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zdrs/downrev.xmlPKykplB   P?Line 5"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK![a d$drs/shapexml.xmlUn0 }:tq.ڠnA}-ˉ] IΥ_?Jr,mQyxtsSluvfpL)2+J]4tfFuNWףNDZWྚk\U.;k)eٰ@hzf^lff(s.hPu*4'z$g@S֮ųA@@/|5_k :FdCؤ4%<vU qLU]N'z F| ހK ljwn@BJ~<l·StL8MsÐmNWa;#E.d2[2)%R^eᗪP>2 dRǦTgsB}pySCli>Te~/ vPC cN#x`B(DZ@1\('oS`a,He[ pe `hố2RkR-ח-bznfů]-dgt;%jaKWдh&xfQ*`J #O|KMI-<[M@ :Q4O-ы40‚?' 8.g`?u2E5M8EH͌&Ŋ5f-J܆ox5;uTx?kkvmfK*IAӤUaf_EƋf=֨.YAiZ;26p8E I{\KcCHG)9HHT?PK!GJtdrs/downrev.xmlD]K0C8w.]Eٺ1Z7؜aMR\^_>c !^AԟӷD!GHD/PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-![a d$*drs/shapexml.xmlPK-!GJt|drs/downrev.xmlPKypB   PJ?Line 6"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yU#drs/shapexml.xmlUn1}Z%,e%(4B~ .l/|}H*evg:M3xh[Yu*T{w `ķ0>a7ܜG9Xl·BpL&ST7q]e3R]KK6 s/cQslHrz_CӃIRHRUyϩ J܅㰥*;?;= |RH.;Îs/tEK)IIɫW\uoاda:HS"tFa ffGFyl|vbh\Ů Ng4;,I_uƴh&3b0dPܑ'BMI-<[M@ :ǣhA/ 0+亜L֍oX֜l6["53>j .+Sy(Ys"!,RZSE)?UŽ zQ3ՋmӴr78$&b I$dO!UnPK!!:rdrs/downrev.xmlDJ1!b3+2mZDSEqw:9sdHBp1c qtǍק;!"k4Iw-ڍ\pH#rTR%az[IFjcFVZ8=CK*cӸS1|<P(u97 "M?>hl}~>|K D/PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!yU#*drs/shapexml.xmlPK-!!:r{drs/downrev.xmlPK{pB   Po?Line 7"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!S͠$drs/shapexml.xmlUn0 }:tq.ڠnA}-ˉ] IΥ_?Jr,mQ!yxtsSluvfpL)2+J]4tfFuNWףNDZWྚk\U.;k)eٰ@hzGͼ`Q洗]^RAaԩМ|#9"v- -vh3^^ ju"4#\IiJ7vU 瘪"bO9t F| ހK ljwn@A9Xl·CpL&Scs5d3R]KK6 s#07%yscA*}RH.aQ ffx|7RFy"]j6c>AW]#]jv\_բAvFDͲ~8r$8] Mf9*VCUZy[lhJjjJ lXHyBo^9 `lWu9 %-R߰9l7)"Ejf|69$\.V6hQ6\ExC 4˥uYܩå" _C_@k3kLmXr1MZf0'/0*~w/~Xfdiȴ/J_pHJܻZzD:JABPK!pdrs/downrev.xmlDN1&CsMi%BF F:LG ۅ˓o]' q@޴h8>,@ĄlLa,4{yclJ})e-9SgÔeh x㮓3abOϖi->݋>]jsn D1[aZǘ(hD/\PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!S͠$*drs/shapexml.xmlPK-!p|drs/downrev.xmlPKypB   P81?Line 8"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!7#drs/shapexml.xmlUn0 }:tq.ڠnA}-ˉ] IΥ_?Jr,mQyxtsSluvfpL)2+J]4tfFuNWףNDZWྚk\U.;k)eٰ@hzf^lff(s.hPu*4'Wz$g@S֮ųA@@/|5_k :FdCؤ4%<vU qLU]N'e#ao@ å6 u;7gc !PN%V? 6SC )B:m&Bs&afYDe@p:,Ғ Ȝ>{o˸rꦄHrz_CӃRHRUyϹ ÕL G0S%A> ).;dG9rB ]tDuJRRjcp)>yscA*}RH.c0F3 ߍz^H͘Olly}tx{Hts5;W/~j ;)Q[]E33*VCUZy[lhJjjJ lXHyBo^9 `lWu9 %-R߰9l7)"Ejf|69՘$\.V6hQ6\ExC 4˥uYܩå" _C_@k3kLmXrPI Ҙ& 3v7/0*~w7^0FT/v Jڑig/J_pHJܻZzD:JABPK!sPdrs/downrev.xmlDN1&CsLIG)$^ ܰ;L\tl0?-t>Vb(E\xpests*&dg2psO~*%#s4PZǢ&q;bJ&6I]Y6;z@˷բ߯˪]Ï1WT!گVzTr>n0& H PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!7#*drs/shapexml.xmlPK-!sP{drs/downrev.xmlPKzpB   PJ?Line 9"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!3$drs/shapexml.xmlUn1}Z%,4B~ .l/|}H*ev=99s|}Uluv3Jfz_dz+J]4tfuNWNDZWM5U*jrǵlQ 4Pz3g6Xi3D9ehPu*4'#i=3 ak€QZxC@@/|5_j :FdCؤxiJ7xo+N☪"ۜbOv9t/(' {J.%)op߹9 r*\:JpHi(FakWݎepͥhoG4-G<3b0TPܑ'BMI-<[=2H;[u<7ңhP[iaNpr]~&F e~7,kNky6- pHMN5& k u(OkUvs ~>|K D/PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!3$*drs/shapexml.xmlPK-!96|drs/downrev.xmlPK|>p?B   R$?Line 10"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!yU"drs/shapexml.xmlUn0 }:tq.ڠnA}-ˉ] IΥ_?Jr,mQyxtsSluvfpL)2+J]4tfFuNWףNDZWྚk\U.;k)eٰ@hzf^lff(s.1YBshuIހ]Gia{h3^^ jטu"6#^IiJ7x*☪"bS9 F| ހK ljwn@BJ,<l·StL8MsÐmN,vF2 0]cidNd\9uSsKP9/}š|eDAdc%=*<\a<݃)!Aȵ4rz*s;!Å)R`hn)qJ$n1pzYFH=YKf'\_<>:0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!%RWT%drs/shapexml.xmlUn0 }:tq.͚nA}-ˉ] IΥ_?Jr,mQ!yxt}WluvfpL)*Ӌ+J]4fuNNDZ5Wྚk\Uծ:k)eٰ@hzG`Q洗](Ѡ0LhN]i]7 aQZaro m&k+XC͗C`M#4DOx&)q4`>0WV *csM9?B`0> (al $Syv|()DTHyn15=TWa;#Eήd 2[((fM -B* T5A!M*<0]i ޔ$[s=U?H_;!)Hv4!(d%jG4AP$%%P,s:z>%'o3}o7a,He[ pe<8L= FHYK'.[~y5%pfջů]-dgt{M,Ö/.Ex~A}EӢbģUPBqG<Zx2H <[u<7ңhQ[iaJpr]~&F e~7,kNky1- pHMN5 "Zl w^ vikwpH PSE)?$iLV;ُ7 ?J/~Xfdiȴ/J_pHJܻZzD:JQBPK! 4drs/downrev.xmlD]k0p†vFݘu۳ 6IIl._/nS;E\q Ddt;HDv w{ɍH#.e )cՒŸ=>X$C#u!NY"-ZRu+cLQ\w\kI+ȳ5cF_02(%6_PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!%RWT%*drs/shapexml.xmlPK-! 4}drs/downrev.xmlPKz7p8B   RJ?Line 12"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! 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Y2 m&>0 d2C   XP < ?"6@ NNN?N  Y4 m&>0 d2C B YP <D1?"0@NNN?NyUB ZP BD1?"0@NNN?NUS B P <D?"0@NNN?Na,$@ 0B  P <D?"0@NNN?NQQ,$@ 0B  P <D?"0@NNN?Nn,$@ 0B  P <D?"0@NNN?NZ ,$D 0H P 0޽h ?MPNPOPPPP6P7P 8P ̙33urmr___PPT10Mr.h`P++KqMDm' = @B DDm' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*+B#style.visibility<*P%(D ' =%(D| ' =%(DC' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-6B#blinds(vertical)*<3<*PDC' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* P%(D' =-6B#blinds(vertical)*<3<* PDC' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* P%(D' =-6B#blinds(vertical)*<3<* PDC' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* P%(D' =-6B#blinds(vertical)*<3<* PD' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*[P%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*:P%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4P%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*;P%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*^P%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*_P%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*mP%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*dP%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*.P%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*qP%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2P%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*lP%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*zP%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0P%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*pP%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*cP%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*1P%(D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*{P%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*tP%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*/P%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*wP%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