FWS x_ C3ff$1$E9$pP3asoDdIUq.DAEGe/GT9.$1$jC$M5g55dREyIYx/DQ1uoWWQ1A*4PX@%oƖ&yKhe ΣF\ 8H-,?ٖ`"u[V86,P pB#DGmM l Pu3{1C8q  0XQ ڷ` @`cGа18a:! bD|hȉ@L-0_! nXZx0h5*2 $>]S m)m-Z_7P)BUUI%G[DMƆA02m%ghkErO 9G/=ysv}Ж߫W8*B8F<b  QOw P(6Ly}i-|Ӱj:7}s鞵z (*sN/h$Ҋ!,fDbIhG_+?`a k XvumQ*'Jsi4r"K<9PEcox &LDpZ:Q1pSѴ>r@[jA-4bnIMǕr1F['m{@-A;mB_ؘw(kr]K}-=OPMyMJ,5WkmIօ:F i5$8=Q]KWË2&n/OD"32H"9t0"TΈFoD&@Ύ3#G PS ^=S" 7'{gEď!/G85GjmvQbEF?G#1EdFe>e;-j^"RH 1 diU !,w̋[W@(tPpZb}_ڳ87%XH "$A`LS߮ΚP:>IF|9td6cBfeFZt@YhQ=63IyC4S>9檰=4 WAkjbxg6ab4y5@oXRR[ވF jYrsP1&Q?x@BnEVv-})](IAM_@,"do%NS+vrZނ @A$(@ VB1,ILv}etɔ'{trǾw:P^đvv;0h; 4"6lfP&LFyD% (he8[t1"]u(+L A]#ZhCaS3Xμ<њ*2\W}bI^PFuˆwU*&3`7őan}HRCRP<]xpp̩ej_32cg"Rԏ6}b:P4eMTb>}4c\ěnY(,Py$P% R컸CNQF- Ȏ^]K"GerF(lgŇڗ= w#9s6/B#)[5!}J:ߔU]ք,9*P2yq$B@`$XKQlDȅ31?2 *4Q&^Z.z*)Ub1, rLv*DW&j̥fm˴-F`V+2'P xS5'uw jv^i {;sW V8C7ۗR{>^]K!AIL`x3'Kt$K zjb(P:8aaPR tFmO  IgI;;Xt]e/D\^[I @wCtǯnr'E )M[b:5\mP֞lufmЪXK]Ȋr\M"c(2';F,1m^yĢMluٺ@$ӖbjdFAPyi(JQ L8d[l䋜Ԟ]z/W~QPffd]gortosw5˶q8)i\#P*ʾ{O,CC(-"GCS.b=m 0JV= )E&mZ5<ˮ{9_Tbpl&G :bv _vԄy%laUN*P޲>Fbz.۱uiarخs&&VHA2XUM#4XAŷe]%6SKISY.?"3a`42(ËD a01GPں{(CJR/:W974H%Dyùj[ {HlȗϩE SE74CdW&-r#rb/jȊ)Ph. '0*&Y 5@#P>bF ԧ•1IՇV^R6G&M6U_m1Xl+ *͛UxY)7cXRjAaKP\c?Ӊ"pl$PK^zF ޿#?ȉ̼Fdivvgg(-(߹4iŔYE0( IEQe`diP+.uzF PmxM PX ?correct_soundR 4?!R!SCɑS0@B SQP8?)Jz*7h@!S/ qkC@^Iܖ(90gMR@N(w@a&Fa4-%q Q A` 7@Tk,cHjI Ƒ D:~3aB%yCL n%8cB~{Hkl$8gJ !#6h D  bs6R*PX ^a hEJFd8Q.^F!B z!{) @@) @%8HcÄhx4iX*JJ;|  A/,1AF JҵB,#Cc)W @/Lk4a bM"8 n$" ^)d%BA33FQITQ  Ic8 ScSQ^(`BC !XōfBl x+8ҁOy, "3EMJE*Tq1Cc "ƆΐBIKaHMB8KUP "e+vp)a7BP#ִ&u!&$ X 21ItHA:#(d1+V!FPq xB"[ZPa]R!!P5RF! (6P0JpB( 14PB)"% 0G-#b!E$Qߜ B c" %)n00o$/pA AXrB29ZJ ANY) eZuLoiG[X'(T H)JAœ!D/-!1C$(YjAJJу nPH0 B@d I ;%"a+Q^V8ӨT“B2  AijHl1Hx+CD(B Z沵"8"HE`)r@D #LOsI֑J[B 2 [FF9aRq_5  W!Qo5JU"dWs "CBpBٔ[A/ V3 ~Af9ZC).f(s$`i91s1i@@fm |! x EdJ&0h!@IxR@@- Hᓀ P5  t]p h `T2]8  0!\  X!I?incorrect_soundD ?X dTotalBytesthisgetBytesTotaldLoadedBytesgetBytesLoadedpercentLoadedMathfloor%HowMuchLoadedi R R d RG?HowMuchLoaded=? r!L3 RWع6S\Dz 0+|Ҁo,pp˃ ]^S u-ylц]@L B*; >5M-G E7]c'"eI[/rlQغѧ<>’+J)d+7M[x<]:yβP-*=uii=3рX.L,=$JV3!#ҠR;뤫5;Y~7 9J{iü2dJ{ iS\(.Xl׽Vrgn.vd6[i6 S.wd,H)q7Q*RR@)! $rP WJO}.aP M?²nI hmtVNbtV!5:l' !ӓzdG]$ dXvR\H*M-W':П@X) G`` y@' 8~? \VerdanaUCf =Xu(& G g )   E d Cb!FUi)TYt/>5IBnMoVM?҄+Mh5d{xI>V =I>V5d{xI>V5gj宒mn#䙻RVEI|S03 3]CCJ&~$rsbf.`^5beF/f`q.w\w#g#Gy7(yE%M@Yn~,YpBH5Cmݽp!|7'BP w8/P5Iy/*졸mvQ[NO5jx*=ikUkpd#+*fL2Z(ZKdrM؂V`?)arv%+RMmD/u(/[(˾׽{j6ۇU.r!-p5gnf/(RTUW@6JRҩ:e& RsZG-͔)r5Ot6ٷ6E3O L-hg1B -Tuз]>;mRIk]A(i@>QDX i|EYĠ-&۔eGz5jZy*W7rI@5gbekq]Bnpȡ))kN?[ϔVZrk}LWdS)&c?V?&.8uwYJP՘UGç.*@"LP9KNs'+y)RxZo- Bi@\ݶ]ۤhCn{dK5fӮǝvp#&nԽI(bH[ "F6auO] ezX٬0 t(͖wd=5qn۴֬~Ҧo\u);Pͱ imvZϛ@`KY{D8dPa9[Nbұt05IfybnQwgTR{]u5JVy/8ˏ75>4N00 ͢w6\r9 f1A @Q댞#D9( RCT\ᴥD)/|4eG>9sb5kfS4h䋉E~? #A  yWTfUFLpYkdk\O[G{S$pLJBmK5hNf@&C$|#N@Y K|7jxi L&(0M}_Mw߉ϻNVcQ5wi; & ]{vQ-MEů6X ӗw >dpQ]fsi_5jw"crj7#E#5kx]a&}a*mnqL@M1 2H;sW5l yѹ)(+A\ťb5lyF䯎 ߞ]g>oF7<Ò"p@5O/-frYx~wzmѽAjq5kxG A@x1~kB&Ƙ5jwR;vs)ۇ"LGq\5dfyVeゲ\ v<5c{yYf"l5f{y^we[혎85dL xWn]w IZI-pB`6Vp!),eԕ3Ųkt]4ہ o;W{~Bdl5fJNHI5 \c[! .A5ig@yMRku90 nܩmů '*J[5&gZb=` ـ-yؿ,(;}$ʌw)|?qj5e"(}$ʎ_6֐m?