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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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B T Ԕ?"6@`NNN?NX ; 2 " B Tm Ԕ?"6@`NNN?N dB #  <D>?"0@NNN?N{{,$D  0B $  <D?"0@NNN?N~rC~,$@ 02 %  H o?"6@`NNN?NgV,$D 0! &  <:  ?"6@ NNN?N,$ 0 Cx&>0 d2BF '  <?  ?"6@ NNN?N ,$ 0 h2 kN&>0 d2CF (  <m  ?"6@ NNN?N,$ 0 h2 kN&>0 d2CH )  <r  ?"6@ NNN?Nt,$ 0 j1 kN/m&>0 d2CG *  <w  ?"6@ NNN?N Y ,$ 0 i4 kNm&>0 d2C-z  4  ,  um ,$D 0B -  BD?"0@NNN?N z  B .  6D?"0@NNN?N  B /  BD?"0@NNN?Nd  F  B 0  BD?"0@NNN?NE   B 1  6D?"0@NNN?N  B 2  6D?"0@NNN?N{  { B 3  6D?"0@NNN?NF  F  4  < P  ?"6@ NNN?NM 4  E2 m&>0 d2C 5  <P  ?"6@ NNN?N L X 3  E2 m&>0 d2C 6  <P  ?"6@ NNN?N5 M 4  E4 m&>0 d2C, 7  <lP  ?"6@ NNN?N P,$ 0 NThe set of loadings acting an a structure has to be in equilibrium (i.e. equal to zero set of forces). Beforehand, kinematic boundary conditions have to be replaced by static boundary conditions (c.f. Theoretical Mechanics)D>0 d2CCC@z s0  8   ,$D 0B 9  <D1?"0@NNN?NsB :  BD1?"0@NNN?N0 F ;  <P  ?"6@ NNN?Norl,$ 0 h4 kN&>0 d2C- =  <pP  ?" # ,$ 0 GTo write equilibrium equations a global coordinate system has to be setH 2HC >  <tP  ?",$ 0 PImportant observations 2CH   0޽h ??0 ! "  3355___PPT10d5.[R+eD3' N = @B D2' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*> %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* i%(D4' =%(D' =%(D' =4@BBBB%(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<* %(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =4@BBBB%(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<* %(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(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<*% %(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$ %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*& %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7 %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*( %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*' %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<** %(D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*) %(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8 %(DA' =%(D' =%(D' =A@BBBB0B%(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+' 0 ++0+( 0 ++0+) 0 ++0+* 0 ++0+7 0 ++0+; 0 ++0+= 0 ++0+> 0 +1\  0 3 3>D$\2(  $^ $ 6u fu ^ $ 6 4 ^ $ 6  ^ $ 6 Z  $ B ?"6@ NNN?ND"D $ B ?"6@ NNN?NY:Y  $ B ?"6@ NNN?N ~ ~  $ <P  ?"6@ NNN?NiN,$D 0 PIn global coordinates the sign of cross-sectional forces depends on the on the assumption on which part of a structure is considered (that  from left or  from right)&>0 d2C@2z [    $ fe+ ,$D 0B  $ <DjJ?"0@NNN?N[  B  $ <DjJ?"0@NNN?N  B $ <DjJ?"0@NNN?N[  B $ <D>?"0@NNN?N[  2z b $  $ fl+ ,$D  0B $B <DjJ?"0@NNN?Nb $ B $B <DjJ?"0@NNN?Nb b B $B <DjJ?"0@NNN?Nb $ B $B <D>?"0@NNN?Nb $ Cz cf  $ >e ,$D 0B $ BD>?"0@NNN?Nf  $ <T@P  ?"6@ NNN?NJFcf  UQ$>0 d2@  Cz HA  $ g`;,$D 0B $ BD>?"0@NNN?NH $ <EP  ?"6@ NNN?N(A  UN$>0 d2@  z I $ 8 ,$D  0 $ <xP  ?"6@ NNN?N)I UM$>0 d2@  Z    $3 2L2 $ 3 BZENGIQ >? _Z2Z`T_Z2Z`T`T2Z`T`T"6@`NNN?N  F2 $ # BfENGxINQ >? ff`Tff`TN`Tf`TN`T"6@`NNN?N  Oz ` @  $ 3t],$D 02 !$ H jJ?"6@ NNN?N@ "$ <H\P  ?"6@ NNN?N`  Uo$>0 d2@  z S<cI  #$ q~,$D  0B $$ <Dg ?"0@NNN?NccI B %$B HDg ?"0@NNN?Nc  &$ <HaP  ?"6@ NNN?NS<# Yn(>0 d2C  Oz ` @ '$ <f,$D  02 ($ H jJ?"6@ NNN?N@ )$ <P  ?"6@ NNN?N`  Uo$>0 d2@  Cz  |=/ *$ eU,$D 0B +$B BD>?"0@NNN?N9=/ ,$ <PP  ?"6@ NNN?N | UQ$>0 d2@  Cz [, -$ "F,$D  0B .$ BD>?"0@NNN?N, /$ <P  ?"6@ NNN?N[t UN$>0 d2@  z E? 0$ ? ,$D 0 1$ <wP  ?"6@ NNN?N,E? UM$>0 d2@  Z    2$3 =L2 3$ 3 BZENGIQ >? _Z2Z`T_Z2Z`T`T2Z`T`T"6@`NNN?N  F2 4$ # BfENGxINQ >? ff`Tff`TN`Tf`TN`T"6@`NNN?N  z   5$ gv,$D 0B 6$ <Dg ?"0@NNN?NJ B 7$B HDg ?"0@NNN?N  8$ <zP  ?"6@ NNN?N1 Yn(>0 d2C   ;$ <DP  ?"6@ NNN?N e3,$ 0 We adopt the following rules for N, Q axis: Positive direction of N coincides with an outward direction of normal n and positive direction of Q is such that couple {N, Q } is left-twisted. >0 d2!CBCB0CBCB C CBC  @ <$ <\P  ?"6@ NNN?N* 3  ,$ 0 dTo avoid this ambiguity system of coordinates has to be connected with the normal outward vector n.4e>0 d2bCB e @z U\  =$  ,$D 0B >$ <D?"0@NNN?N B ?$ <D?"0@NNN?N c =  @$ </P  ?"6@ NNN?NE \  Wx&>0 d2B    A$ <hP  ?"6@ NNN?NU  Wy&>0 d2B  H $ 0޽h ?O@$$3$4$ 33((___PPT10(.[R+|OD(' N = @B D'' = @BA?%,( < +O%,( < +Dt' =%(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<* $%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*5$%(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<*$%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*#$%(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<**$%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0$%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<$%(D' =%(D' =%(D)' =4@BB BB%(D' =-g6B fade*<3<*=$D' =1:Bhidden*o3>+B#style.visibility<*=$%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*;$%(+p+0+;$0 ++0+<$0 +f  0 RRnp(Q(  (^ ( 6% f% ^ ( 6 4 ^ ( 6  ^ ( 6 Z  ( B ?"6@ NNN?ND"D ( B ?"6@ NNN?NY:Y  ( B ?"6@ NNN?N ~ 2  ( <P  ?"6@ NNN?N3,$D  0 TTo define the sign of bending moment we introduce a special case of  axis . It will be given by pointing at upper or lower surface of a bar. It will be called  bottoms and marked by a dashed line drawn along the bar axis. We will consider bending moment as being positive if its action results in