�²GmvX�y~]_�qkxwvo�XKz�TWnbkxw|dgfbTRXrT\[py~jlTWz{]a`bXc` TR]_np��TWj~]akcj¸` krhITWj°²bVp²GdgfbTEXcwlwlTWngylT}TWz ylTWj~jlTWnbk?mskczÁz�f ]_ylk^�kqXcwRmvX�jAXcmWylTWj~�awly~]amvXcwez�Tsmvÿ�n ]amvXcwv�

¹ h jlkc^ VaTWz;Xª`bX«��f nb`bXctvuckª` kxwh�TWj°²GwO�qTWj~y~]amvX�]awhGX�jlTsmsT�wlTWjOhGX�j~y~]amWf VYX�j~z�TWngylT�]_z{hIkcj~yAX�ngylT�nGXcwkc^ jAXcw�` T�TswlmvXv�cXctvuck¾mskcz½mskcn�ylTWnbtvuck�y~]_hIkwÛiTWj~V_]_z!jlTvX�V_]_¬´Xc`bX¾TWz/��kcj~z;Xcts¯�Tsw�mskcz�k�kxw?�xjAX�n ]_ylkxwO` kSUkcj~ylk � � kcnp��kcj~z�T6�¾w�X�^ ]a` k oeTsw~ylTsw®z;X�ylTWj~]YX�]aw�X�h jlTswlTWngyAX�z$hITWj°²Gw�` T©X�V_ylTWjAXctvuckÑd�fbT¾h�k�` TWz wATWj^GXcw~yAX�ngylTe]_j~jlTW�xf VYX�jlTswvo�wlfbmsTs` TWnb` k���wlTxoghIkcj|�qTW¬vTswvo�Xrng»bmWVaTskxw¸^GXcw~yAX�ngylTEjlTsw~]aw~ylTWn�ylTsw¸T}hIkcfbmsk�X�V_ylTWjAXc` kxwvoX�z{h VYXcwr¬vkcnGXcwK` TOwAkcVakxwrjlTsw~]a`pfGX�]awKmskcz/mvX�jAXcmWylTWj~�aw~y~]amvXcwKjlTsw~]aw~ylTWn�ylTswK^GX�]�[bXcwv�\|w~yAX®�bTWylTWjlkc�qTWnbTW]a`bXc` T��X�¬mskcz�d�fbTOkxweh jlkc^ VaTWz;XcwK` T���f nb`bXctvuckà` kxw�h�TWj°²Gw�nbTsw~yAXcwe��kcj~z;Xcts¯�TswrwlT�ºlX�z5z;X�]awe��jlTsdgfbTWn�ylTswK` kdgfbTxophIkcjeT\[ TWz{h Vak o nGXcwi��kcj~z;Xcts¯�Tsw}z{]ak�ms�Wn ]amvXcwe` T�ß:]aw~^IkqXp�6rT¸f z;Xe��kcj~z;XR�qTWjAX�VÊox`p]_j°��wlT\��üpoqXcwAw~]_z�ocdgfbT¶wlT·ylTWz¼jlTW�x]aw~yAXc` k�f z;XEwlTWnbw~]_^ ]_V_]_¬´XctvuckrmWjlTswlmsTWn�ylT·hGX�jAX

X�d�fbTsw~yAuck;`bX�jlTsw~]aw~y%$WnbmW]YX�` kxwEhITWj°²GwRz�TWyAü�V_]amskxw��qTWj~y~]amvX�]awrT?w~fGX��f nb`bXctvuck �RS£Xcwlwlk;hGX�j~y~]amWf VYX�j~z�TWngylT]_z{h�kcj~yAX�n�ylT�mskcnbw~y~]_y~f ]_f¾XO]_nbmWV_fbw�uck{nGX{B�S2jlkchIkxw~yAX{` T?��kcj~z;XcweXd�fbTK` TW�qTWz'kc^�Ts` TsmsTWjEkxw}h jlk�º°TsmWylkxw` T?TswlmvXs�xXctvuckàT?mskcngylTWnbtvuck®h�TWj~]����Wj~]amvX D o�X�h jlTswATWngyAXc`bX®TWz Û¶j~]_ylk;TWyEX�VÊ�.� ÂYl�l Zx�\o�` TKf z;X�jlT\��TWj%$WnbmW]YX®­nbTsmsTswlw~]a`bXc` T¸` T:º�fbw~y~]�²GmvXctvuckE`bXcwTB�mvX�jAXcmWylTWj~�aw~y~]amvXcwQ` kxw.TWVaTWz�TWn�ylkxwQ�qTWj~y~]amvX�]aw.h jlk´��]awl�cj~]akxwQT|` T\²bn ]_y~]_�qkxw D �

³UX�zM^��Wz jlTWVYXcmW]akcnGXc` k6mskcz Tsw~ylT®h jlkc^ VaTWz;Xpo¶TWz�^IkcjAX¾mskcz kc^pº~TsmWy~]_�qkxwz�f ]_ylkªz;X�]aw�X�VYX�j~�gXc` kxwvo��` T�jlT\��TWj~]_j�k�h jl�ch j~]ak©X�hGX�jlTsmW]_z�TWngylkª`bXcw?jlT\��TWj~]a`bXcwMnbkcj~z;Xcwvo.nGX�wlTsd�f4$WnbmW]YX«` k�hITs`p]a` k«��TW]_ylk«hITWVYX� ÿ�z;X�jAX � f n ]amW]_hGX�V�` T�ß:]aw~^IkqX�Xckqj�j~f h�k�` Te³ûjAX�^GX�V_�bk` TøjrTskcylTsmWn ]YX�`bX ¹ jl` TWz ` kxw�\2n �qTWn �bTW]_jlkxwvok�d�fbT�z�kxw~y~jAX¾X«h jlTsk�mWf hGXctvuck¾mskcz kxwOXcwlwlf ngylkxwO`bX�wlTW�xf jAX�nbtvX�nGXcw��xjAX�nb` TswOTswlmvXs�xXcts¯�Tsw�f j~^GX�nGXcwh�kcj}hGX�j~ylT?` TMX�V_�xf nbwRz�f n ]amW�_h ]akxw´�

�eTW�x]aw~yAX�z��wAT�X�]_nb`bXpo·nbk6TWn�yAX�ngylk o¶z�f ]_yAXcw®` T\²GmW]r$WnbmW]YXcw�nGX©��kcj~z;Xªmskcz�k Xªd�fbTsw~yAuck6` k6Tsdgf ]_V_���^ j~]ak®�qTWj~y~]amvX�V2`bXcwrmskcngylTWnbts¯�TswKy~]_hIkHÛiTWj~V_]_z/�My~jAX�yAXc`bXpo:k®d�fbTM�Oz�kcy~]_�xXc` kàh�TWVak;��XcmWylkà` Tk;h jl�ch j~]ak

Page 24: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 þ à Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

h jlkc^ VaTWz;X�TswlyAX�jeX�]_nb`bX]_nbw~fp²GmW]aTWngylTWz�TWn�ylTTsw~y~fb`bXc` k �

ÊÌËaͧÎ�ÏÐ�Ñ!Ò­Ó(Ô!Ï$Õ�Ô!Ö�×�Ô!Ï?Ø=Î�Ö¯ÐAÙÚÕ�ÔvÙÚÏ<Î&Ô Õ�Ò©Û,ÏÐ�Ö�Í���Ñ!Ò

¹ w�h jlkc^ VaTWz;Xcwr`bX;TswlyAX�^ ]_V_]a`bXc` TM�qTWj~y~]amvX�V2`bXcwrmskcngylTWnbts¯�Tswry~]_hIk�ÛiTWj~V_]_z¦nGuck®wlTMmskcVak�mvX�z!X�hITWnGXcwXck«n �_�qTWV¸` T�h jlk�º°TsmWylk oUTsw~yAX�nb` k«z�f ]_yAXcwM�qTW¬vTswKjlTWVYXcmW]akcnGXc` kxwOmskcz½X�h jl�ch j~]YX«T\[ TsmWfbtvuck oUz�TWjlTsmsTWnb` kTsw~yAXpobXcwlwl]_z�o f z;X�X�ylTWnbtvuck�Tsw~hITsmW]YX�VÊ�

¹ h j~]_z�TW]_jlk�Xcw~hITsmWylk«`p]_¬jlTsw~hITW]_ylk�­®wATWVYX��qTWz!` kxwKh�TWj°²Gw´o���f nb`bX�z�TWn�yAX�V|hGX�jAX�k�Xc` TsdgfGXc` kà��f np�mW]akcnGX�z�TWngylk�`bXªwlkcV_fbtvuck ��S£X�jAX X�Va�Wz ` T�` TW�qTWj�wlTWj{T\[pTsmWf yAXc`bXªmskcz k©nbTsmsTswlw�ü�j~]akªjlTsw~h�TW]_ylk©hITWVYXcw]_nb`p]amvXcts¯�Tsw¶` kMh jlk�º~TsmWylk o��e��f nb`bX�z�TWn�yAX�VIylTWj¶TWz±X�ylTWnbtvuckOX�dgfGX�V_]a`bXc` Tr`bX�wlTWVYX��qTWz�opdgfbT�` TW�qTRh jlT\��T\�jlTWnbmW]YX�V_z�TWngylTOwlTWjRjlTvX�V_]_¬´Xc`bX;mskcz jlTsmWf jlwlk;X{z;X�n �xfbTW]_jAXpo ��TW]_yAX{` TswlmsTWjemskcz'k�h�TWj°²bVûz�TWyAü�V_]amsk o�TrnGuckhIkcj�d�fbTs`bX®V_]_��jlT` Tswl` T{X®^�k�mvX®` k;��f jlk � � �GX�z;X���wlT�X�]_nb`bX�X�X�ylTWnbtvuckàhGX�jAX®k®�ÊXcmWylk�` Txo:`pf jAX�ngylT{TX�hI�xwEX{wlTWVYX��qTWz�o�X�yl��­h jlTswAX�`bX{mvX�Va`bXpoGk{hITWj°²bVU` TW�qTWjEwlTWjRz;X�ngy~]a` kàmsTWngy~jAXc` k®nbk{]_n�ylTWj~]akcjE` k{��f jlk oXcw~hITsmWylk�yAX�n�ylk�z;X�]awE]_z{h�kcj~yAX�n�ylTMd�fGX�ngylk;z;X�]akcjR��kcjEk�`p]Yÿ�z�TWy~jlkà` k��f jlk;TKz�TWnbkcjKX{wlTsmstvuck®` T�XctskfbwAXc`bXp�Ùãö]_ngylTWjlTswlwAX�n�ylT�z�TWnbmW]akcnGX�jrd�fbT�TWz'`p]_�qTWjlwAX;^ ]_^ V_]akc�xjAX�²�X®mskcnbw~f V_yAXc`bXpo�wATKjlT\��TWjlTxo�X{h jlkchI�xw~]��ylk�`bX;��f nb`bXctvuck«` kxwrhITWj°²GwvoIkàjlTsmWf jlwlk�X;`p]Yÿ�z�TWy~jlkxw�` T���f jAXctvuck«w~f ^bw~yAX�nbmW]YX�V_z�TWn�ylT�w~f hITWj~]akcjlTsw?Xckxwh jAX�y~]amvXc` kxwRfbwlfGX�V_z�TWngylTOTWz SUkcj~y~f �gX�VÊo�wlTWnb` k�X{wlTWVYX��qTWz'jlTvX�V_]_¬´Xc`bX{mskcz ^ITWyAuck �

¿+]_V_fbw~y~jAX�j}XK]_z{hIkcj~yAÿ�nbmW]YXO`bX?d�fGX�V_]a`bXc` TE`bX?��f nb`bXctvuckM` kxw¶TWVaTWz�TWngylkxwi�qTWj~y~]amvX�]awvo i ylk�mlµqTWjK� ÂYl�lp �jlT\��TWjlT·f zÁmvXcwAk�` Tif z;XEhGX�jlTs` TR` TiTsw~yAXcmvXcw2wATsmvX�ngylTsw|` T<b�b��Ez{zÁ` Ti`p]Yÿ�z�TWy~jlk ogmskcz  Zez�` TRX�V_y~f jAXpohGX�jAX TswlyAX�^ ]_V_]_¬´Xctvuck�` T«f z yAX�V_fb` T��qTWj~y~]amvX�Vrmskcz ÂY� z ` T�X�V_y~f jAXpo}mskcz � n �_�qTW]aw®` T©X�nbmskcjAX��qTWnbwh jl�\��Tsw°��kcjltvXc`bXcwO]_nbmWV_]_nGXc`bXcwvo2nbk©dgfGX�VÊo2X�hI�xwX�T\[pTsmWfbtvuckª`bX�hGX�jlTs` T®T�X�X�h V_]amvXctvuckª`bXcwmvX�j~�gXcwOnGXcwX�nbmskcjAX��qTWnbwvo wlTE�qTWj~]�²Gmskcf�f z±w~» ^ ]_ylkOXcwAwlTWngyAX�z�TWn�ylk�`bXcwiTsw~yAXcmvXcwi` TEd�fGXcwlT  7�mWz��2ú|TW]akX��qTWj~]�²GmvX�j°�wlTEdgfbT�X?mvX�fbwAX?hGX�jAX�Tsw~ylTEmskcz{h�kcj~yAX�z�TWn�ylk]_nbTsw~hITWjAXc` k�y~]_n �GXMw~]a` k�kOXcmWf z�f VYX�j}` T�` TWy~j~]_ylkxw¸nGX�^GXcwlT`bXcwTsw~yAXcmvXcwvo|d�fGX�nb` kª`bX���f jAXctvuck o2ylTWnb` kªk¾h jlkc^ VaTWz;Xªw~]a` k©jlTswlkcV_��]a` k�h jlk�msTs` TWnb` k ­�]_ncº~Tsmstvuck6`bX^GXcwlTK`bXcwETsw~yAXcmvXcwRT?Xck{jlT\�ÊylTWnbw~]akcnGX�z�TWn�ylk®`bXcwEX�nbmskcjAX��qTWnbwv�Û¶j~]_ylk�� ÂYl�l�l �¶jlT\��TWjlTrf z mvXcwlk{` Trf z;XTswlmvXv�cXctvuck�TWz�ßû]aw~^�kqXd�fbT?X�ylTsw~yAX{XM]_z{hIkcj~yAÿ�nbmW]YX�` T�f z

Xc` Tsd�fGXc` k�Tsw~y~fb` k«�qTskcyl�smWn ]amsk¾dgfbTylkcz�T�TWz½` TW��]a`bX«X�ylTWnbtvuck©Xà� ]aw~yl�cj~]YX«` k�Vak�mvX�VÊ� � kczäT\��TW]_ylk o.kh VYX�nbk?` T}h jlkxwlh�TsmstvuckKnGuck�` TWylTsmWylkcf®XKT\[p]aw~y%$WnbmW]YXrnbkKVak�mvX�Vb` T}f z;X?X�n�y~]_�gXrh�Ts`pjlTW]_jAXpo�kKd�fbT}]_z{h V_]amskcfd�fbTxobTWz hGX�j~ylT�wlf ^bw~yAX�nbmW]YX�VU`bX{kc^ jAXpoG` TW��]a` kà­�xjAX�nb` TK]_j~jlTW�xf VYX�j~]a`bXc` T` k�w~f ^bw~y~jAX�ylk�jlTsw~]aw~ylTWngylTxo�kxwhITWj°²Gw£�qTWj~y~]amvX�]aw2²GmvXcwlwlTWz1��f nb`bXc` kxw2nbkrz;X�ylTWj~]YX�Vb` TRX�ylTWj~jlk?d�fbT¶h jlTsTWnbml� ]YXMX�X�n�y~]_�gXr¬vkcnGXKT\[ph VakcjAXc`bXp�6KXc` krdgfbTik�z;X�ylTWj~]YX�V ` T}X�ylTWj~jlk?X�h jlTswlTWngyAXv�cXrmvX�jAXcmWylTWj~�aw~y~]amvXcw|z�Tsmvÿ�n ]amvXcw2z�f ]_ylk���jAXcmvXcwvoqXEhGX�jlTs` T

wlk���jlTWfûoûX�h��xwKX®jlTvX�V_]_¬´Xctvuck«` T{X�V_�xf z;Xcw�X�nbmskcjAX��qTWnbwvo.XcwAwlTWngyAX�z�TWn�ylkxw?T` Tsw~Vak�mvX�z�TWn�ylkxwK�bkcj~]_¬vkcngyAX�]aw]_z{hIkcj~yAX�ngylTswvoxd�fbT2]_z{h V_]amvX�jAX�z1` T\��kcj~z;Xcts¯�TswU` keylTWj~jlTWnbkew~f hIkcj~yAXc` kR^GXcwlyAX�ngylT¶w~]_�xn ]�²GmvX�y~]_�cXcw´�U³UTWnb` k��wlT�mskcnbwlyAX�yAXc` k�Tsw~ylTsw�]_z{h�kcj~yAX�n�ylTswM` Tsw~Vak�mvX�z�TWngylkxw´o.��kcjAX�z!jlTvX�V_]_¬´Xc`bXcwX�nbmskcjAX��qTWnbwOXc`p]amW]akcnGX�]aw´oQd�fbT]_nbmWjlTWz�TWngyAX�jAX�z X�]_nb`bX®kxwr` Tsw~Vak�mvX�z�TWngylkxw´� i ��X�hI�xw�Tsw~ylTTW�qkcV_f ]_jr`bX®w~]_y~fGXctvuck�wlTMh jlk�msTs` TWf X;f z;XmvX�z{hGX�n �GXà` T?h jlkxw~hITsmstvuck�dgfbT�h�TWj~z{]_y~]_fªmvX�jAXcmWylTWj~]_¬´X�j?X;wl]_y~fGXctvuck;�qTskcyl�smWn ]amvXpo�]_ngylTWj~h jlTWyAX�j?k®mskcz�hIkcj~yAX�z�TWngylk�`bXOkc^ jAXOT�h jlk�msTs` TWje­cw¶z�Ts`p]a`bXcwRmskcj~jlTsmWy~]_�xXcwRd�fbTehITWj~z{]_y~]_jAX�z'XOmskcnbmWV_fbwAuck{`bXMz�Tsw~z;X� � TWnbkcjvo ÂYl�l þxXpo ^��\�¹ ]_nbmW]a` TWngylT;z�kxw~y~jlkcf�X�]_nb`bX�d�fbTOkxwry~jAX�^GX�V_�bkxw�` TOT\[ TsmWfbtvuck«` kxwr��f jlkxwrhGX�jAX�Xà]_nbw~yAX�VYXctvuck«` kxw

hITWj°²Gwez�TWyAü�V_]amskxw��qTWj~y~]amvX�]awEnGuck���kcjAX�z'fbwAXc` kxwEhGX�jAX;f z;X;Xs�xX�V_]YXctvuck o�z�Tsw~z�kàdgfbT?wlf z;ü�j~]YXpo�`bXcwEmvX��

Page 25: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â þ�7

jAXcmWylTWj~�aw~y~]amvXcw¸`bXcw£��kcj~z;Xcts¯�Tsw|X�y~jAXs�qTswlwAXc`bXcw´ox��f nbtvuckKhGX�jAXrdgfbT}TswlyAuckrhGX�j~y~]amWf VYX�j~z�TWngylTE�qk�mvXcmW]akcnGXc` kxwv�Àez;XOkcf y~jAXd�fbTsw~yAuckTsw~yAü�jlTWVYXcmW]akcnGXc`bX{mskcz±kMh jlTsTWnbmA� ]_z�TWngylk®mskcz'X�jlTW]YXM` kTsw~hGXctskmskcz{h jlTsTWnp�

`p]a` kOTWn�y~jlTKkOh�TWj°²bV:TKXcwihGX�jlTs` Tsw}` kM��f jlk o Xcw~hITsmWylkdgfbT�z�f ]_yAXcwR�qTW¬vTswinGuckO�rmWf z{h j~]a` k{TWz±kc^ jAXp�2¿h jlkch��xw~]_ylkK` TswlyAXrdgfbTsw~yAuck o��ih jlT\��TWj~�_�qTWVbd�fbT}krz;X�ylTWj~]YX�VG` Tih jlTsTWnbmA� ]_z�TWngylkOwlT�º~X�]_nbmskcz{h jlTswAw~�_�qTWVU��¿ i �� \Ro ÂYl�l Zx�\o:wlTWnb` k o.X�V_]YücwvoIh jAü�y~]amvXà]_n�ylTWj~nGXcmW]akcnGX�V¸mskcj~jlTWngylT;k®h jlTsTWnbmA� ]_z�TWngylk¾` kxw���f jlkxwrmskcz/^ITWyAuckh�kc^ jlTrkcf�mvX�Va`bXM` TrmW]_z�TWn�ylk o mskcngy~jAX�j~]YX�z�TWngylTOXck��GX�^ ]_y~fGX�V_z�TWn�ylTKjlTvX�V_]_¬´Xc` k{TWngy~jlT�nb�xwv��ÄrVakxwl]_nbw~µ�®T�EX��ÊX�Vaw~µ�]|� ÂYl�l�à �¶jlT\��TWjlTWz'XT\[ TsmWfbtvuck�` T���f jlkxwijlTsmskcj~jlTWnb` k®Xw~fbw~hITWnbwAuck^�TWn�ylkcn �_y~]amvXpobmskcnbw~y~]_y~f ]_nb` kX©h jl�ch j~]YX6w~fbw~hITWnbwAuck o·X�hI�xw;X©]_nbw~yAX�VYXctvuck�` kªh�TWj°²bVRT«k6TWnb`pf jlTsmW]_z�TWn�ylk�`bXcd�fbTWVYXpo¶kªz;X�ylTWj~]YX�VE` TTWnbml� ]_z�TWngylk�` k©��f jlk o¶X�h jlTswlTWngyAX�nb` k<X�]_nb`bX©jlTsw~f V_yAXc` kxw�` T«TWnbwAX�]akxw;` T«mvX�j~�gXª` T�h�TWj°²Gwz�TWyAü�V_]amskxw]_nbw~yAX�VYXc` kxwRnbTsw~yAXcwemskcnb`p]ats¯�Tswv�

