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Section 1: Vertical distance from the origin to centroid of \
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Section 2: Vertical distance from the origin to centroid of \
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    \(\(\[Sigma]\_zzB = 
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\>\"", Max[
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    \(Print[\*"\"\<The minimum value at point B is: \!\(\[Sigma]\_zzB\) = \
\>\"", Min[
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Cell[BoxData[
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    \(Print[\*"\"\<          \!\(\[Sigma]\_zzD\)=\>\"", \ \[Sigma]\_zzD\  // 
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        AxesLabel \[Rule] {"\<\[Theta]\>", \*"\"\<\!\(\(\[Sigma]\_zz\)\_D\)\>\
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\>\"", Max[
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\>\"", Min[
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Cell[BoxData[
    \("The maximum bending stress occurs at two locations at two different \
angles"\)], "Print"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(AnsA = 
        ExpandAll[\(180\/\[Pi]\) \(\(Flatten[
                  NSolve[Min[
                        Table[\[Sigma]\_zzA\/10\^6, {\[Theta], 0, \[Pi], 
                            0.001}]] == \[Sigma]\_zzA\/10\^6, \
\[Theta]]]\)[\([1]\)]\)[\([2]\)]];\)\), "\[IndentingNewLine]", 
    \(\(AnsC = 
        ExpandAll[\(180\/\[Pi]\) \(\(Flatten[
                  NSolve[Min[
                        Table[\[Sigma]\_zzC\/10\^6, {\[Theta], 0, \[Pi], 
                            0.001}]] == \[Sigma]\_zzC\/10\^6, \
\[Theta]]]\)[\([1]\)]\)[\([2]\)]];\)\), "\[IndentingNewLine]", 
    \(Print["\<Maximum bending stress occurs at location A at an angle \>", \ 
      AnsA, "\< degs and has a value of \>", \ 
      Min[Table[\[Sigma]\_zzA\/10\^6, {\[Theta], 0, \[Pi], 
            0.001}]], \ "\< MPa in tension\>"]\), "\[IndentingNewLine]", 
    \(Print["\<Maximum bending stress occurs at location C at an angle \>", \ 
      AnsC, "\< degs and has a value of \>", \ 
      Min[Table[\[Sigma]\_zzC\/10\^6, {\[Theta], 0, \[Pi], 
            0.001}]], \ "\< MPa in tension\>"]\)}], "Input"],

Cell[BoxData[
    InterpretationBox[\("Maximum bending stress occurs at location A at an \
angle "\[InvisibleSpace]69.95814678543445`\[InvisibleSpace]" degs and has a \
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tension"\),
      SequenceForm[ 
      "Maximum bending stress occurs at location A at an angle ", 
        69.958146785434451, " degs and has a value of ", -102.90883967293102, 
        " MPa in tension"],
      Editable->False]], "Print"],

Cell[BoxData[
    InterpretationBox[\("Maximum bending stress occurs at location C at an \
angle "\[InvisibleSpace]19.99622705006103`\[InvisibleSpace]" degs and has a \
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tension"\),
      SequenceForm[ 
      "Maximum bending stress occurs at location C at an angle ", 
        19.99622705006103, " degs and has a value of ", -102.90883696845921, 
        " MPa in tension"],
      Editable->False]], "Print"]
}, Open  ]],

Cell[TextData[StyleBox["Problem 7b. Using  thin-walled assumption",
  FontFamily->"Times New Roman"]], "Title",
  CellFrame->{{0, 0}, {0, 3}},
  FontFamily->"Courier"],

Cell[BoxData[
    \(\(newdef\  = \ {h \[Rule] \ \[Alpha]\ b, \ 
          t\_1 \[Rule] \ t\_2\/\[Alpha]};\)\)], "Input"]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Total Cross sectional Area of the beam", "Section",
  FontFamily->"Times New Roman"],