extension of  bottoms .C>0 d2CCCG CaCC` @Gz $   ( $A ,$D 0N b $   ( b$ B  (B <DjJ?"0@NNN?Nb $ B (B <DjJ?"0@NNN?Nb b B (B <DjJ?"0@NNN?Nb $ B (B <D>?"0@NNN?Nb $ N S<cI  ( JZ B ( <Dg ?"0@NNN?NccI B (B HDg ?"0@NNN?Nc  ( <%  ?"6@ NNN?NS<# Yn(>0 d2C #N ` @ ( }2 ( H jJ?"6@ NNN?N@ ( <%  ?"6@ NNN?N`  Uo$>0 d2@ N  |=/ ( %ZB (B BD>?"0@NNN?N9=/ ( <%  ?"6@ NNN?N | UQ$>0 d2@ N [, ( RB ( BD>?"0@NNN?N, ( <%  ?"6@ NNN?N[t UN$>0 d2@ qN E? ( R]  ( <C%  ?"6@ NNN?N,E? UM$>0 d2@ Z     (3 =L2 !( 3 BZENGIQ >? _Z2Z`T_Z2Z`T`T2Z`T`T"6@`NNN?N  F2 "( # BfENGxINQ >? ff`Tff`TN`Tf`TN`T"6@`NNN?N  Gz [b  #( [D ,$D 0N [   $( [ B %( <DjJ?"0@NNN?N[  B &( <DjJ?"0@NNN?N  B '( <DjJ?"0@NNN?N[  B (( <D>?"0@NNN?N[  N cf  )( eT B *( BD>?"0@NNN?Nf  +( <%  ?"6@ NNN?NJFcf  UQ$>0 d2@ N HA  ,( B -( BD>?"0@NNN?NH .( <%  ?"6@ NNN?N(A  UN$>0 d2@ qN I /( @  0( <(%  ?"6@ NNN?N)I UM$>0 d2@ Z    1(3 2L2 2( 3 BZENGIQ >? _Z2Z`T_Z2Z`T`T2Z`T`T"6@`NNN?N  F2 3( # BfENGxINQ >? ff`Tff`TN`Tf`TN`T"6@`NNN?N  #N ` @ 4( L,2 5( H jJ?"6@ NNN?N@ 6( <,%  ?"6@ NNN?N`  Uo$>0 d2@ N   7( b.o B 8( <Dg ?"0@NNN?NJ B 9(B HDg ?"0@NNN?N  :( <#%  ?"6@ NNN?N1 Yn(>0 d2C B ;( BDo?"0@NNN?N b' ,$D 0B <( BDo?"0@NNN?N g, ,$@ 0z : ' =( r ',$D 0N b $  >( b/ $B ?(B <DjJ?"0@NNN?Nb $ B @(B <DjJ?"0@NNN?Nb b B A(B <DjJ?"0@NNN?Nb $ B B(B <D>?"0@NNN?Nb $ N S<cI  C( J: ZGB D( <Dg ?"0@NNN?NccI B E(B HDg ?"0@NNN?Nc  F( <*%  ?"6@ NNN?NS<# Yn(>0 d2C #N ` @ G(  }/2 H( H jJ?"6@ NNN?N@ I( <T/%  ?"6@ NNN?N`  Uo$>0 d2@ N  |=/ J( k ZB K(B BD>?"0@NNN?N9=/ L( <4%  ?"6@ NNN?N | UQ$>0 d2@ N [, M(  RB N( BD>?"0@NNN?N, O( <pZ%  ?"6@ NNN?N[t UN$>0 d2@ qN E? P(  ] Q( <\%  ?"6@ NNN?N,E? UM$>0 d2@ Z    R(3 =F2 S( # BZENGIQ >? _Z2Z`T_Z2Z`T`T2Z`T`T"6@`NNN?N  L2 T( 3 BfENGxINQ >? ff`Tff`TN`Tf`TN`T"6@`NNN?N  B U( BDo?"0@NNN?Nb ' z  a V(  r,$D 0 T [   W(# 4 B X( <DjJ?"0@NNN?N[  B Y( <DjJ?"0@NNN?N  B Z( <DjJ?"0@NNN?N[  B [( <D>?"0@NNN?N[  T cf  \(#  B ]( BD>?"0@NNN?Nf  ^( <:%  ?"6@ NNN?NJFcf  UQ$>0 d2@ T HA  _(#   B `( BD>?"0@NNN?NH a( <x?%  ?"6@ NNN?N(A  UN$>0 d2@ wT I b(# H a c( <]%  ?"6@ NNN?N)I UM$>0 d2@ Z    d(3 2F2 e( # BZENGIQ >? _Z2Z`T_Z2Z`T`T2Z`T`T"6@`NNN?N  L2 f( 3 BfENGxINQ >? ff`Tff`TN`Tf`TN`T"6@`NNN?N  )T ` @ g(#  +2 h( H jJ?"6@ NNN?N@ i( <@%  ?"6@ NNN?N`  Uo$>0 d2@ T   j(#  B k( <Dg ?"0@NNN?NJ B l(B HDg ?"0@NNN?N  m( <8%  ?"6@ NNN?N1 Yn(>0 d2C B n( BDo?"0@NNN?N  T o( Bp%  o?"6@ NNN?N y ,$D  0 pAll figures show: M, Q, N > 06>8 d2C @H ( 0޽h ?2(3(!("(S(T(e(f( 33___PPT10.