Кочетов Сопротивление материалов (968718), страница 11
Текст из файла (страница 11)
WJ DG[Z² hj^bgZlZ gZ wixj_ fhf_glh\ hl _^bgbqghc kbeu ih^ p_gljhf ly`_klb wixju FLh]^Z bgl_]jZe ijbgbfZ_l \b^ ³ Z Ijhba\_^_gb_[. WJ , 0 ]^_ 0 < blh]_ bgl_]jZe FhjZ aZibr_lky \ \b^_GZ0 (,>ey hij_^_e_gby i_j_f_s_gby ih ijZ\bem <_j_sZ]bgZ g_h[oh^bfh agZlviehsZ^v wixju fhf_glh\ hl \g_rg_c gZ]jmadb b gZclb iheh`_gb_ __ p_gljZly`_klb ?keb wixjZ fhf_glh\ bf__l keh`gmx dhgnb]mjZpbx lh __ jZa[b\Zxl gZ ijhklu_ iehsZ^b Z ZZ3 b gZoh^yl iheh`_gb_ p_gljh\ ly`_klb ^ey dZ`^hc iehsZ^b Kljhblky wixjZ fhf_glh\ hl _^bgbqghc kbeu beb_^bgbqgh]h fhf_glZ \ aZ\bkbfhklb hl lh]h hij_^_ey_lky beb T Ih^ p_gljhf ly`_klb wixj fhf_glh\ hl \g_rg_c gZ]jmadb [_jmlky hj^bgZlu gZwixj_ fhf_glh\ hl _^bgbqguo kbeh\uo nZdlhjh\ KmffZ ijhba\_^_gbc¦Z hlg_k_ggZy d `_kldhklb jZkkfZljb\Z_fh]h we_f_glZ ^Zkl i_j_f_s_gb_ \ jZkkfZljb\Z_fhc lhqd_F «mIjbf_j GZclb i_j_f_s_gb_ lhqdb ijbeh`_gby khkj_^hlhq_gghc kbeu \ dhgkhevghc [Zed_ jbk J_r_gb_Kljhbf wixjm fhf_glh\ hl kbeu J jbk [ b hij_^_ey_f __ iehsZ^vZ J Kljhbf wixjm fhf_glh\ hl _^bgbqghc kbeu 3 WlZ kbeZ ijbdeZ^u\Z_lky\ lhqd_ \ dhlhjhc bs_lky i_j_f_s_gb_ ih gZijZ\e_gbx ^_ckl\by aZ^Zgghckbeu ! jbk \ Hj^bgZlZ ih^ p_gljhf ly`_klb wixju F gZ wixj_b fhf_glh\ hl _^bgbqghc kbeu jZ\gZ[m^_l jZ\ghGZ0 .(,F lh]^Z i_j_f_s_gb_ lhqdb3O O O 3O (,(,LZdbf h[jZahf fu ihemqbf lhl `_ j_amevlZl qlh b ijb j_r_gbb wlhc aZ^Zqb\ ij_^u^msbo r_klb kemqZyo Ijbf_j >ey dhgkhevghc [Zedb gZ]jm`_gghc khkj_^hlhq_gghc kbehc Jkhkj_^hlhq_gguf fhf_glhfmF b jZ\ghf_jgh jZkij_^_e_gghc gZ]jmadhc hij_^_eblv ijh]b[ : b m]he ih\hjhlZjbk J_r_gb_T dhgp_\h]h k_q_gby ih ijZ\bem <_j_sZ]bgZKljhbf wixju ba]b[Zxsbo fhf_glh\ hl \g_rg_c gZ]jmadbghc kbeu3 b _^bgbqgh]h fhf_glZ Hij_^_ey_f ijh]b[ \ lhqd_\:Z0 Z 0 Z 0 (,(,(,J F b hl _^bgbq 3O O 0 O O TO O O O (, (, (, 3O 0O TO (, (, (, b m]he ih\hjhlZ dhgp_\h]h k_q_gby [ZedbTÇZ0 ÄÂ(,ÇZ 0 ÄÂ(,ÇZ 0 ÄÂ(, 3O O 0 O TO O (,(, (,3O 0O TO (, (, (,GZ jbk [±_ ihdZaZgu khhl\_lkl\_ggh wixju fhf_glh\ hl khkj_^hlhq_gghc kbeu J khkj_^hlhq_ggh]h fhf_glZ F jZ\ghf_jgh jZkij_^_e_gghcgZ]jmadb 6 _^bgbqghc kbeu ! b _^bgbqgh]h fhf_glZ 0 Ijb bkihevah\Zgbb ijZ\beZ <_j_sZ]bgZ ijboh^blky hi_jbjh\Zlv iehsZ^yfbwixj b iheh`_gbyfb p_gljh\ ly`_klb wixj ba]b[Zxsbo fhf_glh\ dhlhju_fh]ml [ulv kZfufb jZaebqgufbGb`_ ijb\h^ylky ko_fu qZklh \klj_qZxsboky [Zehd bo wixju b iheh`_gbyp_gljh\ ly`_klb < ko_fZo ihdZaZgguo gZ jbk Z hagZqZ_l iehsZ^v wixju fhf_glh\ Z 1 ² gZb[hevrbc ba]b[Zxsbc fhf_gl gZ khhl\_lkl\mxs_c wixj_fhf_glh\ À¿ÄÂÀ½Î¿Í·´ÀÁÂÀÃÍDZdbfb \_ebqbgZfb oZjZdl_jbam_lky ijb ihi_j_qghf ba]b[_ `_kldhklv[Zedb"DZd aZibku\Z_lky ijb[eb`_ggh_ ^bnn_j_gpbZevgh_ mjZ\g_gb_ bah]gmlhc hkb [Zedb"H[tykgbl_ kfukeh\mx klhjhgm f_lh^Z g_ihkj_^kl\_ggh]h bgl_]jbjh\ZgbyDZd aZibku\Z_lky mgb\_jkZevgh_ mjZ\g_gb_ mijm]hc ebgbb [Zedb"Qlh ihgbfZ_lky ih^ nbdlb\ghc gZ]jmadhc ijb hij_^_e_gbb ijh]b[Z ]jZnhZgZeblbq_kdbf f_lh^hf"GZ q_f hkgh\Zg wg_j]_lbq_kdbc f_lh^ hij_^_e_gby i_j_f_s_gbc [Zedb"Knhjfmebjmcl_ l_hj_fm h \aZbfghklb jZ[hlKnhjfmebjmcl_ l_hj_fm DZkl_evyghDZd aZibku\Z_lky bgl_]jZe FhjZ"DZd hij_^_eyxlky i_j_f_s_gby ih ijZ\bem <_j_sZ]bgZ"½²´²£½À¸¿À·ÃÀÁÂÀĺ´½·¿º·ÀÃÀ»º¹µº³JZg__ jZkkfZljb\Zebkv ijhkl_crb_ \b^u ^_nhjfZpbb jZkly`_gb_ ² k`Zlb_k^\b] djmq_gb_ ihi_j_qguc ba]b[ GZ ijZdlbd_ lZdb_ ijhklu_ ^_nhjfZpbb\klj_qZxlky \_kvfZ j_^dh DZd ijZ\beh gZ ^_lZeb fZrbg b we_f_glu dhgkljmdpbc ^_ckl\m_l dhf[bgZpby \g_rgbo kbeh\uo nZdlhjh\ kha^Zxsbo g_kdhevdh ijhkluo ^_nhjfZpbc GZijbf_j ex[hc \Ze h^gh\j_f_ggh bkiulu\Z_l ba]b[ djmq_gb_ b k^\b] ^Z`_ ijhklZy ^_lZev ² [hel jZ[hlZ_l gZ keh`gmx^_nhjfZpbx gZ g_]h h^gh\j_f_ggh ^_ckl\mxl jZkly`_gb_ b djmq_gb_Ijb jZkq_l_ ^_lZe_c fZrbg beb we_f_glh\ dhgkljmdpbc bkihevamxl h[uqghijbgpbi g_aZ\bkbfhklb ^_ckl\by kbe jZkkqblu\Zxl we_f_gl gZ h^bg \b^^_nhjfZpbb aZl_f gZ ^jm]hc b ihke_ wlh]h ^_nhjfZpbb beb gZijy`_gbykmffbjmxlkyDhkhc ba]b[ ² wlh h^bg ba kemqZ_\ keh`gh]h khijhlb\e_gby dh]^Z iehkdhklv ^_ckl\by ba]b[Zxsbo fhf_glh\ g_ kh\iZ^Z_l gb k h^ghc ba ]eZ\guoiehkdhkl_c [ZedbJZkkfhljbf ijbf_j dh]^Z gZ [Zedm ijyfhm]hevgh]h k_q_gby aZs_fe_ggmxh^gbf dhgphf ^_ckl\m_l kbeZ J b iehkdhklv ^_ckl\by wlhc kbeu g_ kh\iZ^Z_lgb k iehkdhklvx [R] gb k iehkdhklvx ohm Wlh b _klv kemqZc dhkh]h ba]b[ZGZ jbk Z ihdZaZgZ dhgkhevgZy [ZedZ gZ dhlhjmx ^_ckl\m_l kbeZ Jijbeh`_ggZy ih^ m]ehf , d \_jlbdZevghc hkb m kha^ZxsZy \ ijhba\hevghfk_q_gbb ba]b[Zxsbc fhf_gl ih Z[khexlghfm agZq_gbx jZ\guc 0 3[Kbem J jZaeh`bf gZ ^\_ khklZ\eyxsb_ Jm b 3] Wlb kbeu ^_ckl\mxl \ ]eZ\guo iehkdhklyo ohm b [R] b kha^Zxl fhf_glu0\3] [J  o  VLQ ,0]3\ [J  o  FRV ,LZdbf h[jZahf kemqZc dhkh]h ba]b[Z fh`gh k\_klb d ^\mf ijhkluf ihi_j_qguf ba]b[Zf bkihevamy ijbgpbi g_aZ\bkbfhklb ^_ckl\by kbe½²´² ?keb \aylv \ jZkkfZljb\Z_fhf k_q_gbb ijhba\hevgmx lhqdm 1 k dhhj^bgZlZfb m b ] lh jZkly]b\Zxsb_ gZijy`_gby \ wlhc lhqd_ \uau\Z_fu_ ba]b[Zxsbfb fhf_glZfb 0\ b 0] [m^ml jZ\gu8 0 ] \ , ] b 8 0 \ ] , \< ^jm]bo lhqdZo jZkkfZljb\Z_fh]h k_q_gby kha^Zxlky k`bfZxsb_ gZijy`_gby [m^_f kqblZlv bo hljbpZl_evgufbMqblu\Zy qlh fhf_glu 0] b 0\ ² khklZ\eyxsb_ fhf_glZ F gZijy`_gb_\ lhqd_ 1 gZc^_f dZd8 8 8 0 ] \ , ] 0 \ ] , \< wlm nhjfmem dhhj^bgZlu m b ] ^he`gu \\h^blvky kh k\hbfb agZdZfb < gZr_f kemqZ_ h[_ dhhj^bgZlu m b ] ² iheh`bl_evgu_ l d lhqdZ 1 gZoh^blky\ i_j\hc q_l\_jlb wlZ ahgZ k_q_gby ih^\_j]gmlZ jZkly`_gbx ?keb `_ lhqdm1 [jZlv \h \lhjhc lj_lv_c b q_l\_jlhc q_l\_jlyo lh __ dhhj^bgZlu [m^mlbf_lv khhl\_lkl\mxsb_ agZdb m ±] ±m ±] ±m ]Ihkdhevdm ij_^_evgufb agZq_gbyfb dhhj^bgZl m b ] [m^ml agZq_gby K b E Z bf khhl\_lkl\mxl lhqdb k_q_gby : < K ' lh ih^klZ\eyy agZq_gbydhhj^bgZl m b ] ^ey wlbo lhq_d \ \ujZ`_gb_ fh`gh m[_^blvky qlhgZb[hevrb_ gZijy`_gby [m^ml \ lhqdZo : b K < lhqd_ : [m^_l gZb[hevr__gZijy`_gb_ k`Zlby Z \ lhqd_ K ² gZb[hevr__ gZijy`_gb_ jZkly`_gbyWlh e_]dh aZf_lblv _keb jZkkfZljb\Zlv \gZqZe_ ^_ckl\b_ gZ [Zedm fhf_glZ 0]£½À¸¿À· ÃÀÁÂÀĺ´½·¿º·jZkly]b\Zxs_]h \_jogb_ \hehdgZ b k`bfZxs_]h gb`gb_ Z aZl_f fhf_glZ 0\jZkly]b\Zxs_]h ijZ\u_ \hehdgZ b k`bfZxs_]h e_\u_ GZ jbk \ wlhihdZaZgh agZdZfb iexk b fbgmkMqblu\Zy qlh \ lhqdZo K b : ^_ckl\mxl khhl\_lkl\_ggh gZb[hevrb_ b gZbf_gvrb_ gZijy`_gby f_`^m gbfb ^he`_g jZkiheZ]Zlvky g_gZ]jm`_gguckehc fZl_jbZeZ [Zedb ?]h ijbgylh gZau\Zlv g_cljZevghc ebgb_c>ey hij_^_e_gby iheh`_gby g_cljZevghc ebgbb ijbjZ\gy_f gmex mjZ\g_gb_0 ]\ , ] 0 \] , \beb3[\ FRVD,]3[] VLQ] VLQD,\Hlkx^Z ihemqbf\ FRV,]DD,\Ihemq_ggh_ mjZ\g_gb_ gZau\Z_lky mjZ\g_gb_f g_cljZevghc ebgbbWlhfm mjZ\g_gbx g_cljZevghc ebgbb m^h\e_l\hjyxl agZq_gby \ b ] ke_^h\Zl_evgh g_cljZevgZy ebgby ijhoh^bl q_j_a p_glj ly`_klb ihi_j_qgh]h k_q_gby?keb \aylv hlghr_gb_ \ ] lh ba \ujZ`_gby ihemqbfWJ-±\ ]±WJ,,] ,\Wlh hagZqZ_l qlh ^ey hij_^_e_gby iheh`_gby g_cljZevghc ebgbb ^hklZlhqgh agZlv m]he , b fhf_glu bg_jpbb jZkkfZljb\Z_fh]h k_q_gby?keb ,] ,\ lh dhkh]h ba]b[Z g_ [m^_l l _ [Zedb djm]eh]h beb d\Z^jZlgh]hihi_j_qgh]h k_q_gby ih^\_j]Zxlky h[uqghfm ihi_j_qghfm ba]b[m ih^ dZdbf [u m]ehf gZ gbo gb ^_ckl\h\Zeb \g_rgb_ gZ]jmadbGZfb jZkkfhlj_g qZklguc kemqZc dhgkhevghc [ZedbNhjfmeZ ^ey hij_^_e_gby gZijy`_gbc [m^_l kijZ\_^eb\Z b ^ey ^jm]bo [Zehd ihwlhfm mkeh\b_ ijhqghklb ijb dhkhf ba]b[_ fh`_l [ulv aZibkZgh ^ey ex[hc [Zedb \ ke_^mxs_f \b^_§ FRV D·VLQ Dr 0 PD[ ¨\] ¸ d >V @ ¨ ,]¸,\©¹]^_ ] b m ² dhhj^bgZlu lhqdb gZb[he__ m^Ze_gghc hl g_cljZevghc ebgbbV PD[½²´² DZkZl_evgu_ gZijy`_gby \ ihi_j_qguo k_q_gbyo [Zedb bkiulu\Zxsbo dhkhc ba]b[ fh]ml [ulv gZc^_gu lZd`_ ih ijbgpbim g_aZ\bkbfhklb ^_ckl\bykbe· §¨ 