*3P%(D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|P%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*bP%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*}P%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*~P%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`P%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*uP%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*vP%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*aP%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D ' =%(D' =%(D)' =4@BB BB%(D' =-g6B fade*<3<*PD' =1:Bhidden*o3>+B#style.visibility<*P%(D)' =4@BB BB%(D' =-g6B fade*<3<*PD' =1:Bhidden*o3>+B#style.visibility<*P%(D' =%(D' =%(D)' =4@BB BB%(D' =-g6B fade*<3<*[PD' =1:Bhidden*o3>+B#style.visibility<*[P%(D' =%(D' =%(D/' =4@BB@BB%()?)?D' =.K7 BBBBB]M -5.55556E-7 7.40741E-7 L -0.00121 -0.03079 *3>*B ppt_xB ppt_y=@0BBAApBBa 6B~<*uPD4' =A@BB@BB0B%()?)?D{' =.C7 BBBBBUM -0.0007 -3.33333E-6 L -0.0007 -0.02939 *3>*B ppt_xB ppt_y=@0BBAApBBBֹr<*vPD' =%(D' =%(D1' =4@BB@BB%()?)?D' =.M7 BBBBB_M 4.72222E-6 4.44444E-6 L 4.72222E-6 -0.03264 *3>*B ppt_xB ppt_y=@0BBAApBBB<*P++0+P0 ++0+.P0 ++0+/P0 ++0+0P0 ++0+1P0 ++0+2P0 ++0+3P0 ++0+:P0 ++0+;P0 ++0+_P0 ++0+`P0 ++0+aP0 ++0+cP0 ++0+vP0 ++0+vP0 ++0+zP0 ++0+{P0 ++0+|P0 ++0+}P0 ++0+~P0 ++0+P0 +8  0 k c ,?$(  $ $ <˪  ?"6@ NNN?NP YTypical simple beams (>0 d2C6z *\ $ gM,$D 0R $ H o?"6@ NNN?N*=B $ <DԔ?"0@NNN?NZT < $# W\R  $ H o?"6@ NNN?NLeB  $ <Do?"0@NNN?N<2  $ H1?"6@`NNN?N2  $ H1?"6@`NNN?NHuPz   $  7,$D 0B $ <DԔ?"0@NNN?NZ  B $ BDԔ?"0@NNN?NVB $ HDԔ?"0@NNN?Na0aB $ HDԔ?"0@NNN?N0z *D  $  ]= ,$D  0R $ H o?"6@ NNN?N* B $ <DԔ?"0@NNN?NZ2 $ H1?"6@`NNN?NHuR $ H o?"6@ NNN?N* T < $# /D R $ H o?"6@ NNN?NLeB $ <Do?"0@NNN?N<2 $ H1?"6@`NNN?NHuPz  X  $  # =,$D  0B $ BDԔ?"0@NNN?N V B $ HDԔ?"0@NNN?Na aX B $ <DԔ?"0@NNN?NZ  B $ HDԔ?"0@NNN?N X B  $ <DԔ?"0@NNN?N{,$@ 0 !$ A*o?Ciemny uko[ny w gr"6@ NNN?N v ,$D 0z   "$ Q  l ,$D 0B #$ <DԔ?"0@NNN?NXYYB $$ BDԔ?"0@NNN?N_T_B %$ HDԔ?"0@NNN?N_i_B &$ <DԔ?"0@NNN?NXYYZ Xf d '$3 o 2 ($ Z% Ԕ?"6@`NNN?N"f I 2 )$B T Ԕ?"6@`NNN?NX ; 2 *$B Tm Ԕ?"6@`NNN?N dF +$ <  ?"6@ NNN?N| %,$ 0 h&Pin-pointed (or simply supported) beam&'>0 d2'C .$ <  ?#" ` =Beams 2C4 =$ <Ц  ?"6@ NNN?N< 4 # ,$  0 VSemi-cantilever beam&>0 d2C/ ?$ <<  ?"6@ NNN?N$| ,$ 0 QCantilever beam&>0 d2CH $ 0޽h ??0($)$*$ ̙33___PPT10.\Ѕ+mnkD' N = @B D' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+$%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* $%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*?$%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* $%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*!$%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*"$%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*=$%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(++0++$0 ++0+=$0 ++0+?$0 +8  0 "}"-Vh "(  h h <  ?"6@ NNN?NP,$ 0 KFundamental assumptions used for drawing diagrams of cross sectional forces(L>0 d2LC L  *h <  ?