[R+*D"' N = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(Dc' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<* (C%(D' =-o6Bwipe(up)*<3<* (CD4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*#(%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<(%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*;(%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*V(%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*=(%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*o(%(+8+0+o(0 +   0 ZYoq,X(  ,^ , 66 f6 ^ , 6 4 ^ , 6   , B ?"6@ NNN?ND"D , B ?"6@ NNN?NY:Y , B ?"6@ NNN?N ~ B  , <D>?"0@NNN?N!mm,$@ 0B  , <D>?"0@NNN?Ng,$@ 0B  , BDo?"0@NNN?Nmm,$@ 0  @    ,# ` ,$@ 0B  , H30Do?"0@NNN?N@ zF  B , H30Do?"0@NNN?Ny B , H30Do?"0@NNN?N x  B , H30Do?"0@NNN?N w  B , H30Do?"0@NNN?NX y^  B , H30Do?"0@NNN?N x  B , H30Do?"0@NNN?N z  B , H30Do?"0@NNN?Ng zm  B , H30Do?"0@NNN?N x  B , H30Do?"0@NNN?Ny" B , H30Do?"0@NNN?Nwy} B , < D?"0@NNN?NW  B , BDo?"0@NNN?N~~,$@ 0B , BDo?"0@NNN?N=2 2 ,$@ 0B , <D>?"0@NNN?N2 2 ,$@ 0B , <D>?"0@NNN?N ,$@  0 Xf d ,3 BHG f,$@  02 , Z% Ԕ?"6@`NNN?N"f I 2 ,B T Ԕ?"6@`NNN?NX ; 2  ,B Tm Ԕ?"6@`NNN?N dB !, <D>?"0@NNN?N'{{,$@  0B ", <D?"0@NNN?NrC,$@  02 #, H o?"6@`NNN?N~V,$@  05 $, <܀%  ?"6@ NNN?N,$ 0 Wx&>0 d2B 8 %, <<%  ?"6@ NNN?N}<? 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_Z2Z`T_Z2Z`T`T2Z`T`T"6@`NNN?N  F2 X, # BfENGxINQ >? ff`Tff`TN`Tf`TN`T"6@`NNN?N  B Y, BDo?"0@NNN?N T ;  Z,#  B [, <DjJ?"0@NNN?N9  B \, <DjJ?"0@NNN?N   B ], <DjJ?"0@NNN?N9  B ^, <D>?"0@NNN?N9; ; B _,B <Dg ?"0@NNN?Nb ^ B `, HDg ?"0@NNN?N    a,B <L)-  ?"6@`NNN?N  Yn(>0 d2C B b, BD>?"0@NNN?N>   c,B <x.-  ?"6@`NNN?N   UQ$>0 d2@ B d,B BD>?"0@NNN?N@ V@  e,B <1-  ?"6@`NNN?Nh) \H  UN$>0 d2@   f,B B -  ?"6@`NNN?NG ;  UM$>0 d2@ Z    g,3 GG / L2 h, 3 BZENGIQ >? _Z2Z`T_Z2Z`T`T2Z`T`T"6@`NNN?N  F2 i, # BfENGxINQ >? ff`Tff`TN`Tf`TN`T"6@`NNN?N  B j, BDo?"0@NNN?N9   k,B S BZA$MCj02805340000[1]"? c l, <g ?"6@ NNN?N [b ,$ 0  M(x)= +2x> >0 d2@A@b m, <,h ?"6@ NNN?N= [b] ,$ 0 Q(x)= +2> >0 d2@A@U n, <0 d2@AB p, BDo?"89,$D  0 q, < ?"zw,$" 0 Z The results have to be the same!! 2!CH , 0޽h ?,, ,W,X,h,i,D, E, G, H, 33GG___PPT10G.[R+x$D E' t= @B DD' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*!,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*",%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*#,%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$,%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%,%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&,%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*',%(D' =A@BBBB0B%(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<*4,%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7,%(D' =%(D' =%(Dg' =4@BB7BB%(D' =1:Bvisible*o3>+B#style.visibility<*:,%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*:,D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*:,D' =-g6B fade*<3<*:,DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*9,%(D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*p,%(D' =-o6Bwipe(up)*<3<*p,D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*;,%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*A,%(D}' =%(D%' =%(D' =4@BB9BB%()?)