{VERSION 3 0 "IBM INTEL NT" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 257 
"" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" 
-1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 
0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 257 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "" 11 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 259 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "" 11 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 261 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 
1 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 8 "Question" }{TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 87 "For what body forces will the following \+
stress field describe a state of   equilibrium." }}{PARA 257 "" 1 "" 
{XPPMATH 20 "6#>%'sigmaxG,(*$)%\"xG\"\"#\"\"\"!\"#*$)%\"yGF)F*\"\"$%\"
ZG!\"&" }}{PARA 258 "" 1 "" {XPPMATH 20 "6#>%'sigmayG,$*$)%\"yG\"\"#\"
\"\"!\"#" }}{PARA 259 "" 1 "" {XPPMATH 20 "6#>%'sigmazG,*%\"xG\"\"$%\"
yG\"\"\"%\"zGF'!\"&F)" }}{PARA 260 "" 1 "" {XPPMATH 20 "6#>%&tauxyG,(%
\"zG\"\"\"*&%\"xGF'%\"yGF'\"\"%!\"(F'" }}{PARA 261 "" 1 "" {XPPMATH 
20 "6#>%&tauyzG\"\"!" }}{PARA 0 "" 1 "" {XPPMATH 20 "6#>%&tauzxG,(%\"x
G!\"$%\"yG\"\"\"F)F)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 262 "" 0 "" 
{TEXT -1 9 "Solution:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 157 " In thi
s  problem , we employ the differential equations of equilibrium to fi
nd out the body forces required to maintain a given stress field in eq
uilibrium." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 8 "restart;" }{TEXT -1 114 "This is done so that eve
ry time you run the program it does not \"remember' the \"previous\" v
alues of the variables." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "sigmax:=
(-2*x^2)+(3*y^2)-5*Z;" }{TEXT -1 88 "These are the given expressions o
f the six stresses which constitute the \"stress field\"." }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 15 "sigmay:=-2*y^2;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "sigmaz:=3*x+y+3*z-5;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 17 "tauxy:=z+4*x*y-7;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "tauyz:=0;
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "tauzx:=-3*x+y+1;" }}{PARA 0 "" 
0 "" {TEXT -1 75 "Now, we write the differential equation of equilibri
um for the X- direction" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "eqn1:= d
iff(sigmax, x)+diff(tauxy, y)+diff(tauxz, z)+Fx=0;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%'sigmaxG,(*$)%\"xG\"\"#\"\"\"!\"#*$)%\"yGF)F*\"\"$%
\"ZG!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sigmayG,$*$)%\"yG\"\"#
\"\"\"!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'sigmazG,*%\"xG\"\"$%
\"yG\"\"\"%\"zGF'!\"&F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&tauxyG,(
%\"zG\"\"\"*&%\"xGF'%\"yGF'\"\"%!\"(F'" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%&tauyzG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&tauzxG,(%\"
xG!\"$%\"yG\"\"\"F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqn1G/%#Fx
G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "solve(eqn1,Fx);" 
}{TEXT -1 72 "This command asks Maple to solve equation-1 for the vari
able(unknown) Fx" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 69 "This is the differential equation of equi
librium for the Y- direction" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "eqn
2:= diff(sigmay,y)+diff(tauxy,x)+diff(tauyz,z)+Fy=0;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%%eqn2G/%#FyG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "solve(eqn2,Fy);" }{TEXT -1 72 "This command asks Mapl
e to solve equation-1 for the variable(unknown) Fy" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "This is
 the differential equation of equilibrium for the Z- direction" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "eqn3:= diff(sigmaz,z)+diff(tauzx,x)
+diff(tauyz,y)+Fz=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqn3G/%#FzG
\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "solve(eqn3,Fz);" }
{TEXT -1 72 "This command asks Maple to solve equation-1 for the varia
ble(unknown) Fz" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 257 12 "Final Answer" }{TEXT -1 19 ": Fx = Fy = \+
Fz = 0." }}}}{MARK "0 11 0" 9 }{VIEWOPTS 1 1 0 1 1 1803 }