#" `F =Beams 2C -h <\9  ?"6@ NNN?NN,$ 0 1. Diagram of bending moment will appear always on the side of a beam which is subjected to the tension caused by this bending moment. Therefore, no sign is necessary.(>0 d2C  ^ .h <y  ?"6@ NNN?NOr6,$D 0 (2. We will make use of q-Q-M dependence:()>0 d2)C )  /h s *A X? ?"`T ; 8 X$D 0 0h s *A Y? ?"`Z9  8 Y$D 0 1h <  ?"6@ NNN?N% U ,$ 0 h3 . Shear and normal forces will be always marked with their sign according to the following convention:(i>0 d2iC i  z   2h  ,$D 0N [   3h  ?B 4h <DjJ?"0@NNN?N[  B 5h <DjJ?"0@NNN?N  B 6h <DjJ?"0@NNN?N[  B 7h <D>?"0@NNN?N[  N cf  8h B 9h BD>?"0@NNN?Nf  :h <`  ?"6@ NNN?NJFcf  UQ$>0 d2@ N HA  ;h B ?"0@NNN?NH =h <Ы  ?"6@ NNN?N(A  UN$>0 d2@ #N ` @ >h  62 ?h H jJ?"6@ NNN?N@ @h <  ?"6@ NNN?N`  Uo$>0 d2@ N   Ah B Bh <Dg ?"0@NNN?NJ B ChB HDg ?"0@NNN?N  Dh <  ?"6@ NNN?N1 Yn(>0 d2C p z & Eh J ,$D  0N b $  Fh B GhB <DjJ?"0@NNN?Nb $ B HhB <DjJ?"0@NNN?Nb b B IhB <DjJ?"0@NNN?Nb $ B JhB <D>?"0@NNN?Nb $ N S<cI  Kh &3B Lh <Dg ?"0@NNN?NccI B MhB HDg ?"0@NNN?Nc  Nh <:  ?"6@ NNN?NS<# Yn(>0 d2C #N ` @ Oh 2 Ph H jJ?"6@ NNN?N@ Qh <t  ?"6@ NNN?N`  Uo$>0 d2@ B RhB BD>?"0@NNN?N  Sh <L  ?"6@ NNN?N? 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,$D' 0 ]\ <Xx ?"6@ NNN?N   Q0, N0 M=0 >8 d2@@D 2 ^\ H Ԕ?"6@ NNN?Nf z f  _\ ?S /,$D) 0 `\ <| ?"6@ NNN?N   Q0, N0 M=0 >8 d2@@D 2 a\ H Ԕ?"6@ NNN?Nf B b\ H o?"6@ NNN?N^,$D& 0B c\ H o?"6@ NNN?NE ,$D( 0 d\ < ?#" ` Gerber s beams 2C*H \ 0޽h ?0\1\2\L\M\N\P\Q\ S\ T\ V\ W\ Y\Z\ ̙33&YY___PPT10X.v]=+)DX' = @B DX' = @BA?%,( < +O%,( < +Dd' =%(D ' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =%(D' =%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-s6Bwipe(down)*<3<*\DQ' =%(D' =%(D7' =4@BB@BB%()?)?D' =.S7 BBBBBeM -1.38889E-6 -1.41536E-6 L -1.38889E-6 -0.16189 *3>*B ppt_xB ppt_y=@0BBAApBBBť<* \D5' =4@BB@BB%()?)?D' =.Q7 BBBBBcM -4.72222E-6 4.76411E-6 L -4.72222E-6 -0.15611 *3>*B ppt_xB ppt_y=@0BBAApBBB<* \D%' =4@BB@BB%()?)?Dy' =.A7 BBBBBSM -2.5E-6 -1.41536E-6 L -2.5E-6 -0.1642 *3>*B ppt_xB ppt_y=@0BBAApBBB#<* \D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*/\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D ' =%(D' =%(D)' =4@BB BB%(D' =-g6B fade*<3<* \D' =1:Bhidden*o3>+B#style.visibility<* \%(D)' =4@BB BB%(D' =-g6B fade*<3<* \D' =1:Bhidden*o3>+B#style.visibility<* \%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*.\%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*!\%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*3\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4\%(D' =%(D' =%(DC' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*R\%(D' =-6B#blinds(vertical)*<3<*R\D' =%(D' =%(DC' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*O\%(D' =-6B#blinds(vertical)*<3<*O\D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*6\%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*5\%(D' =%(D' =%(DC' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