?D!' =.7 BBBBBM 4.72222E-6 -4.44444E-6 L 4.72222E-6 -0.20763 C 4.72222E-6 -0.30092 0.03333 -0.41527 0.06111 -0.41527 L 0.12256 -0.41527 *3>*B ppt_xB ppt_y=D0BB FfFFpBB{=BJT<*A,DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*l,%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*m,%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*n,%(D' =%(D' =%(D)' =4@BB BB%(D' =-g6B fade*<3<*A,D' =1:Bhidden*o3>+B#style.visibility<*A,%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*A,%(D}' =%(D%' =%(D' =4@BB9BB%()?)?D!' =.7 BBBBBM 4.72222E-6 -0.08187 L 4.72222E-6 -0.24861 C 4.72222E-6 -0.32354 -0.14011 -0.41536 -0.25382 -0.41536 L -0.50678 -0.41536 *3>*B ppt_xB ppt_y=D0BB FfFFpBBǁB*<*A,DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*q,%(+h+0+$,0 ++0+%, ++0+&,0 ++0+',0 ++0+(,0 ++0+7,0 ++0+9,0 ++0+l,0 ++0+m,0 ++0+n,0 ++0+q,0 + 0  YYnq0W(  0^ 0 6~ f~ ^ 0 6 4 ^ 0 6   0 B ?"6@ NNN?ND"D 0 B ?"6@ NNN?NY:Y 0 B ?"6@ NNN?N ~ B  0 <D>?"0@NNN?Nimm,$@ 0B  0 <D>?"0@NNN?Ng,$@ 0B  0 BDo?"0@NNN?Nmm,$@ 0  @    0#  ,$@ 0B  0 H30Do?"0@NNN?N@ zF  B 0 H30Do?"0@NNN?Ny B 0 H30Do?"0@NNN?N x  B 0 H30Do?"0@NNN?N w  B 0 H30Do?"0@NNN?NX y^  B 0 H30Do?"0@NNN?N x  B 0 H30Do?"0@NNN?N z  B 0 H30Do?"0@NNN?Ng zm  B 0 H30Do?"0@NNN?N x  B 0 H30Do?"0@NNN?Ny" B 0 H30Do?"0@NNN?Nwy} B 0 < D?"0@NNN?NW  B 0 BDo?"0@NNN?N~~,$@ 0B 0 BDo?"0@NNN?N2 2 ,$@ 0B 0 <D>?"0@NNN?N2 2 \,$@ 0B 0 <D>?"0@NNN?N U,$@  0 Xf d 03 BG ,$@  02 0 Z% Ԕ?"6@`NNN?N"f I 2 0B T Ԕ?"6@`NNN?NX ; 2  0B Tm Ԕ?"6@`NNN?N dB !0 <D>?"0@NNN?No{{,$@  0B "0 <D?"0@NNN?NrC,$@  02 #0 H o?"6@`NNN?NV,$@  05 $0 <h) ?"6@ NNN?N,$ 0 Wx&>0 d2B 8 %0 <8 ?"6@ NNN?N<? 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_Z2Z`T_Z2Z`T`T2Z`T`T"6@`NNN?N  F2 W8 # BfENGxINQ >? ff`Tff`TN`Tf`TN`T"6@`NNN?N  B X8 BDo?"0@NNN?N T ;  Y8#  B Z8 <DjJ?"0@NNN?N9  B [8 <DjJ?"0@NNN?N   B \8 <DjJ?"0@NNN?N9  B ]8 <D>?"0@NNN?N9; ; B ^8B <Dg ?"0@NNN?Nb ^ B _8 HDg ?"0@NNN?N    `8B <J ?"6@`NNN?N  Yn(>0 d2C B a8 BD>?"0@NNN?N>   b8B <Q ?"6@`NNN?N   UQ$>0 d2@ B c8B BD>?"0@NNN?N@ V@  d8B <xS ?"6@`NNN?Nh) \H  UN$>0 d2@   e8B B X ?"6@`NNN?NG ;  UM$>0 d2@ Z    f83 GG / L2 g8 3 BZENGIQ >? _Z2Z`T_Z2Z`T`T2Z`T`T"6@`NNN?N  F2 h8 # BfENGxINQ >? ff`Tff`TN`Tf`TN`T"6@`NNN?N  B i8 BDo?"0@NNN?N9   j8B S BZA$MCj02805340000[1]#" `? < k8 <_ ?"6@ NNN?N= [/] ,$ 0 ^LM(x1)= +4x1 - 1x1x1/2 = 4x1 - x12/2j'>0 d2@H@`h` ` @H`@H@`h`     @  H  H  @  H         l8 <ht ?"6@ NNN?N [P ,$ 0 &0Q(x)= -4 + 1x1= - 4+ x1>0 d2 @`h@  @`hJ   G m8 < ?"6@ NNN?N [b ,$ 0 iN(x)= 0$>0 d2@dz 2 { n8 2 {,$D 0B o8 BDjJ?"0@NNN?N {( p8 < ?"6@ NNN?N2   vx1D>0 d2BJB xz [  q8 [ ,$D 0B r8 <̊ ?"6@ NNN?N[   0 < x1 < 4V >0 d2@@H@@ B s8 <Do?"0@NNN?N  B u8 BDo?"N  ,$D  0 v8 < ?"6@`NNN?N kExample&>0 d2CH 8 0޽h ?88 8V8W8g8h8C8 D8 F8 G8 33>>___PPT10r>.