渽o֘Fa%h@.xg͉]n|5Nl'(f7WYt7a; g5d*{yXV/{n-@5heTd [RgVylb`~rtmN.sͽim` ܩɼ(knա5akMer,B2%JHR n1/z` 4nٺ<7Ŷ6P5jQ/VW)-bMF6vX 'Ep%% F~$sv᜷5j.tc4n~q '5lr<1ܠhn'5mf+-3kG ҵ<ܠ9.sd !"'()+,-./0123456789:;=?ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]abcdefghijklmnopqrstuvwxyz|^ZT--xrrxx R?Z/9cgg!@--[^^<`c-ddXf&`XT@XT 3Xa;SgXS9gXmauP$PnͷPX>LQX8T XNXX]T$XFRT X*V`XRR`XCT(XNR`X2TX4R Xq%<X')W<\X}_XJH X a`X_[`X4V$X_c`X_OT`X_N`X4^T$X__t`X>>T`XL ̒ X!Oa ̒ XN ̒ ~ bD &@4i@@ &@4pi@ @ &@4Ti@D@ &@4TMi@d@ &@4T}@i@@ &@4T@i@@ &@4Ti@@ &@4U i@@ &@4Ui@@ &@4@i@ &@4 i@ &@4%Ni@ &@4 >i@$@ @4R &@4 ni@ԓ &@4%i@< &@4|&i@H@ &@4 .i@ &@4%i@\ &@4|[@i@l@ &@4 i@ &@4i@ &@4|i@@ &@4 i@8 &@48Xi@ &@4|i@@ &@4i@X &@49 i@ē &@4|@i@@ &@4i@| &@49i@ &@4},i@@ &@4i@ &@4:i@  &@4}ai@$ &@4i@@ &@4,*i@ &@4;xi@0 &@4}i@H &@4i@$@ &@4XZ@i@ &@48qi@P &@4}i@l &@4D"i@D@ @4X  &@48t i@t &@4u@i@ &@4DTi@h@ &@48w@i@ &@4,i@ &@4Di@ &@4i@@ &@4pi@ &@4,i@ܓ &@4Di@ &@4i@ @ &@4pi@ܒ &@4,mi@ &@4<i@Г &@4#i@@@ @4p€ &@4,?i@$ &@4=i@ &@4#Gi@`@ &@4Y@i@H &@4=Ni@ &@4#u@i@@ &@4Yӈi@l &@4=i@< &@4#@i@@ &@4Yi@ &@4=i@\ &@4#i@@ &@4Yi@ &@4=i@ &@4#i@@ &@4YXi@ܒ &@4>xXi@ &@4#,i@ &@4Bi@@ @4Y &@4>y i@ē &@4#Zi@  &@4Bi@$@ &@4>yi@ &@4#@i@@ &@4,"i@D@ &@4>zi@  &@4#@i@` &@4,Ti@h@ &@4>{xi@0 &@4#i@ &@4,i@@ &@4|i@P &@4GGi@ &@4,i@@ &@4| i@t &@4Gi@ &@4,|i@@ &@4|@i@ &@4G i@ &@4,}i@@ &@4|`i@ &@4G mi@ &@4,}Ni@@ &@4|݀i@ܒ &@4G %i@  &@4,}i@<@ @4| &@4Fi@@ &@4,}i@\@ &@4Fi@` &@4,}i@@ &@4FKi@ &@4XXi@@ &@4Fi@ &@4X i@@ &@4Fi@ &@4Xi@@ &@4Fqi@ &@4Xi@ @ @4F( &@4Xxi@0@ &@4X@i@P@ &@4Xi@t@ &@4Xi@@ &@4Xi@@ &@4X`i@@ @4X(@ i@ i@̉ i@Љ i@؉ i@܉ i@ i@@ i@ i@ i@ i@ i@ i@ i@@ i@@ i@` i@t i@ i@ i@ i@@ i@ i@( i@D i@\ i@l i@| i@@ i@ i@ i@ i@4 i@H i@\ i@h@ i@ i@ i@ i@  i@$ i@8 i@L@ i@@ i@ i@ i@ i@ i@ i@,@ i@ i@P i@ i@ i@܉ i@ i@@ i@ i@ i@\ i@ i@ i@؉ i@@ i@ i@ i@0 i@h i@ i@ i@@ i@@ i@ i@ i@< i@l i@ i@@ i@ i@x i@Љ i@ i@H i@t i@@ i@ i@D i@ i@ i@$ i@T i@x@ i@ i@  i@t i@ĉ i@ i@0 i@\@ i@@ i@؉ i@D i@ i@܉ i@ i@<@ i@ i@ i@ i@p i@ i@ i@ @ i@l i@ i@H i@ i@Љ i@@ i@4 i@ i@  i@l i@ i@@ i@ i@ i@ i@H i@ i@@ i@\ i@̉ i@$ i@l i@@ i@0 i@ i@ i@L i@@ i@ i@| i@܉ i@( i@h@ i@P i@ i@ i@L@ i@( i@ i@ i@,@ i@ i@l i@ȉ i@@ i@H i@ i@@ i@$ i@ i@@ i@ i@d i@@ i@D i@@ i@  i@x@ i@ i@\@ i@<@ i@ @ i@@ )@HH@@@@@@@@@@@@@?@ ?K-MathcommaFormattedneo.inputStringsplitneoLenlengthneoStartcharAt-neoLenRnoCommasfloorFirstBunchsubstringwithCommasSecondBunch,ThirdBunchneolenFourthBunchformatDecimalsnumisNaNdigitscroppedroundCFtenToPowerpowindexOf.0halveszerosNeededi0toScientificexponentabslogmantissasigDigsoutputeinputString R< NN< < N R I <      R< ? I     IL I> NR<< I    NR<  NR<GG<7 I    NR<   NR<  NR<GGGG<? I*    NR<   NR<   NR<  NR<GGGGGG< NNHGNG>Onumdigits= J>_ H<RK<R<>  R< R K< RI G !R<"!NN <#<"#H$G##PR<>O%numsigDigs.J=>&'R(R k@U  R< I &&  R<) <)* )R+)<& I++,&GG+>O? LocationOfSpace inputStringindexOfoutputStringsForesAftLengthOfStringsubstringoutputstringLocationOfComma,lengthisNaNmyRandomArraymyFlagsFillArraysShellSort2FillArraysSubsetnrtheRandomigapMathflooriflagjswapTemptheIndicestheLengthrandom$StripAnyUnitStringsinputStringR<AAAAI#R   <  R< Ik N R GRG I>J = >J>GenerateFlags{ @ O @ O==GenerateFlagsSubsetv @ O @ O==$ShellSort2theRandomtheIndices N< R<AAA HgI    HGNNHNGNOGONGNOGOP R%TraceArraystheRandomtheIndicesJ N< < HP.FillArraystheRandomtheIndicestheLength < HM ROGOPO  O  O*FillArraysSubsettheRandomtheIndices <H1 ROPO  O  O O?txtInstructions introduction? $SymbolUj8Gk|&|*&<~m ;   G  J fjZdJa/#['K7Rjg  9 V 5ae|$`0 Cet-MZ../^ IPa%LR!H"5h7)x,.