*U\%(D' =-6B#blinds(vertical)*<3<*U\D' =%(D' =%(DC' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X\%(D' =-6B#blinds(vertical)*<3<*X\D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*7\%(D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*9\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*:\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*;\%(D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*=\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*K\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<\%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*J\%(D' =%(D' =%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*b\%(D' =-6B+checkerboard(across)*<3<*b\D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\\%(D' =%(D' =%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*c\%(D' =-6B+checkerboard(across)*<3<*c\D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*_\%(+  0 <<FHd <(  dB d <DԔ?"0@NNN?Nu}u,$@ 0B d BDo?"0@NNN?Ny,$D 0^ d 6 f ^ d 6} )} ^ d 6 t z   d 3,$D 0N   d B  d <DԔ?"0@NNN?NA!!B  d <DԔ?"0@NNN?NT!M !B  d <DԔ?"0@NNN?N !U!2  d HjJ?"6@ NNN?NM@2 d HjJ?"6@ NNN?NS  >R d H o?"6@ NNN?N -R dB H o?"6@ NNN?N-R d H o?"6@ NNN?N&|R dB H o?"6@ NNN?N&u|B dB BDԔ?"0@NNN?NV 8 "T @   d# B d H30Do?"0@NNN?N@ zF  B d H30Do?"0@NNN?Ny B d H30Do?"0@NNN?N x  B d H30Do?"0@NNN?N w  B d H30Do?"0@NNN?NX y^  B d H30Do?"0@NNN?N x  B d H30Do?"0@NNN?N z  B d H30Do?"0@NNN?Ng zm  B d H30Do?"0@NNN?N x  B d H30Do?"0@NNN?Ny" B d H30Do?"0@NNN?Nwy} B  d < D?"0@NNN?NW  B !d BDԔ?"0@NNN?N Z Xf d "d3 B  2 #d Z% Ԕ?"6@`NNN?N"f I 2 $dB T Ԕ?"6@`NNN?NX ; 2 %dB Tm Ԕ?"6@`NNN?N d &d < ?"6@ NNN?N`,$ 0 Formal definition: the set of aligned simple bars, hinged together and supported in the way which assures kinematical stability&>0 d2C @r 'd <L ?"6@ NNN?N,$D 0 Equilbrium equations(>0 d2C4  }z : (d ,$D 0N  y )d B *d <D?"0@NNN?N yB +d <D?"0@NNN?N    ,d <| ?"6@ NNN?N| " WX&>0 d2B   -d < ?"6@ NNN?N2 y  WY&>0 d2B N : .d :2 /d < ?"6@ NNN?N 6  0d <( ?"6@ NNN?N.: YK(>0 d2C 7 1d < ?"6@ NNN?N,$ 0 YA(>0 d2C 7 2d < ?"6@ NNN?N ,$ 0 YB(>0 d2C N 3d <H ?"6@ NNN?N ,$  0 p SX = 04>0 d2 z . )  4d  F ,$D  0" 5d <D ?"6@ NNN?N. N  p SY = 04>0 d2 D 6d <@ ?"6@ NNN?N )  SMK = 0T>0 d2 h 7d <Ul  ?"6@ NNN?N 2,$ 0 MB = 0T>0 d2 h 8d < l  ?"6@ NNN?N 2 ,$ 0 MA = 0T>0 d2 h 9d <hl  ?"6@ NNN?N w ,$  0  1 equation6 >0 d2C C&i :d <0ll  ?"6@ NNN?N  ,$  0  2 equations6 >0 d2C C&  ;d <ql  ?"6@ NNN?N!  ,$  0 4 unknown horizontal reactionsh>0 d2C C G CG 0 d2C C G C  i =d <l  ?"6@ NNN?Ns  Z,$ 0  2 equations6 >0 d2C C& z Z  >d HT/d,$D 0 ?d Bg ?"6@ NNN?NZ r @d S BZA$MCj02805340000[1]G: H Ad H o?"6@ NNN?N[ @ ,$D 0 Bd <l  ?"6@ NNN?N b ,$ 0 IStructure is statically indetermined with respect to horizontal reactionspJ>0 d2C GC G C &B Cd <DԔ?"0@NNN?Nuu,$@ 0B Dd <DԔ?"0@NNN?Nuu,$D 0X Ed <xl  ?"6@ NNN?N )? ,$ 0 z6Number of unknown reactions: 4 horizontal + 4 vertical(7>0 d27C" Fd H o?"6@ NNN?N+> ,$D 0 Hd <Ȗl  ?