[R+#RxDN<' = @B D <' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*!8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*"8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*#8%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$8%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%8%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&8%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'8%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*)8%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*48%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*78%(D' =%(D' =%(Dg' =4@BB7BB%(D' =1:Bvisible*o3>+B#style.visibility<*98%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*98D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*98D' =-g6B fade*<3<*98D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*n8%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*q8%(D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*u8%(D' =-o6Bwipe(up)*<3<*u8D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*:8%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@8%(D}' =%(D%' =%(D' =4@BB9BB%()?)?D!' =.7 BBBBBM 1.94444E-6 -0.08194 L 1.94444E-6 -0.24884 C 1.94444E-6 -0.32384 -0.11893 -0.41574 -0.21511 -0.41574 L -0.42882 -0.41574 *3>*B ppt_xB ppt_y=D0BB FfFFpBB9[BY*<*@8DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*k8%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*l8%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*m8%(++0+$80 ++0+%80 ++0+&80 ++0+'80 ++0+(80 ++0+780 ++0+k80 ++0+l80 ++0+m80 +!F  0 KC "<(  <^ < 6 q ^ < 6 4 ^ < 6  ^ < 6 Z  < B ?"6@ NNN?ND"D < B ?"6@ NNN?NY:Y  < B ?"6@ NNN?N ~   < <( ?"6@ NNN?NX:x,$  0 Before we draw diagrams of cross-sectional forces for our example, we make agreements according to positive directions of axes of the functions M(x), Q(x), N(x)2>0 d2C@2? @*Rs-B  < <D>?"0@NNN?N ,$D 0B  < <D?"0@NNN?N ,$@ 02 < H o?"6@`NNN?N,$D 05 < <8 ?"6@ NNN?N; 4 ,$ 0 Wx&>0 d2B B < BDԔ?"0@NNN?N ,$D 0tz pb  < ,$D  0B < BDjJ?"0@NNN?Npp8 < <d ?"6@ NNN?Nb   Q(x), N(x)$ >0 d2 @4Uz p  < Z ,$D  0B < BDjJ?"0@NNN?Nppe  < < ?"6@ NNN?N   gM(x) $>0 d2@ < < ?"6@ NNN?Ne ge p$D 0<4___PPT9 Positive axis of M points towards  bottoms Positive axes of Q i N  can be chosen arbitrarilyj_?0 d2=C@C@CC&M @8X^ < 6 Z  < B ?"6@ NNN?ND"DB < <D>?"0@NNN?N| ,$D  0B < <D?"0@NNN?N X,$@  02 < H o?"6@`NNN?Nk ,$D 05 < < ?"6@ NNN?N,$ 0 Wx&>0 d2B B < BDԔ?"0@NNN?N e,$D 0Tz pb  <  %,$D 0B  < BDjJ?"0@NNN?Npp !