Cell["Section 1: Web ", "Text",
  FontFamily->"Times New Roman"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(h\_1\  = h;\)\), "\[IndentingNewLine]", 
    \(\(A\_1\  = \ h\_1\ t\_1;\)\), "\[IndentingNewLine]", 
    \(Print[\*"\"\<The redefined web area is \!\(A\_1\) = \>\"", 
      A\_1, "\< = \>", \ 
      A\_1 /. vars\  // N, \*"\"\< \!\(m\^2\)\>\"", "\< = \>", 
      10\^6\ A\_1 /. vars\  // N, \*"\"\< \!\(mm\^2\)\>\""]\)}], "Input"],

Cell[BoxData[
    InterpretationBox[\("The redefined web area is \!\(A\_1\) = "\
\[InvisibleSpace]\(h\ t\_1\)\[InvisibleSpace]" = "\[InvisibleSpace]0.0005`\
\[InvisibleSpace]" \!\(m\^2\)"\[InvisibleSpace]" = "\[InvisibleSpace]500.`\
\[InvisibleSpace]" \!\(mm\^2\)"\),
      SequenceForm[ "The redefined web area is \!\(A\_1\) = ", 
        Times[ h, 
          Subscript[ t, 1]], " = ", .00050000000000000001, " \!\(m\^2\)", 
        " = ", .5*^3, " \!\(mm\^2\)"],
      Editable->False]], "Print"]
}, Open  ]],

Cell["Section 2: Flange", "Text",
  FontFamily->"Times New Roman"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(h\_2\  = t\_2;\)\), "\[IndentingNewLine]", 
    \(\(A\_2\  = \ b\ h\_2\ ;\)\), "\[IndentingNewLine]", 
    \(Print[\*"\"\<The redefined flange area is \!\(A\_2\) = \>\"", 
      A\_2, "\< = \>", \ 
      A\_2 /. vars\  // 
        N, \*"\"\< \!\(m\^2\)\>\"", "\< = \>", \ \(10\^6\) A\_2 /. vars\  // 
        N, \*"\"\< \!\(mm\^2\)\>\""]\)}], "Input"],

Cell[BoxData[
    InterpretationBox[\("The redefined flange area is \!\(A\_2\) = "\
\[InvisibleSpace]\(b\ t\_2\)\[InvisibleSpace]" = "\[InvisibleSpace]0.0005`\
\[InvisibleSpace]" \!\(m\^2\)"\[InvisibleSpace]" = "\[InvisibleSpace]500.`\
\[InvisibleSpace]" \!\(mm\^2\)"\),
      SequenceForm[ "The redefined flange area is \!\(A\_2\) = ", 
        Times[ b, 
          Subscript[ t, 2]], " = ", .00050000000000000001, " \!\(m\^2\)", 
        " = ", .5*^3, " \!\(mm\^2\)"],
      Editable->False]], "Print"]
}, Open  ]],

Cell["Total area", "Text",
  FontFamily->"Times New Roman"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(A\_\(\(Tp\)\(\ \)\) = \ 
      ExpandAll[\[Sum]\+\(j = 1\)\%2 A\_j]\  /. 
        newdef\), "\[IndentingNewLine]", 
    \(Print["\<For thin-walls neglect all higher order terms of thickness\>"]\
\), "\[IndentingNewLine]", 
    \(\(A\_\(\(T\)\(\ \)\) = 
        Normal[Series[
            A\_\(\(Tp\)\(\ \)\), {t\_2, 0, 1}]];\)\), "\[IndentingNewLine]", 
    \(Print[\*"\"\<The total area is \!\(A\_\(\(T\)\(\\\ \)\)\) = \>\"", 
      Expand[A\_\(\(T\)\(\ \)\)\ ], "\< = \>", \ \(A\_\(\(T\)\(\ \)\) /. 
            vars\) /. newdef\  // 
        N, \*"\"\< \!\(m\^2\)\>\"", "\< = \>", \ \(\(10\^6\) 
              A\_\(\(T\)\(\ \)\) /. vars\)\  /. newdef\  // 
        N, \*"\"\< \!\(mm\^2\)\>\""]\)}], "Input"],

Cell[BoxData[
    \(2\ b\ t\_2\)], "Output"],

Cell[BoxData[
    \("For thin-walls neglect all higher order terms of thickness"\)], "Print"],