#" ` Gerber s beams 2C*H d 0޽h ??0#d$d%d ̙33{JsJ___PPT10SJ.v]=+DF' l = @B DF' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*d%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&d%(D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-6B'blinds(horizontal)*<3<*dDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Ed%(D' =%(D' =%(Dg' =4@BB7BB%(D' =1:Bvisible*o3>+B#style.visibility<*Fd%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*FdD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*FdD' =-g6B fade*<3<*FdD4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*'d%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(d%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*3d%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*9d%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*;d%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4d%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*:d%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*1d%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2d%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8d%(Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*>d%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*>dD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*>dDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7d%(D' =%(D' =%(D+' =4@BB?BB%()?)?D' =.G7 BBBBBYM 2.77778E-7 3.9408E-6 L 0.23524 3.9408E-6 *3>*B ppt_xB ppt_y=@0BBAApBB =B<*>dDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*=d%(D2' =%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*>d%(D' =%(D' =%(DK' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*Ad%(D' =-6B+checkerboard(across)*<3<*AdDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+B#style.visibility<*Bd%(Dx ' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Cd%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Dd%(D' =%(D6' =A@BB BB0B%(D' =-g6B fade*<3<*BdD' =1:Bhidden*o3>+B#style.visibility<*Bd%(D' =%(D6' =A@BB BB0B%(D' =-g6B fade*<3<*;dD' =1:Bhidden*o3>+B#style.visibility<*;d%(+H+0+&d0 ++0+1d0 ++0+2d0 ++0+3d0 ++0+7d0 ++0+8d0 ++0+9d0 ++0+:d0 ++0+;d0 ++0+;d0 ++0+Number of unknown reactions to be found: 1 horizontal reaction from 1 equilibrium equation (or we accept indeterminancy with respect to normal cross-sectional forces) (2 + n) remaining reactions (vertical reactions, moment reactions) from 2 equilibrium equations and n equations of vanishing bending moment in hinges?>0 d2*CMCG0CC@CCCC1Cj@   <Pl  ?"6@ NNN?NN,$  0 JNumber of hinges is determined from the second of the above condition: structures appears to be kinemtaically unstable if there are too many hinges, and hyper-stiff  if there are too little hinges). However, the location of hinges  even if their number is correct one  cannot be arbitrary! 