¿���f nbtvuckeh j~]_nbmW]_hGX�Vb`bX�X�jlTW]YX�kcfO` Tikcf y~jlk�z;X�ylTWj~]YX�V ` T¸h jlTsTWnbmA� ]_z�TWngylk o�hGX�jAX�X�Va�Wz�` T¶mskcngy~j~]_^ f ]_jhGX�jAX©X�jlTs`pfbtvuckª` kxw` Tsw~Vak�mvX�z�TWn�ylkxwvo¸`p]_z{]_n�f ]_nb` k X�` T\��kcj~z;Xctvuck6`bXcwOhGX�jlTs` Tsw{` kxwM��f jlkxwvo£�«X¾` TTW��]_yAX�j®X TWnbmWf j~�cXc`pf jAX6` k h�TWj°²bVRnbk�wlTWfÑ]_ngylTWj~]akcjvo}d�fbT«mskcnb`pf ¬´X�Xªf z;X6jlTs`pfbtvuck w~f ^bw~yAX�nbmW]YX�V�`bXw~fGXªmvX�hGXcmW]a`bXc` T«hGX�jAX XªX�^bwlkcjltvuck ` T«Tsw~��kcjltskxw{nbkcj~z;X�]aw´� \¸w~ylT�h jlkc^ VaTWz;X6��nGX�y~f jAX�V_z�TWngylT¾yAX�ngylkz;X�]aw¸]_z{hIkcj~yAX�ngylTrd�fGX�ngylk?z;X�]akcjlTsw·��kcjlTWz�kM`p]Yÿ�z�TWy~jlkM` k?��f jlkMTek�mskcz{h j~]_z�TWn�ylk` k?hITWj°²bV�Ted�fGX�ngylkz�TWnbkcj}��kcjeX�wlTsmstvuck�` T?Xctsk �

¿']_V_fbwly~jAX�j®Tsw~ylT�h jlkc^ VaTWz;X�Tsw~yAüªf z ]_nbmW]a` TWn�ylT¾k�mskcj~j~]a` k6ngf z;X�kc^ jAX6TWz�d�fbTxoi` TW��]a` k�­ª`p]�² �mWf Va`bXc` T�` TO��f jAXctvuck oûz�kcy~]_�cXc`bX�hITWVYX®�bTWylTWjlkc�qTWnbTW]a`bXc` T;`bXcwr��kcj~z;Xcts¯�TswvoûkC\2z{h jlTW]_ylTW]_jlk�jlTsmskcj~jlTWf<XTsdgf ]_hGX�z�TWn�ylk�` T{T\[pTsmWfbtvuck�` T{Tsw~yAXcmvXcwrhGX�jAX«X®jlTvX�V_]_¬´Xctvuck«` kxw���f jlkxwrhGX�jAX«X®]_nbw~yAX�VYXctvuck«` kxwrh�TWj°²Gwz�TWyAü�V_]amskxw�qTWj~y~]amvX�]awv�6¿Àf y~]_V_]_¬´Xctvuck6` Tsw~yAX�yl�smWn ]amvX¾mskcnb`pf ¬s]_fûo¸nbk¾TWn�yAX�ngylk o¶X«��f jlkxwmskcz `p]Yÿ�z�TWy~jlkz�f ]_ylkw~f hITWj~]akcjiXckM�GX�^ ]_y~fGX�V_z�TWngylTrf y~]_V_]_¬´Xc` k opnGuckOwlTEylTWnb` k o�mskcn�y~fb` k oph jlk�msTs`p]a` kXckMh jlTsTWnbml� ]_z�TWnp�ylk{` k{Tsw~hGXctsk{mskcz{h jlTsTWnb`p]a` k;TWn�y~jlT?kOh�TWj°²bV:z�TWyAü�V_]amsk�T?XcwihGX�jlTs` Tswe` kO��f jlk obXcmW]_z;X`bXO¬vkcnGX{wATWVYXc`bXXck�z;XcmW]atsk �}¿1mskcncº�f �gXctvuck®` Tsw~ylTsw�` kc]awRh jlk�msTs`p]_z�TWngylkxwrmskcnb`pf ¬s]_fª­;TWnbmWf j~�cXc`pf jAX®` T�X�V_�xf nbwEh�TWj°²Gwnbk{]_ngylTWj~]akcj�` kxw}jlTsw~hITsmWy~]_�qkxwi��f jlkxw´obmskcz�k{]_V_fbw~y~jAX{X{ýQ]_�xf jAX�þp� Ä�� �

ýQ]_�xf jAX�þp� Ä���� \|nbmWf j~�cXc`pf jAX;` TKf z hITWj°²bV:z�TWyAü�V_]amsk �¿ X�nbkcz;X�V_]YXpoUnbk«TWngyAX�n�ylk oU��TW¬W��wlT{wATWngy~]_j�TWz/h j~]_z�TW]_jlk«V_f �gX�jOX�y~jAXs�q�swO` T�XcwlwlTWngyAX�z�TWn�ylkxwMT{` Tsw~�

Vak�mvX�z�TWn�ylkxwE]_z{hIkcj~yAX�ngylTsw�`bX{hGX�jlTs` TM` T?mskcngylTWnbtvuck � i TWnb` k;Tsw~ylT?k;mvXcwlk obhIk�` TWjAü{�GXs�qTWjKXylTWngyAXctvuck

Page 26: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 þxþ Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

` T{jlT\��kcjltvX�jMX«wlkcV_fbtvuck¾` T�mskcngylTWnbtvuckªX�y~jAXs�q�swM` T{nbkv�xXcwMX�nbmskcjAX��qTWnbw´oUh jlk�msTswlwlk�dgfbT{wlT�jlTW�qTWVYX�]_nGX��` Tsd�fGXc` k«mvXcwlk�k®h jlkc^ VaTWz;X�wlT�º~Xpo:` TM�ÊXcmWylk o:k«Tsdgf ]_V_�_^ j~]ak��qTWj~y~]amvX�VÊoûf z;Xà�qTW¬d�fbTOyAX�V¸Xcmstvuck�]_z{h V_]amvXf z XcmWjl�swAmW]_z�kM` T�mvX�j~�gX?�qTWj~y~]amvX�VId�fbTR]_jAüpo�h jlkv�xXs�qTWV_z�TWngylTxo�X��xjAXs�xX�j¶k�h jlkc^ VaTWz;Xp�|SQX�jAXOkMwlkcV_fbmW]akcnGX�jjlTsmskcj~jlTWfp��wlT?XOTswlmskcjAXcw¶]_nbmWV_]_nGXc`bXcwvoGX�hIkc]YXc`bXcw}TWz±wAX�hGX�yAXcwUº~üM^ITWylkcnGXc`bXcwinGXM¬vkcnGXMmsTWn�y~jAX�Vû` TrTswlmvXs�xX��tvuck o�hGX�jAX;TW��]_yAX�jrX;k�mskcj~j%$WnbmW]YX®` TXcwlwlTWngyAX�z�TWn�ylkxw?Xc`p]amW]akcnGX�]awv��Á�X�jlTOTWy�X�VÊ�£� ÂYl Z � �RjlT\��TWjlTMyAX�z�^I�WzkjlTsmWf jlwlk;X�Tsw~yAXwlkcV_fbtvuck �Ürü�]_�xfGX�V_z�TWngylTànbkcy~�amW]YX�` T�kcf y~jAXcwM`pfGXcwMkc^ jAXcw�jlTsmsTWn�ylTsw�nGX�mW]a`bXc` T;` k¾SUkcj~ylk¾mskczä]_nbmW]a` TWngylTsw

jlTWVYXcmW]akcnGXc` kxwRmskcz±XO` T\²GmW]aTWngylTKTsw~yAX�^ ]_V_]a`bXc` TrTWzÀjlTWVYXctvuck{­cw¶mvX�j~�gXcwi�qTWj~y~]amvX�]aw´o�ylTWnb` k���wATEn�f z;X` TWVYXcwjlTW�x]aw~yAXc` k X©TWnbmWf j~�xXc`pf jAXª�qTWnbTWjAX�V_]_¬´Xc`bX6` kxwhITWj°²Gwz�TWyAü�V_]amskxw{�qTWj~y~]amvX�]awvo¸mskcz X©mskcnbwlTsd�f4$WnbmW]YX6` TTWVaTW�xXc` kxwe` Tsw~Vak�mvX�z�TWngylkxwe�qTWj~y~]amvX�]aweTK�bkcj~]_¬vkcn�yAX�]awE`bXmskcj~y~]_nGX;TK` kxweX�j~j~fGX�z�TWngylkxwE��]_¬s]_n �bkxw´�� kcnbw~]a` TWjAX���wATR]_�xfGX�V_z�TWngylTr` T}hGX�j~y~]amWf VYX�j¶]_z{hIkcj~yAÿ�nbmW]YX?f z mskcj~jlTsmWylkMhIkxw~]amW]akcnGX�z�TWngylkO` kxw|hITWj°²Gwvo

nbkªdgfbTàjlTsw~hITW]_yAX©dgfbTWj{­©w~fGX¾Vak�mvX�V_]_¬´Xctvuck6TWz h VYX�n�yAXpo¸d�fbTWj{­©w~fGX��qTWj~y~]amvX�V_]a`bXc` Tx� Àez hITWj°²bVid�fbTwlT�X��ÊXcw~ylT�w~]_�xn ]�²GmvX�y~]_�xX�z�TWngylTà`bX��qTWj~y~]amvX�V¸�xoUnGX�y~f jAX�V_z�TWngylTxoQf z!hITWj°²bV|z;X�]aw?��kcj~ylTWz�TWn�ylT;w~fcº~TW]_ylk�XT\��TW]_ylkxw·` TEwlTW�xf nb`bX�kcjl` TWz�o�hITWVak�d�fbTR�GüMdgfbTETW��]_yAü��ÊVak �2SQkcjikcf y~jlk�VYXc` k o�f z�hITWj°²bVGz;X�V�hIkxw~]amW]akcnGXc` kTWz h VYX�n�yAX{hIk�` T?`p]�²GmWf V_yAX�jrXy~jAX�nbw~z{]awlw�uck�`bXcwemvX�j~�gXcwe�qTWj~y~]amvX�]awEkcf¾X�]_nb`bX�h jlkv�qk�mvX�j�XnbTsmsTswAw~]a`bXc` T` T·]_ngf y~]_V_]_¬´X�j|XRw~fGXEXcmstvuck�X�y~jAXv�q�sw2` kewlTWfOmskcj~ylTxocylkcyAX�V�kcfOhGX�jlmW]YX�VÊoxd�fbT¸wlTWjAüRnbTsmsTswlwAü�j~]akEhGX�jAXRhITWj~z{]_y~]_jXmskcVak�mvXctvuck;`bXmsk���jAX��qTWz'kcf�`bX{X�j~z;Xc`pf jAX�` kxwRhGX�]_nb�W]awv�i TWjAü®X�]_nb`bX;` TMTW��]_yAX�j�k{jlTsmWf jlwlk�Xh�TWj°²GwrXcwlw~f z{]a`bX�z�TWn�ylTMT\[pylTWj~]akcjlTswr­{hGX�jlTs` Txo�mskcz�k;��k®mvXcwlk

` kxwihITWj°²GweX�h jlTswlTWngyAXc` kxwenGXOýU]_�xf jAX{þp� Ä�à � ¹ jlTsmWf jlwlk�XOTsw~yAXwlkcV_fbtvuck{�xo�h�kcj}�qTW¬vTsw´o�º�fbw~y~]�²GmvXc` khITWVYX`p]�²GmWf Va`bXc` T}` T¶jlTvX�V_]_¬´XctvuckK` kxwQ��f jlkxwQyAX�n �qTWn�ylTsw|kcfz�f ]_ylkrh jl�s[p]_z�kxw|`bXETWz{h�TWnGXr` T¶f z�Ts`p]����amW]akE��]_¬s]��n �bk � � kcz�k��|��ücmW]_Vp` T¶mskcz{h jlTsTWnb` TWjvoqkR��f nbmW]akcnGX�z�TWngylkK` T¸yAX�]awQh�TWj°²GwQwlTWjAüEwlTWz{h jlT¸z�TWnbkxw2Xc` Tsd�fGXc` k` k�dgfbT·kE` T¸h�TWj°²GwU]_nbmskcj~h�kcjAXc` kxw£nGXehGX�jlTs` TiXRmskcnbw~y~j~f ]_jvochITWVakEd�fbT¸wAT¸mskcnbw~]a` TWjAXEyAX�VpT\[�hITs`p]aTWngylTiX�V_yAX��z�TWngylTr` TswAXcmskcnbwATWV_�Güs�qTWVÊo yAX�n�ylkMz;X�]awihITWVak���XcmWylkO` TET\[p]aw~y~]_jlTWz XcmWy~fGX�V_z�TWngylTKTsd�f ]_hGX�z�TWngylkxwe` kcyAXc` kxw` TKmvX�jAXcmWylTWj~�aw~y~]amvXcw�Trz;X�nbkc^ jAX�^ ]_V_]a`bXc` T�hGX�jAXOjlTvX�V_]_¬´X�jEkxwi��f jlkxwRnbkxw}Vak�mvX�]awEXc` TsdgfGXc` kxwv� � �GX�z;X���wlT�XX�ylTWnbtvuckOhGX�jAXOk��ÊXcmWylkO` TEyAX�zM^��Wz±kxw¶hITWj°²Gw·jlTWh jlTswATWngyAXc` kxw}nGXMýQ]_�xf jAXOþp� Ä�à T\[p]_^ ]_jlTWz X�V_�xf nbw}w~]_nGX�]aw` T?TWnbmWf j~�xXc`pf jAXp�

ÀEz;X}kcf y~jAXijAX�¬´uck}hGX�jAXRwlT2TW��]_yAX�jUTsw~yAXiwlkcV_fbtvuckR�|Xiz;X�]akcjUT\[�hIkxw~]atvuck}` kxwûhITWj°²Gw.XckxwûTsd�f ]_hGX�z�TWngylkxwTiz;X�ylTWj~]YX�]aw¶dgfbT}mW]_jlmWf VYX�z�nbkr]_ngylTWj~]akcji`bXrTswlmvXs�xXctvuck o�kKd�fbTxogTWzÁmvXcwAk?` Ti]_z{hGXcmWylk oghIk�` TWjAürh jlkv�qk�mvX�j`bX�nbkxweTK`p]_z{]_n�f ]_j�XmvX�hGXcmW]a`bXc` TM` kxwRhITWj°²Gw}hGX�jAX�XOy~jAX�nbw~z{]awlw�uck�` TKmvX�j~�gXcwR�qTWj~y~]amvX�]awv�

¿&h jlkch��xw~]_ylk{` TswlylTrXcwlh�TsmWylk opjlT\��TWjlTWz��wlT?X�]_nb`bXkxwi]_z{hGXcmWylkxwe` kxw}Tsd�f ]_hGX�z�TWngylkxwE` TrTswlmvXs�xXctvuck�T` TOjlTWz�k�tvuck«` TOylTWj~jAXcwvo:mskcz/Tsw~hITsmW]YX�VQ$Wnp��XcwATMhGX�jAXàkxwrh j~]_z�TW]_jlkxwvo:d�fbTOnbTsmsTswlw~]_yAX�z/` TOf z;Xà�xjAX�nb` Th jlks[p]_z{]a`bXc` T�Xckxw¶hITWj°²Gw¶TrwAuck o�hIkcj~yAX�ngylk o w~fbwAmsTWh y~�_�qTW]aw}` TEV_�bTsw}mvX�fbw�X�j¶]_z{hIkcj~yAX�ngylTswe`bX�nbkxwvo�z�Tsw~z�kd�fGX�nb` k?yAX�]aw·h�TWj°²Gw¸nGuck�wAuck?T\[pylTWj~]akcjlTsw}­rhGX�jlTs` TrXKmskcnbw~y~j~f ]_jv�Q\|w~ylT�Xcw~hITsmWylk��R` TehGX�j~y~]amWf VYX�j·]_z{hIkcj°�yAÿ�nbmW]YX?`bXc`bX�Xrh�kcy%$WnbmW]YX�` kxw¸Tsd�f ]_hGX�z�TWngylkxwid�fbTxoq�bk�º~TRTWz `p]YXpogTswlyAuck?`p]aw~hIkcn �_�qTW]aw¸hGX�jAX?XKjlTvX�V_]_¬´Xctvuck`bX®TswlmvXs�xXctvuck oIwlTWnb` k®X�]_nb`bX;jlTWVYX�y~]_�cX�z�TWn�ylTO��jlTsd�fbTWngylTOkc^bwlTWj~�xX�j°��wlTMh�TWj°²Gw�mskcz�` T\��kcj~z;Xcts¯�Tsw�` TMyAX�V��kcj~z;X{w~]_�xn ]�²GmvX�y~]_�xXcwed�fbTKkxw}ylkcj~nGX�z'mskcz{h VaTWyAX�z�TWngylTM]_nbT\²GmvX�¬vTswv�6rTKf z;X{��kcj~z;X�qTWjAX�VÊo�X�T\[ TsmWfbtvuck;` TKf z;X;kc^ jAX{` Tsw~ylT�y~]_h�k�ÊX�¬W��wlT?mskcz'z;X�]akcjlTswEmWf ]a`bXc` kxwEnGXcw

h jlks[p]_z{]a`bXc` Tswi` kxw¸Ts`p]����amW]akxw¸T}nbkxw¸h j~]_z�TW]_jlkxw¸n �_�qTW]aw¶` TRTswlmvXv�cXctvuck o�TWzÁhGX�j~y~]amWf VYX�j¶nbk?d�fbT}jlTsw~hITW]_yAX�­`p]_z�TWnbwAuck{`bXcw·��jlTWngylTsw}TswlmvXv�cXc`bXcwRkcf«Xckxwi]_ngylTWj~�xX�VakxwR` T�ylTWz{hIkOTWz±d�fbTETswlyAXcwih�TWj~z;X�nbTsmsTWz'X�^ITWj~yAXcwwlTWz�dgfbTOX{^ITWylkcnGX��qTWz¦wAT?jlTvX�V_]_¬vTx�e¿�Xc` kchItvuck®` TswlyAXcwez�Ts`p]a`bXcw�nGXcwEh j~]_z�TW]_jAXcwe�ÊXcwlTsw�`bX�kc^ jAX®Tsw~yAü

Page 27: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â þXZ

ýQ]_�xf jAX�þp� Ä�Ã4� SQTWj°²GweT\[pylTWj~]akcjlTswemskcz5X�V_�xf nbwew~]_nGX�]awR` T?TWnbmWf j~�xXc`pf jAXpobn�f z;X{kc^ jAX{TWzHß:]awl^�kqXp�nGX�y~f jAX�V_z�TWngylT?jlTWVYXcmW]akcnGXc`bXmskcz XMz;X�]akcj}h jlks[p]_z{]a`bXc` T?`bXcw·��f nb`bXcts¯�Tsw}` kxw}Ts`p]����amW]akxwi��]_¬s]_n �bkxw´o�mskczf z z�TWnbkcj�mskcn �bTsmW]_z�TWngylk<`bXcw{mskcnb`p]ats¯�Tsw�` kªylTWj~jlTWnbk6T«mskcz�X���jlTsdgfbTWn�ylT�k�mskcj~j%$WnbmW]YXªw~f h�TWj°²GmW]YX�V` Tn �_�qTW]aw?` T�X�ylTWj~jlk«kcf ` T{wlkcVakxw?` Tswlmskcz{h j~]_z{]a` kxw´oUX�T\[p]_�x]_jlTWz!Tsw~h�TsmW]YX�V¸X�ylTWnbtvuck � � kcz!k«TW�qkcV_f ]_j`bX6kc^ jAX6T�mskcz X6z�TWV_�bkcj~]YX `bXcw;mvX�jAXcmWylTWj~�awly~]amvXcw®` kxw�wAkcVakxw;d�fbT«wlT��cX�]Êo¶jlTW�xjAXª�qTWjAX�VÊo¶�qTWj~]�²GmvX�nb` k­©z�Ts`p]a`bXªdgfbT«XªTswlmvXv�cXctvuckªh jlkc�xj~]a` Txo·�Gü6X¾ylTWnb`#$WnbmW]YXpoiX�V_]Yücw{mskcz{h jlTsTWnbwl�_�qTWVÊo·hGX�jAX©]_j�X�VYX�j~�gX�nb` kXcw��jlTWn�ylTsw�` T�TswlmvXv�cXctvuck o¶TWz hGX�j~y~]amWf VYX�j;nGXcw�¬vkcnGXcw{z;X�]aw;X��ÊXcw~yAXc`bXcw�` kxw�Ts`p]����amW]akxw{��]_¬s]_n �bkxwvo·wAkc^h jlTWylT\[�ylk�` TOz�TWV_�bkcjlTswKmskcnb`p]ats¯�TswK` k®ylTWj~jlTWnbk�TOz�TWV_�bkcjrmskcn �bTsmW]_z�TWn�ylk�` Tsw~ylTx�K�ruck;nbTW�gX�nb` k�Tsw~ylTsw��XcmWylkxwvopmA�GX�z;X���wlT�nbkOTWn�yAX�ngylk�XOX�ylTWnbtvuckhGX�jAX�d�fbTrXMwl]_y~fGXctvuckOmskcnb`p]amW]akcnGX�n�ylT?wlkc^�k�hIkcngylk` TE��]awlyAX` k?Tsdgf ]_V_�_^ j~]ak?�qTWj~y~]amvX�V��xoqh jlTsmW]aw�X�z�TWngylTxo X�» V_y~]_z;Xr�ÊXcwlT}` TRTswlmvXv�cXctvuck o�TWz d�fbTeXKXcmstvuck?�qTWj~y~]amvX�VbylkcyAX�VylTWz!k®�xX�Vakcjrz;X�]aw?TWVaTW�xXc` k oû`bXc` k�dgfbTOylk�`bXcw?Xcw?X�nbmskcjAX��qTWnbw�Tsw~yAuckMºlü;jlTvX�V_]_¬´Xc`bXcw�TXàhGX�jlTs` T{TswlyAüpoTWz �xjAX�nb` TKhGX�j~ylTxobT\[ TsmWf yAXc`bXp�

Àez T\[ TWz{h Vak6TWz dgfbT�Tsw~ylT�h jlk�msTs`p]_z�TWngylk ylTW�qT��xjAXs�qTsw�mskcnbwlTsd�f4$WnbmW]YXcw��kc]}k6dgfbT�k�mskcj~jlTWfÑnbk]_n �amW]akM`bX�` �smvXc`bX�` T?b��po�TWzZß:]aw~^IkqXp�£SQX�jAXOXKjlTvX�V_]_¬´Xctvuck` k?n �_�qTWVI` TeTswAmvXs�xXctvuckOX�dgfbTEmskcj~jlTsw~h�kcnb`p]YXX6h jlk���f nb`p]a`bXc` T©` T ÂvÄ z���kc]�T\[pTsmWf yAXc` k�]_n ]amW]YX�V_z�TWngylT X�hITWnGXcw®f z hGX�]_nbTWVr` T�mvX�n�ylk oRylTWnb` k<TWzwlTW�xf ]a`bX;wl]a` k�jlTvX�V_]_¬´Xc`bX;ylk�`bX®X{jlTsw~yAX�n�ylTMTswlmvXv�cXctvuck oITWz5ylk�`bX®X�T\[pylTWnbwAuck;` T�f z�` kxwrX�VatvXc` kxwvoIX�yl�Xck;kcf y~jlk;mvX�n�ylk �R¿ÁX��xjAXs�xX�jETswlylT�mskcz{hIkcj~yAX�z�TWngylk oûX{kc^ jAX®Tsw~yAXs�xX;X;wlTWjRjlTvX�V_]_¬´Xc`bX;nGuck�jlTsmskcj~jlTWnb` k­f y~]_V_]_¬´Xctvuck;` TKhITWj°²GwR�qTWj~y~]amvX�]aw´obhITWVak�dgfbTxobnGXjlT\��TWj~]a`bX�hGX�jlTs` TxoGTWjAX�X�hITWnGXcwEX{jlTsw~]aw~y%$WnbmW]YX�Xck�mskcj~ylT`bX{]_ngylTWj°�ÊXcmsTOh�kxwlylTWj~]akcj�X®w~f h�kcj~yAX�jEylk�`bX®X�mvX�j~�gX;�qTWj~y~]amvX�V£X�h V_]amvXc`bXp� � kcz�k;jlTswlf V_yAXc` k o�k�mskcj~jlTWf©nbkX�VatvXc` k�TWz'mvX�fbwAX{k{mskcVYX�hbwAk�`bXTswlmvXs�xXctvuck¾��ýQ]_�xf jAX�þp� Ä 7q�\�

¿ k�mskcj~j%$WnbmW]YXª` Tà` TswlVak�mvX�z�TWn�ylkxw{]_z{h�kcj~yAX�n�ylTswvo|hGX�jAX6X�Va�Wz ` Tàh jlkv�qk�mvX�j�`bX�nbkxw{w~]_�xn ]�²GmvX�y~]_�qkxw

Page 28: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 þ�b Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

ýQ]_�xf jAX«þp� Ä 7 � �Ekcy~f jAX®�qTWj~y~]amvX�V|` TMhGX�jlTs` T{` Tmskcn�ylTWnbtvuck�y~]_h�kCÛiTWj~V_]_z!` T\²bn ]_y~]_�cXpoûnGuck�X�hIkc]YXc`bX�TWzhITWj°²Gw}z�TWyAü�V_]amskxwv�

nGXcw¶Tsw~y~j~f y~f jAXcw¸��]_¬s]_n �GXcwvo�h�k�` TeX�]_nb`bX�]_z{h V_]amvX�jiXKjlkcy~f jAX�` TEwlTWj~��]atskxw´ogmskcz�kMh�kcj¸T\[ TWz{h VakOmskcnb`pf yAXcw` T�ü��xfGXªkcf Tsw~�qkcylkªd�fbTxo¸wlTWnb` k6` T«TWVaTW�xXc`bXª`p]_z�TWnbwAuck o·h jlkv�qk�dgfbTWz f z T\[ msTswlw~]_�qk X�f z�TWn�ylk `bXcwh jlTswlwl¯�Tswwlkc^ jlT«X¾hGX�jlTs` Tx� ã�kªmvXcwlkª`bX¾kc^ jAX©d�fbT�wlTàX�h jlTswATWngyAX©nGX©ýQ]_�xf jAX6þp� Ä þ¾d�fbTxo|mskcnp��kcj~z�TwlTMh�k�` TOkc^bwlTWj~�cX�jvoIjlTswlf V_ylkcf©nbk«XcmW]a` TWn�ylT^�TWz���]awl�_�qTWVQnGX���kcylkc�xjAX�²�Xp�?��uck�wlTMhIk�` TX�²bj~z;X�jKdgfbTkh jlkc^ VaTWz;X©`bX�Tsw~yAX�^ ]_V_]a`bXc` T®�qTWj~y~]amvX�ViylTWn �GX�wl]a` k�k«�ÊXcmWylkcjMd�fbT�z;X�]awmskcn�y~j~]_^ f ]_f<hGX�jAX¾X�jlkcy~f jAX¾`bXTsw~y~j~f y~f jAX{` T�mskcngylTWnbtvuck oxº°f V_�gX�nb` k���wlT?d�fbT?`p]_�qTWjlwlkxw}��XcmWylkcjlTsweylTWjAuck�mskcngy~j~]_^ f �a` k;hGX�jAX{k;XcmW]a` TWngylTx�

¿ÀmvX�fbwAX�`p]_jlTsmWyAX�` k¾XcmW]a` TWn�ylT���kc]ÊoQmskcz�k�wlT{jlT\��TWj~]_fûoQk�]_nbmWjlTWz�TWngylk©` T�h jlTswAwl¯�TswMmvX�fbwAXc` k�hITWVYXü��xfGX©X�h��xwX�jlkcy~f jAX¾`bX¾mskcnb`pf yAXp�¾³Uk�` kªk�h jlk�msTswlwlk¾` T;jlkcy~f jAX©` Tsmskcj~jlTWfÑTWzähIkcfbmsk¾z;X�]awO` T � �z{]_ngf ylkxw´ogylTWnb` k�XKhGX�j~y~]amWf VYX�j~]a`bXc` Te` T}ylTWj¸wl]a` k?Xcwlw~]aw~y~]a` kKhIkcj2f z�\2n �qTWn �bTW]_jlk � ]_��]_VÊo�dgfbTekK` TswlmWjlTW�qT`bXKwlTW�xf ]_n�ylT}��kcj~z;X � jlkcy~f jAX?` kK^ITWyAuckKnbkxw|hGX�]_nb�W]aw·]_np��TWj~]akcjlTswvoq]_nbmWV_f ]_nb` kX�jlkcy~f jAXKhIkcj|h f nbtskqX�z�TWngylk`bXcw}X�nbmskcjAX��qTWnbwY"ph jlkchGX��gXctvuck`bXMjlkcy~f jAX�` kO^ITWyAuckOX�j~z;Xc` kOhGX�jAXMkxw·hGX�]_nb�W]awiw~f hITWj~]akcjlTswY"�jlkcy~f jAXO`bXcwTswlmskcjAXcwK` T{mvX�n�ylk�nGXcwKV_]_�gXcts¯�Tsw?Xck�^ITWyAuck#":jlkcy~f jAX«` kà^ITWyAuck�nGX®¬vkcnGX�` Tf z�hITWj°²bV2z�TWyAü�V_]amsk o.d�fbTxoV_]_^ITWj~ylk{` kOmskcnp²bnGX�z�TWn�ylk oGTWnbmWf j~�xXOhGX�jAXkO]_ngylTWj~]akcje`bXOTswlmvXv�cXctvuck obwAkc^«XXcmstvuck{`bXcw}mvX�j~�gXcwRd�fbTrw~fp�hIkcj~yAXs�xX�"�jlkcy~f jAXM` TEX�V_�xf z;XcwiX�nbmskcjAX��qTWnbwY"ph jlkc�xjlTswlw�uck�w~fbmsTswlwl]_�cX�`bXr��TWnb`p]_V_�GXctvuckM` k�^�TWyAuckX�j~z;Xc` k o` T?wlTW�xf nb` k®XwlTW�xf nb` k oGX�^ITWj~y~f jAX{` Tr��TWnb`bXO�qTWj~y~]amvX�VUTWz ylk�`bX{X{X�V_y~f jAX�`bXOhGX�jlTs` Txo�mskcnb`pf ¬s]_nb` k®XckmskcVYX�hbwlk�mskcz{h VaTWylk �

Page 29: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â þ l

ýQ]_�xf jAX�þp� Ä þ � \|w~y~j~f y~f jAX;` TKmskcngylTWnbtvuck®y~]_h�kêÛiTWj~V_]_z5X�hI�xw}jlkcy~f jAXp��ETswlyAXK²b�xf jAXO�E]_�xfGX�V_z�TWngylTr��]aw~�_�qTWV�kMz�k�` k` TEjlkcy~f jAXpopdgfbT�TW��]a` TWnbmW]YXXMk�mskcj~j%$WnbmW]YXO` T�` Tsw~Vak�mvX��

z�TWngylkxw¶�qTWj~y~]amvX�]aw¶Xcmskcz{hGX�n �GXc` kxwi` TE` Tsw~Vak�mvX�z�TWn�ylkxw¶�bkcj~]_¬vkcngyAX�]awvopwlTWnb` kMTsw~ylTsw|» V_y~]_z�kxw·z;X�]akcjlTswiTWzh jlk���f nb`p]a`bXc` TK` kd�fbTeh jl�v[�]_z�k{`bXOw~f hITWj°���amW]aTx� ¹ ^bwATWj~�cXctvuckwlTWz�TWV_�GX�n�ylTrh�k�` TR�ÊX�¬vTWj°��wlTKX�h jlkch��xw~]_ylk`bX{ýQ]_�xf jAX�þp� Ä 7p�

ÊPØ!ÔM�ÚÙÚÔ���Ñ!Ò Ó(ÒMÕ�ÒR����Ò©ÖAÐ�ÔM�­Î�Û=Ð�Ò���Ò©Ö$اÙÚÔMÛ Í�����Ö#ÙÚÕ�Ô�ETswlyAX�wlTsmstvuck¾` TswlmWjlTW�qT\��wlTàk«�ÊXcwlTvX�z�TWngylkªT®X�h jlTswATWngyAX���wlTàkxw�jlTswlf V_yAXc` kxwM`bX�z�k�` TWVYXctvuck©` T;Tsw~�

y~j~f y~f jAXcw¶` T�mskcngylTWnbtvucky~]_hIk{ÛiTWj~V_]_z±` T\²bn ]_y~]_�xXcwvopmskcz ` Tsw~yAXcd�fbTEhGX�jAX�k�z�TsmvX�n ]aw~z�k` TEmskcVYX�hbwlkMhIkcjh�TWjl`bX{` TKTsd�f ]_V_�_^ j~]ak��qTWj~y~]amvX�VÊ�

SQX�jAX;X�fp[�]_V_]YX�jRXO` TswlmWj~]atvuck{`bXcw}`p]_�qTWjlwAXcw¶�ÊXcwlTswimskcnbw~y~j~f y~]_�xXcwvo mskcnbw~]a` TWjlT\��wlTKkOTswld�fbTWz;X�y~]amvX�z�TWngylTX�h jlTswlTWngyAXc` k;nGX{ýQ]_�xf jAX�þp� Ä ZT?XwlTsd�f4$WnbmW]YX{d�fbTKwlTr]_nb`p]amvX�TWz wlTW�xf ]a`bX �

! �ÊXcwlT����®mvü�VamWf Vak�`bXcw}ylTWnbwA¯�Tsw}]_n ]amW]YX�]aw�"! �ÊXcwlT  ��TswlmvXv�cXctvuck�]_n ]amW]YX�VphGX�jAXKXemskcnbwly~j~fbtvuckK`bXe��]_�gXE` T¶mskcjlkqX�z�TWn�ylk;��jlTWy~]_jAXc`bXr` T¶TWVaTWz�TWngylkxw` T?wlkcVakg�¶T?]_nbw~yAX�VYXctvuck�` kxw}hITWj°²Gw}z�TWyAü�V_]amskxwE�qTWj~y~]amvX�]aw �

� Tsw~ylTsw;h�TWj°²Gw{z�TWyAü�V_]amskxw;]_n ]amW]YX�V_z�TWngylT¾]_nbw~yAX�VYXc` kxw�y%$Wz XªjlTsw~]aw~y%$WnbmW]YX6`bXc`bX6h�TWVYXªylTWnbw�uck` TmsTs`#$WnbmW]YXàz��s`p]YX��"���ÁTX�j~]_�x]a` TW¬;X�[p]YX�VUjlTvX�V���G�".X;ylTWnbwAuck�` TmsTs`#$WnbmW]YX®z��s`p]YXànGuckmskcnbw~]a` TWjAXpopnbTsw~yAX?�ÊXcwlTxo�XMhIkxwlw~]_^ ]_V_]a`bXc` T�` TETWnbmWf j~�xXc`pf jAX` kMh�TWj°²bVÊo�f z;XM�qTW¬�d�fbT�Tsw~ylTEwATTWnbmskcngy~jAX®mskcnp²bnGXc` k#"

� kxwihITWj°²Gw}wAuckMwl]_z�f VYXc` kxw}hIkcjif z;XMwATsdgf4$WnbmW]YX` TrTWVaTWz�TWngylkxwR^GX�j~jAXOnGXM`p]_jlTsmstvuck�qTWj~y~]amvX�VÊowlTWnb` k�kn�» z�TWjlk;` TK^GX�j~jAXcwR]_�xfGX�VUXck{ng» z�TWjlk®` T���XcwATswR` TKTswlmvXs�xXctvuck#"

Page 30: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 Z�� Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

��Xq�¸�ÊXcwlT�� �J�R�{���������

�;�����������y  ¡;¢¤£{¥�¦�§�¨|©

¡;¨�£�¥�¦�§�¨|ª «E¬®­L¬%¯�°�±}²

«J³´­L¬%¯�°�±yµ ¶J·R¸{¹�º�»�¼y½

¶J¾J¸L¹%º�»�¼y¿ ÀÂÁ�ÃLÄ%Å�Æ�ÇyÈ

É�Ê#Ë�Ì�Í ÅÏÎ>Ð�ÑHÒÔÓ6Õ)Ç®Ö Í ÇxÆ�Ç®×HØ�Å�ÙwÚ�ÛÜÇxÆ�Ý Ì Ç®Þàß"Ø Ê+á ÅàâMÅãÞãÛÔâ�Ç®äåÅ�ÙwÚ�ÛÜâMÅ�Æ2Ä%Å�Æ�ÇxÆ á Û�×MÆ�Ø Í�Ì Ø Ê#æ Å�Æ�â�Ç Ì ÞàÅãÖçÅ Í Çxâ�Çâ�Ç á Û�×ÔØ�Ç®×MÙwÚ�ÛãØ Ê ÖèÛêé�Ç Í ä Ê ÞëÐ

ì Û�Æ}Å"ÖèÛ Ê Û�Æ Í Ç®Ö Í ÇxÆ�Ç®×HØ�Å�â�Û�Æ}×çÅ�Æ�í Ë�Ì�Í Å�Æ Í ÇxÆ�Ø Í�Ê × Ë Ç®ÞGÛ�Æ|â�ÇxÆ�ä+Û á Å"ÞãÇ®×HØ�Û�ÆyîMÛ Í�Ê#ï Û�×HØ�Å Ê ÆyÇ�Æ�Ú�Û×MÇ á ÇxÆ�Æ�ß Í�Ê Û�Æ0ÖèÇ®ä+Û�Ä�Å á Ø�Ûàâ�Ç}Û�Æ0Ç®ä+Ç®ÞãÇ®×HØ�Û�Æ)ðçÅ Í�Í ÅãÅ"ÖèÇ®×çÅ�Æ2Ø Í Å"×MÆ�Þ Ê Ø Ê#Í Ç®ÞñÇxÆ�Ä;Û Í ÙxÛê×MÛ Í ÞàÅ"ä%ò

ì ÛàÇ®ä+Ç®ÞãÇ®×HØ�ÛãðçÅ Í�Í Å Ê ×>Ä;Ç Í�Ê Û Í Æ Ê Þ Ì äåÅãÅ�Æ á Å Í Å á Ø�Ç Í�ó Æ�Ø Ê+á Å�Æ)âMÅ�Ä Ì ×MâMÅ�ÙwÚ�Û�ò

Page 31: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â Z Â

� k�TWVaTWz�TWn�ylk�]_np��TWj~]akcje�rf n ]a` k;Xf z±hIkcngylk�d�fbTxo nbTsw~yAXM�ÊXcwlTxo �r² [ k#"� kxw£TWVaTWz�TWngylkxw2^GX�j~jAX�wAuck oqXcwAw~]_z�o�nbTsw~yAXe��XcwlTxocmskcz{h VaTWyAX�z�TWn�ylT}]_nb` TWh�TWnb` TWn�ylTsw|`bXEjlTsw~yAX�ngylTz;X�V_�GX©` T®TWVaTWz�TWn�ylkxwO²bn ]_ylkxwY"|nGuck©wlTàmskcnbw~]a` TWjAXpo£]_�xfGX�V_z�TWngylTxo·dgfGX�Vad�fbTWjT\��TW]_ylk©`bX�wlfGX]_nbw~yAX�VYXctvuck#"

! �ÊXcwlT Ä �;^ITWylkcnGX��qTWz'`bX��]_�gX` T?mskcjlkqX�z�TWngylk �� mskcVak�mvXctvuckM` TRTWVaTWz�TWn�ylkxwUº�f n�yAXK�bkcj~]_¬vkcngyAX�]aw¶nbkr��f y~f jlk�mskcn�yAXcmWylkM`bXK��]_�gXK` TEmskcjlkqX�z�TWngylkmskcz5X{wlf h�TWj°���amW]aTK` kylTWj~jlTWnbk;TswlmvXv�cXc` k#"� X�h V_]amvXctvuck�`bXcw·mvX�j~�gXcw|�qTWj~y~]amvX�]aw·` TW��]a`bXcw¸Xck?h�TswlkK`bXK��]_�gXK` T}mskcjlkqX�z�TWn�ylk�nbkxw¸TWVaTWz�TWngylkxwº°f ngyAX�"GTswlylTswRTWVaTWz�TWngylkxw|º�f n�yAXnGuck{y%$Wz'd�fGX�VadgfbTWjeV_]_�gXctvuck;Xckxw}hITWj°²Gw}z�TWyAü�V_]amskxwY"

� X�hITswAX�j�` Txo|nGX©z;X�]akcj{hGX�j~ylT«` kxw{mvXcwlkxw´o·XªX�h V_]amvXctvuck `bXcw�mvX�j~�gXcw{` TW��]a`bXcw;XckªhITswlkª`bX��]_�gX�nGuck�ylTWj?�xjAX�nb` T{]_npZbf4$WnbmW]YX�nbkxw?` Tsw~Vak�mvX�z�TWngylkxwOTxo:h�kcj~yAX�n�ylk oUTswlylT{T\��TW]_ylk«nGuck�ylTWjvonbTsw~yAX«��XcwlTxoUmskcnbwlTsd�f4$WnbmW]YXcwMw~]_�xn ]�²GmvX�y~]_�xXcwOmskcnbw~]a` TWjAX���wlTxo2X�hGX�j~y~]_jM` TswlyAXà��XcwATxoQX�X�h V_]amvX��tvuck«` T` Tsw~Vak�mvX�z�TWngylkxwMXckànb�à]_np��TWj~]akcj?` kxwKTWVaTWz�TWngylkxw?^GX�j~jAX®]_�xfGX�]aw�XckxwKd�fbTkànb�àmskczmsk�kcjl` TWnGXc`bXcwez;X�]aw}h jl�v[�]_z;XcwE` k{ylTWj~jlTWnbk�wlk���jlTWjY"