%ĞZ";ʳF\ԙoUFʬ~5K3`t"5F)^VUhfe1`<-֭4ޔydgUk#F=>S"J5)Fa%SNL4URnrfVXh;dnnհ)5`^tkA$$@ i } 7ѮWדŘNa:` ـ${śk@5d]V;-n؞KV~v#5+=S'@/K&,ѪV\t{oMeiI(,' ӾDl P4t5@A/5+@/B$ 0 @)C p$\Q\5dv𵫩cz5D`:p`N`$lg  #,#,0%)J|AXRԘ`Lso)-,O`Fπ/3X%pO) 5au@9 :29xtR܀ݭ߃FP@DG3_5e75IS1}fIVC5@ ,9)@ +0 ʖ 2op.kfThFW%|@M[(1OM5f x[}]՞n7R_pq%Cq5fV&tB$&B=pk+ bɮI+xVBH + YRLW`ԕe0e7EysױZsK|n<쪀5g2tS\RZ+1Eڑ#dP3fVN6hk Zp` bJ+0&C?4Fot@iP%C:`U"{[С\@5axC#ʳ۔ic6Z 5bsd5ڤ+D0C M,K_&3THȶVK9l&'6apT8#(l: 42$i@R?Ra4v%`Y/J.0 <7+`1J ۙrrGL`5DT ׀dV,5( $KF,Rh^Q6@x+1vFd`ـrXb@քB=A8cKqJl7md 3fR.w1ڨʀh5F4BKШ ) $) QD/\ dA,^/` IHa%LR!zH#"5D\SBDi_$ @/L0 $C,̦_(MYf5T)ˀ,4V1Ly;JG@5!9zP'B VV5ad#ې:@43$ ~%Y5U&g0<" ywku/)x"BA^`rkmRL-sKPrN D/\ dAFKФ ) $) Q5ei0 )t!L7m^ۤ.Hg(lh*ѺU~tk~ߘZ &xKq5ff֣L‚m](T _e`V0|S. ̎FC1p_.J͐+`hݠԪ(#R˄5Z6 . 2d"rT.\C\0ו}p%g]u۟m@ `(5hvfnZ{ѷq㢜qJ]JmHzVoHf=ZuRtn֯֔5{^Z-% ir[kԸܪSSޠo&ɱymNtSC#@0y9gj5OürG2uRkj5gV|nQPĬ) h'ж_3{]}ܶn ȥZ`{T$k)0tUr_]Py>` ?wlByNJWB{JL`5fZ٘24_3*l̩V.ܯM$q1!Loߎ|9* (T@ZE. kFJHZi_.i`"mp Y/3e-e.YRdSz?( yKeh4n%.?L|4 %򖡝Lɀ.:o5i>-n.[P 7*d$IP RഴnFU a@Wۺ]۩пFDo 5fx-( %@`0JJA-Py=ٗΘ <:RRgE. wF%TyFpK[\i@h觡*P|erUhQh5gg?SVR=zNRߩwK#@2ѺԽ/xI6qt~)#$]ܔIPNeɹMXUTjkkY@0&1ӘI8WČ40IlTunEe7$q-MH5gvͳe|,\:F{^ѝaҕ*)p[7h1*3|2T&VF zK\ Czv2e5w:)K`5e)gJXp:)p_z7JޒJvvIK@J8bpz)nLn'қ6~@5lnx[@>BRETcE. F%ViE:羑ކq%i IPA"7h1*J/2,#l.ݔfSF1+۸OBjj^95gw)Q-PKԀ2ˌuN5crNH0'0 |'g@)$M+f4NczO*Srȋ@/N>ڀ,*[\t`Pe!5j~x^i@*$JRdKE. GFXI_R~P %4KѻAV'R{Vᆥ_nwnByzKPR$H5c*   :d$ '$j@Ʀlk 0Yzs@c" rLE7W|cFfI@(/5[ w5byYV3U^䓖@n75U]5I'FL ) $) QD0\ $ALw `,(H/ PRI~R )J@ 0 d0EA @|5`rIWq5.z@5JܙxӰ~և0hP|8(7Gk M7%DMtv˩^?t|4eٖSIL{x+ Lx 6u8QΖşT\WZזz5gbZiu&rt1̍%yg[/Z86UfQ^ج!YgKVRUcec LX-Q$#e#14#.2HxpV0]X;Rf#”7v cn5D4]@%.tZT#akm M8PRRdЀ(-%a.sI e%X}㽠m3o\7\uΞ$9 h@,,^R|ќF}.MǤ 8}kn\-C6u` R-QؐD0H 8+'f*;ZYMx&G.ٜ@ROc]Up <5d^2!h(}KFXI:q(~ֿٌ:;WBJx2W3kksv!$? U#0^4 zn (1xeio:\e5AE ,,Ѫ` JfFGM)E -dó {ʽl:s{n3ްc0',Q2RgJ ҏ~rd5F{P+k~ƈKyBɂ/%9X U,baap4 meG0 W<^SŤ(o0(3Uk o %0ߟT$ BITd5FSZ` 9@#x9E [AIyG%r $טv[hZM^i}=_L5JmJeU/Jam )teV +$HTzGyۥ & ]Cr"W 0p42`h S!pK}fVn$ff,%+DINASL5Lw`$pOR@32$ <7\)X*|AmC襹 ѺD>р^@1Mb]d@t>ތh)ގb5bvD  I,H )-*'&A(A%.98%uwbRo~i'$ ՗YO+. ȗFSW5EmHeAi ]cdXՀ|%I%aO.$G(P#h9Et oAYej mզ]ZȖkeZ uCPm2 oK5^5Y֘>BKn@!-`5 k nkmN\G$f Gؚ\2PUQ}$) R{}H5Kmo%O侹Ll#>p<&\cfRNVI{7DޮFM^#-4%nfٖmf5&etp缏2"1@s=JE*G 5g&%k$muٵey}%41 ߚ_V #|` B %9/ #Wi 5`yje+%ٷ vmXWm\P (ɩ&'P-sL+%% $#,FRSDL*݅iTh`,5a]&nX5pDKʠ90-@5pDKʠ90-@5bB&ꐨRDrT R=qLtУx>ݴ"Poҽr@il (5A85hWuXpA:8pP=#'KY|_sE0I !"'()+,-./0123456789:;=?ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]abcdefghijklmnopqrstuvwxyz|UUU222srjU:^r.rUtU22jQj22N222jNgg2Xru,X1U5hP:EX*'nX%tnXDHݙUXDI%qX#X%;0Xx0u0X:0X*5u0X;0X17hX-;50X&:uhX>80X):0PcEpPm%XXDX,3,X [U,XNuhX [5hX L,XK5hX$]5hXIhXZhX'hX'KX]hX V,Xouh_ZhX&W,X`UhX%ZU,XChXG5hXJhX W5hPH&X^,X!NhXcHX JuhXT&,eXWX% 5,eX*MX=@nX#AnX#;PJEX$>tnPXCXnPD X#InX EXCTX>GnP(pX,@ؤXAX-=tX5@ؠnX'JP,X$BؤX!WX(RؤX.;nXTؠnX.<pXRnX4FX4FX5.5/7XB qg'g 3@text