Cell[BoxData[
    InterpretationBox[\("The total area is \!\(A\_\(\(T\)\(\\ \)\)\) = "\
\[InvisibleSpace]\(2\ b\ t\_2\)\[InvisibleSpace]" = "\[InvisibleSpace]0.001`\
\[InvisibleSpace]" \!\(m\^2\)"\[InvisibleSpace]" = "\[InvisibleSpace]1000.`\
\[InvisibleSpace]" \!\(mm\^2\)"\),
      SequenceForm[ "The total area is \!\(A\_\(\(T\)\(\\ \)\)\) = ", 
        Times[ 2, b, 
          Subscript[ t, 2]], " = ", .001, " \!\(m\^2\)", " = ", .1*^4, 
        " \!\(mm\^2\)"],
      Editable->False]], "Print"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
  "Centroid: ",
  Cell[BoxData[
      FormBox[
        SubscriptBox[
          FormBox[\(x\&_\),
            "TraditionalForm"], "G"], TraditionalForm]]],
  " (let's place the origin at point B)"
}], "Section",
  FontFamily->"Times New Roman"],

Cell[TextData[{
  "Centroid: ",
  Cell[BoxData[
      \(\(\(x\&_\_G\)\(=\)\(\(Sum\ of\ all\ \(A\_j\) 
              x\&_\_j\)\/\(Total\ Area\)\)\(\ \)\)\)]]
}], "Text",
  FontFamily->"Times New Roman"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(x\&_\_1 = \ 0;\)\), "\[IndentingNewLine]", 
    \(\(x\&_\_2 = \ b\/2\ ;\)\), "\[IndentingNewLine]", 
    \(\(Qx = 
        ExpandAll[\ \((\[Sum]\+\(j = 1\)\%2\( A\_j\) 
                x\&_\_j\ )\)];\)\), "\[IndentingNewLine]", 
    \(Print["\<The first moment of area about the B'C' is:\>"]\), "\
\[IndentingNewLine]", 
    \(ExpandAll[\ \((Qx\ )\)] /. newdef\), "\[IndentingNewLine]", 
    \(Print["\<The centroid is located at \>"]\), "\[IndentingNewLine]", 
    \(x\&_\_Gp = 
      ExpandAll[\ \((Qx\/A\_T\ )\)] /. newdef\), "\[IndentingNewLine]", 
    \(Print["\<For thin-walls neglect all higher order terms of thickness\>"]\
\), "\[IndentingNewLine]", 
    \(\(x\&_\_G = 
        Normal[Series[x\&_\_Gp, {t\_2, 0, 1}]];\)\), "\[IndentingNewLine]", 
    \(Print[\*"\"\<\!\(x\&_\_G\) =\>\"", x\&_\_G, "\< = \>", 
      x\&_\_G /. vars\  // N, "\< m\>", "\< = \>", 
      ExpandAll[\(10\^3\) x\&_\_G /. vars\  // 
          N], \ "\< mm to the right of the origin\>"]\)}], "Input"],

Cell[BoxData[
    \("The first moment of area about the B'C' is:"\)], "Print"],

Cell[BoxData[
    \(\(b\^2\ t\_2\)\/2\)], "Output"],

Cell[BoxData[
    \("The centroid is located at "\)], "Print"],

Cell[BoxData[
    \(b\/4\)], "Output"],

Cell[BoxData[
    \("For thin-walls neglect all higher order terms of thickness"\)], "Print"],

Cell[BoxData[
    InterpretationBox[\("\!\(x\&_\_G\) ="\[InvisibleSpace]b\/4\
\[InvisibleSpace]" = "\[InvisibleSpace]0.025`\[InvisibleSpace]" m"\
\[InvisibleSpace]" = "\[InvisibleSpace]25.`\[InvisibleSpace]" mm to the right \
of the origin"\),
      SequenceForm[ "\!\(x\&_\_G\) =", 
        Times[ 
          Rational[ 1, 4], b], " = ", .025000000000000001, " m", " = ", 25.0, 
        " mm to the right of the origin"],
      Editable->False]], "Print"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
  "Centroid: ",
  Cell[BoxData[
      FormBox[
        SubscriptBox[
          FormBox[\(y\&_\),
            "TraditionalForm"], "G"], TraditionalForm]]],
  " (let's place the origin at point B)"
}], "Section",
  FontFamily->"Times New Roman"],

