(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 4.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 41642, 941]*) (*NotebookOutlinePosition[ 42306, 964]*) (* CellTagsIndexPosition[ 42262, 960]*) (*WindowFrame->Normal*) Notebook[{ Cell["16.21 Techniques of structural analysis and design", "Title", TextAlignment->Center, FontSize->18], Cell["\<\ Home assignment 7 \ \>", "Subtitle", TextAlignment->Center, FontSize->18], Cell["Question 1: Problem 7.22 from textbook", "Subtitle"], Cell[TextData[{ StyleBox["The unknown displacement field for this problem is the deflection \ of the beam's neutral axis ", "Subsubtitle", FontSize->18], StyleBox[Cell[BoxData[ \(TraditionalForm\`\((w\_0)\) . \ We\ approximate\ this\ field\ using\ a\ Ritz\ approximation\ of\ \ the\ \(type : \[IndentingNewLine]w\_0\ ~\ c\_i \[Phi]\_i\)\)], "Subsubtitle", FontSize->18], "Subsubtitle"], StyleBox["The essential boundary conditions for the simply-supported beam \ require:\n", "Subsubtitle", FontSize->18], StyleBox[Cell[BoxData[ \(TraditionalForm\`\(\[Phi]\_i\)(0)\)], "Subsubtitle", FontSize->18], "Subsubtitle"], StyleBox["=0, ", "Subsubtitle", FontSize->18], StyleBox[Cell[BoxData[ \(TraditionalForm\`\[Phi]\_i\)], "Subsubtitle", FontSize->18], "Subsubtitle"], StyleBox["(L) = 0\nA good candidate family of functions ", "Subsubtitle", FontSize->18], StyleBox[Cell[BoxData[ \(TraditionalForm\`\[Phi]\_i\)], "Subsubtitle", FontSize->18], "Subsubtitle"], StyleBox["would be: ", "Subsubtitle", FontSize->18], StyleBox[Cell[BoxData[ \(TraditionalForm\`\[Phi]\_i = \ \(x\^i\)(L - x), \ i = 1, n\)], "Subsubtitle", FontSize->18], "Subsubtitle"], StyleBox[". 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