ab lot

D @ I@6@dummy_symbol{nO* )ST>?:; 0^uQ?R{q>lcfm\u,8eA$h؃=.A c6+(80% jIA/&7o-*f(As'?o>[8eg@f`(*J~Ogi8-/-~X.X7) US  ?0@0-¿xȑ^@~ce߀Ѫė53hi! :'Led3339GYb]32ģ& mȀ}ac_Ⲗ 6D3B1)=)u$%_?bpZ"C[$D{ַzfQP\qCq?oYEg '<$Ԟ{6kxX31oӷ BD9n .5G| x&]Ro%\+"|O> ;VĆČvn\_9/ğ?Dfԝ#7uq54(ki'qv};DV M?KutgzqփPi*zBPJؿ5JR"G흫{ \)j<@'v.A~{ĜXc@^Nx>˸ z"Ir$xK梞wXb@jty333%nBoP  PՉ  P  P4 .vÌBy`"@ '0#Dj kD ŷ۟B`P-3 0Ŷ۟2x3 Ŷ۟7*&3 @\L(\YkꃅyrcYkYl9PXkYkǂ7u'XkYk} jv#YkYl}JZ]wOYkYkes_܀YkYljVitKǀYkYk u)WYkYkJUH YkYl|{7YkYkJRYkYk%vYkYl|ڃ%tYkYlJRBPBP|jGD;BPBPk+~BPBPă e1BPBP|[Q/}PBPBPU `BPBPk+~XkYk|jGD;YkYk_0Sp~c|bz3qYkYl.2Vܗq@~cd|QYkYlP 쮿]C[b3j)4yyO\bGLL ]3(%[D }4ѳ&3.&sT%\wg|Goԍ1TDmDLA䨈|CfC!tRں w'[@b/{`#5%$3á3іތ]q㡒CT$f{#8˅'=dt֌^ *FِJ~aV"sҽm=WV@άShxxvZ& J~Z&8 ̶\'.ou?qA%>w#27Ѿa`:P@s \PPD,mCP/BJ|*q~g?wX#(sO֦jřkƛ)sOƺp!%I8&J9zjP+yS+yTzjP Z> Z?;AX5!]A!_B"&J9%I88U Z? Z>8U+yT+yS@v{t jęjŚ6jękƚ<3jÙjŚDM$`jęjÙ@W;Q{'dւoFhEF&!'B^"vx#5xl&gƲ&m|v{[(GUe ~em=C􂨛Ũ "oV‹wYP@m/\hul(}%H~{/ >?v? TahomaK?Mxs=XuUv 9 z r q R j  6 U %].jgi 'T}5HBnNoPVD?؄,\]c5c{xI>Qk=I>Q5c~{xI>Q5f尒mn#ԙRVEI|S0+ 3]Iҥ/<)q:`lLDG*TRL[5ef8C9 J`4izN]mJjv,BwS ]UL]q7m,a[-6.fqo=TM<5Hy㨯F*qn5L7n f,5/uOݞn,@5g{yYpID5iZfH^&oo0fl 2y啞n&tB`]%`-iS&Ri.5J݁o?/SݺPe kɺ؜WRj<5i&x,Mi?Ak\E#/*e0\([KI(B@?)brvDK[u!7 Md\{ }pn05ff.DZTr7%6ʌY<] s:&O&__f7mۓj^MxC0¶%p̓$[ sZ3ez@A9G@>CLlȤ!4+KWP p 'q\Cf3"J2ShJ#6HXb=%`90#Cų_siK J䤮$*,8Li>VcH$Ts\:!?*kED?m-K!84-/ tkI6y-O@5ifC_>n#nGoovc8vڎT]΢7#|4l6[fm-Kg3tZ1I򔜒.51b BR$4EB`Xw|L+ə/s H p]jIH8h(Zc5HybnSgT{u5Iy㨯F*qn :OrFFѹ5f8WOڇ"lMpl q*JM m\UP)"TX(KUrC8v;>iUJP.ۼ~r5]`K( ɕmwWy5ij-з]z.]oc7qE^xN$*1J_5ɠ]|!z;=RgSyyYe@j.@mʀ5fed&֯UOUMc4` ~|s˗2IyZJ 4iMvY615^p+r/F7`B 5ix,-KW ;85ix,}gA8T 7-|Q5gel~\Gzg #鐏@4ݷn\7n / ߶}'=@Ϙ(Ӏ*&挲2Д>=п]Z_' vz5k yWF܀[^Z1D775gv%x^M߻~k6%wo 5abx^T(˽]E4٢h6tּ%d)ȹ 76[v5N,⊱9=n.T'um{+ 5hwQ-]5iwr ;ŅT9hcJ))5k.yWF3<rF7N֫VU5g*u-Kfd;ɄFS"9is0xjR6S^KʎRQ YB'T &p@g>h'4yp:p4T5f^dJ?}.1֧=JqLiVp_.O뮒JQrm>rF8Ԫ_0p5g*u-Kfd;ɄFS"9is0xjR6S^KʎRQ YB'T &p^%zpP-W`5'=P B ,P_Lܼ~=ϥ*S) 5fu_H;FP$o,Bl[$ֹhJuN &mߐq>ؽDw(ܴc,*̀5ge u;LLI) * GjPÄ'LR>ko{ݧ#1ȃG֫:d7' *Jk̛k4` (z2iBk݉5f^yRnI7n\u$5jʌx]*}*mNqwL:M02 snW5jyѹ=( Dq(5knC]>#;`5Nxے}srcx~cz g֠5jx oEr.W$q#/mp5iwQܖvWx+ۗ")Gq5dFHc Wʖ]x c]2:?:l I@B3fS6å z;eJ{6ۆm̎jv_`T: 3FL@',>RԀpF6Rݘ5hgmNk) wf\ܬrm '?.U4$|I(ִ++L?Y0g6K5h2wRiwk\^nͶ^09T( yKiZR\v"5?|U-kzdђk0xDc*w{WB\-yp5fN{w+r]X~fȰ^ʔV%=qfUbj@V!؈*\d}w>Kp'4K)k_ESL5e@$i$P U($HsK">}o3 &Zىֿċp;-x;kX 0)$5hf-6g[w*7V}gI񮟍uIQnTyg⿅];%S 5c޿(}$+ʌw* ğtRDA(Irj"}Wsn ȊQ@K&5h@imNk) wfr@wʣ[@1狙Za` ɀ+nX tDIH|j5i WGdq8$  yRħ,*L@J{PG>.2>%ɸ S%W5" &|5fTz~FWʏ-WkEZl'\k_A=)5fNb1 vdvZGm6IMiL-`mp:W&PjIw$b[/Y7y=beq@5i>UDUWsqqvX85hwPo27oˏ:D !"'(),-./0123456789:;?ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz,_@@OttDvSJs~e`5ti5xQkNXL"t`X@6X<X753gX(3SgWPnWI!<X;>sQX'L$XbIXXLM$X4K XN`X_&3jXCNXCSXCrVXCJ6XK XCMVgXHVgXC74X?X 4X?I<XJ7<Xq<_M<_ISߴ^_ɺ8tV!@W#BGC%$0~5XϩXA1@00~5XϩXW#BV!@ɺ8t@0A1_?].C2D3u]`L+y7b_`iNdW]^0j/_^@D]DGЁ@@j! Cc1V֓v?|w$ȝ 簁?`U@4/F߅CQS 4"q6.]qo#{T5!ositEul6@Z(#%\H/ w@ ED &Xˀoffset&0force@/ g}*7dx +E *jOfLtLu6~KsLtD/A"B*E+E%i(X%Ja%h7)[KsLs2)6RKsLtTLsLt@B;QB8Eڄ#o< 0kw q( '|q2h` Qx D"q=Q7H0<_%x}~ze A!D  &offset&force@)"UW*@ 6NV.W/$ꀴ:\i0Fh62 YU.V.)ڡ-*H  )r*")%  =tY!R?eڱ:"k@ (:q80 .CDm^}8 g<Cڸ_:%Kh}pt{ᥐy"NU qX -#g4g P1text12345 lb-ft !$D ?#3x@ +%D "&$force@ &D ?Fj U*Oi@h& Ivgreen&purple&!blue&%`orange@'_t_<%ny#(Ulo<%VsmNp )D (@*P4  +P4 >,f(FےHU %+0:"HY+XzP @UYU:G@Vo@#-g <0վ+ַַ{T_q-'$s%nvh8+`V4a@Jgb+El>6l8lVSg$r| %Q0G)xP.D$  @;)9yqKg? p#9 ` $)]p%Fl 0D ?,@Y ,-#.h#%h.!& $W 1=@depth& W (dzwidth /J#*6J+#)6J@? k1VerdanaUB^y/LhVw = u s i Q i 3 Q p 8\"GV_%U^x0? 5/ܿebkf_a*185c{ximf {q-?U5c{xio5dV{vVZn0ln#䩻RVGI}SS3$Wb6jpc!bh5b^eBżreq&xe؎ɽvw3 \UL]m7u8z 5Kl8aOD6T8/Gb5I㹨Eza5L-6ix5/kurw5f{yES̲텀5ggqlZ 1 =%ޗӹON4+RJe"YOdU6e%\4k_R7YeΆG?|Ozp3 E8B5b.o6}ʓ.nWyTce3mٴMP5hYzև]'p3m[dvUx 4X`$ʘ$P`k~Z`%Y r/f^T3 & 5hej.3%# L Q4=ʥڮm#FYa ,N6<9'+M@mC'R$^^`ci3eZku̘[*!&YgGz{ DeFٗڿkTE"-*CJM5L]8 @ D+D7lHv(7e5h* 6u.U“A&+BM n#Nl; ^rgv̾CʤrR$_iP5E.)EbP9\m[mg l5ffCUYڽP&Ta.C"kT@ dZ{ޛW_n 'Em&/Řdn lkP'e"7TNlB*]?+ ҐZt܋Z Rb@ @Q^Xpj$\o`5i.+̳V cfo5ff x9@$(nRcJ;% Ĕ<,eW20)dĥ0ZMj48 򀄒tę\xX1ڗEș!f3YRRm料ȨY &.,H$jb @Rٖ]"3X5fdvųk)Jxҍ<ڟ*i 0( э]`.T4&9~\١]jGkvf鏯B%rʹk}ijaFn #&Kle\A)EЀ5I.GlDnܶRK0lDnܶ7Q5JN㹨Eza$Fau5k3-~͇"QPk3ve\pf W_t}ӟ6-ܶR [5pc1~z'<|@^;I%ușaMl>5fnlQݯҵ$00L<83 S0>bـuR.iCց۔NZ1ޮLX85i>x'g