Cell[TextData[{
  "Centroid: ",
  Cell[BoxData[
      \(\(\(y\&_\_G\)\(=\)\(\(Sum\ of\ all\ \(A\_j\) 
              y\&_\_j\)\/\(Total\ Area\)\)\(\ \)\)\)]]
}], "Text",
  FontFamily->"Times New Roman"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(y\&_\_1 = \ ExpandAll[\(-\((h\/2)\)\)];\)\), "\[IndentingNewLine]", 
    \(\(y\&_\_2 = \ 0\ ;\)\), "\[IndentingNewLine]", 
    \(\(Qy = 
        ExpandAll[\ \((\[Sum]\+\(j = 1\)\%2\( A\_j\) 
                y\&_\_j\ )\)];\)\), "\[IndentingNewLine]", 
    \(Print["\<The first moment of area about the B'A' is:\>"]\), "\
\[IndentingNewLine]", 
    \(\(-ExpandAll[\ \((Qy\ )\)]\)\  /. newdef\), "\[IndentingNewLine]", 
    \(Print["\<The centroid is located at \>"]\), "\[IndentingNewLine]", 
    \(y\&_\_Gp = \(-ExpandAll[\ \((Qy\/A\_T\ )\)]\)\  /. 
        newdef\), "\[IndentingNewLine]", 
    \(Print["\<For thin-walls neglect all higher order terms of thickness\>"]\
\), "\[IndentingNewLine]", 
    \(\(y\&_\_G = 
        Normal[Series[y\&_\_Gp, {t\_2, 0, 1}]];\)\), "\[IndentingNewLine]", 
    \(Print["\<The centroid is located at \>"]\), "\[IndentingNewLine]", 
    \(Print[\*"\"\<\!\(y\&_\_G\) =\>\"", y\&_\_G, "\< = \>", 
      y\&_\_G /. vars\  // N, "\< m\>", "\< = \>", 
      ExpandAll[\(10\^3\) y\&_\_G /. vars\  // 
          N], \ "\< mm below the origin\>"]\)}], "Input"],

Cell[BoxData[
    \("The first moment of area about the B'A' is:"\)], "Print"],

Cell[BoxData[
    \(1\/2\ b\^2\ \[Alpha]\ t\_2\)], "Output"],

Cell[BoxData[
    \("The centroid is located at "\)], "Print"],

Cell[BoxData[
    \(\(b\ \[Alpha]\)\/4\)], "Output"],

Cell[BoxData[
    \("For thin-walls neglect all higher order terms of thickness"\)], "Print"],

Cell[BoxData[
    \("The centroid is located at "\)], "Print"],

Cell[BoxData[
    InterpretationBox[\("\!\(y\&_\_G\) ="\[InvisibleSpace]\(b\ \[Alpha]\)\/4\
\[InvisibleSpace]" = "\[InvisibleSpace]\(0.025`\ \[Alpha]\)\[InvisibleSpace]" \
m"\[InvisibleSpace]" = "\[InvisibleSpace]\(25.`\ \[Alpha]\)\[InvisibleSpace]" \
mm below the origin"\),
      SequenceForm[ "\!\(y\&_\_G\) =", 
        Times[ 
          Rational[ 1, 4], b, \[Alpha]], " = ", 
        Times[ .025000000000000001, \[Alpha]], " m", " = ", 
        Times[ 25.0, \[Alpha]], " mm below the origin"],
      Editable->False]], "Print"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
  "Second Moment of Area ",
  Cell[BoxData[
      \(\[CapitalIota]\_xx\)]],
  " about the neutral axis ( which is located at centroid C)"
}], "Section",
  FontFamily->"Times New Roman"],