� nbTWn �gf z�mvX�j~jlTW�gX�z�TWngylk®�xopnbkOTWn�yAX�ngylk o�X�h V_]amvXc` k;Xckxw}hITWj°²Gwiz�TWyAü�V_]amskxwvo f z;XO�qTW¬?d�fbT�wATh jlTWylTWnb` T�wl]_z�f VYX�jEXO^ITWylkcnGX��qTWz�obTWz d�fbTKk^�TWyAuckO��jlTswlmsk{�KmskcVak�mvXc` k{TWz'mskcngyAXcmWylk�mskczkxw}hITWj°²Gw}z;XcwRnbTWn ��f z;X�mvX�j~�gXV_�bTswe�Ky~jAX�nbw~z{]_y~]a`bX�"

! �ÊXcwlT � �;h jlTswAX` k{^ITWyAuck�`bXO��]_�gX` T?mskcjlkqX�z�TWngylk �� ]_nbw~yAX�VYXctvuck�` kxw}TWVaTWz�TWn�ylkxwe^ ]a`p]_z�TWnbwl]akcnGX�]awed�fbT�wl]_z�f VYX�z5XM��]_�gXTK` kxw}TWVaTWz�TWngylkxw2º°f ngyAX�qTWj~y~]amvX�]aw�dgfbT¾w~]_z�f VYX�z�k�mskcn�yAXcmWylk�TWn�y~jlT©X ��]_�gX�T¾X�w~f h�TWj°���amW]aT��qTWj~y~]amvX�Vr` k ylTWj~jlTWnbkTswlmvXv�cXc` k#"�kxw2TWVaTWz�TWngylkxw|^ ]a`p]_z�TWnbwl]akcnGX�]aw2nGuckry%$Wz1h�Tswlk ocf z;X��qTW¬Rd�fbT}Xcw£mvX�j~�gXcw|` TW��]a`bXcwXck{hITswlkO��kcjAX�z1º~ü{X�h V_]amvXc`bXcw�` T���kcj~z;X{]_nb` TWh�TWnb` TWn�ylT?nGXO�ÊXcwlT Ä "

� X;hGX�j~y~]_j�` Tsw~yAX{��XcwATMX{��]_�gX®` T�mskcjlkqX�z�TWngylkà²GmvX;wlkcV_]a`bX�j~]_¬´Xc`bXàmskcz�kxwEhITWj°²Gwez�TWyAü�V_]amskxwY"hGX�jAXw~]_zMf VYX�jekmskcngyAXcmWylk{jlTsmskcj~jlT\��wlT?XMf z;XO^GX�j~jAX` T��xjAX�nb` TKj~]_�x]a` TW¬?T�jlTsw~]aw~y%$WnbmW]YXOz;Xcw` T;mskcz{h j~]_z�TWn�ylk©z�f ]_ylk¾h�Tsd�fbTWnbk#"2Tsw~yAX«^GX�j~jAX�nGuck�ylTWz�oQnbTsw~ylT�mvXcwAk oQd�fGX�Vad�fbTWjMT\��TW]_ylk of z;X;�qTW¬Od�fbT�wlTWjAü�jlTWy~]_jAXc`bX®nGX{�ÊXcwlT?mskcnbw~y~j~f y~]_�xX®wlTW�xf ]_ngylTT?nGuck®�GüàX�]_nb`bX®X�nbmskcjAX��qTWnbw]_nbw~yAX�VYXc`bXcwY"Unbk�TWn�yAX�ngylk oUh�kcj?w~]_z{h V_]amW]a`bXc` T®kch ylkcfp��wlThIkcjKfbwAX�j?T\[ XcmWyAX�z�TWn�ylT;k�z�Tsw~z�kh jlk�msTs`p]_z�TWngylk6d�fbT;wlT®f y~]_V_]_¬´X�jAü�nGX��ÊXcwlT®þpo£nGX�dgfGX�V¶�GXs�qTWjAü©mvX�j~�gX��qTWj~y~]amvX�Vi` TW��]a`bX©Xckh j~]_z�TW]_jlk�n �_�qTWVU` T�X�nbmskcjAX��qTWnbwY"

! �ÊXcwlT à �iQxô��ÊXcwlTK` TKTswlmvXs�xXctvuck �� X�^GX�j~jAX�` TEh�Tsd�fbTWnbkOmskcz{h j~]_z�TWngylk{Te` T�TWVaTW�xXc`bX?j~]_�x]a` TW¬qo Xcwlw~]_zÀmskcz�kXK^GX�j~jAXOw~f hITWj~]akcj` k hITWj°²bVe]_n ]amW]YX�V_z�TWn�ylT©]_nbw~yAX�VYXc`bX wAuck�jlTWy~]_jAXc`bXcw®T¾w~f ^bw~y~]_y~f �a`bXcw®h�kcj;f z;X6^GX�j~jAX mskczmskcz{hIkcj~yAX�z�TWngylkÑTWVYücw~y~]amsk�h�TWj°��TW]_yAX�z�TWngylT©h VYücw~y~]amsk<mWfcºlX mvX�j~�gX�V_]_z{]_ylT©�©X mvX�hGXcmW]a`bXc` TjlTsw~]aw~ylTWn�ylT6­�TWnbmWf j~�xXc`pf jAX�"?Xck�z�Tswlz�k�ylTWz{hIk<X�y~j~]_^ f ]���wATª­ nbkv�xX�^GX�j~jAX�k<Tsw~yAXc` k<` TylTWnbwAuck�`bX{^GX�j~jAX]_n ]amW]YX�V_z�TWngylTOT\[�]awlylTWngylT�"

� h jlk�msTs` T\��wlT©X�]_nb`bX nbTsw~yAXª�ÊXcwlT�­ TswlmvXs�xXctvuck�` k n �_�qTWV�wlTW�xf ]_n�ylTxo}k�d�fbT�wlT«y~jAXc`pf ¬©hITWVYXjlTWy~]_jAXc`bX®` T�TWVaTWz�TWngylkxwr` TMwlkcVak;TM` kxweTWVaTWz�TWngylkxwK` TRº�f n�yAX{�bkcj~]_¬vkcn�yAX�]awY"ITsw~yAX�TswlmvXv�cXctvuck` TW�qTWjAü{h jlk´�qk�mvX�j�Xy~jAX�nbw~z{]awlwAuck{` T�mvX�j~�gXcwR�qTWj~y~]amvX�]awEXckhITWj°²bVûz�TWyAü�V_]amsk#"

Page 32: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 Z Ä Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

! �ÊXcwlT�7õ�®^ITWylkcnGX��qTWz'` k�Qt�KhGX�]_nbTWV �� ]_nbwlyAX�VYXctvuck®` TOTWVaTWz�TWngylkxw·º°f ngyAX;�bkcj~]_¬vkcngyAX�]aw�nbk®mskcn�yAXcmWylk®` kSQ � hGX�]_nbTWV£`bX{hGX�jlTs` TOmskczX�w~f h�TWj°���amW]aTr�bkcj~]_¬vkcngyAX�VQ` k{ylTWj~jlTWnbk�TswlmvXv�cXc` k o�­wlTWz�TWV_�GX�nbtvX{` k�` TswAmWj~]_ylk{nGXO�ÊXcwlT Ä "� X�h V_]amvXctvuck;nbTsw~ylTswRTWVaTWz�TWn�ylkxw|º°f ngyAX{`bXcwemvX�j~�gXcwR�qTWj~y~]amvX�]awe` TW��]a`bXcwEXckhITswlk{` k{^ITWyAuck#"

! �ÊXcwlT?þõ�®h jlTsw�X` k{^�TWyAuck{` k&Qt�KhGX�]_nbTWV.T�X�h V_]amvXctvuck�` k{h jl�\��Tsw~��kcjltsk �� ]_nbwlyAX�VYXctvuckà` kxw�TWVaTWz�TWngylkxwK` TMhGX�jlTs` TOT�` kxwrTWVaTWz�TWngylkxw¶º°f ngyAX;�qTWj~y~]amvX�]awrdgfbTMw~]_z�f VYX�z/kmskcn�yAXcmWylk«TWngy~jlTk;wAkcVak®TX�w~f hITWj°���amW]aT��qTWj~y~]amvX�V2TswlmvXv�cXc`bX�":kxw�TWVaTWz�TWngylkxwr^ ]a`p]_z�TWnbw~]akcnGX�]awd�fbTw~]_z�f VYX�z X;hGX�jlTs` TnGuck�y%$Wz¦hITswlk oIf z;Xà�qTW¬{dgfbT{XcwKmvX�j~�gXcw?` TW��]a`bXcw?XàTsw~yAX�Xcmstvuck��kcjAX�z'mskcnbw~]a` TWjAXc`bXcwenGXO�ÊXcwlT?X�ngylTWj~]akcjY"

� X�^GX�j~jAX�d�fbTr��kc]û]_nbw~yAX�VYXc`bX;nGXO��XcwAT à �KjlTWy~]_jAXc`bX�":XV_]_�gXctvuck®`bX{hGX�jlTs` TOXckxwehITWj°²Gw}�ÊX�¬W��wlTX�y~jAXv�q�swi`bX?XcmWy~]_�cXctvuckM` TRf z;X?nbkv�xXK^GX�j~jAX?` TRh�Tsd�fbTWnbk�mskcz{h j~]_z�TWn�ylkOd�fbT}f nbT�XrhGX�jlTs` TXck�ylkch�k{` k{hITWj°²bV:]_n ]amW]YX�V_z�TWngylTM]_nbw~yAX�VYXc` k#"

� XcwemvX�j~�gXcwe` TW��]a`bXcweXck{h jl�\��Tsw°��kcjltsk�wAuck�X�h V_]amvXc`bXcw�X�y~jAXs�q�sw�` Trf z;XO��kcjltvX�mskcnbmsTWngy~jAXc`bX�"! �ÊXcwlTsw{ZàX l ��w~]_z{]_VYX�jlTsw�Xck®��XcwATvX�z�TWngylk�` TswlmWj~]_ylk�nGXcw��ÊXcwlTsw à X�þpo:hIk�` TWnb` kàjlTWhITWy~]_j°��wlThGX�jAXkcf y~jlkxwen �_�qTW]awe` TKTswlmvXv�cXctvuck o�mvXcwlk{T\[p]aw~yAX�z��S£X�jAXOz�TWV_�bkcj}mskcz{h jlTsTWnb` TWjek�h jlkc^ VaTWz;XTrkxw·��TWnb�cz�TWnbkxw}TWng�qkcV_��]a` kxwinbkOTsd�f ]_V_�_^ j~]akO�qTWj~y~]amvX�Vû`bXcw

hGX�jlTs` TswK` TOmskcngylTWnbtvuck«y~]_hIkHÛiTWj~V_]_z�oIVaTW�qkcfp��wlT{X®mvX�^�kàf z/Tsw~y~fb` k®ngf z��Wj~]amsk�d�fbTOwlTOX�h jlTswATWngyAX�TWzwlTW�xf ]a`bXp�

³.jAX�yAX���wlT{` TOf z;X�TswlmvXs�xXctvuck«w~]_z��Wy~j~]amvXpo:Tswld�fbTWz;X�y~]amvX�z�TWngylT;jlTWh jlTswlTWngyAXc`bX�nGXàýQ]_�xf jAX�þp� Ä bpoû` TÂYl zä` T�h jlk���f nb`p]a`bXc` TàT Ä ��zä` T�VYX�j~�xf jAXpo.jlTvX�V_]_¬´Xc`bX¾TWz!ylTWj~jlTWnbk¾X�j~�x]_VakxwAk�mskczäjlTsw~]awly%$WnbmW]YX�nGuck`pjlTWnGXc`bX®mskcnbw~yAX�ngylTTWz'h jlk���f nb`p]a`bXc` TxoImskcz5f z�msk�T\²GmW]aTWn�ylT` T?]_z{h f VawlkàTWz'jlTWhIkcfbwlk oRöà÷xoG` Tn�p�[Z�omskcz±f zÀh�TswAkM�qkcV_» z{]amsk o�øQop` T����0������� �Trmskcz kOn �_�qTWVI��jlTvü�y~]amsk�­Ow~f hITWj°���amW]aTx� � kcnbwl]a` TWjlkcfp��wlTrf zz���`pf Vak�` T¶` T\��kcj~z;X�^ ]_V_]a`bXc` T}nGuckr`pjlTWnGXc` k��úù�` TÉ������û(ù?T·f z;X�Xc` Tsw�uck�wAkcVak��ÊhGX�jlTs` T¶` T à �EµpSQXp� i kc^krz;XcmW]atskMX�j~�x]_VakxwAk?mskcnbw~]a` TWjlkcfp��wlTEdgfbT}T\[p]aw~y~]YX�f z Tsw~y~jAX�ylk�mskcz TWVaTW�cXc`bXcw·mvX�jAXcmWylTWj~�aw~y~]amvXcw·z�Tsmvÿ�n ]amvXcwv�

¿�hGX�jlTs` T2��kc]qmskcnbw~]a` TWjAXc`bX}mskcz �p� à �}z&` T|Tsw~hITswlw~f jAX¶T|kih jl�\��Tsw°��kcjltskR`bXcwQX�nbmskcjAX��qTWnbw:��kc]g` T\²bn ]a` khIkcj}��kcj~z;X;X{dgfbTMXcwRw~fGXcwemskcz{hIkcnbTWngylTswE�bkcj~]_¬vkcngyAX�]awrTsd�f ]_V_]_^ jAXcwlwlTWz�k�`p]YX��xjAX�z;X�wlTWz{]���TWz{h �_j~]amskà` T³.TWj~¬´X��x� ]�T�SQTsmlµÑhGX�jAX X�j~�x]_VYXcw;j~] º~Xcw;X `pf jAXcwvo·` T«��kcj~z;Xªy~jAX�hITW¬vkc]a`bX�VET«mskcz�ylTWnbwAuck6z;ü�[p]_z;X ` T�>ü[��øRý<� � kcnbw~]a` TWjAX�nb` k�XcwKX�nbmskcjAX��qTWnbwK]_nbmWV_]_nGXc`bXcw?X9R�T � oI`p]aw~y~j~]_^ f �a`bXcw?TWz 7;n �_�qTW]awvo:TXc`pz{]_y~]_nb` k ohIkcjMw~]_z{h V_]�²GmvXctvuck o¸f z;X�mvX�j~�gX�]a`#$Wngy~]amvX©TWz ylk�`bXcw{XcwX�nbmskcjAX��qTWnbwvo|�\��wlT®mskcnb`pf ¬s]a` kªX¾mvX�j~�gXcwOnGXcwX�nbmskcjAX��qTWnbw?` TRHþ��0���������S£X�jAX«Xcw?X�j~z;Xc`pf jAXcw?`bXcw?X�nbmskcjAX��qTWnbwr��kc]2mskcnbw~]a` TWjAXc`bX�f z;XàwlTsmstvuck«` TR�ü[�0����������2¿}`pz{]_y~]_fp��wlTKX�]_nb`bXOXMj~]_�x]a` TW¬KT\��TsmWy~]_�cXO`bXcw}X�nbmskcjAX��qTWnbwi]_�xfGX�V.X l �XW�`bX�j~]_�x]a` TW¬KylTs�cj~]amvX�"Tsw~yAX;jlTs`pfbtvuck���kc]Q]_ngy~jlk�`pf ¬s]a`bXàX�y~jAXv�q�swK`bX®X�V_ylTWjAXctvuck�` k®�cX�Vakcjr` k�z���`pf Vak�` T�TWVYXcw~y~]amW]a`bXc` T` k�Xctsk ohITWVak{dgfbT?k�xX�Vakcj}fbwAXc` k��kc]û` T��>ü Þêÿ]�/Q��n� Q��EÞ��������i f h�\xw°��wlTrd�fbT�kxwihITWj°²Gw¶�qTWj~y~]amvX�]awRTWjAX�z Ü?\�Û ÂvÄ �M` T?XctskýbT � þ��pobX��ÊXcw~yAXc` kxwvo TWzÀz��s`p]YXpo ` T  z�o

mskcz'wlTsmstvuck;` T���R��������� Trz���`pf Vak�` T?TWVYXcw~y~]amW]a`bXc` TM` T Äp ��jrS£Xp�¿+ýQ]_�xf jAX�þp� Ä br]_nbmWV_f ]�]_�xfGX�V_z�TWngylTEhGX�j~ylTe`bXrz;X�V_�GX�` TeTWVaTWz�TWn�ylkxw|²bn ]_ylkxw·f y~]_V_]_¬´Xc`bXKnbkxw·mvü�VamWf Vakxwv�

¿�w�z;X�V_�GXcwà` T�TWVaTWz�TWngylkxw®²bn ]_ylkxwàmskcz{h VaTWyAXcwvo}hGX�jAX�X w~]_y~fGXctvuck�]_n ]amW]YX�VET�hGX�jAX�X6» V_y~]_z;X6��XcwAT�` T

Page 33: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â Z �

10m 0.4m

19m

6m

���� ���������� ��������� ���� ���������� � ������ !#"$ � ����� %&'��(�����)+*-, �. ��/ � �0!1� (�23, ( *-,.547638-9':<; ���-!52�, ( *-,

ýQ]_�xf jAX�þp� Ä b � jKTskcz�TWy~j~]YX{` k�mvXcwlk{` T?Tswly~fb` k�Trh jlkch j~]aTs`bXc` TswE` kxwRz;X�ylTWj~]YX�]awv�TswlmvXs�xXctvuck ogwAuckKX�h jlTswlTWn�yAXc`bXcw2nGXrýQ]_�xf jAXrþp� Ä�l � ¹ wAkcVak�Tik�ylTWj~jlTWnbk���kcjAX�z�z�k�` TWVYXc` kxw£hIkcj2TWVaTWz�TWngylkxw` Tnb;nb�xwvo�k®mskcn�yAXcmWylkàTWn�y~jlTk®wlkcVakàTMX;hGX�jlTs` Tmskcz�TWVaTWz�TWn�ylkxw¶º�f n�yAXà` TOþ�nb�xw�TXcwrX�nbmskcjAX��qTWnbwKTkxw}h�TWj°²GwRz�TWyAü�V_]amskxwR�qTWj~y~]amvX�]awrX�y~jAXs�q�swe` T�TWVaTWz�TWngylkxwR^GX�j~jAX�` T Ä nb�xwv�6KXc` k�dgfbT®XcwK¬vkcnGXcw?` T�wlTWVYX��qTWz½`bXcwMX�nbmskcjAX��qTWnbw�T;` kxwKh�TWj°²Gw��qTWj~y~]amvX�]aw�Tsw~yAuck�Vak�mvX�V_]_¬´Xc`bXcwMnbk

w~f ^bw~y~jAX�ylke` T¸TWVaTW�cXc`bXcwQmvX�jAXcmWylTWj~�aw~y~]amvXcwUz�Tsmvÿ�n ]amvXcwvo�nGuckeT\[p]aw~ylTWz�o´h jAX�y~]amvX�z�TWn�ylTxoxz�kv��]_z�TWngylkxw£` Tsw~yAXcw¬vkcnGXcwv�USQkcjUTswlylT|z�kcy~]_�qk ockxwûhIkcngylkxwUjlTWh jlTswlTWngyAX�y~]_�qkxw£`bXcw.¬vkcnGXcwU` T|wATWVYX��qTWz&hIk�` TWz"wlTWj.mskcnbw~]a` TWjAXc` kxw² [pkxwv��¿eVa�Wz/`p]awlwlk o�nbk�d�fbTMjlTswlh�TW]_yAX�XckxwrhITWj°²GwEz�TWyAü�V_]amskxw?�qTWj~y~]amvX�]awvo.Xc`pz{]_y~]_fp��wlT{d�fbTOnGuck®hIk�` TWj~]YXk�mskcj~jlTWj¶jlkcy~f jAXO`bX�w~fGX?��f nb`bXctvuck o�hITWVakOdgfbTrX?]_nbwlyAX�^ ]_V_]a`bXc` TE�qTWj~y~]amvX�VÊobXM`bX�j°��wlTxo�wlTWjAü�z�kcy~]_�cXc`bXMhITWVYXTWnbmWf j~�cXc`pf jAXp�

¿Ew}X�nGü�V_]awlTsw·��kcjAX�z±T\��TsmWy~fGXc`bXcwiTWzÀylTWnbwl¯�Tsw·ylkcyAX�]aw´opXc`pz{]_y~]_nb` kmskcz{hIkcj~yAX�z�TWngylk�TWVYücwly~]amskMhITWj°��TW]��yAX�z�TWngylT{h VYücw~y~]amsk oIfbw�X�nb` kàk�mWj~]_yl�Wj~]ak«` TOmsTs`#$WnbmW]YX�` T³ûjlTswlmvXp�M¿�hGX�jlTs` TO��kc]£mskcnbw~]a` TWjAXc`bX�TWVYücw~y~]amvXV_]_nbTvX�jvobmskcz5Xcw}h jlkch j~]aTs`bXc` Tsw�` TKf z Û Ä 7����x\�Û¶¿�SQo ÂYl bxþq�\�

¿Ñj~]_�x]a` TW¬iyAX�n �qTWnbmW]YX�V ` kxwQTWVaTWz�TWn�ylkxwIº°f ngyAXR��kc]pTswlmskcV_� ]a`bX�` T¸z�k�` krXed�fbT¸z�kc^ ]_V_]_¬´XcwAwlT}XRjlTsw~]awly%$Wnp�mW]YX�hGX�jAX;f z�` TswlVak�mvX�z�TWn�ylk®jlTWVYX�y~]_�qkà` T Ä z{z�o�ylTWnb` k���wlTMfbwAXc` k;f z��xX�VakcjETWVaTW�xXc` k;hGX�jAXàX�j~]_�x]a` TW¬nbkcj~z;X�VÊ� ¹ w{TWVaTWz�TWngylkxw{^GX�j~jAX���X�nbmskcjAX��qTWnbw�T®hITWj°²Gw��?��kcjAX�z mskcnbw~]a` TWjAXc` kxw{mskcz mskcz{hIkcj~yAX�z�TWngylkTWVYücw~y~]amsk{hITWj°��TW]_yAX�z�TWn�ylT?h VYücw~y~]amsk �

¿¼TswAmvXs�xXctvuck{��kc]:z�k�` TWVYXc`bX;` T?Xcmskcjl` k;mskcz'kh jlk�msTs`p]_z�TWngylkàTswld�fbTWz;X�y~]amvX�z�TWngylTMjlTWh jlTswlTWngyAXc` knGX{ýQ]_�xf jAX�þp� Ä Z�� ¹ mvü�VamWf Vak��kc]ûjlTvX�V_]_¬´Xc` k�TWz ÂYl �ÊXcwlTswvo wlf z;X�j~]YX�z�TWngylTO` TswlmWj~]_yAXcw}nbk9]EfGXc`pjlk;þp�  �

ýbkcjAX�z"]_n ]amW]YX�V_z�TWngylT·jlTvX�V_]_¬´Xc`bXcwU`pfGXcw£X�nGü�V_]awlTswè�r¿<T�Û��´��XRX�nGü�V_]awAT¸¿<nGucki��kc]�Xc`pz{]_y~]a`bXed�fGX�Vad�fbTWjV_]_z{]_yAXctvuckhGX�jAXOXcwimvX�j~�gXcw}d�fbTehIk�` TWzÀwATWj¶w~f hIkcj~yAXc`bXcwihITWVakxw·hITWj°²Gw¶z�TWyAü�V_]amskxwvo kOdgfbTrw~]_�xn ]�²GmvXOd�fbTxonbTsw~yAXKX�nGü�V_]awlTxoqnGuck���kc] mskcnbw~]a` TWjAXc`bX?XrTWnbmWf j~�xXc`pf jAXp�2¿ X�nGü�V_]awATÉÛ<�¶]a`#$Wn�y~]amvX�­KX�ngylTWj~]akcjvo�mskcz T\[ msTWhp�tvuckà` TOd�fbT?��kc]Qmskcnbwl]a` TWjAXc` k«mskcz{h�kcj~yAX�z�TWn�ylk«TWVYücw~y~]amskàh�TWj°��TW]_yAX�z�TWngylTh VYücw~y~]amskàhGX�jAXàkxw�TWVaTWz�TWngylkxwdgfbT®w~]_z�f VYX�z kxw?hITWj°²GwM�qTWj~y~]amvX�]awv��¿±mvX�j~�gX�V_]_z{]_ylT;hGX�jAX¾Tsw~ylTswMTWVaTWz�TWngylkxw{` TWhITWnb` T®`bX�T\[�]aw~y%$WnbmW]YX` T�mskcnp²bnGX�z�TWngylk�` k;h�TWj°²bVÊ�Ù6rTsw~yAX��kcj~z;XpobnGXcw�w~]_y~fGXcts¯�TsweTWz�dgfbT?k;h�TWj°²bVQwlT?TWnbmskcn�y~jAX;mskcnp²bnGXc` k o��kc]|mskcnbw~]a` TWjAXc`bX�X;V_]_z{]_yAXctvuck�nGX®ylTWnbwAuck�mskcj~jlTsw~hIkcnb` TWngylT;Xck��xX�VakcjKz��s`p]ak �"��� �M��R�Þ>=?�@��o:k«d�fbTmskcnb`pf ¬à­�mvX�j~�gX�` T�b à Z�µp�BA�z�� ¹ h ylkcfp��wlT;h�kcj�fbwAX�jMk«�xX�Vakcj?z��s`p]ak o£TWzäV_f �gX�jO` k�mvX�jAXcmWylTWj~�aw~y~]amsk`bXc` k�d�fbT�wlT�Tsw~yAü�X X�nGX�V_]awAX�j;f z;X�w~]_y~fGXctvuck�` T�jlkcy~f jAXpoiz;Xcw®k ` TWyAX�V_�bT�nGuck��«zMf ]_ylk�jlTWVaTW�xX�ngylT

Page 34: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 Z à Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

0. 10. 20. 30. 40. 50. 60. 70. 80. 90.

0.

5.

10.

15.

20.

25.

ÀrÁtÂDCYÏ¡Î � Á���¾ÈÉÏ���Ï�� Ï[Á¾Ê

0. 10. 20. 30. 40. 50. 60. 70. 80. 90.

0.

5.

10.

15.

20.

25.

À�Í� � Ï[Ç�ÆAÁpÅ����OÁ��¾Á���eÈ

ýU]_�xf jAX;þp� Ä�l���� X�V_�GXcwe` T?TWVaTWz�TWngylkxwe²bn ]_ylkxwRnbk]_n �amW]ak�Trnbk{²bnGX�V.`bX{TswlmvXv�cXctvuck �]EfGXc`pjlk®þp� Â�� ýGXcwATvX�z�TWngylkàmskcnbw~y~j~f y~]_�qk;Xc` kch yAXc` k�nGXcwEX�nGü�V_]awlTswv�

� Á��éÅ �0Å����`ÄJÏ���eÈ Å���� Á��¾Á���¾ÈÉÐ�Á%Ä)ÁÙÁpÅ���Å�� � ��eÈÉÆ�Á{��Ï��EÁÉÆAÅ�� ÈeÄJÈtÁeÇÉÅ���ÎJÈøÀE'7 3(. ÇxÂ� ÁeÐ�Ê8Ï��OÁ���eÈ<Æ�Á�� � ÁeÄ%�tÁ��0Æ�Å��YÏ ÆAÁ��=ÁeÈÙÐ�Å��éÈ<Æ�Á{�YÏ��EÁ� Ð�ÄJÅ��JÁÙÆAÈ�Í�Å`Î�¾È<ÆAÁ��YÏ��tÁ& �1F � Á��éÅ�Æ�ÅQÅ����OÁ��EÁ���¾ÈÀ � 7 EpÇxÂ. ÁeÐ�Ê8Ï��OÁ���eÈ<Æ�Á�� � ÁeÄ%�tÁ��0Æ�Å��YÏ ÆAÁ��=ÁeÈÙÐ�Å��éÈ<ÆAÈ�Í�Å`Î�¾ÈÙÆAÈ�� Ð�Á¾Ï���Å`Ê�ÆAÁ�Ð�Á%ÄJÅOÆAÅ1 Ð�ÄJÅ��JÁÙÆAÈ�Í�Å`Î�¾È<Æ�È)� Ð�Á¾Ï���Å`ʦÅQÐ�Ä%$�-¼Å�� � ÈeÄ%� È<ÆAÈú� �"!��tÅ Ê�Æ�Å�Á��"�`ȾÄ)Á��¾Å��"�3 / F � Á��éÅ�Æ�ÅQÅ����OÁ��EÁ���¾ÈÀ 1 7 EpÇxÂ5 ÁeÐ�Ê8Ï��OÁ���eÈ<Æ�Á�� � ÁeÄ%�tÁ��0Æ�Å��YÏ ÆAÁ��=ÁeÈÙÐ�Å��éÈ<ÆAÈ�Í�Å`Î�¾ÈÙÆAÈ0/� �Ð�Á¾Ï���Å`Ê�ÆAÁ�Ð�Á%ÄJÅOÆAÅG Ð�ÄJÅ��JÁÙÆAÈ�Í�Å`Î�¾È<Æ�È2/ Ð�Á¾Ï���Å`ʦÅQÐ�Ä%$�-¼Å�� � ÈeÄ%� È<ÆAÈ6/ �"!��tÅ Ê�Æ�Å�Á��"�`ȾÄ)Á��¾Å��"� E 4 F � Á��éÅ�Æ�ÅQÅ����OÁ��EÁ���¾ÈÀ G 7 EpÇxÂ( ÁeÐ�Ê8Ï��OÁ���eÈ<Æ�Á�� � ÁeÄ%�tÁ��0Æ�Å��YÏ ÆAÁ��=ÁeÈÙÐ�Å��éÈ<ÆAÈ�Í�Å`Î�¾ÈÙÆAÈ24� �Ð�Á¾Ï���Å`Ê�ÆAÁ�Ð�Á%ÄJÅOÆAÅ�� Ð�ÄJÅ��JÁÙÆAÈ�Í�Å`Î�¾È<Æ�È64� �Ð�Á¾Ï���Å`ʦÅQÐ�Ä%$�-¼Å�� � ÈeÄ%� È<ÆAÈ�4( ��"!��tÅ Ê�Æ�Å�Á��"�`ȾÄ)Á��¾Å��"��� H F � Á��éÅ�Æ�ÅQÅ����OÁ��EÁ���¾ÈÀ �� 7 EpÇx & ÁeÐ�Ê8Ï��OÁ���eÈ<Æ�Á�� � ÁeÄ%�tÁ��0Æ�Å��YÏ ÆAÁ��=ÁeÈÙÐ�Å��éÈ<ÆAÈ�Í�Å`Î�¾ÈÙÆAÈ H Ð�Á¾Ï���Å`Ê�ÆAÁ�Ð�Á%ÄJÅOÆAÅ�. Ð�ÄJÅ��JÁÙÆAÈ�Í�Å`Î�¾È<Æ�È H �Ð�Á¾Ï���Å`ʦÅQÐ�Ä%$�-¼Å�� � ÈeÄ%� È<ÆAÈ H ��"!��tÅ Ê�Æ�Å�Á��"�`ȾÄ)Á��¾Å��"��1 I F � Á��éÅ�Æ�ÅQÅ����OÁ��EÁ���¾ÈÀ �. 7 EpÇxÂ�3 ÁeÐ�Ê8Ï��OÁ���eÈ<Æ�Á�� � ÁeÄ%�tÁ��0Æ�Å��YÏ ÆAÁ��=ÁeÈÙÐ�Å��éÈ<ÆAÈ�Í�Å`Î�¾ÈÙÆAÈ I Ð�Á¾Ï���Å`Ê�ÆAÁ�Ð�Á%ÄJÅOÆAÅ�5 Ð�ÄJÅ��JÁÙÆAÈ�Í�Å`Î�¾È<Æ�È I Ð�Á¾Ï���Å`ʦÅQÐ�Ä%$�-¼Å�� � ÈeÄ%� È<ÆAÈ I �"!��tÅ Ê�Æ�Å�Á��"�`ȾÄ)Á��¾Å��"��G J F � Á��éÅ�Æ�ÅQÅ����OÁ��EÁ���¾ÈÀ 1G 7 EpÇxÂ

Page 35: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â Z�7

hGX�jAX�k�XcwAw~f ngylk«TWz/Tsw~y~fb` k �O��Xcwrw~]_y~fGXcts¯�Tsw?wlTWz/mskcnp²bnGX�z�TWn�ylk�kc^ yl�Wz��wlTf z;XàmvX�hGXcmW]a`bXc` T{jlTsw~]aw~�ylTWngylT�­®TWnbmWf j~�cXc`pf jAX�` T{þ���7;µ��BA�z�oûXc` kch yAX�nb` k�f z�mskcz{h j~]_z�TWn�ylk�` TTWnbmWf j~�cXc`pf jAX�` T Ä �8�®z ��Xh jlk���f nb`p]a`bXc` TM` T?TswlmvXs�xXctvuck�TWz mvXc`bXO�ÊXcwlTK�?` T � z®�\�i Txo|` T®f z;X���kcj~z;X¾w~]_z{h V_]�²GmvXc`bXpo¸wlTà` Tsw~]_�xnGX�jhIkcj�B�mvX�j~�gX¾�qTWj~y~]amvX�ViylkcyAX�V D �·y�zr|-zr}¾~���k¾VYXc` k©Tsw~�

dgfbTWjl` k�`bX®TsdgfGXctvuck«þp� Ä TB�Tsw~��kcjltskàjlTsw~]aw~ylTWn�ylT D �·yLKU�Ek®�cX�Vakcj�z;ü�[�]_z�k�` kàVYXc` k�`p]_jlTW]_ylk�`bX�z�Tsw~z;XTsdgfGXctvuck o�ylTWz��wlTxo Xc`pz{]_y~]_nb` k{d�fbTEXcwimvX�j~�gXcw¶nGXcwiX�nbmskcjAX��qTWnbw}w�uckMmskcnbw~yAX�n�ylTsw}XckMVakcn �qkO` kMh jlk�msTswlwAkmskcnbw~y~j~f y~]_�qk o£kxw?jlTsw~f V_yAXc` kxwOdgfbT®wlT;X�h jlTswlTWn�yAX�z½nbkS]EfGXc`pjlk©þp� Ä ���ruck���hIkxwlw~�_�qTWV·X�h jlTswATWngyAX�jOf zdgfGXc`pjlk�wlTWz�TWV_�GX�ngylT�hGX�jAX�X X�nGü�V_]awlT�¿'f z;X �qTW¬�dgfbT�wlT�mskcnbw~]a` TWjAXpo¶nbTsw~yAX X�nGü�V_]awATxo¶d�fbT�X6mvX�j~�gXjlTsw~]aw~ylTWngylT��K]_np²bn ]_yAXp�

]EfGXc`pjlk®þp� Ä�� ú|TWj~]�²GmvXctvuck O}<¤A�:�=�A(:·w~]_z{h V_]�²GmvXc`bX;` k{Tsdgf ]_V_�_^ j~]ak�hGX�jAX�X�X�nGü�V_]awlT�ÛMON

P !��tŠʦÆAÅ � Á��éÅ M�QSR#QST1U M@V1WYX#Z�[\U ] T M@V�W^X�Z�[<U`_a] TÅ����OÁ��¾Á���eÈ Àcb P>d Çx Àcb P>d Çx Àcb P>d Çx Àcb P�d ÇxÂ

� 3 �(.(. 1 E . �� E 3(��.� E 3x E 1 E . � & E 5 & .& �� E 1®. 1 E . ��1 E G(1(.. �1 & � E 1 E . & 5 E E 5(.1 �G �3(3(. 1 E . 1 E�E �� E .

M QSR#QST1U0e �OÁ%Ä%�tÁ6�tÅ`ÄéÎJÏ��OÁeÊ�ÎJÈeÎ)Á¾Ê3À�Ð�Å��éÈÉÆAÁpÐ�Á%ÄJÅOÆAÅOf9� ȾÇÉÐ�È(�AÅ���ÎJÅ��tÅ`ÄéÎJÏ��OÁeÊ�Æ�ÈpÐAÄ%$�-'Å�� � ȾÄ%�`È2��Á���Á��"� ÈeÄ)Á��EÅ��"�)Â�*] T e � ȾÄ%�OÁÉÆ�Å�� ȾÄéÎJÅQÇhg��AÏ8Ç<ÁL��ÁpÏ���ÎJÅ`Ä � Á�� Å��éȾÊ[È�-¼Ð�ÁeÄJÅ ÆAÅ(*M@V1WYX#Z�[\U e � ȾÄ%�OÁÉÁ���Ï ÁeʦÇhg���Ï[Ç<Á{��È���Ð�Å-Ä����1ÇÉÅ`Î#geÊ[Ï�� È���7

6KXKX�nGü�V_]awlT}` k�]EfGXc`pjlk�þp� Ä oqmskcnbmWV_f ]���wlT}d�fbTxoxnbkxw£h jlTswlw~f hIkxw~ylkxw|X�h jlTswlTWn�yAXc` kxwvogkrTsd�f ]_V_�_^ j~]ak?` TW]�[bX` T;wlTWj?hIkxwlw~�_�qTWV2hGX�jAX¾XcwK�ÊXcwlTsw ÂY� T�wlTW�xf ]_ngylTsw´oQk�dgfbT�wl]_�xn ]�²GmvX�d�fbT�wlTWjAuck�` T;Tsw~h�TWjAX�jvoUnGX�X�nGü�V_]awlTÛ�oQh VYXcw~y~]�²GmvXctvuck6` kªylTWj~jlTWnbk6T�` Tsw~Vak�mvX�z�TWngylkxw;TWVaTW�cXc` kxwvo|z�kcy~]_�cXc` kxw{hITWVYX¾h VYXcw~y~]�²GmvXctvuck6` kªhITWj°²bVz�TWyAü�V_]amsk�TxoQTW�qTWngy~fGX�V_z�TWngylTxo¸`bX�]_ngylTWj°�ÊXcmsT®wAkcVak��ÊhGX�jlTs` TxoQmskcz½mskcnbwlTsdgfbTWn�ylT®`p]_z{]_n�f ]atvuck¾`bXcw?��kcjltvXcwnGXcweX�nbmskcjAX��qTWnbwv�

¿eh jlTswATWngyAX���wlT;nGX«ýQ]_�xf jAX�þp� � ��Xcw�ylTWnbwl¯�Tsw?yAX�n �qTWnbmW]YX�]aw�nbk¾mskcngyAXcmWylk�wAkcVak«hGX�jlTs` T�nGXcw?��XcwlTsw�` TTswlmvXs�xXctvuck�Z�o  �po ÂY� o  þOT ÂYl o�hGX�jAXOXcwRX�nGü�V_]awATsw}¿�TkÛr�pS£X�jAX{X?�ÊXcwlT ÂYl o X�h jlTswlTWngyAX�z��wlTryAX�zM^��Wz kxwjlTsw~f V_yAXc` kxwe`bX�X�nGü�V_]awAT�Û Â " y~jAX�yAX���wlT�` T?f z;X�X�nGü�V_]awlTKjlTvX�V_]_¬´Xc`bX;mskcz h jlTsmW]awAuck�w~f hITWj~]akcjE­�X�nGü�V_]awAT�ÛT?dgfbT�wl���KjlTWVaTW�xX�ngylT�nGX�ÊXcwlT ÂYl o �ÊXcwlTKTWz5d�fbT?k�mskcj~jlT�Xjlkcy~f jAXp� ¹ Xcwlwlf ngylk�nGuck;Tsw~yAüpo nbk;TWn�yAX�ngylk onbk�ÿ�z�^ ]_ylk�` Tsw~ylTrylT\[pylk �2SQk�` Tr�qTWj~]�²GmvX�j°��wlT�dgfbTxopnGXcw¶�ÊXcwlTswxZMT  �po mskcj~jlTsw~hIkcnb` TWngylTswEXckxwih j~]_z�TW]_jlk;TwlTW�xf nb` kàn �_�qTW]awK` TOTswAmvXs�xXctvuck oûXcwrX�nGü�V_]awATsw�¿ TnÛ"X�h jlTswlTWngyAX�z/jlTswlf V_yAXc` kxwr]_�xfGX�]awvo:wlTWnb` k�` T�nbkcyAX�jdgfbT{wlTOz�kc^ ]_V_]_¬´X�nGXàh j~]_z�TW]_jAX���XcwlT` T{TswlmvXv�cXctvuck�f z;XàhGX�j~ylT;w~f ^bw~yAX�nbmW]YX�V|`bXàjlTsw~]aw~y%$WnbmW]YX«Xck«mskcj~ylTnGX?]_n�ylTWj°��XcmsT{��]_�xfGX�V:X à �?µ�S£Xq�\�|ýGX�¬W��wlTE]_�xfGX�V_z�TWngylTrnbkcyAX�j}X�]_j~jlTW�xf VYX�j~]a`bXc` T�d�fbT�wlTR�qTWj~]�²GmvXMnGXK¬vkcnGX]_np��TWj~]akcj¸` T}mvXc`bX�n �_�qTWV�` T}TswlmvXs�xXctvuck ogTWzÁmvXc`bXrf z;Xr`bXcw2��XcwlTsw£jlTWh jlTswATWngyAXc`bXcw¶T¶d�fbT}wlTQº°fbw~y~]�²GmvX�hITWVYXh�TWj~y~f j~^GXctvuck;h jlkv�qk�mvXc`bX{hITWVYXT\[�]aw~y%$WnbmW]YXpobnGX^GXcwlTK`bXhGX�jlTs` Txob` T�TWVaTWz�TWngylkxw2º°f ngyAX{�bkcj~]_¬vkcngyAX�]awv�

¿ X�nGü�V_]awlTà`bX�ýQ]_�xf jAX¾þp� � ��h�TWj~z{]_ylT®]_�xfGX�V_z�TWngylTà�qTWj~]�²GmvX�j{d�fbTxoUnGX«��XcwAT ÂY� �ªylTWjlmsTW]_jAX«�ÊXcwlT®` TTswlmvXs�xXctvuck �<kxw;jlTsw~f V_yAXc` kxw;kc^ y~]a` kxwà`p]���TWjlTWz�w~f ^bw~yAX�nbmW]YX�V_z�TWn�ylT�nGXcwàX�nGü�V_]awlTsw;¿¦TwÛro2hITWVakª�ÊXcmWylk` T{nbTsw~yAXà» V_y~]_z;X«wlTylTWj��qTWj~]�²GmvXc` k¾X�msTs`#$WnbmW]YX«` k«hITWj°²bV2z�TWyAü�V_]amsk oU]_z{h V_]amvX�nb` k¾X�z�kc^ ]_V_]_¬´Xctvuck¾`bXjlTsw~]aw~y%$WnbmW]YX{`bX]_n�ylTWj°��XcmsT�wlkcVak��ÊhGX�jlTs` Tx�

ú|TWj~]�²GmvX���wlTxo Xcwlw~]_z�o�dgfbTRnbTsw~yAXK�ÊXcwlTeX?jlTsw~]aw~y%$WnbmW]YX�nGXK]_n�ylTWj°��XcmsT�wlkcVak��ÊhGX�jlTs` T�wlTeTWnbmskcn�y~jAX�h jAX�y~]amvX��

