{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "#problem 3b: distrib uted load is w(x)=wa - 2*(wa-wb)x/d with wa=109kN/m and wb=57kN/m" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "restart;w:= wa - 2*(wa-wb)* x/d; e1:=ax+bx; #RHS sum forces in x-dir. symmetry says by=0 Cx=-Ax, B y=Cy." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG,&%#waG\"\"\"**\"\"#F', &F&F'%#wbG!\"\"F'%\"xGF'%\"dGF,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#e1G,&%#axG\"\"\"%#bxGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "e2:=ay=int(w,x=0..d/2);e3:=-bx*h-int(x*w,x=0..d/2); #RHS sum force s in y-dir and moments about A" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e 2G/%#ayG,&*(\"\"#!\"\"%#waG\"\"\"%\"dGF,F,*(\"\"%F*,&F+F,%#wbGF*F,F-F, F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e3G,(*&%#bxG\"\"\"%\"hGF(!\" \"*(\"#7F*,&%#waGF(%#wbGF*F(%\"dG\"\"#F(*(\"\")F*F.F(F0F1F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "reactions:=solve(\{e1,e2,e3 \},\{ax,bx,ay\}); #solve for reactions" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*reactionsG<%/%#bxG,$**\"#C!\"\"%\"dG\"\"#,&%#waG\"\"\"*&F-F0% #wbGF0F0F0%\"hGF+F+/%#ayG,&*&#F0\"\"%F0*&F/F0F,F0F0F0*&F8F0*&F,F0F2F0F 0F0/%#axG,$**F*F+F,F-F.F0F3F+F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "evalf(subs(\{d=90,h=13,wa=109,wb=57\},reactions));assign(react ions);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%#bxG$!+xIU*y&!\"'/%#ayG$ \"%NP\"\"!/%#axG$\"+xIU*y&F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "fx:=n*cos(t)-v*sin(t)+ax;fy: =n*sin(t)+v*cos(t)+ay-int(w,x=0..x); #sum forces on arch from 0 to x" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#fxG,(*&%\"nG\"\"\"-%$cosG6#%\"tGF (F(*&%\"vGF(-%$sinGF+F(!\"\"**\"#CF1%\"dG\"\"#,&%#waGF(*&F5F(%#wbGF(F( F(%\"hGF1F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#fyG,.*&%\"nG\"\"\"-% $sinG6#%\"tGF(F(*&%\"vGF(-%$cosGF+F(F(*(\"\"%!\"\"%#waGF(%\"dGF(F(*(F2 F3F5F(%#wbGF(F(*&F4F(%\"xGF(F3*(,&F4F(F7F3F(F5F3F9\"\"#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "nvsols:=solve(\{fx,fy\},\{n,v\}); # solve for axial force and shear as a funct of theta (t)" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#>%'nvsolsG<$/%\"nG,$*&#\"\"\"\"#CF+*(,0*(-%$cosG 6#%\"tGF+)%\"dG\"\"$F+%#waGF+F+**\"\"#F+F0F+F4F+%#wbGF+F+*,\"\"'F+F7F+ )F5F9F+-%$sinGF2F+%\"hGF+F+*,FF+F@F+F+*.F,F+F7F+%\"xGF+F5 F+F>F+F@F+!\"\"*,F,F+)FCF9F+F7F+F>F+F@F+F+*,F,F+FFF+F:F+F>F+F@F+FDF+F5 FDF@FDF+FD/%\"vG,$*&#F+F,F+*(,0*(F7F+F4F+F>F+FD**F9F+F4F+F:F+F>F+FD*,F " 0 "" {MPLTEXT 1 0 15 "assign(nvsols);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "m:=ay*x-int(subs(x=xx,w)*(x-xx),xx= 0..x)-ax*y; #internal moment (taken about cut \011x)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG,,*&,&*&#\"\"\"\"\"%F**&%#waGF*%\"dGF*F*F**&F) F**&F.F*%#wbGF*F*F*F*%\"xGF*F**,\"\"#F*\"\"$!\"\",&F-F*F1F6F*F.F6F2F5F 6*(F4F6,&F-F6**F4F*F7F*F2F*F.F6F6F*F2F4F6*&)F2F4F*F-F*F6*,\"#CF6F.F4,& F-F**&F4F*F1F*F*F*%\"hGF6%\"yGF*F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "t:=arctan((d/2-x)/(y+r-h));y:=sqrt(r^2-(x-d/2)^2)-r+h ;r:=d^2/h/8+h/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tG-%'arctanG6# *&,&*&\"\"#!\"\"%\"dG\"\"\"F.%\"xGF,F.,(%\"yGF.%\"rGF.%\"hGF,F," }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,(*&\"\"#!\"\",**&\"\"%\"\"\")% \"rGF'F,F,*&F+F,)%\"xGF'F,F(*(F+F,F1F,%\"dGF,F,*$)F3F'F,F(#F,F'F,F.F(% \"hGF," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG,&*(\"\")!\"\"%\"dG\" \"#%\"hGF(\"\"\"*&F*F(F+F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "h:=13;d:=90;wa:=109;wb:=57;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"hG\"#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG\"#!*" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#waG\"$4\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#wbG\"#d" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "plot(n,x=0.. d/2,labels=[\"x (m)\",\"N (kN)\"]);plot(v,x=0..d/2,labels=[\"x (m)\", \"V (kN)\"]);plot(m,x=0..d/2,labels=[\"x (m)\",\"M (kN-m)\"]);" }} {PARA 13 "" 1 "" {GLPLOT2D 518 518 518 {PLOTDATA 2 "6%-%'CURVESG6$7S7$ $\"\"!F)$!3%=p\"3NxH*)o!#97$$\"3-*****\\P>(3)*!#=$!3)>z]T<#=KoF,7$$\"3 )***\\ilLKM=!#<$!3aK7)>aMRy'F,7$$\"31++Dc(=Tz#F6$!3x'yR=7y7t'F,7$$\"3] ++v$Hw-w$F6$!3OP78@w(*zmF,7$$\"3\\**\\7`=%=s%F6$!3SQc4?%31j'F,7$$\"3'* **\\i:iL8cF6$!3eps#['*Hje'F,7$$\"3V**\\i!*pUOlF6$!3rWnLiT)>a'F,7$$\"3m **\\i!z)3\"\\(F6$!3SOba\\^r(\\'F,7$$\"32+]7y*)oU%)F6$!37[jLd]=bkF,7$$ 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