4 ] 6 \¸¸ ¹ ¨© , \ K§ 4\ 6 ]¨¨© , ]EW PD[·¸ d >W@ ¸¹Ba \ujZ`_gby \b^gh qlh \ g_f bkihevam_lky nhjfmeZ @mjZ\kdh]hIh dZkZl_evguf gZijy`_gbyf ijh\_jdZ [Zedb jZ[hlZxs_c gZ dhkhc ba]b[ijhba\h^blky djZcg_ j_^dh Á·¶·½·¿º·Á·Â·¾·Ë·¿º»Áº¼ÀÃÀ¾º¹µº³·I_j_f_s_gby ijb dhkhf ba]b[_ fh]ml [ulv hij_^_e_gu dZd b gZijy`_gbyih kihkh[m g_aZ\bkbfhklb ^_ckl\by kbe Ijb jZkkfhlj_gbb ijbf_jZ ijb\_^_ggh]h \ ij_^u^ms_f iZjZ]jZn_ ijh]b[ \ lhqd_ ijbeh`_gby kbeu J fh`_l[ulv gZc^_g dZd ]_hf_ljbq_kdZy kmffZ ijh]b[h\ I] b I\ khhl\_lkl\_ggh jZ\guo3 O 3O VLQ ,I] I\](, \3\ O(, \3O(, ] FRV D(, ]Lh]^Z kmffZjguc ijh]b[ gZc^_f ih nhjfme_IMqblu\Zy qlh hlghr_gb_ I] I\I]I\I]WJ-D ,]FRV D , \VLQI\,],\WJDWJEIjb kjZ\g_gbb nhjfme b \b^gh qlh m]he f_`^m iehkdhklvxba]b[Z b hkvx m ih Z[khexlghc \_ebqbg_ jZ\_g m]em f_`^m g_cljZevghc ebgb_c k_q_gby b hkvx ] Ke_^h\Zl_evgh iheguc ijh]b[ I ijb dhkhf ba]b[_i_ji_g^bdmeyj_g d g_cljZevghc ebgbb k_q_gbyIjbf_j ;ZedZ ^\mlZ\jh\h]h k_q_gby aZs_fe_ggZy h^gbf dhgphf ba]b[Z_lky kbehc 3 G dhlhjZy ijbeh`_gZ gZ k\h[h^ghf dhgp_£½À¸¿À· ÃÀÁÂÀĺ´½·¿º·Iehkdhklv ^_ckl\by kbeu khklZ\ey_l m]he , k ]eZ\ghc iehkdhklvx oHmHij_^_eblv gZijy`_gb_ \ hiZkghf k_q_gbb [Zedb b gZclb ihegh_ i_j_f_s_gb_k\h[h^gh]h dhgpZ [Zedb _keb O O f Z >8@ FIZ jbk J_r_gb_Ih =HKL ± \u[bjZ_f agZq_gby fhf_glh\ bg_jpbb ^ey [Zedb ,] kf ,m kf HiZkgh_ gZijy`_gb_ [m^_l \hagbdZlv \ aZ^_ed_ [Zedb \ lhqdZo k_q_gby : b <l d \ lhqd_ : [m^_l gZb[hevr__ jZkly]b\Zxs__ gZijy`_gb_ Z \ lhqd_ < ²gZb[hevr__ k`bfZxs__ gZijy`_gb_GZoh^bf gZb[hevrbc ba]b[Zxsbc fhf_gl0PD[ 3O b b Gf b GffIh nhjfme_ gZoh^bf hiZkgh_ gZijy`_gb_ \ aZ^_ed_ [Zedb§ FRV D·VLQ DPD[ ¨¨ , \ , ] ¸¸ d >V@\© ]¹Kh]eZkgh =HKLm ± rbjbgZ [Zedb E ff __ \ukhlZke_^h\Zl_evgh dhhj^bgZlu ] ff Z \ ffV PD[V PD[0Kff§ · ¨ ¸ © ¹ nq¶ ! >V @ nq¶ GZijy`_gby \ hiZkguo lhqdZo k_q_gbc : b < ij_\urZxl ^himklbfh_ gZ qlh \iheg_ ijb_fe_fh½²´² GZoh^bf \_ebqbgm ihegh]h ijh]b[Z [Zedb ih nhjfme_ I] I\ 3O VLQ , b b b  ÂÂ(, \ b b b b3O FRV , b b b  ÂÂ(, ] b b b b  ff y\ey_lky ^himklbfuf b [Zedm fu \u[jZebIIjh]b[ [Zedb\_jghI ¿·È·¿Ä·¿¿À·Ã¸²Äº·º½ºÂ²ÃÄѸ·¿º·Ij_^iheh`bf qlh gZ kl_j`_gv ijyfhm]hevgh]h k_q_gby ^_ckl\m_l k`bfZxsZy kbeZ J kf_s_ggZy hlghkbl_evgh p_gljZ ly`_klb k_q_gby H gZ \_ebqbgm _gZau\Z_fmx wdkp_gljbkbl_lhf jbk Z Ijb ijbeh`_gbb kbeu J \ lhqd_ : k_q_gby kl_j`gy [m^ml bkiulu\Zlv k`Zlb_ b ihi_j_qguc ba]b[ KbeZ J ijb\_^_ggZy d p_gljm k_q_gby H [m^_lk`bfZlv kl_j`_gv b \uau\Zlv \ _]h k_q_gbyo gZijy`_gby jZ\gu_8k` ±3 )IjhkljZgkl\_ggZy wixjZ wlbo gZijy`_gbc