Page 36: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 Zcþ Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

8

10

12

14

16

18

20

22

24

−40 −20 0 20 40

z (m

)

Fase 7

AB

−40 −20 0 20 40

Fase 10

−40 −20 0 20 40Tensão tangencial (kPa)

Fase 13

−40 −20 0 20 40

Fase 16

−40 −20 0 20 40

Fase 19

ABB1

ë�ì�í�î#ïeð�ñ�ò �E��õ�0�÷tþ4ù7i�÷�ùkÿeð�þ#íX÷tþ4ütì¼ð�ìrùkþ4ûHü�û�þ�ÿeð�ütÿ%û ù%û�úrû�.��3ð�ï%÷�#÷�þ3ð�ùkð�þkj�ú�ìrù%÷�ù�� ÷ml^34þ3ð�ù% Jð�ù%÷�ù���3=ó��/3ó��/3=óYñq÷�ó���ò

ý�÷tþ�ÿ%÷{ý�û#-#ì�ú�ì���ð#�4ð$�3ð�ïeð�ð�ð�þkj�ú�ìrù%÷ml^33ð�ûêúrû�þ#íXû<�#÷ÿ%û��4ð�ð�3ð�ï%÷�#÷�òJ0�ð�ú=þ�C�û�û�ü�û�ïOï%÷tïOì¼ð�ù%÷�ðêð#�#÷�ù*C�û éû�ù%ù%÷øú�ì�íX÷tì�ïeð�ý�÷tþ�ÿ%÷�ý�ð�ìrû�ï>�ºì�í�î3ð�ú;ðonE�`p�q0ð/3v�Tû�ï<÷65�÷tý?�#úrûi�#rkî4÷tïOïeð�÷tÿxð�úJò�33ôE�E��ó¯�:�tsxî3ð�þ�ÿ%û¨Oêð�þkj�ú�ìrù%÷��34ü�û�þ�ÿOïeð�ïOì¼ð�ý�÷tþ¦ÿ%÷$Oêý�û#-#ì�ú�ì���ð#B�C�û ùOî!-4ùOÿeð�þ4ütì¼ð�ú,@¦î4÷{û�ü�û�ïOï%÷�þ3ð? éð�ùe÷���3v�X÷tïOìGF3üYð¯.)ù%÷{þ3ð�ù� Jð�ù%÷�ù�ó��/3�ó��÷nóYñî#ývùOî4ü�÷�ù%ùOì��Xû>�#÷�ütï8)�ù%ütì�ý�û�4ð�ï%÷�ùOìrù%ÿ87tþ4ütì¼ð�ð�ûnü�û�ïOÿ%÷xý�û#-#ì�ú�ì���ð#�4ð�ò+I�ùOÿ%÷��#÷�ütï8)�ù%ütì�ý�û> éð��2.)ù%÷xþ4û�ÿeð�ï�#÷� Jð�ù%÷P�3ð�ïeð� Jð�ù%÷�O?ý�÷��ì;�4ð�@¦î4÷Éû�ü�j�úrütî#úrû�÷<ðø÷�ù%üYð���ð#B�C�û��#ï%û�ù%ù%÷tí�î4÷tý�÷E3X÷tý üYð#�4ð^ éð�ù%÷E3¦ð�ûúrû�þ#íXû��4ðð�ú�ÿOî#ïeð9�4ð$�3ð�ï%÷�#÷E3Tý�ð�þ¦ÿ%÷tþv�#û�.)ù%÷êð�ï%÷�ùOìrù%ÿ87tþ4ütì¼ð�ý�û#-#ì�ú�ì���ð#�4ð ÷tý þ!���X÷tìrùkï%÷tú¼ð�ÿOì���ð�ý�÷tþ�ÿ%÷ê÷túr÷2��ð#�#û�ù?þ3ð�ù�Yû�þ3ð�ùøý�ð�ìrùøùOî!�T÷tï"F3ütì¼ð�ìrù÷nð�ù%ù%î#ýêì�þv�#û9��ð�úrû�ï%÷�ù^-3ð�ìG5#û�ùkþ3ð�ù?ý�ð�ìrù^�#ï%û� ·î#þv�4ð�ù�31û�þv�#÷qü8�4÷tí�ðCðCð�ÿOì�þ#í�ì�ï��ð�úrû�ï%÷�ùÙþ4÷tí�ð�ÿOì��Xû�ù�3!@�î4÷?ùOì�í�þ#ìGF3üYð�ý�@¦î4÷øû�ù%û�úrûnÿ%÷tývý�û���ì�ý�÷tþ�ÿ%û<�#÷�ù%ü�÷tþv�#÷tþ�ÿ%÷÷tývï%÷tú¼ð#B�C�û$O>�3ð�ï%÷�#÷�ò

uøð�ù� Jð�ù%÷�ù?ù%÷tí�î#ì�þ�ÿ%÷�ù�O? éð�ù%÷Hó���ü�û�þ¦ÿOì�þ�î3ðCð<�X÷tïOìGF3üYð�ï".)ù%÷êðêÿ%û�ÿeð�ú�ý�û#-#ì�ú�ì���ð#B�C�û¨�4ð�ì�þ�ÿ%÷tï" Jð�ü�÷qù%û�úrû�.�3ð�ï%÷�#÷�þ3ð�ð�þkj�ú�ìrù%÷vl^34û#-4ù%÷tï:��ð�þv�#û�.)ù%÷E35÷tý ü�û�þ�ÿOïeð��3ð�ïOÿOì;�4ð/3Òþ3ð� Jð�ù%÷�ó��/33î#ý�ðqí�ïeð�þv�#÷�ì�ïOï%÷tí�î#ú¼ð�ïOì;�4ð#�#÷þ4û�ù���ð�úrû�ï%÷�ù%�4ð�ùpÿ%÷tþ4ù7i�÷�ùP�#÷øü�û�ïOÿ%÷�ò�I�ùOÿ%÷� Jð�ütÿ%û>)?ý�û�ÿOì���ð#�#û>�Tû�ïÙþ�C�ûqù%÷xÿ%÷tïÉü�û�þ4ù%÷tí�î#ì;�#ûnþ4û��#ï%û�ü�÷�ù%ù%ûì�ÿ%÷tïeð�ÿOì��Xû�û ý�÷�ùOý�û�þ!���X÷tú��#÷Ýü�û�þ��X÷tïOí�7tþ4ütì¼ð û#-#ÿOì;�#û �3ð�ïeðÚð�ù¨ éð�ùe÷�ùCð�þ¦ÿ%÷tïOìrû�ï%÷�ùYòwq�ð�ïeðÚð Jð�ù%÷ ó��/3ð��#ï%÷�ù%÷tþ¦ÿeð�ý.)ù%÷�ð�ù<ütî#ï:��ð�ù<ü�û�ïOï%÷�ù:�Tû�þv�#÷tþ�ÿ%÷�ùøð�û�ü�j�úrütî#úrûaløò

x�÷tïOìGF3üYð�þv�#û�.)ù%÷��4ð� Jð�ù%÷{ó����3ð�ïeðqð^ Jð�ù%÷�ó��{î#ý�ð{ý{î#ì�ÿ%ûqùOì�í�þ#ìGF3üYð�ÿOì���ð{ý�û���ìGF3üYð#B�C�ûnþ3ð�ï%÷�ù%ìrùOÿ87tþ4ütì¼ðð�û?ü�û�ïOÿ%÷�ý�û#-#ì�ú�ì���ð#�4ðkþ4û?ü�û�þ�ÿeð�ütÿ%ûøù%û�úrû�.��3ð�ï%÷�#÷E3�ð��#ï%÷�ù%÷tþ¦ÿeð¯.)ù%÷pþ3ðxë�ì�í�î#ïeð?ñ�ò ��ópðk÷2�Xû�ú�îvB�C�û��4ð<ï%÷6 é÷tïOì;�4ðí�ïeð�þv�#÷2��ði�3ð�ïeð]ÿ%û��4ð�ùqð�ù> éð�ù%÷�ùn÷tþ�ÿOï%÷^ð�ó��]÷ ð�ó��/3Qü�û�ý û]û#-zy ÷�ütÿOì��XûN�#÷ ù%÷<�T÷tï%ü�÷2-T÷tïnü�û�ýÔý�ð�ìrû�ï�#÷tÿeð�ú��4÷^ûS é÷tþ|{�ý�÷tþ4û �#÷Hý�û#-#ì�ú�ì���ð#B�C�û­�4ðæï%÷�ùOìrùOÿ87tþ4ütì¼ðæþ3ð]ì�þ�ÿ%÷tï" Jð�ü�÷�ò �kù%ù%ì�ý�30þ3ði éð�ù%÷ ó�óE3�÷tý @¦î4÷ù%÷qý�û��#÷tú¼ð^ð~-T÷tÿ%û�þ3ð�íX÷tý¶�4ð¨�3ð�ï%÷�#÷E3,@¦î4÷êü�û�þ4ùOìrùOÿ%÷qþ3ð^ð��#ú�ìrüYð#B�C�ûi�4ð�ù�üYð�ïOí�ð�ù��#÷2��ì;�4ð�ù�ð�û~�T÷�ù%ûD�#û-T÷tÿ*C�û!3Xð�ù0ð�ú�ÿ%÷tïeð#B�i�÷�ù�þ3ð�ù�ÿ%÷tþ4ù7i¦÷�ù�ÿeð�þ#íX÷tþ4ütì¼ð�ìrù0ý�û�ÿOì���ð#�4ð�ù´�Òû�ï0÷�ùOÿ%÷püYð�ïOï%÷tí�ð�ý�÷tþ�ÿ%ûù*C�û��#ïeð�ÿOìrüYð�ý�÷tþ�ÿ%÷ì�þ4÷65�ìrùOÿ%÷tþ�ÿ%÷�ùYò}u?ð& Jð�ù%÷]óYô]ùOì�ý�î#ú¼ð¯.)ù%÷wði�#ï%÷�ùeð&�#ûS-T÷tÿ*C�ûÝð�ÿOïeð��)�ù$�4ðæð�ütÿOì���ð#B�C�û �#û�ùq÷túr÷tý�÷tþ¦ÿ%û�ù<�4ð�3ð�ï%÷�#÷�÷��#ûêü�û�þ¦ÿeð�ütÿ%û�ù%û�úrû�.��3ð�ï%÷�#÷�÷øï%÷Yð�ú�ì���ð¯.)ùe÷�û?�#ï8)6.)÷�ù" éû�ï8B�û?�4ð�ùxð�þ4ü�û�ïeð�íX÷tþ4ù �#û�ÿ%÷tï%ü�÷tì�ï%ûêþ!���X÷tú�34û

Page 37: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â Z�Z

8

10

12

14

16

18

20

22

24

−40 −20 0 20 40

z (m

)

Fase 10

AB

−40 −20 0 20 40

Fase 11

−40 −20 0 20 40Tensão tangencial (kPa)

Fase 12

−40 −20 0 20 40

Fase 13

−40 −20 0 20 40

Fase 14

8

10

12

14

16

18

20

22

24

−40 −20 0 20 40

z (m

)

Fase 15

AB

−40 −20 0 20 40

Fase 16

−40 −20 0 20 40Tensão tangencial (kPa)

Fase 17

−40 −20 0 20 40

Fase 18

−40 −20 0 20 40

Fase 19

ABB1

~��c���������z���>���B�����M�7�´�x�B���`��� ���M���å�`�+�m�|� �������������7�ë�7����`���ç�`���������ç���õ�`�k�`�c�+���x�B� �L�����ç�����������x�ê��� ����z�

� �M���k ��¡���7��¢+�´�w�z���`�ç�`����������£ã���0�����{�¤���å���7���¦¥ç�w��§� ��¨�����è���1¥|��£ã���'�`�c�+��� �;��£ ���c���ç��§� ��ë�����z¥|�ç���M�H�©��R���� � �M���ç�`�7ªy�x�������%�������M���ú�`�k�`�c�+���x�h� �v� ���������c�0�ç�`£ � �����c�M����z�c���

�«���å�������¦¥ç�w��§� ��¤���¬�R���1¥|�>�´���������v�ç�ã�������Ï���z�¤�%�����v�����x���w��¢���§� �����£ � �M�­�o�è���1¥|��¥ç�w�à��®z�¯���7�7��ë��£ � �M���°���������`�0�7���±�c²M�?ªë�`�����#����³�M� �´���x�7�+���7µ��M���å� ���������x�������|�����0���´¶ �w�`�ç������M�����¡���x�7�+�������0���·¶���M������¢����z�����z�¸¢ �����¦¥ç�w�`�|���`�����?�����a�+���7� � �M� �´£a�����c�c�c¹'��§� ��º�M�´���x���+���7µ��M���å� �������������¡�M�»�c�������������x��7����`���ç�`�������à���ê���`¹o���a��£à���-����£à� ��¼����c���z��£à�`�0�����|���`�����¬�ç���}�%�����x�õ���������c�0���x���½�¾�è���ç���m�ç���y�������x�

Page 38: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 Z�b Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

` T�X�h V_]amvXctvuck�` Th jl�\��Tsw~��kcjltsk ��T�` Th jlTsw�X�` k�^�TWyAuckg�Ef z;X�hGX�j~ylT;` k«mskcngyAXcmWylk�wAkcVak��ÊhGX�jlTs` T{nGuck«wlTTWnbmskcngy~jAX�mskcz/XàjlTswl]aw~y%$WnbmW]YX�Xck«mskcj~ylTMylkcyAX�V_z�TWn�ylT�z�kc^ ]_V_]_¬´Xc`bXpoUkàd�fbTwlTOT\[�h V_]amvXàhITWVYX®]_ngy~jlk�`pfbtvuck` Tnbkv�qkxw�TWVaTWz�TWngylkxw?nbk«mvü�VamWf Vak �nã�k«d�fbTwlTkc^bwlTWj~�cXànGXcw��ÊXcwlTsw  7àT  bp�O¿Ew��ÊXcwlTswrwlTW�xf ]_ngylTsw´o.` TTswlmvXv�cXctvuck o �xuck o nbk{TWn�yAX�ngylk o�h jlkv�qk�mvX�j�XOz�kc^ ]_V_]_¬´Xctvuck�ylkcyAX�VU` Tsw~yAXjlTsw~]aw~y%$WnbmW]YXp�

¿äX�nGü�V_]awAT���TW]_yAX<X�ngylTWj~]akcj~z�TWngylT nbk<d�fbT©`p]_¬¾jlTsw~hITW]_ylkÑ­ jlTswl]aw~y%$WnbmW]YX�Xck�mskcj~ylT©z�kc^ ]_V_]_¬´Xc`bX<nGX]_ngylTWj°�ÊXcmsTàwlkcVak��ÊhGX�jlTs` TàylTW�qT;TWz X�ylTWnbtvuck¾kxw��cX�VakcjlTswO`bXcw�ylTWnbwA¯�TswOT;`bX�w~fGX�TW�qkcV_fbtvuck6Xck�Vakcn �qk©`bX]_ngylTWj°�ÊXcmsTxoqhGX�jAX�mvXc`bXE�ÊXcmsTimskcnbw~y~j~f y~]_�cXp� ¹ d�fbT¶wAT·z�kxwly~jAXenGXrýQ]_�xf jAXrþp� �xÄ ��Xq�Qmskcnbw~]a` TWjAXKXEjlTsw~f V_yAX�n�ylT`bXcwi��kcjltvXcw}` T?mskcj~ylTrz�kc^ ]_V_]_¬´Xc`bXcwe`p]_��]a`p]a`bXhITWVYXOjlTsw~]aw~y%$WnbmW]YX{Xck{mskcj~ylTKylkcyAX�V:nGX{]_ngylTWj°�ÊXcmsTKhGX�jAXmvXc`bX�ÊXcwlTRmskcnbw~y~j~f y~]_�xXp�2¿ jlTsw~f V_yAX�ngylTE`bXcw|��kcjltvXcw¸` TRmskcj~ylTE�ekc^ y~]a`bXMX�y~jAXs�q�sw¶`bXK]_ngylTW�xjAXctvuckOTWz X�V_y~f jAX�`bXcwylTWnbwl¯�TswU` T¶mskcj~ylT}X�h jlTswlTWngyAXc`bXcw2TiXejlTsw~]aw~y%$WnbmW]YXeylkcyAX�VpX�y~jAXv�q�sw2`bXR]_n�ylTW�xjAXctvuckK`bXcwUylTWnbwA¯�TswUjlTsw~]aw~ylTWn�ylTswv��rX«Xs�xX�V_]YXctvuck�` Tsw~yAXcw�jlTsw~f V_yAX�ngylTswM�Gü«d�fbTylTWj�TWz½X�ylTWnbtvuck�k«��XcmWylk«` T�k�mskcz{h j~]_z�TWngylk©`bX�hGX�jlTs` TTWz mskcngyAXcmWylk6mskcz k¾ylTWj~jlTWnbkª�cX�j~]YX�j{` T;��XcwlT®hGX�jAX���XcwATxo|` TW��]a` k6­¾mskcnbw~y~j~fbtvuck6`bX�hGX�jlTs` T�X�h��xw{XT\[ TsmWfbtvuck�`bX{TswlmvXv�cXctvuck �

ú|TWj~]�²GmvX���wlTxo�yAX�V£mskcz�k®wATWj~]YX;` TOTsw~hITWjAX�jETWz5��XcmsTM` kxwEjlTswlf V_yAXc` kxwrX�n�ylTWj~]akcj~z�TWngylT{` TswlmWj~]_ylkxw´o�d�fbTXcwEX�nGü�V_]awATswE¿1T{Û�X�h jlTswATWngyAX�z�o:Xck�Vakcn �qk®` k{�ÊXcwlTvX�z�TWngylk®mskcnbw~y~j~f y~]_�qk oIk{z�Tsw~z�k;mskcz{hIkcj~yAX�z�TWngylk`bX«]_n�ylTWj°��XcmsT�X�yl�®­���XcwlT ÂvÄ oQmskcnbwlyAX�yAX�nb` k���wlTxo|X�hGX�j~y~]_j`bX��ÊXcwlT ÂY� oQdgfbT;nGX�X�nGü�V_]awlT®¿ mskcn�y~]_ngfGXªXylTWnb`#$WnbmW]YX;hGX�jAX�X{`p]_z{]_ngf ]atvuck�`bXjlTswl]aw~y%$WnbmW]YX;Xck�mskcj~ylT�z�kc^ ]_V_]_¬´Xc`bXpo�Xck�hGXcwlwlk�d�fbTKnGX;X�nGü�V_]awAT�Û4wlTkc^bwlTWj~�xX?f z±w~]_�xn ]�²GmvX�y~]_�qk{X�f z�TWn�ylk{` Tsw~yAXM�xjAX�nb` TW¬´Xpo�²GmvX�nb` kMylkcyAX�V_z�TWn�ylTrz�kc^ ]_V_]_¬´Xc`bX{X?jlTswl]aw~y%$WnbmW]YXXck�mskcj~ylTx�

−40

−20

0

20

40

60

80

100

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Res

istê

ncia

mob

iliza

da (%

)

Fase de construção

ABB1

ÀrÁtÂ�¿E�YÎJÅ-Ä � Á��`Å

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Res

istê

ncia

mob

iliza

da (%

)

Fase de construção

BB1

À�Í�ÂTÃ�Å`Ä����

ýQ]_�xf jAX�þp� �xÄ�� �eTsw~]awly%$WnbmW]YX�z�kc^ ]_V_]_¬´Xc`bXànGX;]_ngylTWj°�ÊXcmsT{wlkcVak��ÊhGX�jlTs` TT�nbkxw�hITWj°²Gw�nGXcwrX�nGü�V_]awATsw�¿Oo�T�Û�è�ÊXcwlT ÂYl �\�� kcnp²bj~z;X�nb` kMk�d�fbTQºlüEwAT·jlT\��TWj~]_fûoqnGXKX�nGü�V_]awAT}¿öXEjlTsw~]aw~y%$WnbmW]YX?Xckrmskcj~ylT}nGX�]_n�ylTWj°��XcmsTewlkcVak��ÊhGX�jlTs` T

z�kc^ ]_V_]_¬´X���wlT�ngf z;XhITWjlmsTWngyAX��qTWz�TWVaTW�cXc`bX���msTWjlmvX{` T�b��XW �;nbk{h j~]_z�TW]_jlk{n �_�qTWVU` T?TswlmvXs�xXctvuck��è�ÊXcwlTZx�\oR` TsmWjlTswlmsTWnb` k<nGXcw;��XcwATsw®wlTW�xf ]_n�ylTswàhGX�jAX�msTWjlmvX<` T]7�7XW nGX ��XcwlT  ��T¾hGX�jAX � �XW nGX6��XcwlT ÂY� �ú|TWj~]�²GmvX���wlTxo¸nbk¾TWn�yAX�ngylk o·f z X�f z�TWn�ylk `bX�hITWjlmsTWngyAX��qTWz `bX¾jlTsw~]awly%$WnbmW]YX©Xckªmskcj~ylTàz�kc^ ]_V_]_¬´Xc`bX©nGX]_ngylTWj°�ÊXcmsT?nGXcw}��XcwlTsw}` T?h jl�\��Tsw°��kcjltsk;mskcz�k;Xcwi�ÊXcwlTsw  7{T  bp�ã&nbTsw~yAXcwKz�Tsw~z;Xcwr�ÊXcwlTsw?d�fbTxo:nGX�X�nGü�V_]awAT�ÛroûX�h��xw?wATylTWjKz�kc^ ]_V_]_¬´Xc` k  ���XW¦`bX�jlTswl]aw~y%$WnbmW]YX�Xck

mskcj~ylTxo£wlT{�qTWj~]�²GmvX�f z½` TsmWjl�swlmW]_z�k oQz�kcy~]_�xXc` k�nGuck�h jlkch j~]YX�z�TWn�ylTàh�TWVak«h jl�\��Tsw~��kcjltsk �ªd�fbT�` TW�qTWj~]YX

