{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart;with(linalg) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "K:=(EA/L/2/sqrt(2))*ma trix([[1,-1],[-1,2*sqrt(2)+1]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"KG,$*&#\"\"\"\"\"%F(**%#EAGF(%\"LG!\"\"\"\"##F(F.K%'matrixG6#7$7$F(F -7$F-,&*&F.F(F.F/F(F(F(Q(pprint06\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 36 "Pv:=vector([P*cos(phi),P*sin(phi)]);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#PvGK%'vectorG6#7$*&%\"PG\"\"\"-%$cosG6#%$phiG F+*&F*F+-%$sinGF.F+Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "u:=linsolve(K,Pv);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uGK% 'vectorG6#7$**%\"PG\"\"\"%\"LGF+,(-%$sinG6#%$phiGF+-%$cosGF0F+*(\"\"#F +F5#F+F5F2F+F+F+%#EAG!\"\"**F*F+F,F+,&F.F+F2F+F+F7F8Q(pprint06\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "kinv:=inverse(K);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%kinvGK%'matrixG6#7$7$*(%#EAG!\"\"%\"LG\" \"\",&*&\"\"#F.F1#F.F1F.F.F.F.*&F+F,F-F.7$F3F3Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "multiply(kinv,Pv);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'vectorG6#7$,&*,%#EAG!\"\"%\"LG\"\"\",&*&\"\"#F, F/#F,F/F,F,F,F,%\"PGF,-%$cosG6#%$phiGF,F,**F)F*F+F,F1F,-%$sinGF4F,F,,& **F)F*F+F,F1F,F2F,F,F6F,Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "M:=(EA/L)*matrix([[0,1],[-1/2,1/2]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG*(%#EAG\"\"\"%\"LG!\"\"K%'matrixG6#7$7$\"\"! F'7$#F)\"\"##F'F2Q(pprint06\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "forces:=multiply(M,u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'f orcesGK%'vectorG6#7$*&%\"PG\"\"\",&-%$sinG6#%$phiGF+-%$cosGF/F+F+,&*&# F+\"\"#F+*&F*F+,(F-F+F1F+*(F6F+F6#F+F6F1F+F+F+F+!\"\"*&F:F+F)F+F+Q(ppr int06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "simplify(forces) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'vectorG6#7$*&%\"PG\"\"\",&-%$s inG6#%$phiGF)-%$cosGF-F)F),$*(F(F)\"\"##F)F3F/F)!\"\"Q(pprint06\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "K2:=(EA/L/2/sqrt(2))*matrix( [[2*sqrt(2)+1,-1],[-1,2*sqrt(2)+1]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#K2G,$*&#\"\"\"\"\"%F(**%#EAGF(%\"LG!\"\"\"\"##F(F.K%'matrixG6#7$ 7$,&*&F.F(F.F/F(F(F(F-7$F-F5Q(pprint06\"F(F(F(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 20 "u2:=linsolve(K2,Pv);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#u2GK%'vectorG6#7$,$*&#\"\"\"\"\"#F,*,%#EAG!\"\",&*$F -F+F,F,F,F0%\"PGF,%\"LGF,,(-%$sinG6#%$phiGF,-%$cosGF8F,*(F-F,F-F+F:F,F ,F,F,F,,$*&#F,\"\"%F,*.F-F+F3F,F4F,,(*&F@F,F6F,F,*&F-F+F:F,F,*&F-F+F6F ,F,F,F/F0F1F0F,F,Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "M2:=(EA/L)*matrix([[0,1],[-1/2,1/2],[-1,0]]);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#M2G*(%#EAG\"\"\"%\"LG!\"\"K%'matrixG6#7%7$\"\"!F'7 $#F)\"\"##F'F27$F)F/Q(pprint06\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "forces:=multiply(M2,u2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'forcesGK%'vectorG6#7%,$*&#\"\"\"\"\"%F,**\"\"##F,F/% \"PGF,,(*&F-F,-%$sinG6#%$phiGF,F,*&F/F0-%$cosGF6F,F,*&F/F0F4F,F,F,,&*$ F/F0F,F,F,!\"\"F,F,,&*&#F,F-F,*(FF1F,,(F4F,F9F,*(F/F,F/F0F9F,F,F,F, F>*&#F,\"\")F,F.F,F,,$*&#F,F/F,FBF,F>Q(pprint06\"" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 17 "simplify(forces);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#K%'vectorG6#7%,$*&#\"\"\"\"\"%F***\"\"##F*F-%\"PGF*,(*& F+F*-%$sinG6#%$phiGF*F**&F-F.-%$cosGF4F*F**&F-F.F2F*F*F*,&*$F-F.F*F*F* !\"\"F*F*,$*&#F*F-F***F/F*F-F.,&F2F " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "7 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }