% vim: ft=tex tw=0

% arara: lualatex: { synctex: true, shell: true }
% arara: tikzmake: { options: ['-j2'] }
% arara: lualatex: { synctex: true, shell: true }

\RequirePackage{shellesc}
\documentclass{article}

%% e-TeX tools
\usepackage{etoolbox}

%% Maths typography — re-enable these if we need maths support
\usepackage{xfrac}
\usepackage{physics}
\usepackage{mathtools}
\usepackage{unicode-math}
\usepackage{siunitx}
\sisetup{%
  detect-all,
  per-mode=symbol,
  bracket-unit-denominator=false
}
\DeclareSIPostPower\inv{-1}

\usepackage{tikz}

\usetikzlibrary{calc}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{decorations.shapes}
\usetikzlibrary{intersections}
\usetikzlibrary{positioning}
\usetikzlibrary{external}
\usetikzlibrary{patterns}
\usepgflibrary{arrows.meta}
\usetikzlibrary{bending}
\usetikzlibrary{angles}
\usetikzlibrary{hobby}

\tikzexternalize[prefix=tikz/,shell escape=-enable-write18]
\tikzset{external/system call={lualatex \tikzexternalcheckshellescape -halt-on-error -interaction=scrollmode -jobname "\image" "\texsource"}}
\tikzset{external/mode=list and make}
\tikzset{
  % Defines a custom style which generates BOTH, .pdf and .png export
  % but prefers the .png on inclusion.
  png export/.style={%
    external/system call/.add=%
    {}
    ; convert -density 300 -transparent white "\image.pdf" "\image.png",
  },
  png images/.style={%
    external/system call/.add=%
    {}
    ; convert -density 300 -transparent white "\image.pdf" "\image.png",
    /pgf/images/external info,
    /pgf/images/include external/.code={%
      \includegraphics
      [width=\pgfexternalwidth,height=\pgfexternalheight]
      {##1.png}%
    },
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}

\DeclareGraphicsExtensions{.pdf,.png,.jpg,.ppm}

\usepackage{xsim}

\xsimsetup{
  exercise/within = part,
  exercise/print = true,
  solution/print = false,
  print-solutions/headings = true,
}

%% Define all TikZ styles here
\tikzset{%
  dim edge/.style={%
    densely dashed, line width=0.5pt, shorten >= -2.5mm, color=black!75!white
  },
  dim length/.style={
    draw, line width=0.5pt, arrows={Stealth-Stealth}, 
    every node/.style={above=2pt, midway, fill=white, node font=\footnotesize, inner sep=1pt},
  },
  force/.style={draw, line width=1pt, arrows = {Stealth-}},   % Force with arrow tip at start
  force'/.style={draw, line width=1pt, arrows = {-Stealth}},  % Force with arrow tip at end
  pin support/.pic={
    \draw[line width=1pt] (0, 0) -- ++(0.2,-0.5) -- ++(-0.4, 0) -- cycle;
    \draw[line width=1pt, fill=white] (0, 0) circle[radius=0.10];
    \fill[black!20] (-0.4, -0.5) -- ++(0.8, 0) -- ++(0, -0.4) -- ++(-0.8, 0) -- cycle;
    \draw[line width=1pt] (-0.4, -0.5) -- ++(0.8, 0);
  },
  roller support/.pic={
    \draw[line width=1pt] (0, 0) -- ++(0.2,-0.30) -- ++(-0.4, 0) -- cycle;
    % \draw[line width=1pt, fill=white] (0, 0) circle[radius=0.10];
    \draw[line width=1pt, fill=white] (-0.10, -0.4) circle[radius=0.10];
    \draw[line width=1pt, fill=white] (0.10, -0.4) circle[radius=0.10];
    \fill[black!20] (-0.4, -0.5) -- ++(0.8, 0) -- ++(0, -0.4) -- ++(-0.8, 0) -- cycle;
    \draw[line width=1pt] (-0.4, -0.5) -- ++(0.8, 0);
  },
  fixed support/.pic={
    \fill[black!20] (-0.4, 0) -- ++(0.8, 0) -- ++(0, -0.4) -- ++(-0.8, 0) -- cycle;
    \draw[line width=1pt] (-0.4, 0) -- ++(0.8, 0);
  },
  pin connection/.pic={
    \draw[line width=1pt, fill=white,pic actions] (0, 0) circle[radius=0.10];
  },
  fixed connection/.pic={
    \path[pic actions] (0, 0) -- (0.25, 0) -- (0, -0.25) -- cycle;
  },
  % png export,
}