Page 39: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â Z l

mskcnb`pf ¬s]_j;X�f z ]_nbmWjlTWz�TWngylk�`bX�ylTWnbw�uck¾yAX�n �qTWnbmW]YX�V}z�kc^ ]_V_]_¬´Xc`bX � z;XcwOhITWVak��ÊXcmWylkª` Txo2nbTsw~yAXcwM�ÊX��wlTswrk�mskcj~jlTWjK]_�xfGX�V_z�TWn�ylT;X®h jlTswAXà` k®^ITWyAuck o:mskcnp��kcj~z�T�X�ngylTWj~]akcj~z�TWngylT;jlT\��TWj~]a` k o:k�d�fbTO]_z{h V_]amvXàf zX�f z�TWngylk;`bX;ü�jlTvX{`bXO]_ngylTWj°�ÊXcmsT�Txo mskcnbwlTsd�fbTWngylTWz�TWn�ylTxoI`bXOjlTsw~]aw~y%$WnbmW]YX�Xck�mskcj~ylT?z�kc^ ]_V_]_¬´üs�qTWVÊ�

SQX�jAX X�Va�Wz)`bX<jlTsw~]aw~y%$WnbmW]YX<z�kc^ ]_V_]_¬´Xc`bX�nGX<]_n�ylTWj°��XcmsT�wlkcVak��ÊhGX�jlTs` Txo?X�ýQ]_�xf jAXÑþp� �xÄ X�h jlTswlTWngyAX]_�xfGX�V_z�TWngylT�X«hITWjlmsTWngyAX��qTWz `bXà��kcjltvX«jlTsw~]aw~ylTWngylT;z�kc^ ]_V_]_¬´Xc`bX�nbkxw�h�TWj°²Gw��qTWj~y~]amvX�]awv� ¹ w?jlTsw~f V_yAXc` kxwdgfbT}wlT}X�h jlTswlTWn�yAX�z `p]_¬vTWz X�hITWnGXcw2jlTsw~hITW]_ylkr­KX�nGü�V_]awATÉÛ�o�f z;X��qTW¬Rd�fbT¶nGXKX�nGü�V_]awlT}¿ kxw£hITWj°²Gw£��kcjAX�zmskcnbw~]a` TWjAXc` kxwemskcz jlTswl]aw~y%$WnbmW]YX]_V_]_z{]_yAXc`bXp�

¿1kc^bwlTWj~�cXctvuck®`bX²b�xf jAX�h�TWj~z{]_ylTMmskcnbmWV_f ]_j�d�fbT�X�mvX�j~�gX®XcmWy~fGX�ngylTMnbkxwehITWj°²GwRz�TWyAü�V_]amskxw���mWjlTsw~�msTWngylTxo.X�f z�TWn�yAX�nb` k�TWz¦hGX�j~y~]amWf VYX�jKnGXcw���XcwATsw�` TOh jl�\��Tsw°��kcjltsk ��mskcz�k«Xcw���XcwATswrþàT l �ET` TX�V_�xf z;X��kcj~z;X�yAX�z�^I�Wz�nGXcwe�ÊXcwlTswe` TMTswlmvXs�xXctvuck � ¹ X�f z�TWngylkà`bX{��kcjltvX{nbkxwEh�TWj°²GwEnGXcwe��XcwlTswE` T�TswlmvXv�cXctvuck` TW�qT\��wlT?XckO��XcmWylk` TxopnbTsw~yAXcw¶�ÊXcwlTswvopwlTWjijlTWy~]_jAXc` k�k{X�hIkc]ak�qTWj~y~]amvX�Vû` kxwihGX�]_nb�W]awR` Tr^ITWyAuckX�j~z;Xc` k�nbkwlkcVak og�GXv�qTWnb` k oph�kcjiTsw~ylTEz�kcy~]_�qk o X?nbTsmsTswlwl]a`bXc` TE` TEy~jAX�nbw°��TWj~]_j¶Tsw~yAXMmvX�j~�gX�hGX�jAX�kxw·h�TWj°²Gw¶z�TWyAü�V_]amskxwv�

]EfGX�nb` ke`bX}TswAmvXs�xXctvuckR` k}ylTWjlmsTW]_jlkRn �_�qTWVÊocX}d�fbT|mskcj~jlTsw~hIkcnb` T¸X¶�ÊXcwlT  �po��qTWj~]�²GmvX���wlT¸Xiz�kc^ ]_V_]_¬´Xctvuck` T?dgfGXcwAT  ���XWÀ`bXOjlTsw~]aw~y%$WnbmW]YX{` k�h�TWj°²bV:�qTWj~y~]amvX�VÊ��ã ` TKnbkcyAX�jed�fbTxopnbTsw~yAXO�ÊXcwlTxo Tsw~yAXv�cXOz�kc^ ]_V_]_¬´Xc`bXmsTWjlmvX;` Tq7��XW `bX;jlTsw~]aw~y%$WnbmW]YX;VYX�ylTWjAX�VÊ����X{��XcwlTMwlTW�xf ]_ngylTxo:mskcj~jlTswlh�kcnb` TWn�ylT­àX�h V_]amvXctvuck�` k;hITswlk®` khGX�]_nbTWVÊo�nGuckM�bkcf �qTxo�h jAX�y~]amvX�z�TWngylTxobX�V_ylTWjAXctvuck opz;Xcw·nGXK�ÊXcwlT ÂvÄ op` Teh jl�\��Tsw°��kcjltsk o X�mvX�j~�gX?z�kc^ ]_V_]_¬´Xc`bX�xo�` TrXcmskcjl` kmskcz±k��xjAü�²Gmsk�X�h jlTswlTWn�yAXc` k o ` TrmsTWjlmvXM` T ÂWà �XW�`bX?jlTswl]aw~y%$WnbmW]YXp��â�w~ylkM` TW�qT\��wAT�XckM�ÊXcmWylk` Txo nbTsw~yAXO�ÊXcwlTxobkhITWj°²bV.wlT?TWnbmskcn�y~jAX�j�mskcnp²bnGXc` k oGh�TWVak;dgfbT�XwlfGXjlTsw~]aw~y%$WnbmW]YXjlTswlf V_yAX�`bXylTWnbwAuck;` TmsTs`#$WnbmW]YXOz��s`p]YXpo w~f h�TWj~]akcjvopnGX�y~f jAX�V_z�TWn�ylTxo�­MylTWnbwAuck{XOdgfbTrmskcj~jlTsw~hIkcnb` T?XMmvX�hGXcmW]a`bXc` TKjlTsw~]aw~ylTWn�ylT?­TWnbmWf j~�cXc`pf jAXpo:TWz5jlTWVYXctvuck�­;dgfGX�V2XcwEjlTsw~]aw~y%$WnbmW]YXcw�z�kc^ ]_V_]_¬´Xc`bXcw�nbkxwEhITWj°²GwEz�TWyAü�V_]amskxwrX�h jlTswATWngyAXc`bXcwnGXO²b�xf jAX{wAuckjlT\��TWj~]a`bXcw�À´�

³UX�V}w~]_�xn ]�²GmvXpo2hIkcj~yAX�ngylk o¸dgfbT�X�hGX�j~y~]_j{`bX���XcwAT  �¾Txo2Tsw~h�TsmW]YX�V_z�TWn�ylTxo·X�hGX�j~y~]_j{`bX«�ÊXcwlT ÂY� o2wAT�qTWj~]�²GmvX¾X�ylkcyAX�V·z�kc^ ]_V_]_¬´Xctvuck©`bX«jlTsw~]awly%$WnbmW]YX�` kxwMh�TWj°²Gw��qTWj~y~]amvX�]awvo2d�fbTWjMTsw~ylT�ºlX�z½mskcnp²bnGXc` kxwd�fbTWjnGuck oGXcwlw~]_z mskcz�k�wATr�qTWj~]�²GmvX�XylkcyAX�Vûz�kc^ ]_V_]_¬´Xctvuck®`bXjlTsw~]aw~y%$WnbmW]YX{` k{mskcn�yAXcmWylk;wlkcVak��ÊhGX�jlTs` Tx�Ü�Xv�qTWnb` k�XàylkcyAX�V2z�kc^ ]_V_]_¬´Xctvuck�`bXàjlTswl]aw~y%$WnbmW]YX�` kxwKhITWj°²Gwrz�TWyAü�V_]amskxw�T{`bXà]_ngylTWj°�ÊXcmsTxoûylTWnb` k�TWz

X�ylTWnbtvuck�X®Tsd�fGXctvuckàþp� Ä o�ylTWz��wlTOdgfbTX®mvX�j~�gX®XcmWy~fGX�n�ylTnGuck;hIk�` TOX�f z�TWngyAX�jvoûkàd�fbT�w~]_�xn ]�²GmvXàd�fbTxomskcngy~]_ngfGX�nb` k�XjlTvX�V_]_¬´X�j°��wlTMX{TswlmvXs�xXctvuck�T�XT\[ TsmWf yAX�jek{h jl�\��Tsw~��kcjltsk o f z5` TsmWjl�swlmW]_z�k�`bX{mvX�j~�gXnGXcwX�nbmskcjAX��qTWnbweylTWjAüd�fbT?k�mskcj~jlTWjv�ã�TswlylTRkr��TWnb�cz�TWnbk�mWVYX�jAX�z�TWngylT�TW��]a` TWnbmW]YXc` k�hITWVYXKýQ]_�xf jAX�þp� ��� �£¿iyl�E­r��XcwlT ÂvÄ nGuckK�Gü?d�fGX�Vad�fbTWj

`p]���TWjlTWnbtvX¾TWngy~jlT�k�mskcz{hIkcj~yAX�z�TWngylk6`bXcw{X�nbmskcjAX��qTWnbwOnGXcw{X�nGü�V_]awlTswO¿±THÛø"UX�hGX�j~y~]_j{` Tsw~yAX��ÊXcwlT®Xcw�cX�j~]YXcts¯�TswE` TOmvX�j~�gX;nGXcw�X�nbmskcjAX��qTWnbwrnGX®X�nGü�V_]awlTM¿�mskcn�y~]_ngfGX�zäX;wlTWjEz�k�` Tsw~yAXcwvoGz;Xcw�nGX;X�nGü�V_]awlTnÛ�qTWj~]�²GmvX���wlTOf z;X®wl]_�xn ]�²GmvX�y~]_�cXà`p]_z{]_ngf ]atvuck�`bXcdgfbTWVYX®mvX�j~�gXp�\|w~ylTT\��TW]_ylk®�eº~ü;^ITWz¦TW��]a` TWngylTOnGX���XcwATÂY� z;Xcw·X�f z�TWn�yAX�` Ti��kcj~z;XrzMf ]_ylk�w~]_�xn ]�²GmvX�y~]_�xX�X�hGX�j~y~]_j¶` Tsw~yAX��ÊXcwlTx�Qú|TWj~]�²GmvX���wlTRd�fbTeXcw·X�nbmskcjAX��qTWnbwz;X�]aw.h jlk���f nb`bXcw2X�h jlTswlTWngyAX�z"z;X�]akcjlTswQ�cX�j~]YXcts¯�Tsw.` T¶mvX�j~�gXpocmskcnbw~yAX�yAX�nb` k���wlT¶` TsmWjl�swlmW]_z�kxw£` T¸msTWjlmvXE` T� �XWÁnGX��ÊXcwlT  þOT�` TrdgfGXcwlT  ���XW nGXK�ÊXcwlT ÂYl �Q6rTe�ÊXcmWylk opkxwi` TsmWjl�swlmW]_z�kxw}` TEmvX�j~�gXMnGXcwRX�nbmskcjAX��qTWnbw` kxw}n �_�qTW]aw  X à w�uck opnGX�X�nGü�V_]awlT�Ûro ` T  ���XWà�

¿ z;X�]akcj|�cX�j~]YXctvuckM` TRmvX�j~�gXrnGXcw¶X�nbmskcjAX��qTWnbw·`bX?X�nGü�V_]awATR¿Mog` TRmsTWjlmvXK` T ÂvÄ Wào��eXKd�fbTRk�mskcj~jlTRnGX» V_y~]_z;XE��XcwlTL�r��XcwlT ÂYl �?nGXEX�nbmskcjAX��qTWz ` kE» V_y~]_z�krn �_�qTWVÊ�£¿Ñz�kc^ ]_V_]_¬´XctvuckK`bX�mvX�hGXcmW]a`bXc` TijlTsw~]aw~ylTWn�ylTR­Á# �¾Á¾Ê8ȾÄ0ÆAÅ & E�Ã�ÄJÅ�� � Ê¡Î)ÁkÆAÁÙÄJÅ Ê[Á���eÈ?Å���ÎéÄJÅ�Á<ÎJÅ��"�%¾È<Ç2$OÆ�Ï[Á2- � & GtÄ Ã#Á2-TÅ�Á<ÎJÅ����%¾È0� ÈeÄéÄJÅ��éÐ�È(��ÆAÅ���ÎJÅ°Åú�OÁ%Ä%�tÁÆ�ÅQÅ��"� � Ä%�¾ÁEÆ � Ä)ÁL- �3�5hÄ Ã#Á5Æ � & G d �3�5�Ç� 7 & 7

Page 40: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 b�� Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

−100

−80

−60

−40

−20

0

20

40

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Var

iaçã

o de

car

ga (%

)

Fase

Nível 1

ABB1

8 9 10 11 12 13 14 15 16 17 18 19Fase

Nível 2

11 12 13 14 15 16 17 18 19Fase

Nível 3

14 15 16 17 18 19Fase

Nível 4

17 18 19Fase

Nível 5

ë�ì�í�î#ïeð�ñ�ò �E��õ>x�ð�ïOì¼ð#B�C�û9�#÷�üYð�ïOí�ðqþ3ð�ùxð�þ4ü�û�ïeð�íX÷tþ4ùxþ3ð�ùkð�þkj�ú�ìrù%÷�ù�� ÷Bløò

÷tþ4ütî#ï:��ð#��î#ïeð�þ4û�ù+�Ò÷tï"F3ù�ý�÷tÿ'j�ú�ìrü�û�ù�ì�ý?�#ú�ìrüYðnð�û�ü�û�ïOï87tþ4ütì¼ð��#÷��#÷�ùOúrû�üYð�ý�÷tþ�ÿ%û�ù��X÷tïOÿOìrüYð�ìrù�ì�ý?�Tû�ïOÿeð�þ�ÿ%÷�ùA3@¦î4÷& Jð��Y÷tý ��ì�ýêì�þ�î#ì�ïFð üYð�ïOí�ð þ3ð�ùwð�þ4ü�û�ïeð�íX÷tþ4ùYòÉÈkùD�#÷�ùOúrû�üYð�ý�÷tþ�ÿ%û�ù��X÷tïOÿOìrüYð�ìrù�3xþ4û�÷tþ¦ÿeð�þ�ÿ%û!3øù*C�ûð�ü�û�ý?�3ð�þ!�3ð#�#û�ùJ�Òû�ï+�#÷�ù%úrû¦üYð�ý�÷tþ¦ÿ%û�ù��4û�ïOì��Yû�þ�ÿeð�ìrùP@¦î4÷E3�þ3ð� Jð�ù%÷ó��/3�ù4C�û^-3ð�ùOÿeð�þ�ÿ%÷kùOì�í�þ#ìGF3üYð�ÿOì��Xû�ù�÷�@¦î4÷ÿ%÷tþv�#÷tý ð% Jð��Y÷tïQð�î#ý�÷tþ�ÿeð�ï�ðküYð�ïOí�ðxþ3ð�ùQð�þ4ü�û�ïeð�íX÷tþ4ùYò�uøð% Jð�ù%÷kó��/3�þ3ðkð�þkj�ú�ìrù%÷¸l ÷�ùOÿ%÷�÷6 é÷tì�ÿ%ûøð�üYð�-3ð �Tû�ïù%÷tï�ü�û�þv��ìrütìrû�þ3ð�þ¦ÿ%÷xþ4û�ü�û�ý?�Tû�ïOÿeð�ý�÷tþ�ÿ%û��4ð�ð�þ4ü�û�ïeð�íX÷tý��#ûøþ!���X÷túÊn/3�ü�û�þ4ùOÿeð�ÿeð�þv�#û�.)ùe÷<î#ý�ð�î#ý�÷tþ�ÿ%û��#÷üYð�ïOí�ð¨@�î4÷��Tû��#÷tï'jHù%÷tïøý�÷�ùOý�û ý{î#ì�ÿ%û^ù%ì�í�þ#ìGF3üYð�ÿOì��Xû#òLÈ ý�÷�ùOý�û ÿOì��Òû~�#÷qü�û�ý?�Òû�ïOÿeð�ý�÷tþ¦ÿ%û½ËwüYð�ïOí�ð�ùþ3ð�ù�ð�þ4ü�û�ïeð�íX÷tþ4ù�ùOî!�T÷tïOìrû�ï%÷�ù÷qð�ý�÷tì¼ð^ð�ú�ÿOî#ïeð ü�û�ý ÿ%÷tþv�!7tþ4ütì¼ð~�3ð�ïeð¨��ì�ýêì�þ�î#ì�ï�÷{þ3ð�ùøì�þ/ é÷tïOìrû�ï%÷�ùü�û�ýÿ%÷tþv�!7tþ4ütì¼ð9�3ð�ïeð�ð�î#ý�÷tþ¦ÿeð�ï� éû�ïeð�ÿeð�ý�-�)tý û#-4ù%÷tï:��ð#�#û9�Òû�ï��?ð�þ#þ3ð�÷�� ð�ÿeð�ú�ú¼ð�þ3ðS� ó��������43Ò÷tý ÷tþ4ùeð�ìrû�ù÷tý ý�û��#÷túrûqï%÷��î!��ì;�#û#ò

���#ï%÷�ù%÷tþ�ÿeð¯.)ùe÷�þ3ðÉë�ì�í�î#ïeðkñ�ò �`Ì?ð�ù éû�ï8BYð�ùa�X÷tïOÿOìrüYð�ìrù�þ3ðP�3ð�ï%÷�#÷��#÷�ü�û�þ¦ÿ%÷tþvB�C�ûøð�û<úrû�þ#íXû �4ð�ù(��ì��X÷tï%ùeð�ù Jð�ù%÷�ù�ü�û�þ4ùOÿOïOî#ÿOì���ð�ù�3��3ð�ïeð�û�ù�ü�j�úrütî#úrû�ù��×÷hløòzÈkùJ�#û�ìrù�í�ï'j¯F3ü�û�ù��#û�ú¼ð#�#û{÷�ù*@�î4÷tï8�#û��4ð�F4í�î#ïeðï%÷6 é÷tï%÷tý.ù%÷�O ð�þkj�ú�ìrùe÷�� ÷^û�ù<�#û�ìrù<�4ðM��ì�ï%÷tì�ÿeðMO ð�þkj�ú�ìrù%÷¡l^L�û�ù�í�ï'j¯F3ü�û�ùHùOî!�T÷tïOìrû�ï%÷�ù�ï%÷6 é÷tï%÷tý.)ù%÷&O�ù�üYð�ïOí�ð�ùð��#ú�ìrüYð#�4ð�ù�3¦ü�û�ïOï%÷�ù:�Òû�þv�#÷tþ¦ÿ%÷�ùpð�ûøú¼ð#�#û{÷�ù8@�î4÷tï8�#û��4ðø÷@�î3ð#B�C�û{ñ�ò8ôø÷Éû�ù�í�ï'j¯F3ü�û�ù�ì�þ/ é÷tïOìrû�ï%÷�ùJO�ù0ï%÷Yð�üB�i�÷�ù�3ü�û�ïOï%÷�ù:�Tû�þv�#÷tþ�ÿ%÷�ùøð�ûqú¼ð#�#û$��ì�ï%÷tì�ÿ%û<�4ðný�÷�ù%ý�ðê÷@�î3ð#B�C�û#ò

� ð�þkj�ú�ìrùe÷%�4ð�ù0ð�üB�i�÷�ùQ÷��4ð�ù0ï%÷Yð�üB�i¦÷�ù´�3ð�ïeð?ûøü�j�úrütî#úrû�� �T÷tïOýêì�ÿ%÷+ Jð��Y÷tï�ð�ù0ù%÷tí�î#ì�þ�ÿ%÷�ù�û#-4ùe÷tï:��ð#B�i�÷�ùYõ

K ð>@¦î3ð�ù%÷xÿ%û�ÿeð�ú�ì;�4ð#�#÷^�4ð�ùÙüYð�ïOí�ð�ù��X÷tïOÿOìrüYð�ìrù%)xüYð�î4ùeð#�4ð>�T÷tú¼ð�ùpð�þ4ü�û�ïeð�íX÷tþ4ùA34ð�û{úrû�þ#íXû�#÷kÿ%û��4ð�ùÙð�ù Jð�ù%÷�ù<ü�û�þ4ù%ÿOïOî#ÿOì���ð�ù�33û$@�î4÷{ùOì�í�þ#ìGF3üYð?@¦î4÷û?�Ò÷�ùeû?�4ð�3ð�ï%÷�#÷�ÿ%÷tý î#ý�ð�ð�üB�C�û?�Òû�î4ü�û�ï%÷túr÷2��ð�þ¦ÿ%÷þ4û�ùxüYð�ù%û�ùx÷�ùOÿOîv�4ð#�#û�ùAL