}Vf)OVj 3t&丛zp8љј[7!lf_]<`eͶs5jzyWF )Fpca$]8m͆05avm8m͉TŲmll0 5e֌yQ< Xb̀m{ID#{dX${@xd͏5J1[6k?u;F6XN+LƴW5hvV8"Z1ʤ8@5kyWF-㘶xrg*أ~&;= 5jryWF7=?YT-Ms(Il.5j>.2Ia r`΄t%F&O:m<.(b2biy@&P@h+[>HI!&Lg9dS_M5fdze=”*ma7R$bNPk92[ZK2c\a?- M'`;ŠNэV W HbUgK\5kVfH\f^%(&Bֵs(qR6^>CP3Y`sMͧ6EsR\L1p]1fz4<ɠ( ̀4Xa1qH+V}8!BMo rmo즿8<5fwŒ2mRs:Z^@4kY2]yYe\&FL5a{yWEUL텀5ej{y^ws;=5feV)yP R)6^(bc]cR\$m3:l )@A9fSvjϥ#zg)@`MkI,O5*ZBȽY%`@0:bS;vin6̈́m5b{xQiS[U2q0]/&z%Rh {nب AN,͘4J` ٷ-%)ks@A#5gZr.Zn&6D`RiM5iiv̅gz6 r.l7fH /e2]ݪ 5h{yXVikNZ&p~.wW&RY%[ R;ax.,w$_}5چ 2LDf* w5DWP&כobk@ Bɴ~Q ̗^3Ǩ@Z&Y@3R ф6JRcVBKDfg6[Y[Ppܗ5f&}U/]{ FOqSZw(b  f1˘)t[z5hx^ ~Sf!e.%ݬSeAЎyeYkF 1n'ـ.s%)-P]_Uڤ{Hl,Pm3@9L&!1MH<%Sn>[[yہ5ef[/7jآᰶKMg];k[ +`aQrmjU~ 5byQv-^c lKl5l5dyQ YSgVk\4 0kuE. I6{6;0VBĶV5J ⋥pn(g v߈5b{yXV,^5kbf\,8jآᰶmi]z[,;'ސ^Yv(l-RdV\Y'-v;\Ka{U-*lJ0Q\h/*M@5ef[/7jآᰶKMg];k[ +`aQr-WҬd5I,*b i%5r˴XmSPɀJ*6LA8F̍`32bx8't4PՌ5bu]J r̠ <2qu<)-2mk7][\ax(=seLL76uW#Ȼ=A#5hyW -DIKTNbOـ/3\ VB+rdv1@+j8XKA*2p؛n6\o6 DfJ5fvX2/]: N3bl/lJ⚽Ҫڴ`u 5ff1\Yp fR['2e*Ixnkj.d 2IR%` d%gfqf[!eZI[dWenv\۳n\6Iؤ:h敜ymf 5a~wk ۪~u @1Y Q2&%@ l R@+* 5iy]Cϐ]-n%kyī65lny]SpMvO>t.PNGFCax5K-m{[2ėj]ӭ=nw5iy7ȯn7V[ `5OcOvn/eY@5dR{y^vO,2W5gƼv,70 -*Ö5hqx e@5fΚ:ݷn  fj6= s%i@]Ͷ\i %?@٦ڟ׵_eyWP t&5fevܔ'%@p @%vKܑr'mpFڏkf!(IX\V@nWqbfaW )>%y gK"vimX\ĊV5܇ !"'()+,-./0123456789:;=?ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]abcdefghijklmnopqrstuvwxyz|hFuuF/M:_&j&wvg~~bh~a^n~~^F^^++X T`XT0S XR3 X[1gXJ.gXi[ PnEPѷ@Ir_5LXEI$XCTXQI4 XTG X'KT`X^Ht`XEJ(XMIt`X=IX9I$X$HXs)7H\X{YXP>$X U`XdR`X:Tt(Xd[4`XdI`XdH`X:Z4(XdS`XE-t`X.`XgWt`XdGt`Xd_t`XdS`X:] XdIt`X:_ bXdY`XCP4(XN`XYR`X U`X.x`X"S`XNt`X?P`Xx/bX#<LXV+SbX4AX]IX5?WX6DSX5FX"13X6DWjX]FXXTL_!tLjXaKX^X]qX]FX5G7X]IgX6DWgX]77HX7=X/XYEHXHHX+cwHXHHXHHgX/>WHX"bX>2XMGKqXh<'rXh;#|? $2SymbolUj8Gk|&|*&<~m ;   G  J fjZdJa/#['K7Rjg  9 V 5ae|$`0 Cet-MZ../^ IPa%LR!H"5h7)x,.%ĞZ";ʳF\ԙoUFʬ~5K3`t"5F)^VUhfe1`<-֭4ޔydgUk#F=>S"J5)Fa%SNL4URnrfVXh;dnnհ)5`^tkA$$@ i } 7ѮWדŘNa:` ـ${śk@5d]V;-n؞KV~v#5+=S'@/K&,ѪV\t{oMeiI(,' ӾDl P4t5@A/5+@/B$ 0 @)C p$\Q\5dv𵫩cz5D`:p`N`$lg  #,#,0%)J|AXRԘ`Lso)-,O`Fπ/3X%pO) 5au@9 :29xtR܀ݭ߃FP@DG3_5e75IS1}fIVC5@ ,9)@ +0 ʖ 2op.kfThFW%|@M[(1OM5f x[}]՞n7R_pq%Cq5fV&tB$&B=pk+ bɮI+xVBH + YRLW`ԕe0e7EysױZsK|n<쪀5g2tS\RZ+1Eڑ#dP3fVN6hk Zp` bJ+0&C?4Fot@iP%C:`U"{[С\@5axC#ʳ۔ic6Z 5bsd5ڤ+D0C M,K_&3THȶVK9l&'6apT8#(l: 42$i@R?Ra4v%`Y/J.0 <7+`1J ۙrrGL`5DT ׀dV,5( $KF,Rh^Q6@x+1vFd`ـrXb@քB=A8cKqJl7md 3fR.w1ڨʀh5F4BKШ ) $) QD/\ dA,^/` IHa%LR!zH#"5D\SBDi_$ @/L0 $C,̦_(MYf5T)ˀ,4V1Ly;JG@5!9zP'B VV5ad#ې:@43$ ~%Y5U&g0<" ywku/)x"BA^`rkmRL-sKPrN D/\ dAFKФ ) $) Q5ei0 )t!L7m^ۤ.Hg(lh*ѺU~tk~ߘZ &xKq5ff֣L‚m](T _e`V0|S. ̎FC1p_.J͐+`hݠԪ(#R˄5Z6 . 2d"rT.\C\0ו}p%g]u۟m@ `(5hvfnZ{ѷq㢜qJ]JmHzVoHf=ZuRtn֯֔5{^Z-% ir[kԸܪSSޠo&ɱymNtSC#@0y9gj5OürG2uRkj5gV|nQPĬ) h'ж_3{]}ܶn ȥZ`{T$k)0tUr_]Py>` ?wlByNJWB{JL`5fZ٘24_3*l̩V.ܯM$q1!Loߎ|9* (T@ZE. kFJHZi_.i`"mp Y/3e-e.YRdSz?( yKeh4n%.?L|4 %򖡝Lɀ.:o5i>-n.[P 7*d$IP RഴnFU a@Wۺ]۩пFDo 5fx-( %@`0JJA-Py=ٗΘ <:RRgE. wF%TyFpK[\i@h觡*P|erUhQh5gg?SVR=zNRߩwK#@2ѺԽ/xI6qt~)#$]ܔIPNeɹMXUTjkkY@0&1ӘI8WČ40IlTunEe7$q-MH5gvͳe|,\:F{^ѝaҕ*)p[7h1*3|2T&VF zK\ Czv2e5w:)K`5e)gJXp:)p_z7JޒJvvIK@J8bpz)nLn'қ6~@5lnx[@>BRETcE. F%ViE:羑ކq%i IPA"7h1*J/2,#l.ݔfSF1+۸OBjj^95gw)Q-PKԀ2ˌuN5crNH0'0 |'g@)$M+f4NczO*Srȋ@/N>ڀ,*[\t`Pe!5j~x^i@*$JRdKE. GFXI_R~P %4KѻAV'R{Vᆥ_nwnByzKPR$H5c*   :d$ '$j@Ʀlk 0Yzs@c" rLE7W|cFfI@(/5[ w5byYV3U^䓖@n75U]5I'FL ) $) QD0\ $ALw `,(H/ PRI~R )J@ 0 d0EA @|5`rIWq5.z@5JܙxӰ~և0hP|8(7Gk M7%DMtv˩^?t|4eٖSIL{x+ Lx 6u8QΖşT\WZזz5gbZiu&rt1̍%yg[/Z86UfQ^ج!YgKVRUcec LX-Q$#e#14#.2HxpV0]X;Rf#”7v cn5D4]@%.tZT#akm M8PRRdЀ(-%a.sI e%X}㽠m3o\7\uΞ$9 h@,,^R|ќF}.MǤ 8}kn\-C6u` R-QؐD0H 8+'f*;ZYMx&G.ٜ@ROc]Up <5d^2!h(}KFXI:q(~ֿٌ:;WBJx2W3kksv!$? U#0^4 zn (1xeio:\e5AE ,,Ѫ` JfFGM)E -dó {ʽl:s{n3ްc0',Q2RgJ ҏ~rd5F{P+k~ƈKyBɂ/%9X U,baap4 meG0 W<^SŤ(o0(3Uk o %0ߟT$ BITd5FSZ` 9@#x9E [AIyG%r $טv[hZM^i}=_L5JmJeU/Jam )teV +$HTzGyۥ & ]Cr"W 0p42`h S!pK}fVn$ff,%+DINASL5Lw`$pOR@32$ <7\)X*|AmC襹 ѺD>р^@1Mb]d@t>ތh)ގb5bvD  I,H )-*'&A(A%.98%uwbRo~i'$ ՗YO+. ȗFSW5EmHeAi ]cdXՀ|%I%aO.$G(P#h9Et oAYej mզ]ZȖkeZ uCPm2 oK5^5Y֘>BKn@!-`5 k nkmN\G$f Gؚ\2PUQ}$) R{}H5Kmo%O侹Ll#>p<&\cfRNVI{7DޮFM^#-4%nfٖmf5&etp缏2"1@s=JE*G 5g&%k$muٵey}%41 ߚ_V #|` B %9/ #Wi 5`yje+%ٷ vmXWm\P (ɩ&'P-sL+%% $#,FRSDL*݅iTh`,5a]&nX5pDKʠ90-@5pDKʠ90-@5bB&ꐨRDrT R=qLtУx>ݴ"Poҽr@il (5A85hWuXpA:8pP=#'KY|_sE0I !"'()+,-./0123456789:;=?ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]abcdefghijklmnopqrstuvwxyz|WWW444utlW<`t0tWvW44lSl44P444lPii4Xru,X1U5hP:EX*'nX%tnXDHݙUXDI%qX#X%;0Xx0u0X:0X*5u0X;0X17hX-;50X&:uhX>80X):0PcEpPm%XXDX,3,X [U,XNuhX [5hX L,XK5hX$]5hXIhXZhX'hX'KX]hX V,Xouh_ZhX&W,X`UhX%ZU,XChXG5hXJhX W5hPH&X^,X!NhXcHX JuhXT&,eXWX% 5,eX*MX=@nX#AnX#;PJEX$>tnPXCXnPD X#InX EXCTX>GnP(pX,@ؤXAX-=tX5@ؠnX'JP,X$BؤX!WX(RؤX.;nXTؠnX.<pXRnX4FX4FX5.5/7XB 3w L31explain