6&>0 d2CC`  z ] 0     ] ` ,$D 0B   <DԔ?"0@NNN?N x    A*o?Ciemny uko[ny w gr"6@ NNN?N] 0 R   H o?"6@ NNN?N7  R B H o?"6@ NNN?NI  2  HjJ?"6@ NNN?NAr y 2  HjJ?"6@ NNN?Nku   z  0    ` ,$D  0B  <DԔ?"0@NNN?Nv    A*o?Ciemny uko[ny w gr"6@ NNN?N 0 R  H o?"6@ NNN?N  R B H o?"6@ NNN?N ) 2  HjJ?"6@ NNN?N{  2  HjJ?"6@ NNN?Nou  z  f W  7 f ,$D 0B  BD1?"0@NNN?N WB  BD1?"0@NNN?N| |WB  BD1?"0@NNN?N^ ^WB  BD1?"0@NNN?N WB  BD1?"0@NNN?Nf  f Wz   W  7  ,$D  0B  BD1?"0@NNN?N WB   BD1?"0@NNN?N WB ! BD1?"0@NNN?N WB " BD1?"0@NNN?N   WB # BD1?"0@NNN?N Wz ( D  $  (t ,$D 0B % <DԔ?"0@NNN?N^  R &B H o?"6@ NNN?NG D R 'B H o?"6@ NNN?N( D z Z(  ( a Z ,$D 0B ) <DԔ?"0@NNN?N( _ ( R *B H o?"6@ NNN?N$ , R +B H o?"6@ NNN?NZ/  (z ] ^] , ' ]^i ,$D 0B - <DԔ?"0@NNN?N ^  . A*o?Ciemny uko[ny w gr"6@ NNN?N] ]z    /   ,$D 0B 0 <DԔ?"0@NNN?N  R 1 H o?"6@ NNN?N  R 2 H o?"6@ NNN?N^  z Z   3  0 ,$D 0B 4 <DԔ?"0@NNN?NZ Z R 5 H o?"6@ NNN?Nj  Dz  /  6  _ ,$D  0R 7 H o?"6@ NNN?N + N    8  / B 9 <DԔ?"0@NNN?Nz : :  : A*o?Ciemny uko[ny w gr"6@ NNN?N z {, ;  F,$D 0B < <DԔ?"0@NNN?N,,R = H o?"6@ NNN?N{:z a/ > / a ,$D 0R ? 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=1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*G%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*G%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*6%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*/%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*3%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D?' =%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*H%(D4' =%(D' =%(D' =4@BBBB%(D' 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uko[ny w gr"6@ NNN?NYJ B  @ BD1?"0@NNN?NY&&,$@ 0B @ BD1?"0@NNN?NY,$@ 0B @ BD1?"0@NNN?NY,$@ 0B @ BD1?"0@NNN?NY]],$@ 0B @ BD1?"0@NNN?NYY Y ,$@ 0B @ BD1?"0@NNN?NY ,$@  0B @ BD1?"0@NNN?NY  ,$D  0B @ BD1?"0@NNN?NP ,$@  0 z    ,$D 0B  <DԔ?"0@NNN?N-GGR B H o?"6@ NNN?N`cR B H o?"6@ NNN?NgWB  <DԔ?"0@NNN?NG]GT J  # wB  <DԔ?"0@NNN?Nb  A*o?Ciemny uko[ny w gr"6@ NNN?NYJ N  Gs   GsB  <DԔ?"0@NNN?N GsGR  H o?"6@ NNN?N T T  H  # dG B ! <DԔ?"0@NNN?N R "B H o?"6@ NNN?NK  H2 # HjJ?"6@`NNN?N_%c2 $ HjJ?"6@ NNN?NF&~d2 % HjJ?"6@ NNN?N $ b2 & HjJ?"6@ NNN?N$bz V ' {,$D  0B ( <DԔ?"0@NNN?N(VVR )B H o?"6@ NNN?No^R *B H o?"6@ NNN?Nbfz _>  + {_ ,$D 0R ,B H o?"6@ NNN?N F T  H -# _> B . <DԔ?"0@NNN?N R /B H o?"6@ NNN?NK  Hz lt 0 lV,$D 0B 1 <DԔ?"0@NNN?NtXtR 2B H o?"6@ NNN?N${R 3B H o?"6@ NNN?Nl{z  v 4  b,$D 0B 5 <DԔ?"0@NNN?N nR 6 H o?"6@ NNN?N  vR 7B H o?"6@ NNN?N<pB 8 <D1?"0@NNN?N](],$D  0z \ 9 O,$D9 0B :B BD1?"0@NNN?N\B ; BD>?"0@NNN?NWz , <  ~ ,$D 0  = < ?"6@ NNN?NF WM&>0 d2B 2 > N jJ?"6@`NNN?N,z    ? m ),$D2 0B @B 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H?#"  `] *H,$D: 0H  0޽h ? 33___PPT10.[R+ D' N = @B DP' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* q%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(Do' =%(D' =%(DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B'blinds(horizontal)*<3<* DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*DG' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' 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