< </ ?"6@ NNN?Nb  fM(x)$>0 d2@H < 0޽h ? 33~*v*___PPT10V*.[R+Q!7D)' ?= @B D=)' = @BA?%,( < +O%,( < +D ' =%(D' =%(Dp' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<* <%(D'  =-o6Bwipe(up)*<3<* <D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<,%(D' =%(D' =%(Dg' =4@BB7BB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*<D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*<D' =-g6B fade*<3<*<D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<,_%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =%(D' =%(Dg' =4@BB7BB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*<D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*<D' =-g6B fade*<3<*<D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(++0+ <0 ++0+<0 ++0+<0 +y  0 ; ;SU[:(  ^  6} *} ^  6 4 ^  6  ^  6 Z   B ?"6@ NNN?Nd"d  B ?"6@ NNN?NY:Y  B ?"6@ NNN?N ~ ]z D'    \' ,$D  0!N $    D$  N b $    b$ B  B <DjJ?"0@NNN?Nb $ B  B <DjJ?"0@NNN?Nb b B B <DjJ?"0@NNN?Nb $ B B BD1?"0@NNN?Nb $ N S<cI   JZ B  <Dg ?"0@NNN?NccI B B HDg ?"0@NNN?Nc   <M ?"6@ NNN?NS<# Yn(>0 d2C #N ` @  }2  H jJ?"6@ NNN?N@  <$S ?"6@ NNN?N`  Uo$>0 d2@ N  |=/  %ZB B BD>?"0@NNN?N9=/  <V ?"6@ NNN?N | UQ$>0 d2@ N [,  RB  BD>?"0@NNN?N,  < [ ?"6@ NNN?N[t UN$>0 d2@ qN E? 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BD1?"O*W,$D  0lB @ 6D?"H~P  A T Ԕ?#" `~ -,$D  0 @ z  e = B  l,$D 0zB C <Do?" _ zB D <Do?"` ` =zB E <Do?"=e =z  e = F (s u,$@  0zB G <Do?" _ zB H <Do?"` ` =zB I <Do?"=e = J <  ?"  ,$ 0 QM<0 2D B K BDjJ?"DaD,$D  0B L <D?"gmi,$D  0 M <d ?"=,$ 0 QM>0 2D z  ^  N yx +,$D  0zB O <DԔ?" ^ zB P <DԔ?" zB QB <DԔ?"] ]  R  x0e0e    BdCDE4F @  Ԕ 8c8c     ?A)BCD|E|| ;w}r_\5Yl{l]Ed @    "<  ]  S < ?" Uw ,$ 0 QM<0 2D  X < ?" a  D 2A. Y <<-2 ?" ,$  0 Conclusion: The diagram of M(x) appears always on the same side of a bar  independent from assumption according to the choice of  bottoms . 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0B : 6D?"0@NNN?N5 o5 B ; <DjJ?"0@NNN?Nff,$@ 0B <@ BDo?"0@NNN?Nf ,$@ 05 = <-  ?"6@ NNN?NN 0H ,$ 0 WM&>0 d2B B > BDo?"0@NNN?N R ,$D  0B ? <DjJ?"0@NNN?NS S ,$@ 05 @ <l-  ?"6@ NNN?N} w ,$ 0 WQ&>0 d2B 2z *  A * ,$D! 0B B <D?"0@NNN?NB C <D?"0@NNN?N  B D <D?"0@NNN?NG G B E <D?"0@NNN?N* * ; F <-  ?"6@ NNN?N { ,$# 0 ]02468(>0 d2C  B G <D?"0@NNN?N  ,$@' 0B H <D?"0@NNN?N66,$D) 0B I <D?"0@NNN?N  ,$@( 0A J <-  ?"6@ NNN?N  ,$* 0 c 2 0 -2 -4* >8 d2 C  B K BqDo?"0@NNN?NKZc ,$@$ 0B L <Do?"0@NNN?NE Z6E ,$@% 0l2 M  BkNENGHݞIQ o? 1UkN11UkN1`TkN1`T"6@ NNN?N$)) ,$D& 0B N BDo?"0@NNN?N  ,$D- 0B O <Do?"0@NNN?N f ,$@+ 0B