1

2S

ss

4

5

6

7

8

9

10

11

12 mm in kips kN 13 MPa ksi

= + ? 13

14

15

16

17

=

;4]"<f3%z>Y{U,,KZI?Ui P5P4   v?6D ? ZbsLoadsOffsetorangeLoadforceSteporangeMaxorangeMinRandomValueblueLoadblueMaxblueMinblueOffsetoffsetStepoffsetMaxoffsetMingreenLoadgreenMaxgreenMingreenOffsetpurpleLoadpurpleMaxpurpleMinpurpleOffsetconfigtreeorange_visiblesForceDigitsMathformatDecimalssForceUnitforcetextsOrangeLoadsMbluesLengthUnitoffsetsBlueLoadsBlueMomentsP()()greensGreenLoadsGreenMomentpurplesPurpleLoadsPurpleMomentForcePsForcePMomentMsMomentMsLengthDigitssMomentUnitsMomentMAbsabsAreatreeWidthtreeDepthInertiapowcsAreasInertia4sCAxialStressForceMultiplierBendingStressNormalHNormalKsAxialStresssStressDigitssStressUnitsBendingStressHsBendingStressKsNormalHsNormalKStepSizewidthMaxwidthMinAspectRatioNoStepsroundsTreeWidthsTreeDepthsectionwidthdepthrangeValueMaxValueMinRNrandomtheValueGenerateTree orangeMinorangeMaxblueMinblueMaxgreenMingreenMaxpurpleMinpurpleMaxforceStepoffsetMinoffsetMaxoffsetStepAA= =    ==I   ==ILI   =`kNORGNNO !G+NO  "`#NORG  R$G#NNO#N%NO&!G'()GG*GG+G3#NO &"'"`,NORG R$G,NNO,N%NO-!G.()GG*GG+G3,NO -"."`/NORG R$G/NNO/N%NO0!G1!)GG*GG+G3/NO 0"1"2GGG32RG4    56G4R7G86G49RR7G:;< =<;>R  ?; @6:R$GAGB6G=R$GCGD6?R$G E2 F : G4F ? = HEGGIEG JKERLGMKGRLGNK G RLGOKHRLGPKIRLGBGenerateTreeDimensionswidthMinwidthMaxStepSizeAspectRatio;QRS=<;T U<Q VR<<UQ W6;R$GX6<R$GYZNWOY[NXO+RandomValueValueMinValueMaxStepSizew\]^ < _`R<a^_\ G<UaQ VR<aUQ a>?V! CurrentQuestionNumberthis_currentframeForcePUserResponseIsItCorrectAttaboyexplain sForceP is the axial force produced in the tree for these loads. The axial force will produce compression stresses that are uniformly distributed across the entire cross section._rootSeries1_CorrectCounterngForceEquilcheckmarkgotoAndStopMomentM M = sMomentM is the bending moment produced in the tree for these loads. Note that this bending moment will produce compression bending stresses at H and tension bending stresses at K.Note that this bending moment will produce tension bending stresses at H and compression bending stresses at K.MomentEquilAxialStresssSigmaSubAxialsEsAxialStress is the uniformly distributed normal stress produced in the tree for these loads. The axial stress is compression.Series2_CorrectCounterAxialStressExplanationInertia The moment of inertia needed for these calculations is sIsubzsInertia. You were correct in recognizing that was needed here because the bending occurs about the z-axis.InertiaExplanationBendingStress At H, the bending stress is sBendingStressH. Compression bending stresses are produced at H and tension bending stresses are produced at K. Tension bending stresses are produced at H and compression bending stresses are produced at K. The bending stresses are linearly distributed across the width of the cross section between H and K.BendingStressExplanationNormalK At K, the axial stress is and the bending stress is sBendingStressKSince these stresses are the same type (i.e., normal stresses) and they both act in the same direction (i.e., the x-direction), they can simply be added together to give the combined stress at K.CombinedStressExplanationNormalHSeries3_CorrectCounter Combined stress calculation for point StressAtHH sSigmaSubHK sSigmaSubKsPsSigmaSubBending = ()sNormalHsNormalK Bending stress calculation for point HK |M| c / sMomentMAbsUnitIndex(1,000 N/kN)sC) / ( (compression by inspection)tension by inspection) Moment of inertia about z-axis sTreeDepth)(sTreeWidth) / 12 = Axial stress calculation P / A)(1,000 N/kN) / (sArea / (compression by inspection)LineOfTextPsOrangeLoad sFysBlueLoadEquationFormatsPurpleLoadsGreenLoadsE0sThereforeMsBlueMomentsMzLineOFTextsPurpleMomentsGreenMomentReturnStringklugeCurrentTextlengthNextText indexMathrandomround Correct! Nice work...That's right! Way to go...Good job! You're getting the hang of this stuff...Primo! I'm stoked...Marvelous! Simply marvelous...Most excellent...Sweet...Oh, yeah. You're kickin' it now...responseuserparseFloatisNaNtolerancediffcorrectabsunitIndexsLengthUnit mmsForceUnit NForceMultipliersMomentUnit N-mmsLengthDigitssForceDigitssStressDigitssStressUnit MPa kN kN-mm in lbs lb-in psi kip kip-in ksisGreekargumentssSubsSsubscriptGiveTheAnswerUserResponseNI=G =G G G    NPO6  =  NRI= =GGG HGG    NPO6  =  NRI=G =G G G    NPO6  =  NRI= =GGG HGG    NPO6  =  NR-I=U =GGGGG  NPOF  = =  NR[I=b = G!GG"G#G!G$G  NPO6  %=  NRI&= ='G(G)G H*G+G,G  NPOD  = -=  NRI.=c =/GG0G1G)G2G  NPO  = = = %= -= 3=  NRc I4=+ = 5 5NPOR  = -= 3=  NR I.=+ = 5 5NPOR  = -= 3=  NR(CombinedStressExplanationStressAtH6G78G9G:G;GGG<G=G>GG<G?G7)(G@GGAG$1G@GGBG'BendingStressExplanationStressAtHCG7DGEGFG=GGGG!G>G?GHG@GIIJG?GKGLG"G@G>G7(G1GMG7? HNGOG= HNGOGInertiaExplanationgPG!GG?GQGRGSGTGUG"G  NRAxialStressExplanationVGGGWG>GII.?G GXGYG@G GZGYG>GG[GForceEquil\A\]^G_G`G\G\a\b=\c\b=\d\b=\e\b=fG]GG GMomentEquil\A\ghG_GiGjG\k\b=\l\b=\e\b=fGgGGG(EquationFormatCurrentTextNextTextmAnAIH n nopNqpNG,nGH%qGmoqG"rGqGmsqGm> AttaBoy tuvR <ttuwRt IxGyGDtIxGzGtIxG{GtIxG|GtIxG}GtIxG~GYtIxGG*tIxGG  NRIsItCorrectusercorrectA=== O> z?{G<  <uRH O>>MakeUnitStringsIY  9IU IY  aILMakeHTMLgreekp NGG<pNI NGG<<G> MakeHTMLsubscriptsubscriptGG<>?5-sMsubzMzMakeHTMLsubscriptsMzSMakeHTMLgreek = sFsubxFxsFysSigmassSigmaSubAxialasSigmaSubBendingbsSigmaSubHHsSigmaSubKKsIsubzIsP + sM sEsE00sQ1sQ0sTherefore \ngNope... Here's the solution:explainDetermine the axial force P (in lbs) at section H-K.UnitIndexMakeUnitStringsGenerateTree =G =GG   =G  =GG   =  =  =  =  = =GG !" #$%=G&'()G!G* +=Cd    ,=@BB@i@ŷ۽j: c1Ŷ۽4E `Ŷ۽8` `2EL[T 6JF ^'& &@0tree('T|1ڌZ))T|1ڌ+*@' :.+2EL[T.6J./0ȏrOPi@section?3@D@)+?explainsQ1eDetermine the bending moment M (in N-mm) about the z-axis at section H-K (include the proper sign).GsQ0GUnitIndexMakeUnitStrings=Od    GenerateTree=(45T` \ )5@MY@)?explainsQ17Determine the axial force P (in kips) at section H-K.GsQ0GUnitIndexMakeUnitStrings=O (2  GenerateTree=('T|1ڌZ))T|1ڌ+*@' :@)+?explainsQ1fDetermine the bending moment M (in kN-mm) about the z-axis at section H-K (include the proper sign).GsQ0GUnitIndexMakeUnitStrings=O2d  GenerateTree=(45T` \ )5@MY@()?{explainsQ1Determine the axial stress (in ksi) at section H-K. The cross-sectional dimensions are shown on the sketch. (Note: + = tension, = compression)GUnitIndexMakeUnitStrings=5? GenerateTreeDimensions=S ?   GenerateTree= P꿠 /@?yexplainsQ1VDetermine the moment of inertia needed to compute the bending stress at section H-K.GsQ0G@?explainsQ1}Compute the bending stress (in ksi) produced at point H by the loads shown. (Note: + = tension, = compression)G@?explainsQ1|Compute the normal stress (in ksi) produced at point K by the loads shown. (Note: + = tension, = compression)G@?ZexplainsQ1|Compute the normal stress (in MPa) produced at point H by the loads shown. (Note: + = tension, = compression)GUnitIndexMakeUnitStrings=5?dGenerateTreeDimensions=S2,?  GenerateTree=@?VexplainsQ1|Compute the normal stress (in MPa) produced at point K by the loads shown. (Note: + = tension, = compression)GUnitIndexMakeUnitStrings=5?PGenerateTreeDimensions=O2h  0u' GenerateTree=@ ^('T|1ڌZ))T|1ڌ +*@' : /i@@)+(45T` \ )5@MY@)('T|1ڌZ))T|1ڌ +*@' :@)+(45T` \ )5@MY@)('T|1ڌZ))T|1ڌ+*@' : /@()+ P꿠@ ^(45T` \ )5@MY@(5T` z )@MY.*'T|1ڌZ+)T|1ڌ-*@' : /i@h@ /@@>6?Mi@theTree 7d>ar0rC7̀Lӕ~y3`D7͂=US~ fc2d#8x I<f%E-ȔS%E8E9xd6 uppw#Hi-t"%pwHހ䖙F9@ uL3 0G9@ m3`h:p  fjh%Xz@%$r=@n H%{:;ܟDŽ='9?pH:$I&j10 4;h})3ffUserResponse123456.12I;`J73`(<wү$` 3fB@6tD7! FSI$m6t=9 S!mrI$1@8$AN迎D pC qt_0$! l`C2gEr$0c2 y#b! ːS\;a t_12GN,A- # ˒?>"P̰!q[0#/.ANqm Ll`H)d5L @f O1Ykv\g)ARt짏)rw~%_)qf n41ʴ8fkir_ZɓxL;RGֽʼn@+Sj%kMgę@= fni|z,Z77<|yM0>@4_ K,z<?a  C1k 3/f8И=<d?