ihdZaZgZ gZ jbk [IZjZ kbe fhf_gl dhlhjhc jZ\_g \uah\_l qbkluc ba]b[ kl_j`gy hlghkbl_evgh hkb m GZijy`_gby \ua\Zggu_ iZjhc kbe hij_^_eyxlky ih nhjfme_03H8 H0 :\ H3H :\IjhkljZgkl\_ggZy wixjZ wlbo gZijy`_gbc ihdZaZgZ gZ jbk \ Mkeh\b_ijhqghklb ^ey jZkkfZljb\Z_fh]h gZ]jm`_gby kl_j`gy aZibr_f \ ke_^mxs_f\b^_8 ±3 ) H 3H :\ @ >8k`@Hq_\b^gh qlh k`bfZxsb_ gZijy`_gby ih fh^mex [m^ml [hevr_ q_f jZkly]b\Zxsb_ KmffZjgZy wixjZ gZijy`_gbc ij_^klZ\e_gZ gZ jbk ] Bawlhc wixju \b^gh dZd kf_klbeky g_cljZevguc kehc hlghkbl_evgh hkb ] dhlhjZy ijb h[uqghf ihi_j_qghf ba]b[_ k gbf kh\iZ^Z_l;he__ h[sbc kemqZc \g_p_glj_ggh]h k`Zlby gZ[ex^Z_lky dh]^Z \g_rgyykbeZ J g_ e_`bl gb \ h^ghc ba ]eZ\guo iehkdhkl_c kbff_ljbb jbk bijbeh`_gZ \ dZdhclh ijhba\hevghc lhqd_ : k dhhj^bgZlZfb P b Q Ijb\_^_f aZ^Zggmx kbem J d p_gljm k_q_gby H Ijb wlhf kbeZ h[hagZq_ggZy^\mfy q_jlhqdZfb [m^_l k`bfZlv kl_j`_gv b \uau\Zlv gZijy`_gb_ jZ\gh_± Z iZjZ kbe k fhf_glhf jZ\guf J b :H [m^_l ba]b[Zlv kl_j`_gv3) JZaeh`bf wlm iZjm gZ ^\_ khklZ\eyxsb_ Ijb wlhf h^bg khklZ\eyxsbc fhf_gl jZ\guc J [m^_l ba]b[Zlv kl_j`_gv hlghkbl_evgh hkb m Z \lhjhc ²k fhf_glhf J ² [m^_l ba]b[Zlv kl_j`_gv hlghkbl_evgh hkb GZc^_f kmffZjgh_ gZijy`_gb_ 8 \ ijhba\hevghc lhqd_ < k_q_gby k dhhj^bgZlZfb b m hl ^_ckl\by k`bfZxs_c kbeu J b khklZ\eyxsbo fhf_glh\ JbJ PQ]]PQGZijy`_gby \ djZcgboxlky dZd8< ±3 ) ± 3Q\ , ± 3P] ,\lhqdZo k_q_gby K ' ? ) ih½°), ], \°33QK3PE °V' °), ], \°¾33QK3PE°V( °), ], \°33QK3PE °V) °), ], \¿Ijb wlhf mqblu\Zeky agZd dhhj^bgZl lhq_d K ' ? )\b^gh qlh lhqdZ K bkiulu\Z_l gZb[hevr__ k`Zlb_ Z[m^_l ih^\_j]Zlvky jZkly`_gbxV&33QK3PEZgZeh]bbhij_^_eyBa nhjfme lhqdZ ? \_jhylgh>ey hij_^_e_gby agZdZ gZijy`_gbc \ djZcgbo lhqdZo ijhba\hevgh]h k_q_gbygZ^h agZlv iheh`_gb_ g_cljZevgh]h kehy l _ gme_\hc ebgbbMjZ\g_gb_ gme_\hc ebgbb fh`_l [ulv ihemq_gh ijb jZ\_gkl\_ gmex \ujZ`_gby l d ih g_cljZevghfm kehx gZijy`_gby g_ ^_ckl\mxl±3 ) ± 3Q\ , ± 3P] ,\ Ij_h[jZam_f wlh \ujZ`_gb_ \ughky 3 ) aZ kdh[db±3 ) )Q\ , )P] ,\ Hlghr_gb_ 3 ) g_ fh`_l [ulv jZ\gh gmex l d J b ) ² j_Zevgu_ \_ebqbguKe_^h\Zl_evgh gmex fh`gh ijbjZ\gylv lm qZklv dhlhjZy gZoh^blky \ kdh[dZo )Q\ ,] )P] ,\ Gh hlghr_gb_ , ) L dZd ba\_klgh _klv jZ^bmk bg_jpbb k_q_gby \ d\Z^jZl_kf jZa^ <\h^y ,] ) L] b ,\ ) L\ \ mjZ\g_gb_ ihemqbf Q\ L P] L\ <ujZ`_gb_ y\ey_lky hdhgqZl_evguf mjZ\g_gb_f g_cljZevghc ebgbb?keb \ wlh mjZ\g_gb_ ihhq_j_^gh \\h^blv agZq_gby b lh fh`gh gZclb hlj_adb H b H hlk_dZ_fu_ g_cljZevghc ebgb_c gZ hkyo dhhj^bgZl m b Ijb ± ].