P <Do?"0@NNN?NQ e.Q ,$@, 02 Q B jJ?"6@ NNN?NN ?,$D/ 0B R <DjJ?"0@NNN?Nhh,$D2 0 S <-  ?"6@ NNN?NuI ,$6 0 4 [kNm]R>0 d2C BBB& T < -  ?"6@ NNN?NtH ,$5 0 4 [kNm]R>0 d2C BBB& U <-  ?"6@ NNN?N<| ,$7 0 8 [kNm]R>0 d2C BBB&B V <Do?"0@NNN?NE 11) ,$D8 07 W <D-  ?"6@ NNN?NqX ,$9 0 Y+(>0 d2C 2 X B jJ?"6@ NNN?Ni ,$D; 0B Y <DjJ?"0@NNN?NS S ,$D= 0e Z <H-  ?"6@ NNN?Nr  F,$D 0 4[kN]R>0 d2C BBB Z [ <t-  ?"6@ 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In the light of the above assumptions regarding sing convention  we do not need to assign signs to the bending moments diagrams. It is just enough to be sure that there are drawn on the side of fibres subjected to tension. Thus we need only to mark  bottoms for writing down the bending moment equations, but not for making its final diagram!&]>0 d2]C c <P$?"6@ NNN?N ( ,$D]  0 3. Parts of diagrams marked in red have no physical meaning: the values of corresponding cross-sectional forces are not determined in these points&>0 d2CB d <D>?"0@NNN?N` ` ,$DM 0B e BDԔ?"0@NNN?N ,$DN 0B f BDjJ?"0@NNN?N`  ,$@O 0E g <$ ?"6@ NNN?Nw  ,$P 0 gM(x) $>0 d2@0    h3  | ,$DQ 0L2 i 3 BZENGIQ >? _Z2Z`T_Z2Z`T`T2Z`T`T"6@`NNN?N  F2 j # BfENGxINQ >? ff`Tff`TN`Tf`TN`T"6@`NNN?N  B k <Do?"0@NNN?N` 1 ,$DS 06 l < ?"6@ NNN?N" 8B ,$R 0 XM>0 $>0 d2@ B m <D>?"0@NNN?N\ \ ,$DT 0B n BDԔ?"0@NNN?N) ) ,$DU 0Uz r  o 7d ,$DV 0B p BDjJ?"0@NNN?N)] )  q <` ?"6@ NNN?Nr  gM(x) $>0 d2@0    r3 i ,$DW 0L2 s 3 BZENGIQ >? _Z2Z`T_Z2Z`T`T2Z`T`T"6@`NNN?N  F2 t # BfENGxINQ >? ff`Tff`TN`Tf`TN`T"6@`NNN?N  B u <Do?"0@NNN?N\ - ,$DY 06 v <  ?"6@ NNN?N %> ,$X 0 XM<0 $>0 d2@  w <, ?"6@ NNN?N ( C ,$\  0 2. 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,$ 0 WQ&>0 d2B 2 9 B jJ?"6@ NNN?N(N O ,$D 02 F B jJ?"6@ NNN?N ,$@ 06 z  Z  G  Z w,$D 0B H <DjJ?"0@NNN?N  B I BDo?"0@NNN?N   B J <Do?"0@NNN?N0 f0 B K <Do?"0@NNN?Ne . B L <DjJ?"0@NNN?N    M < ?"6@ NNN?N Z f [4*>8 d2C    N <  ?"6@ NNN?NE   Y2(>0 d2C  B O <Do?"0@NNN?Nc/ c B P <Do?"0@NNN?N/  B Q <Do?"0@NNN?N   R < ?"6@ NNN?N   Y+(>0 d2C   S < ?"6@ NNN?N~c <J Y-(>0 d2C  T <( ?"6@ NNN?N F,$  0 AAnalysis of the obtained diagrams implies following observations:FB>0 d2CG2C U <  ?"6@ NNN?NA U p$D! 0<4___PPT9 Linear part of M diagram corresponds to constant Q and q=0 Constant value of M corresponds to zero value of Q Linear part of Q diagram corresponds to constant loading q but M diagram for this part is second order parabola?0 d2CB!CBCBCBCBCB/CB0C@8X V <  ?"6@ NNN?N` 5,$'  0 ?The above observations suggest that q-diagram is first derivative of bending moment M and distributed loading q is first derivative of tangential (shear) force Q. 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