@d6Ԇ7BB%](eI@%*ٸfo.q"ܫIEYj'ԋ km jYu0Bp[[~G'G9ԇV2Q3)J U(D2EeD(g'uY^uAd6= <3%j=e ٦V5ݕqZ4ѻAIgš@ 6ZYMZGez% Xnj~[( qJ{*Nx;.RҠ4Bh5.P 3 pztpĈ|`ǒ;Ca 3oSfN91`<,&Л#<` Ӎ 34Dh5.P  pztpĈ|`ǒE>3`?@uUŒ@AB@' A>&I >`C@uUŒ@D=? BHowManyFlagsHaveBeenUsedQuestionsInPreceedingSeriesQuestionsInThisSeriesGenerateFlagsSeries1_CorrectCounterSeries2_CorrectCounterSeries3_CorrectCounterFrameInSet  =   ME@U@DEFGHIJKLM? txtInstructionsEnter your answer without units.FrameInSettheTreegotoAndStopconfigmyFlagsHowManyFlagsHaveBeenUsedcheckmarkUserResponsequestionNumDisplayPRGNO R    series1 v?FD ? ZbsLoadsOffsetorangeLoadforceSteporangeMaxorangeMinRandomValueblueLoadblueMaxblueMinblueOffsetoffsetStepoffsetMaxoffsetMingreenLoadgreenMaxgreenMingreenOffsetpurpleLoadpurpleMaxpurpleMinpurpleOffsetconfigtreeorange_visiblesForceDigitsMathformatDecimalssForceUnitforcetextsOrangeLoadsMbluesLengthUnitoffsetsBlueLoadsBlueMomentsP()()greensGreenLoadsGreenMomentpurplesPurpleLoadsPurpleMomentForcePsForcePMomentMsMomentMsLengthDigitssMomentUnitsMomentMAbsabsAreatreeWidthtreeDepthInertiapowcsAreasInertia4sCAxialStressForceMultiplierBendingStressNormalHNormalKsAxialStresssStressDigitssStressUnitsBendingStressHsBendingStressKsNormalHsNormalKStepSizewidthMaxwidthMinAspectRatioNoStepsroundsTreeWidthsTreeDepthsectionwidthdepthrangeValueMaxValueMinRNrandomtheValueGenerateTree orangeMinorangeMaxblueMinblueMaxgreenMingreenMaxpurpleMinpurpleMaxforceStepoffsetMinoffsetMaxoffsetStepAA= =    ==I   ==ILI   =`kNORGNNO !G+NO  "`#NORG  R$G#NNO#N%NO&!G'()GG*GG+G3#NO &"'"`,NORG R$G,NNO,N%NO-!G.()GG*GG+G3,NO -"."`/NORG R$G/NNO/N%NO0!G1!)GG*GG+G3/NO 0"1"2GGG32RG4    56G4R7G86G49RR7G:;< =<;>R  ?; @6:R$GAGB6G=R$GCGD6?R$G E2 F : G4F ? = HEGGIEG JKERLGMKGRLGNK G RLGOKHRLGPKIRLGBGenerateTreeDimensionswidthMinwidthMaxStepSizeAspectRatio;QRS=<;T U<Q VR<<UQ W6;R$GX6<R$GYZNWOY[NXO+RandomValueValueMinValueMaxStepSizew\]^ < _`R<a^_\ G<UaQ VR<aUQ a>?V! CurrentQuestionNumberthis_currentframeForcePUserResponseIsItCorrectAttaboyexplain sForceP is the axial force produced in the tree for these loads. The axial force will produce compression stresses that are uniformly distributed across the entire cross section._rootSeries1_CorrectCounterngForceEquilcheckmarkgotoAndStopMomentM M = sMomentM is the bending moment produced in the tree for these loads. Note that this bending moment will produce compression bending stresses at H and tension bending stresses at K.Note that this bending moment will produce tension bending stresses at H and compression bending stresses at K.MomentEquilAxialStresssSigmaSubAxialsEsAxialStress is the uniformly distributed normal stress produced in the tree for these loads. The axial stress is compression.Series2_CorrectCounterAxialStressExplanationInertia The moment of inertia needed for these calculations is sIsubzsInertia. You were correct in recognizing that was needed here because the bending occurs about the z-axis.InertiaExplanationBendingStress At H, the bending stress is sBendingStressH. Compression bending stresses are produced at H and tension bending stresses are produced at K. Tension bending stresses are produced at H and compression bending stresses are produced at K. The bending stresses are linearly distributed across the width of the cross section between H and K.BendingStressExplanationNormalK At K, the axial stress is and the bending stress is sBendingStressKSince these stresses are the same type (i.e., normal stresses) and they both act in the same direction (i.e., the x-direction), they can simply be added together to give the combined stress at K.CombinedStressExplanationNormalHSeries3_CorrectCounter Combined stress calculation for point StressAtHH sSigmaSubHK sSigmaSubKsPsSigmaSubBending = ()sNormalHsNormalK Bending stress calculation for point HK |M| c / sMomentMAbsUnitIndex(1,000 N/kN)sC) / ( (compression by inspection)tension by inspection) Moment of inertia about z-axis sTreeDepth)(sTreeWidth) / 12 = Axial stress calculation P / A)(1,000 N/kN) / (sArea / (compression by inspection)LineOfTextPsOrangeLoad sFysBlueLoadEquationFormatsPurpleLoadsGreenLoadsE0sThereforeMsBlueMomentsMzLineOFTextsPurpleMomentsGreenMomentReturnStringklugeCurrentTextlengthNextText indexMathrandomround Correct! Nice work...That's right! Way to go...Good job! You're getting the hang of this stuff...Primo! I'm stoked...Marvelous! Simply marvelous...Most excellent...Sweet...Oh, yeah. You're kickin' it now...responseuserparseFloatisNaNtolerancediffcorrectabsunitIndexsLengthUnit mmsForceUnit NForceMultipliersMomentUnit N-mmsLengthDigitssForceDigitssStressDigitssStressUnit MPa kN kN-mm in lbs lb-in psi kip kip-in ksisGreekargumentssSubsSsubscriptGiveTheAnswerUserResponseNI=G =G G G    NPO6  =  NRI= =GGG HGG    NPO6  =  NRI=G =G G G    NPO6  =  NRI= =GGG HGG    NPO6  =  NR-I=U =GGGGG  NPOF  = =  NR[I=b = G!GG"G#G!G$G  NPO6  %=  NRI&= ='G(G)G H*G+G,G  NPOD  = -=  NRI.=c =/GG0G1G)G2G  NPO  = = = %= -= 3=  NRc I4=+ = 5 5NPOR  = -= 3=  NR I.=+ = 5 5NPOR  = -= 3=  NR(CombinedStressExplanationStressAtH6G78G9G:G;GGG<G=G>GG<G?G7)(G@GGAG$1G@GGBG'BendingStressExplanationStressAtHCG7DGEGFG=GGGG!G>G?GHG@GIIJG?GKGLG"G@G>G7(G1GMG7? HNGOG= HNGOGInertiaExplanationgPG!GG?GQGRGSGTGUG"G  NRAxialStressExplanationVGGGWG>GII.?G GXGYG@G GZGYG>GG[GForceEquil\A\]^G_G`G\G\a\b=\c\b=\d\b=\e\b=fG]GG GMomentEquil\A\ghG_GiGjG\k\b=\l\b=\e\b=fGgGGG(EquationFormatCurrentTextNextTextmAnAIH n nopNqpNG,nGH%qGmoqG"rGqGmsqGm> AttaBoy tuvR <ttuwRt IxGyGDtIxGzGtIxG{GtIxG|GtIxG}GtIxG~GYtIxGG*tIxGG  NRIsItCorrectusercorrectA=== O> z?{G<  <uRH O>>MakeUnitStringsIY  9IU IY  aILMakeHTMLgreekp NGG<pNI NGG<<G> MakeHTMLsubscriptsubscriptGG<>?5-sMsubzMzMakeHTMLsubscriptsMzSMakeHTMLgreek = sFsubxFxsFysSigmassSigmaSubAxialasSigmaSubBendingbsSigmaSubHHsSigmaSubKKsIsubzIsP + sM sEsE00sQ1sQ0sTherefore \ngNope... Here's the solution:explainDetermine the axial force P (in lbs) at section H-K.UnitIndexMakeUnitStringsGenerateTree =G =GG   =G  =GG   =  =  =  =  = =GG !" #$%=G&'()G!G* +=Cd    ,=@BB@i@ŷ۽j: c1Ŷ۽4E `Ŷ۽8` `2EL[T 6JF ^'& &@0tree('T|1ڌZ))T|1ڌ+*@' :.+2EL[T.6J./0ȏrOPi@section?3@D@)+?explainsQ1eDetermine the bending moment M (in N-mm) about the z-axis at section H-K (include the proper sign).GsQ0GUnitIndexMakeUnitStrings=Od    GenerateTree=(45T` \ )5@MY@)?explainsQ17Determine the axial force P (in kips) at section H-K.GsQ0GUnitIndexMakeUnitStrings=O (2  GenerateTree=('T|1ڌZ))T|1ڌ+*@' :@)+?explainsQ1fDetermine the bending moment M (in kN-mm) about the z-axis at section H-K (include the proper sign).GsQ0GUnitIndexMakeUnitStrings=O2d  GenerateTree=(45T` \ )5@MY@()?{explainsQ1Determine the axial stress (in ksi) at section H-K. The cross-sectional dimensions are shown on the sketch. (Note: + = tension, = compression)GUnitIndexMakeUnitStrings=5? GenerateTreeDimensions=S ?   GenerateTree= P꿠 /@?yexplainsQ1VDetermine the moment of inertia needed to compute the bending stress at section H-K.GsQ0G@?explainsQ1}Compute the bending stress (in ksi) produced at point H by the loads shown. (Note: + = tension, = compression)G@?explainsQ1|Compute the normal stress (in ksi) produced at point K by the loads shown. (Note: + = tension, = compression)G@?ZexplainsQ1|Compute the normal stress (in MPa) produced at point H by the loads shown. (Note: + = tension, = compression)GUnitIndexMakeUnitStrings=5?dGenerateTreeDimensions=S2,?  GenerateTree=@?VexplainsQ1|Compute the normal stress (in MPa) produced at point K by the loads shown. (Note: + = tension, = compression)GUnitIndexMakeUnitStrings=5?PGenerateTreeDimensions=O2h  0u' GenerateTree=@ ^('T|1ڌZ))T|1ڌ +*@' : /i@@)+(45T` \ )5@MY@)('T|1ڌZ))T|1ڌ +*@' :@)+(45T` \ )5@MY@)('T|1ڌZ))T|1ڌ+*@' : /@()+ P꿠@ ^(45T` \ )5@MY@(5T` z )@MY.*'T|1ڌZ+)T|1ڌ-*@' : /i@h@ /@@F@ theTreeA7̀Lӕ~y3` Gx.3133(txtInstructions

Click on the button to the left of an answer to select it. continue

BG[ "Hx%K<f%KN xECHpQ5\D9pȸs5 3 0E9pȸs53`?DIk]<%@<335!2jUMWW5]XD s*ռLFI 1JW 133(questionNumDisplay10GJz@' oQXKe-mWfIUotS:;|%A{U8zukv{9x\yfӜ& &LD ?@?q0correctSoundcorrect_soundattachSoundstart @ R R@32f`@?u4incorrectSoundincorrect_soundattachSoundstart @ R RK[z0@6HL@nQ@checkmark 5Mh)3ffUserResponse123456.128JM@i1ؠ%N` 00 0ff$= ´tP 0"OX{!!M 133tntw&Pg`$< f3tǒtQ` 0  34Åi&Rg`$< 33tǒtCS|N@)0 0O@' f+ N@)03 4P@' f QN@)03 4 BR@' f_UserNumericUserResponseStripAnyUnitStringstheTreeGiveTheAnswer_currentframegotoAndStop=RN GRKS@K?:4txtInstructionsClick continue to proceed.AT\`|continue to proceed to the next series of problems.DrunningScoreYou have correctly answered Series1_CorrectCounterG of the GQuestionsInThisSeriesG problems in this series.G setup_series26@dummy_symbol>6?Mi@theTreeC7̀Lӕ~y3`D7͂=US~ fc2dE8F9@ uL3 0G9@ m3`VYxT33@ a&C0U`@'_-T33@ a 0V`@'`/ T32@ a 0W`@'`/HowManyFlagsHaveBeenUsedQuestionsInPreceedingSeriesQuestionsInThisSeriesGenerateFlagsSubsetFrameInSetSeries2_CorrectCounter  = HY Zx.31(txtInstructions

Click on the button to the left of an answer to select it. continue

KZ[ L:$I&j10 4[h})3ffUserResponse123456.12M[`N73`i\qΥ   1B@6߂X|Xpq@ pztp׊|m䒒1@q~q~qlxl|XtO\J0u]d6= <3%j=e ٦V5ݕqZ4ѻAIgš@ 6ZYMZGez% Xnj~[( qJ{*Nx;.RҠ^>3`?@‹u]B@' O>&I >`C@‹uD? O}HowManyFlagsHaveBeenUsedQuestionsInThisSeriesGenerateFlagsFrameInSetQuestionsInPreceedingSeriesSeries1_CorrectCounterG GH = P^@V͞ >_w u6133runningScore0 out of 10 2 3 4 5X_@ AC@DEFGHKLMNOPX? txtInstructionsEnter your answer without units.FrameInSettheTreegotoAndStopconfigmyFlagsHowManyFlagsHaveBeenUsedcheckmarkUserResponsequestionNumDisplayPRNO R    series2F@ theTreeA7̀Lӕ~y3` `x.3133(txtInstructions

Click on the button to the left of an answer to select it. continue

B`[ CHpQ5\D9pȸs5 3 0E9pȸs53`FI 1aW 133(questionNumDisplay10Gaz@' oQ6HL@nQ@checkmark 5bh)3ffUserResponse123456.128Jb@i1ؠKS@K?:4txtInstructionsClick continue to proceed.cxT33@ a&C0U`@'_-T33@ a 0V`@'`/ T32@ a 0W`@'`/ FrameInSetQuestionsInPreceedingSeriesQuestionsInThisSeriesGH Kc@ABDEFGHJK?}. txtInstructionsClick continue to proceed to the next series of problems.TotalCorrectSeries1_CorrectCounterSeries2_CorrectCounterrunningScoreYou have correctly answered of the QuestionsInThisSeries problems in this series. In total, you have answered of the 8 problems correctly.GGGG G GG G setup_series36@dummy_symbol>6?Mi@theTreeC7̀Lӕ~y3`D7͂=US~ fc2dE8F9@ uL3 0G9@ m3`]dxT33@ a&C0U`@'_-T33@ a 0V`@'`/ T32@ a 0W`@'`/HowManyFlagsHaveBeenUsedQuestionsInPreceedingSeriesQuestionsInThisSeriesGenerateFlagsSubsetFrameInSetSeries3_CorrectCounter G = Hd ex.31(txtInstructions

Click on the button to the left of an answer to select it. continue

Ke[ L:$I&j10 4fh})3ffUserResponse123456.12Mf`N73`O\J0gg>3`?@‹u]B@' O>&I >`C@‹uD? OmHowManyFlagsHaveBeenUsedGenerateFlagsSubsetFrameInSetQuestionsInPreceedingSeriesSeries2_CorrectCounterPH =  Pg@V͞ >hw u6133runningScore0 out of 10 2 3 4 5Xh@ AC@DEFGHKLMNOPX? txtInstructionsEnter your answer without units.FrameInSettheTreegotoAndStopconfigmyFlagsHowManyFlagsHaveBeenUsedcheckmarkUserResponsequestionNumDisplayPRNO R    series3F@ theTreeA7̀Lӕ~y3` ix.3133(txtInstructions

Click on the button to the left of an answer to select it. continue

Bi[ CHpQ5\D9pȸs5 3 0E9pȸs53`FI 1jW 133(questionNumDisplay10Gjz@' oQ6HL@nQ@checkmark 5kh)3ffUserResponse123456.128Jk@i1ؠKS@K?:4txtInstructionsClick continue to proceed.lxT33@ a&C0U`@'_-T33@ a 0V`@'`/ T32@ a 0W`@'`/ FrameInSetQuestionsInPreceedingSeriesQuestionsInThisSeriesGH Kl@ABDEFGHJK?B txtInstructionsClick continue to go to the printout page and finish.TotalCorrectSeries1_CorrectCounterSeries2_CorrectCounterSeries3_CorrectCounterrunningScoreYou have correctly answered of the QuestionsInThisSeries problems in this series. In total, you have answered of the 10 problems correctly.GGGG G G GG G after_series36@dummy_symbol>6?Mi@theTreeC7̀Lӕ~y3`D7͂=US~ fc2dE8F9@ uL3 0G9@ m3`mxT33@ a&C0U`@'_-T33@ a 0V`@'`/ T32@ a 0W`@'`/Hm nx.31(txtInstructions

Click on the button to the left of an answer to select it. continue

Kn[ L:$I&j10 4oh})3ffUserResponse123456.12Mo`N73`O\J0gp>3`?@‹u]B@' O>&I >`C@‹uD? OmHowManyFlagsHaveBeenUsedGenerateFlagsSubsetFrameInSetQuestionsInPreceedingSeriesSeries3_CorrectCounterPH =  Pp@V͞ >qw u6133runningScore0 out of 10 2 3 4 5Xq@ AC@FHKLMNPX?L TotalCorrectSeries1_CorrectCounterSeries2_CorrectCounterSeries3_CorrectCounterrunningScoreEquilibrium considerations: correct out of 4 problems Partial stress calculations: correct out of 4 problems Complete stress calculations: correct out of 2 problems In total, you have answered of the 10 problems correctly.GGGGGGGGG G printout??myDateDatetxtDatetoStringtxtIdentifierMathrandomround @ R R R #P6@dummy_symbol>6?M i@theTree C0G*U? D̀Lӕ~y3`E7͂=US~ fc2dF8 G@ uL3 0H9@ m3`&ro__f% 7fa5YIr@ 0'sa6 $  1333wtwnJs@'U&t]_]([3333%t Z<4Bp "uX` 1f|B_*v]_]([333335t Z^`|8V&w_f@쐀X 333w|Rm$x\`]_z(5kZ}!Lt/ &y_f@쐀X w|Rmz]_0ZfkZz(C_~{Vtue@ 5`vwe@ 5`xye@ 5`zN=8printasbitmap:_level0K{ 4|xĘ11333txtDate12 pt VerdanaN|@Af}pK  3$PfM3躆c QȰ!(ǎE!틸ICv`G" LH[$`J1GO}&@` %~w ! )3txtNameP~%@LN 1g+' 013txtIdentifier999999QjR:$I&j10 Q?M933runningScore0 out of 10 You've answered ser S@  @