Cell["Section 1: Web", "Text",
  FontFamily->"Times New Roman"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(dy\_1 = \(-\((h\/2 - \((y\&_\_G\ )\))\)\);\)\), \
"\[IndentingNewLine]", 
    \(\(\[CapitalIota]\_xc1 = \(\(t\_1\) h\^3\)\/12;\)\), \
"\[IndentingNewLine]", 
    \(\[CapitalIota]\_xx1p = \ 
      ExpandAll[\ \[CapitalIota]\_xc1\  + \ \(A\_1\) dy\_1\^2\ ]\  /. 
        newdef\), "\[IndentingNewLine]", 
    \(Print["\<For thin-walls neglect all higher order terms of thickness\>"]\
\), "\[IndentingNewLine]", 
    \(\[CapitalIota]\_xx1 = 
      Normal[Series[\[CapitalIota]\_xx1p, {t\_2, 0, 
            1}]]\), "\[IndentingNewLine]", 
    \(Print["\<The second moment of area about the neutral axis for the web \
is: \>"]\), "\[IndentingNewLine]", 
    \(Print[\*"\"\<\!\(\[CapitalIota]\_xx1\) =\>\"", \[CapitalIota]\_xx1 /. 
          vars\  // 
        N, \*"\"\< \!\(m\^4\)\>\"", "\< = \>", \(10\^12\) \[CapitalIota]\_xx1 \
/. vars\  // N, \*"\"\< \!\(mm\^4\)\>\""]\)}], "Input"],

Cell[BoxData[
    \(7\/48\ b\^3\ \[Alpha]\^2\ t\_2\)], "Output"],

Cell[BoxData[
    \("For thin-walls neglect all higher order terms of thickness"\)], "Print"],

Cell[BoxData[
    \(7\/48\ b\^3\ \[Alpha]\^2\ t\_2\)], "Output"],

Cell[BoxData[
    \("The second moment of area about the neutral axis for the web is: "\)], \
"Print"],

Cell[BoxData[
    InterpretationBox[\("\!\(\[CapitalIota]\_xx1\) \
="\[InvisibleSpace]\(7.291666666666668`*^-7\ \[Alpha]\^2\)\[InvisibleSpace]" \
\!\(m\^4\)"\[InvisibleSpace]" = "\[InvisibleSpace]\(729166.6666666667`\ \
\[Alpha]\^2\)\[InvisibleSpace]" \!\(mm\^4\)"\),
      SequenceForm[ "\!\(\[CapitalIota]\_xx1\) =", 
        Times[ .72916666666666685*^-6, 
          Power[ \[Alpha], 2]], " \!\(m\^4\)", " = ", 
        Times[ 729166.66666666674, 
          Power[ \[Alpha], 2]], " \!\(mm\^4\)"],
      Editable->False]], "Print"]
}, Open  ]],

Cell["Section 2: Flange", "Text",
  FontFamily->"Times New Roman"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(dy\_2 = y\&_\_G;\)\), "\[IndentingNewLine]", 
    \(\(\[CapitalIota]\_xc2 = \(\(\ \)\(\(t\_2\^3\) b\)\)\/12;\)\), "\
\[IndentingNewLine]", 
    \(\[CapitalIota]\_xx2p = \ 
      ExpandAll[\ \[CapitalIota]\_xc2\  + \ \(A\_2\) dy\_2\^2]\  /. 
        newdef\), "\[IndentingNewLine]", 
    \(Print["\<For thin-walls neglect all higher order terms of thickness\>"]\
\), "\[IndentingNewLine]", 
    \(\[CapitalIota]\_xx2 = 
      Normal[Series[\[CapitalIota]\_xx2p, {t\_2, 0, 
            1}]]\), "\[IndentingNewLine]", 
    \(Print["\<The second moment of area about the neutral axis for the \
flange is: \>"]\), "\[IndentingNewLine]", 
    \(Print[\*"\"\<\!\(\[CapitalIota]\_xx2\) =\>\"", \[CapitalIota]\_xx2 /. 
          vars\  // 
        N, \*"\"\< \!\(m\^4\)\>\"", "\< = \>", \(10\^12\) \[CapitalIota]\_xx2 \
/. vars\  // N, \*"\"\< \!\(mm\^4\)\>\""]\)}], "Input"],

Cell[BoxData[
    \(1\/16\ b\^3\ \[Alpha]\^2\ t\_2 + \(b\ t\_2\%3\)\/12\)], "Output"],