\2.\.]]L\Pijb H ? ± Hleh`b\ hlj_adb b H khhl\_lkl\_ggh ih hkyf b m b kh_^bgb\ lhqdbb ihemqbf iheh`_gb_ g_cljZevghc beb gme_\hc ebgbb KijZ\Z hl gme_\hcebgbb [m^_l ahgZ k`Zlby Z ke_\Z ² ahgZ jZkly`_gbyGZ jbk [ ihdZaZgZ wixjZ ghjfZevguo gZijy`_gbc kl_j`gy gZ]jm`_ggh]h kbehc J].L]\2.Q.]..?¡À¿Ñĺ·ÀѶ·÷ɷ¿ºÑY^jh k_q_gby ² wlh lZdZy ahgZ ijbeh`_gby k`bfZxs_c beb jZkly]b\Zxs_c\g_p_glj_gghc gZ]jmadb ijb ^_ckl\bb dhlhjhc \k_ \hehdgZ kl_j`gy bkiulu\Zxl h^bg \b^ ^_nhjfZpbb jZkly`_gb_ beb k`Zlb_ GZf ba\_klgh qlhkljhbl_evgu_ dhgkljmdpbb \ [hevrbgkl\_ k\h_f ba]hlZ\eb\Zxlky ba ojmidbofZl_jbZeh\ dbjibq [_lhg `_e_ah[_lhg Wlb fZl_jbZeu ohjhrh jZ[hlZxlgZ k`Zlb_ b ijZdlbq_kdb g_ l_jiyl jZkly]b\Zxsbo mkbebc ihwlhfm ijb bobkihevah\Zgbb g_h[oh^bfh hij_^_eylv iheh`_gb_ y^jZ k_q_gbyJZkkfhljbf ijyfhm]hevguc kl_j`_gv gZ]jm`_gguc k`bfZxs_c gZ]jmadhcjbk k_q_gb_f K E K < ij_^u^ms_f iZjZ]jZn_ gZfb ihemq_gu nhjfmeu ^ey hij_^_e_gbyiheh`_gby gme_\hc ebgbb Ij_^iheh`bf qlh k`bfZxsZy kl_j`_gv kbeZ J gZ jbk hgZ g_ ihdZaZgZ ijbeh`_gZ gZ hkb dh]^Z g_cljZevguc kehc kh\iZ^Z_l k ]jZgvx ZELh]^Z bkihevamy nhjfmem ± fh`gh gZclb jZkklhygb_ hl lhqdbijbeh`_gby kbeu ^h hkb Ihkdhevdm ± ± ± lh HldeZ^u\Zy wlh jZkklhygb_ ih hkb ihemqbf lhqdm O b jZkkm`^Zy ZgZeh]bqgh \ hlghr_gbb kh\iZ^_gby g_cljZevgh]h kehy k ]jZgvx fh`gh ihemqblv\lhjmx lhqdm ij_^_evgh]h ijbeh`_gby k`bfZxs_c gZ]jmadb < wlhf kemqZ_± l _ ihiZ^Z_f \ lhqdm L_i_jv ij_^iheh`bf qlh g_cljZevguc kehc kh\iZe k ]jZgvx k_q_gby Ba \ujZ`_gby ± bf__f ± hlkx^Z HldeZ^u\Z_f wlh agZq_gb_ ih hkb m ihemqZ_f lhqdm ?keb `_ ij_^iheh`blv qlh ijb k`Zlbb kl_j`gy g_cljZevguc kehc kh\iZ^Z_l k ]jZgvx k lhjZkkm`^Zy ZgZeh]bqgh gZc^_f lhqdm _Kh_^bgb\ gZc^_ggu_ lhqdb _ ihemqbf nb]mjm dhlhjZy b ij_^klZ\ey_ly^jh k_q_gbyIjb ^_ckl\bb k`bfZxs_c kbeu J \gmljb y^jZ k_q_gby kl_j`_gv [m^_l bkiulu\Zlv lhevdh k`Zlb_ ?keb `_ k`bfZxsZy gZ]jmadZ [m^_l ijbeh`_gZ aZij_^_eZfb y^jZ k_q_gby lh qZklv k_q_gby [m^_l bkiulu\Zlv k`Zlb_ Z dZdZylhqZklv ² jZkly`_gb_Ijbf_j Qm]mgguc kl_j`_gv jbk ijyfhm]hevgh]h ihi_j_qgh]h k_q_gby KK ff k`bfZ_lky ijh^hevghc kbehc J dG ffkbeZ ijbeh`_gZ \ lhqd_ : dhhj^bgZlu dhlhjhc jZ\gu ffm:]]L\P]]EEL\PPL\PEL\EE]FGPEIDG\L]QKEKQQEKQKNEO N IE K]$Q P Lj_[m_lky Hij_^_eblv gZb[hevr__ jZkly]b\Zxs__ b k`bfZxs__ gZijy`_gby ihkljhblv wixjm gZijy`_gbc GZclb ^himklbfu_ gZ]jmadb gZ k`Zlb_ b jZkly`_gb_ ijb aZ^Zgguo ^himkdZ_fuo gZijy`_gbyo gZ k`Zlb_ b jZkly`_gb_>8 @ FIZ >8 @ FIZ Ihkljhblv y^jh k_q_gbyk`jJ_r_gb_>ey hij_^_e_gby gZb[hevrbo jZkly]b\Zxsbo k`bfZxsbo gZijy`_gbcbkihevam_f nhjfmem 8 ±3 ) ± 3Q\ ,] ± 3P] ,\% & ' b ? k khhl\_lkl\mxsbfbIh^klZ\eyy \ wlm nhjfmem dhhj^bgZlu lhq_dagZdZfb ihemqbfV&3) nq¶ nÅD nq¶ 3QK,]3PE,\V'3)3QK3PE,],\V(3)3QK3PE,],\Hleh`bf ihemq_ggu_ agZq_gby gZijy`_gbc \ khhl\_lkl\mxs_f fZkrlZ[_ ih\_jlbdZevguf ]jZgyf kl_j`gy ijbq_f hljbpZl_evgu_ agZq_gby gZijy`_gbchleh`bf \gba Z iheh`bl_evgu_ \\_jo Kh_^bgb\ djZcgb_ agZq_gby gZijy`_gbc ijyfufb ihemqbf ijhkljZgkl\_ggmx wixjm gZijy`_gbcjbk[Ba \uqbke_gbc b wixju gZijy`_gbc \b^gh qlh gZb[hevrb_ k`bfZxsb_gZijy`_gby ^_ckl\mxl \ lhqd_ < Z gZb[hevrb_ jZkly]b\Zxsb_ gZijy`_gby\hagbdZxl \ lhqd_ ' k_q_gby² >ey hij_^_e_gby ^himklbfuo k`bfZxsbo b jZkly]b\Zxsbo gZ]jmahd bkihevam_f mkeh\b_ ijhqghklb ^ey lhq_d k_q_gby < b 'hlkx^Z3B %3§)QK)PE ·¸ d >V §Ç @V % ¨¨ ),],\ ¸©¹ ) >Vk` @)QK )PE, ] , \ V')QK, ] ) >V S @3B ' §¨) ¨©3)QK, ] , \\·¸ d >V S @¸¹ )PE+ )PE, + >ey ihkljh_gby y^jZ k_q_gby bkihevam_f \ujZ`_gbydhlhju_ iha\heyxl gZclb ij_^_evgh_ iheh`_gb_ lhq_d ijbeh`_gby k`bfZxs_c kbeu dh]^Z g_cljZevguc kehc kh\iZ^Z_l k h^ghc ba ]jZg_c k_q_gbyPQL\ ]L ] \,\ )E,] )KE K ÂÂPÂÂc ÂÂQc ÂÂHldeZ^u\Zy ihemq_ggu_ agZq_gby lhq_d ijbeh`_gby k`bfZxs_c kbeu ihhkyf dhhj^bgZl ] b m b kh_^bgyy bo f_`^m kh[hc ihemqbf y^jh k_q_gbyjbk £À´¾·ÃÄ¿À·¶·»ÃÄ´º·º¹µº³²º¼ÂÅÉ·¿ºÑKh\f_klghc ^_nhjfZpbb ihi_j_qgh]h ba]b[Z b djmq_gby ih^\_j]Zxlky \k_\b^u \Zeh\ \klj_qZxsboky gZ ijZdlbd_ G_evay imlZlv ihgylby \ZeZ b hkbDhgkljmdlb\gh wlb ^_lZeb fZrbg g_ hlebqZxlky Bo jZaebqb_ khklhbl \ \hkijbylbb gZ]jmadb ?keb we_f_gl dhgkljmdpbb \hkijbgbfZ_l h^gh\j_f_gghihi_j_qguc ba]b[ b djmq_gb_ lh wlh \Ze _keb lhqgh lZdhc `_ we_f_gl dhgkljmdpbb g_k_l lhevdh ba]b[Zxsmx gZ]jmadm lh wlh hkvIj_^iheh`bf qlh gZ \Zem `_kldh ihkZ`_gZ r_kl_jgy q_j_a dhlhjmx i_j_^Z_lky djmlysbc fhf_gl am[qZlhfm dhe_km jbk F_`^m am[vyfb r_kl_jgb b dhe_kZ \hagbdZ_l mkbeb_ 5 dhlhjh_ jZaeh`bf gZ^\_ kbeu J b L>ey m^h[kl\Z jZkkm`^_gbc [m^_f mqblu\Zlv lhevdh khklZ\eyxsmx J hdjm`gh_ mkbeb_ Ijb\_^_f wlh mkbeb_ d p_gljm \ZeZ gZ dhlhjhf aZdj_ie_gZk ihfhsvx rihgdb r_kl_jgy >ey wlh]h ^hklZlhqgh \ p_glj_ \ZeZ ijbeh`blvkbeu \aZbfgh mjZ\gh\_r_ggu_ b iZjZee_evgu_ aZ^Zgghc kbe_ Ijb wlhfdZd ba\_klgh ba l_hj_lbq_kdhc f_oZgbdb ^_ckl\b_ aZ^Zgghc kbeu \ gZr_fkemqZ_ hdjm`gZy kbeZ aZf_gy_lky ^_ckl\b_f ijb\_^_gghc kbeu kbeZk ^\mfy q_jlhqdZfb b iZju kbe fhf_gl dhlhjhc jZ\_g J' Ijb\_^_ggZy kbeZ J [m^_l kha^Z\Zlv gZ \Zem gZ dhlhjhf aZdj_ie_gZ r_kl_jgy ^_nhjfZpbx ihi_j_qgh]h ba]b[Z Z iZjZ kbe [m^_l kdjmqb\Zlv \ZeIj_^iheh`bf qlh \jZsZxsbc fhf_gl ihklmiZ_l gZ \Ze hl we_dljh^\b]Zl_eyjbkZ q_j_a fmnlm Z \Ze ihdhblky \ ih^rbigbdZoKqblZ_f qlh r_kl_jgy aZdj_ie_gZ ihkj_^bg_ ^ebgu \ZeZ WixjZ djmlysbofhf_glh\ \hagbdZxsbo \ ihi_j_qguo k_q_gbyo \ZeZ Z lZd`_ wixju ihi_j_qguo kbe b ba]b[Zxsbo fhf_glh\ ihdZaZgu gZ jbk[ \ ] Ba kdZaZggh]h \b^gh qlh k_q_gby \ZeZ ij_l_ji_\Zxl ljb \b^Z ^_nhjfZpbb djmq_gb_ k^\b] b ihi_j_qguc ba]b[ ?keb jZkkfZljb\Zlv mqZklhd \ZeZ \ djmighffZkrlZ[_ lh gZ _]h k_q_gbb jbkfh`gh ihdZaZlv ^_ckl\by gZijy`_gbc hl dZ`^hc ba i_j_qbke_gguo ^_nhjfZpbc >ey k_q_gby dhlhjh_ kqblZ_lky hiZkguf l _ k_q_gby ]^_ ^_ckl\m_l gZb[hevrbc djmlysbc fhf_gl gZijy`_gb_ hij_^_ey_f ih \ujZ`_gbxWdj PZo Fdj PD[ :SgZijy`_gb_ k^\b]ZWF^ PD[ b " GZijy`_gb_ \uau\Z_fh_ gZb[hevrbf ba]b[Zxsbf fhf_glhf hij_^_ey_lkyba \ujZ`_gbyVba] PZo Fba] PD[ :]Ba wixj gZijy`_gbc ihdZaZgguo gZ jbk]jm`_ggufb lhqdZfb k_q_gby [m^ml lhqdb : b < Z\b^gh qlh gZb[he__ gZ H[uqgh ijb jZkq_l_ \ZeZ mqblu\Zxlky gZijy`_gby djmq_gby b ihi_j_qgh]hba]b[Z K^\b]Zxsbf dZkZl_evguf gZijy`_gb_f ij_g_[j_]Zxl \\b^m _]h fZehklb hgh khklZ\ey_l ijbf_jgh gZijy`_gby djmq_gbyLZd dZd gZijy`_gby djmq_gby b ihi_j_qgh]h ba]b[Z ^_ckl\mxl h^gh\j_f_ggh lh\k_ lhqdb ihi_j_qgh]h k_q_gby aZ bkdexq_gb_f lhq_d e_`Zsbo ih hkb o [m^mlgZoh^blvky \ iehkdhf gZijy`_gghf khklhygbb jbk[ Lhqdb e_`Zsb_ ihhkb o dZd \b^gh ba wixj gZijy`_gbc g_ gZ]jm`_guMqblu\Zy \ur_kdZaZggh_ jZkq_l \Zeh\ \_^ml ih lj_lv_c beb q_l\_jlhc l_hjbyf ijhqghklbMkeh\b_ ijhqghklb ih lj_lv_c l_hjbb aZibku\Z_lky \ \b^_ aZ\bkbfhklb VS V V d >V@Ijb iehkdhf gZijy`_gghf khklhygbb ]eZ\gu_ gZijy`_gby fh]ml [ulv hij_^_e_gu ba \ujZ`_gbcVVV WV VVV WIh^klZ\eyy agZq_gby ]eZ\guo gZijy`_gbc \ mkeh\b_ ijhqghklb ih lj_lv_cl_hjbb bf__fV W d >V@V S?keb \ wlh mjZ\g_gb_ \\h^blv agZq_gby V 0ba] :] b W 0dS :S b mqblu\Zlv qlh iheyjguc fhf_gl khijhlb\e_gby djm]eh]h ihi_j_qgh]h k_q_gby\ ^\Z jZaZ [hevr_ hk_\h]h fhf_glZ khijhlb\e_gby wlh]h `_ k_q_gby:] lh ihemqbf:S V W V S0 ÀÆ0 ¾½¹0 ¾½¹ 0 ÀÆd >V@:::]]] dj ij ijbgylh gZau\Zlv ijb\_^_gguf fhf_glhf<_ebqbgm ba]ke_^h\Zl_evghVj 0ij :] d >V@ AgZy qlh :] G gZc^_f ^bZf_lj \ZeZ/ t >V@ijIhemq_ggh_ agZq_gb_ ^bZf_ljZ hdjm]ey_lky ih =HKL ±Ijb jZkq_l_ \ZeZ ih q_l\_jlhc l_hjbb mkeh\b_ ijhqghklb aZibku\Z_lky\ \b^_ V5V V V VV VV V V d >V@Ih^klZ\eyy \ wlh \ujZ`_gb_ agZq_gby V V b V gZoh^bfoV 5o§ V V W · § V V W · ¨¸ ¨¸© ¹ © ¹V V §¨ V W ·¸§¨ V W ·¸ V W d >V@©¹© ¹<\h^y \ ihemq_ggh_ \ujZ`_gb_ V ba] b W @ bf__fV 5V W00 ¾½¹ÀÆ: :0 ÀÆ d >V@: 0 ¾½¹ .