K ð<@�î3ð�ùe÷�ÿ%û�ÿeð�ú�ì;�4ð#�#÷��4ð�ùküYð�ïOí�ð�ù��X÷tïOÿOìrüYð�ìrù�){ùOî!�Tû�ïOÿeð#�4ð$�T÷túrû�ù��T÷tï"F3ù��X÷tïOÿOìrüYð�ìrù�3��X÷tïOìGF3üYð�þv�#û�.)ùe÷@¦î4÷Cðwý�û#-#ì�ú�ì���ð#B�C�û �4ðFÿ%÷tþ4ù*C�û]ÿeð�þ#íX÷tþ4ütì¼ð�úÉþ4û]ü�û�þ¦ÿeð�ütÿ%ûÝù%û�úrû�.��3ð�ï%÷�#÷~)<�Tû�î4ü�û]ù%ì�í�þ#ìGF3üYð�ÿOì��Xû!L÷�ù%ÿeð ÿ%÷tþ4ù*C�ûwð�î#ý�÷tþ�ÿeðCþ4û ì�þ!�rütìrû��4ðCð�þkj�ú�ìrù%÷E3=ý�ð�þ�ÿ8)tý.)ù%÷?�#ïeð�ÿOìrüYð�ý�÷tþ¦ÿ%÷�ü�û�þ4ùOÿeð�þ¦ÿ%÷êþ3ð�ù^ Jð�ù%÷�ùü�û�þ4ù%ÿOïOî#ÿOì���ð�ù^ì�þ¦ÿ%÷tïOý$)��ì¼ð�ùF÷ ÿ%÷tþv�#÷ ð �#÷�ütï%÷�ù%ü�÷tï^þ3ð�ù¤Í#ú�ÿOì�ý�ð�ùD éð�ù%÷�ùAL�÷�ùOÿ%÷S Jð�ütÿ%û!3kü�û�þ/ éû�ïOý�÷ð�þ¦ÿ%÷tïOìrû�ïOý�÷tþ�ÿ%÷xì�þv��ìrüYð#�#û!3Xì�þv��ìrütì¼ð?ý�û���ì�ý�÷tþ�ÿ%û�ï%÷tú¼ð�ÿOì��Xû÷tþ�ÿOï%÷Éû?ù%û�úrûø÷Ùð��3ð�ï%÷�#÷É÷tý½@¦î4÷pð#@¦î4÷túr÷�#÷�ùeü�÷�÷tý ï%÷tú¼ð#B�C�ûHðq÷�ùOÿeð/33û?@�î4÷� Jð��{ð�î#ý�÷tþ�ÿeð�ïðqüYð�ïOí�ðqþ4û�ù%�T÷tï"F3ùÉý�÷tÿ'j�ú�ìrü�û�ùYò

u?û<@¦î4÷�ï%÷�ù:�T÷tì�ÿeð9OHð�þkj�ú�ìrù%÷­l�35÷�ÿ%÷tþv�#ûHì�í�î3ð�ú�ý�÷tþ�ÿ%÷ê÷tý ð�ÿ%÷tþvB�C�ûHû¨@�î4÷�ù%÷{û#-4ùe÷tï:�Xû�î]þ3ðHð�þkj�ú�ìrù%÷>��3�Tû��#÷ü�û�þ4ùOÿeð�ÿeð�ï".)ùe÷�û�ù%÷tí�î#ì�þ¦ÿ%÷�õ

Page 41: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â b Â

0

500

1000

1500

2000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Forç

a ve

rtic

al (k

N/m

)

Fase de construção

Força totalPeso da parede (Pparede)Força vertical nas ancoragens (Fanc,v)

ÀrÁt v -5Á����1Î�Å��

0

500

1000

1500

2000

0 1 2 3 4 5 6 7 8 9 10111213141516171819

Forç

a ve

rtic

al (k

N/m

)

Fase de construção

Força totalPeso da parede (Pparede)Força vertical nas ancoragens (Fanc,v)

À�Í�ÂTÑÜ-5Á����1Î�Å��

0

500

1000

1500

2000

0 1 2 3 4 5 6 7 8 9 10111213141516171819

Forç

a ve

rtic

al (k

N/m

)

Fase de construção

Força totalForça de adesão solo−parede (Fa)Força no perfil (Fperfil)

À#�% v -4ÄJÅOÁ����1Î�Å��

0

500

1000

1500

2000

0 1 2 3 4 5 6 7 8 9 10111213141516171819

Forç

a ve

rtic

al (k

N/m

)

Fase de construção

Força totalForça de adesão solo−parede (Fa)Força no perfil (Fperfil)

ÀrÆ�ÂTÑÜ-4ÄJÅOÁ�����Î�Å��

ýU]_�xf jAX�þp� ��Ã4� \2�qkcV_fbtvuck«`pf jAX�ngylT{k®h jlk�msTswAwlk®mskcnbwly~j~f y~]_�qk«`bXcw�mvX�j~�gXcwr�qTWj~y~]amvX�]awKTO`bXcwE��kcjltvXcw�jlTsw~]aw~�ylTWngylTswRnbkxweh�TWj°²GweTrnGXO]_ngylTWj°�ÊXcmsT! Xcw�mvX�j~�gXcw{�qTWj~y~]amvX�]aw;mskcngy~]_ngfGX�z�XªwlTWj{wlkc^ jlTWy~fb` k mvX�fbwAXc`bXcwhITWVYXªmskcz{hIkcnbTWngylT«�qTWj~y~]amvX�Ve`bXcwmvX�j~�gXcw{nGXcw{X�nbmskcjAX��qTWnbwvo¶TWz�^IkcjAXªkxwO�cX�VakcjlTsw�X�y~]_n �x]a` kxw{hIkcjTsw~yAXcw{wlT�ºlX�z wlf ^bw~yAX�nbmW]YX�V_z�TWngylTz�TWnbkcjlTswRnGX;X�nGü�V_]awlT�Û+` k�d�fbTrnGX{X�nGü�V_]awlT?¿OobX�h��xwRk]_n �amW]ak®`bXOh VYXcw~y~]�²GmvXctvuck#"

! `bXc` k�d�fbT��;X�h V_]amvXc` k¾TWz½X�z�^GXcwXcwMX�nGü�V_]awATsw�k«z�Tsw~z�k�n �_�qTWV¸` T{h jl�\��Tsw°��kcjltsk oQ]awlwlk«w~]_�xn ]�²GmvXd�fbTMXcwemvX�j~�gXcwEnGXcwEX�nbmskcjAX��qTWnbwrwlk���jlTWz5wl]_�xn ]�²GmvX�y~]_�qkxwE` TsmWjl�swlmW]_z�kxwKXck{Vakcn �qkà` k{h jlk�msTswlwlk®` TTswlmvXv�cXctvuck#"

! X�hI�xw?Xàh VYXcw~y~]�²GmvXctvuck�` kxwrhITWj°²Gwrz�TWyAü�V_]amskxwvoû�qTWj~]�²GmvX���wlT{k«wlfbmsTswlw~]_�qk«X�f z�TWngylk¾`bX®mvX�j~�gXàyAX�np��qTWnbmW]YX�VIz�kc^ ]_V_]_¬´Xc`bXOnGX?]_n�ylTWj°��XcmsTrwlkcVak��ÊhGX�jlTs` TxobXcwAw~f z{]_nb` k��xX�VakcjlTswvo�nbTsw~yAXOX�nGü�V_]awlTxop`bX?z�Tsw~z;Xkcjl` TWz ` T��xjAX�nb` TW¬´X6` kxw;d�fbT«wlT«kc^bwlTWj~�xX�z nbkxw�hITWj°²Gw{z�TWyAü�V_]amskxwvoimskcn�y~jAX�j~]YX�z�TWngylT6Xck d�fbTXcmskcngylTsmsT�nGX�X�nGü�V_]awlT?¿n"

! nGXà» V_y~]_z;X®�ÊXcwlTxoI` TW��]a` k�Xck�mskcVYX�hbwlk�` k«wlkcVak o:` TW]�[bXà` TOwATWj�hIkxwlw~�_�qTWV|X®z�kc^ ]_V_]_¬´Xctvuck�` TM��kcjltvX` T?mskcj~ylTKnGXO]_n�ylTWj°��XcmsTMwlkcVak��ÊhGX�jlTs` Tx��Ek{d�fbTrjlTsw~hITW]_yAX{Xckxw}` Tsw~Vak�mvX�z�TWngylkxw�` kylTWj~jlTWnbk obmskcnp��kcj~z�T�wlT�h�k�` TKkc^bwlTWj~�xX�j}nGXýU]_�xf jAX{þp� � 7po

Page 42: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 b Ä Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò

kxw2jlTsw~hITW]_yAX�ngylTsw¶­KX�nGü�V_]awlTR¿öz;X�ngy%$Wz��wlTETWz��cX�VakcjlTsw¶XcmsTW]_yAüs�qTW]awvo�TWnbd�fGX�ngylk?kxw|`bX�X�nGü�V_]awlT<ÛÑX�y~]_n �qTWz�xX�VakcjlTsw¸^GXcw~yAX�n�ylTEwl]_�xn ]�²GmvX�y~]_�qkxw¶Tez�Tsw~z�kMz�f ]_ylkOTWVaTW�cXc` kxw·nGXr�ÊXcwlT  þ�TxogTsw~hITsmW]YX�V_z�TWngylTxopnGXK��XcwAT ÂYl �S£X�jAXKX�Va�WzÁ` T¶k�mskcj~jlTWjlTWzÁ` Tsw~Vak�mvX�z�TWngylkxw¸�bkcj~]_¬vkcngyAX�]aw2^GXcw~yAX�n�ylT}z;X�]aw2w~]_�xn ]�²GmvX�y~]_�qkxw2nGXrX�nGü�V_]awlTÉÛ<` kd�fbTKnGX�X�nGü�V_]awlT?¿OobXhGX�j~y~]_j�`bXO��XcwAT ÂY� obk�mskcj~jlTWz']_�xfGX�V_z�TWngylTXcwlwlTWngyAX�z�TWn�ylkxwr` k{ylTWj~jlTWnbk�^GXcw~yAX�n�ylTz;X�]aw}]_z{hIkcj~yAX�ngylTswEnGXcdgfbTWVYX;X�nGü�V_]awlT?` k�d�fbTrnbTsw~yAXp�

2.5m; 0.10m

fase 4/nível 1fase 7/nível 2

fase 10/nível 3fase 13/nível 4fase 16/nível 5fase 19/nível 6

ÀrÁt v ��g¾Ê8Ï��éÅ v

2.5m; 0.10m

fase 4/nível 1fase 7/nível 2

fase 10/nível 3fase 13/nível 4fase 16/nível 5fase 19/nível 6

À�Í� v �`g¾Ê8Ï��éÅ�Ñ

ýQ]_�xf jAX�þp� � 7 � 6rTsw~Vak�mvX�z�TWngylkxw�` k{wlkcVak{nGXcweX�nGü�V_]awlTswe¿¼TÛr�¿Eh�Tsw�X�jO` Tàkxw` Tsw~Vak�mvX�z�TWn�ylkxw�bkcj~]_¬vkcngyAX�]aw�wATWjlTWz½yAX�zM^��Wz mskcnbw~]a` TWjAXv�qTWV_z�TWngylT�wlf h�TWj~]akcjlTswOnGX

X�nGü�V_]awlT?Ûroq�ÊX�¬W��wlTEnbkcyAX�jikxw·jlTsw~f V_yAXc` kxw}` kxw¶` Tsw~Vak�mvX�z�TWngylkxw}�qTWj~y~]amvX�]awikc^ y~]a` kxwinbTsw~yAXOX�nGü�V_]awlTxo�h�k�` TWnp�` kàmskcnbw~yAX�yAX�j°��wlTxo�nGX�ÊXcwlT ÂY� Txo�` T?��kcj~z;X�hGX�j~y~]amWf VYX�j~z�TWn�ylT{TW��]a` TWn�ylTxoInGX�ÊXcwlT  þpo:X;k�mskcj~j%$WnbmW]YXà` Tf z;X�¬vkcnGXK` TiylTWj~jlTWnbkKnGXcw|]_z�Ts`p]YXcts¯�Tsw·`bX�hGX�jlTs` TR` T}mskcngylTWnbtvuck o�mskczÁ` Tsw~Vak�mvX�z�TWngylkxw·�qTWj~y~]amvX�]aw2hGX�j°�y~]amWf VYX�j~z�TWngylT�TWVaTW�xXc` kxw·TRd�fbT}wAuckKz�kcy~]_�xXc` kxw·h�TWVakxw2z�k´��]_z�TWn�ylkxw¶�qTWj~y~]amvX�]aw·`bXrhGX�jlTs` Txo�d�fbT}hGX�jlTsmsTWzX�j~jAXcw~yAX�jemskcnbwl]_�qk�k{wlkcVak �\|wlylT;T\��TW]_ylk�mWf V_z{]_nGXpo£nGX��ÊXcwlT ÂYl oQmskcz Xà��kcj~z;Xctvuck©` T�f z;X�mWf n �GX�` T®wlkcVak�mskcz½�cX�VakcjlTswO` kxw

` Tsw~Vak�mvX�z�TWngylkxwrzMf ]_ylkàwl]_�xn ]�²GmvX�y~]_�qkxwvoITWng�qkcV_�qTWnb` k«kàwlkcVak®X;f z;X;`p]awlyAÿ�nbmW]YX;`bX;hGX�jlTs` TOz�f ]_ylkàz;X�]awmskcnbw~]a` TWjAüv�qTWV.` k{dgfbTKX�n�ylTWj~]akcj~z�TWngylTxo��qTWj~]�²GmvX�nb` k���wlTxobhIkcj~yAX�ngylk oGXM]_z{]_n4$WnbmW]YX{` k{mskcVYX�hbwAk{` TEylk�`bX{XTswlmvXv�cXctvuck �

Ï�Ò©Û,ÕH��Í,Ï�Ð Î�Ϲ z�TsmvX�n ]aw~z�k®` TMmskcVYX�hbwlkà` T?hGX�jlTs` Tsw�` T�mskcngylTWnbtvuckày~]_hIk�ÛiTWj~V_]_z5��kc]Êo�Xcwlw~]_z�oG` TswAmWj~]_ylkàX�y~jAXv�q�sw

`bXMmskcz{hGX�jAXctvuck{` TE` kc]aw¶mvXcwlkxwi` TETswly~fb` k�n�f z��Wj~]amskxw � f zÀTWz d�fbTenGuckO�Eh�TWj~z{]_y~]a`bXXKh VYXcwly~]�²GmvXctvuck` kxweTWVaTWz�TWn�ylkxwEd�fbTKz�k�` TWVYX�z5kxweh�TWj°²Gw}�qTWj~y~]amvX�]aw�TKf z'kcf y~jlk®TWz'd�fbT�X{mvX�j~�gX{nbTswlylTswRTWVaTWz�TWngylkxwr�V_]_z{]_yAXc`bX;­mvX�hGXcmW]a`bXc` T�jlTsw~]aw~ylTWn�ylT�­{TWnbmWf j~�xXc`pf jAXp�¸S(\�` TxoGXcwAw~]_z�o mskcnbw~yAX�yAX�j°��wlT?d�fbT �

! X©jlTswl]aw~y%$WnbmW]YXªnGXª]_n�ylTWj°��XcmsT���ylkcyAX�V_z�TWn�ylT�z�kc^ ]_V_]_¬´Xc`bX�X�h��xw;X©h VYXcwly~]�²GmvXctvuck�` kªhITWj°²bVJ"RTsw~yAXz�kc^ ]_V_]_¬´XctvuckO�ÊX�¬W��wlT�` TR��kcj~z;XMw~» ^ ]_yAX�TEz;X�ngyl�Wz��wAT?X�yl��XckOmskcVYX�hbwlk`bX�TswAmvXs�xXctvuck#"pnbkMmvXcwlkO`bX

Page 43: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

Å2ÆWÇ�ÈÊÉ~ËcÌ�ÍàÎqÏ�Ð|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò�Ô ÕKÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò Â b �

X�nGü�V_]awlTrTWzÀdgfbTEnGuck�ehITWj~z{]_y~]a`bXX?h VYXcw~y~]�²GmvXctvuck obX?��kcjltvX?nGX�]_ngylTWj°�ÊXcmsTr�cX�]�wlk���jlTWnb` kMjlTs`pfbtvuckw~fbmsTswlwl]_�cXpobXck{Vakcn �qk;`bX{X�nGü�V_]awlT�"

! Xcw|mvX�j~�gXcw2nGXcw|X�nbmskcjAX��qTWnbw·wlk���jlTWzÁw~]_�xn ]�²GmvX�y~]_�qkxw|` TsmWjl�swlmW]_z�kxwvo�ml�bTW�gX�nb` k�z�Tsw~z�k?XrX�ngf VYX�j°��wlTxod�fGX�nb` k{wlT��qTWj~]�²GmvX{kmskcVYX�hbwlk{`bXTswlmvXs�xXctvuck obmskcz T\[ msTWh�tvuck`bX{X�nbmskcjAX��qTWz'` k» V_y~]_z�kn �_�qTWVÊod�fbT?wlk���jlTKw~]_�xn ]�²GmvX�y~]_�qkxwEX�f z�TWn�ylkxwE` TKmvX�j~�gX�"

! XE��kcjltvXr` T}mskcj~ylTinGX�]_ngylTWj°�ÊXcmsTRwlkcVak��ÊhGX�jlTs` T}z;X�n�yl�Wz��wlTeTWz��xX�VakcjlTsw£z�f ]_ylkK^GX�]�[ kxw|T}` TsmWjlTswlmsTWnp�ylTswrdgfGX�nb` kànGuck�wlTXc`pz{]_ylT{X�hIkxwlw~]_^ ]_V_]a`bXc` T` TOh VYXcw~y~]�²GmvXctvuck�` kàh�TWj°²bVQz;Xcw?Xcwlw~f z�TM�cX�VakcjlTswmWjlTswlmsTWn�ylTsw�T«X�y~]_n �x]_nb` k�X¾z�Tsw~z;X©kcjl` TWz ` T®�xjAX�nb` TW¬´X `bXcw{mvX�j~�gX�y~jAX�nbwlz{]_y~]a`bXcw;Xckxwh�TWj°²Gwd�fGX�nb` k�wlTKmskcnbw~]a` TWjAX®XOh�kxwlwl]_^ ]_V_]a`bXc` T?` TKTsw~ylTsw}h VYXcw~y~]�²GmvX�jlTWzw"

! kxw|` Tsw~Vak�mvX�z�TWngylkxw¸�bkcj~]_¬vkcngyAX�]aw¶Ti�qTWj~y~]amvX�]aw¸wlk���jlTWzÁw~]_�xn ]�²GmvX�y~]_�qkxw¶XcmWjl�swlmW]_z�kxw·X�hGX�j~y~]_j¸`bX�h VYXcw~�y~]�²GmvXctvuck�` kxw?h�TWj°²Gwrz�TWyAü�V_]amskxwvoQX�y~]_n �x]_nb` k��xX�VakcjlTsw?T\[py~jlTWz;X�z�TWngylT;TWVaTW�xXc` kxw?Ty~jAXc`pf ¬s]_nb` k¾kmskcVYX�hbwlk«`bXàTswlmvXv�cXctvuck#"UkxwK` Tsw~Vak�mvX�z�TWn�ylkxwK�qTWj~y~]amvX�]aw?`bX®hGX�jlTs` T{wAuck�w~f hITWj~]akcjlTsw?XckxwK` Tsw~Vak�mvX��z�TWngylkxwE�qTWj~y~]amvX�]awe` k{wAkcVak;Xc`�º~XcmsTWn�ylT�"

! X�hGX�j~y~]_j¶`bX?h VYXcw~y~]�²GmvXctvuck` kxw¸hITWj°²Gw¸�qTWj~]�²GmvX���wATef z±X�f z�TWngylkw~fbmsTswlwl]_�qk�`bX�¬vkcnGX?h VYXcw~y~]�²GmvXc`bX` k�wlkcVak{wlf h�kcj~yAXc` k obd�fbTKmskcngy~]_n�fGX®X�yl�MXck{mskcVYX�hbwlk#"

Page 44: ÙgÍOÚIÕ~ÛÈÊÜ ÕlÝaÒ Þ¶ÖsÍvÓvÉ Ý × Æ ÒRßàËcÌÊÉ ÝYáÊÆ …jaime/capitulo6.pdf · Å2ÆWÇ ÈÊÉ~ËcÌ ÍàÎqÏÐ|ÒvÉ ÓvË É~ËcÓ Æ Ò Ô ÕKÖsÍv×

 b à Å2ÆWÇ�ÈÊÉ~ËcÌ�Í®ÎqÏÑÐ|ÒvÉ�ÓvË É~ËcÓ�Æ�Ò?Ô Õ?ÖsÍv×�É�Õl×IØ\ÙgÍOÚIÕ~Û�ÈÊÜ�ÕlÝaÒ�Þ¶ÖsÍvÓvÉ�Ý_×�Æ�ÒRßàËcÌÊÉ�ÝYáÊÆ�×IÖsÍvÓ�ÆgÔ�Æ�Ò