Cell[BoxData[
    \("For thin-walls neglect all higher order terms of thickness"\)], "Print"],

Cell[BoxData[
    \(1\/16\ b\^3\ \[Alpha]\^2\ t\_2\)], "Output"],

Cell[BoxData[
    \("The second moment of area about the neutral axis for the flange is: \
"\)], "Print"],

Cell[BoxData[
    InterpretationBox[\("\!\(\[CapitalIota]\_xx2\) \
="\[InvisibleSpace]\(3.125000000000001`*^-7\ \[Alpha]\^2\)\[InvisibleSpace]" \
\!\(m\^4\)"\[InvisibleSpace]" = "\[InvisibleSpace]\(312500.00000000006`\ \
\[Alpha]\^2\)\[InvisibleSpace]" \!\(mm\^4\)"\),
      SequenceForm[ "\!\(\[CapitalIota]\_xx2\) =", 
        Times[ .31250000000000008*^-6, 
          Power[ \[Alpha], 2]], " \!\(m\^4\)", " = ", 
        Times[ 312500.00000000006, 
          Power[ \[Alpha], 2]], " \!\(mm\^4\)"],
      Editable->False]], "Print"]
}, Open  ]],

Cell["Total", "Text",
  FontFamily->"Times New Roman"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\[CapitalIota]\_xxp = 
      ExpandAll[\ \[CapitalIota]\_xx1p + \[CapitalIota]\_xx2p]\), "\
\[IndentingNewLine]", 
    \(\[CapitalIota]\_xx = 
      ExpandAll[\ \[CapitalIota]\_xx1 + \[CapitalIota]\_xx2]\), "\
\[IndentingNewLine]", 
    \(Print[\*"\"\<For thin-walls neglect all higher order terms of \
thickness: \!\(\[CapitalIota]\_xx\) =\>\"", \[CapitalIota]\_xx]\), "\
\[IndentingNewLine]", 
    \(Print["\<The second moment of area about the neutral axis is: \>"]\), "\
\[IndentingNewLine]", 
    \(Print[\*"\"\<\!\(\[CapitalIota]\_xx\) =\>\"", \[CapitalIota]\_xx /. 
          vars\  // 
        N, \*"\"\< \!\(m\^4\)\>\"", "\< = \>", \(10\^12\) \[CapitalIota]\_xx /. 
          vars\  // N, \*"\"\< \!\(mm\^4\)\>\""]\)}], "Input"],

Cell[BoxData[
    \(5\/24\ b\^3\ \[Alpha]\^2\ t\_2 + \(b\ t\_2\%3\)\/12\)], "Output"],

Cell[BoxData[
    \(5\/24\ b\^3\ \[Alpha]\^2\ t\_2\)], "Output"],

Cell[BoxData[
    InterpretationBox[\("For thin-walls neglect all higher order terms of \
thickness: \!\(\[CapitalIota]\_xx\) ="\[InvisibleSpace]\(5\/24\ b\^3\ \
\[Alpha]\^2\ t\_2\)\),
      SequenceForm[ 
      "For thin-walls neglect all higher order terms of thickness: \!\(\
\[CapitalIota]\_xx\) =", 
        Times[ 
          Rational[ 5, 24], 
          Power[ b, 3], 
          Power[ \[Alpha], 2], 
          Subscript[ t, 2]]],
      Editable->False]], "Print"],

Cell[BoxData[
    \("The second moment of area about the neutral axis is: "\)], "Print"],

Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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\>\"", Min[
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Cell[BoxData[
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Cell[BoxData[
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      Editable->False]], "Print"],

Cell[BoxData[
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Cell["Point C = Point D = (C+D)/2", "Subsubsection",
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\"", Max[Table[\[Sigma]\_zzC\/10\^6, {\[Alpha], 0.7, 1.30, 
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    \(Print[\*"\"\<The minimum value at point C' is: \!\(\[Sigma]\_zzC\) = \>\
\"", Min[Table[\[Sigma]\_zzC\/10\^6, {\[Alpha], 0.7, 1.30, 
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Cell[BoxData[
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(*******************************************************************
End of Mathematica Notebook file.
*******************************************************************)