\begin{document}

\begin{exercise}
  Draw the deflection of the following beam:
  \begin{center}
    \tikzsetnextfilename{week3-1}
    \begin{tikzpicture}
      \coordinate (A) at (0, 0);
      \coordinate (D) at ($(A) + (8, 0)$);
      \coordinate (B) at ($(A)!0.3!(D)$);
      \coordinate (C) at ($(A)!0.7!(D)$);
      \path pic at (B) {roller support};
      \path pic at (C) {roller support};
      \draw[line width=3pt, blue!75] (A) -- (D);
      \path pic at (A) {pin support};
      \path pic at (D) {pin support} ;
      \node[above=1mm] at (A) {A};
      \node[above=1mm] at (B) {B};
      \node[above=1mm] at (C) {C};
      \node[above=1mm] at (D) {D};
      \draw[force] (4, 0) -- ++(0, 1) node[above] {\textbf{P}};
    \end{tikzpicture}
  \end{center}
\end{exercise}

\begin{solution}
  \begin{center}
    \tikzsetnextfilename{week3-1a}
    \begin{tikzpicture}
      \coordinate (A) at (0, 0);
      \coordinate (D) at ($(A) + (8, 0)$);
      \coordinate (B) at ($(A)!0.3!(D)$);
      \coordinate (C) at ($(A)!0.7!(D)$);
      \path pic at (B) {roller support};
      \path pic at (C) {roller support};
      \draw[line width=3pt, blue!75] (A) -- (D);
      \path pic at (A) {pin support};
      \path pic at (D) {pin support} ;
      \node[above=1mm] at (A) {A};
      \node[above=1mm] at (B) {B};
      \node[above=1mm] at (C) {C};
      \node[above=1mm] at (D) {D};
      \draw[force] ($(A)!0.5!(D)$) -- ++(0, 1) node[above] {\textbf{P}};

      \draw[force', red] (A) -- ++(0, -1) node[below] {$V_A$};
      \draw[force, red] (B) -- ++(0, -1) node[below] {$V_B$};
      \draw[force, red] (C) -- ++(0, -1) node[below] {$V_C$};
      \draw[force', red] (D) -- ++(0, -1) node[below] {$V_D$};
      \draw[red, line width=1pt] (A) to[curve through={(B) .. ($(B)!0.5!(C) - (0, 0.5)$) .. (C)}] (D);
    \end{tikzpicture}
  \end{center}
\end{solution}

\begin{exercise}
  Draw the deflection of the following beam:
  \begin{center}
    \tikzsetnextfilename{week3-2}
    \begin{tikzpicture}
      \coordinate (A) at (0, 0);
      \coordinate (D) at ($(A) + (8, 0)$);
      \coordinate (B) at ($(A)!0.3!(D)$);
      \coordinate (C) at ($(A)!0.7!(D)$);
      \path pic at (B) {roller support};
      \path pic at (C) {roller support};
      \draw[line width=3pt, blue!75] (A) -- (D);
      \path pic at (A) {pin support};
      \path pic at (D) {pin support} ;
      \node[above=1mm] at (A) {A};
      \node[above=1mm] at (B) {B};
      \node[above=1mm] at (C) {C};
      \node[above=1mm] at (D) {D};
      \draw[force] ($(A)!0.5!(B)$) -- ++(0, 1) node[above] {\textbf{P}};
    \end{tikzpicture}
  \end{center}
\end{exercise}

\begin{solution}
  \begin{center}
    \tikzsetnextfilename{week3-1b}
    \begin{tikzpicture}
      \coordinate (A) at (0, 0);
      \coordinate (D) at ($(A) + (8, 0)$);
      \coordinate (B) at ($(A)!0.3!(D)$);
      \coordinate (C) at ($(A)!0.7!(D)$);
      \path pic at (B) {roller support};
      \path pic at (C) {roller support};
      \draw[line width=3pt, blue!75] (A) -- (D);
      \path pic at (A) {pin support};
      \path pic at (D) {pin support} ;
      \node[above=1mm] at (A) {A};
      \node[above=1mm] at (B) {B};
      \node[above=1mm] at (C) {C};
      \node[above=1mm] at (D) {D};
      \draw[force] ($(A)!0.5!(B)$) -- ++(0, 1) node[above] {\textbf{P}};

      \draw[force, red] (A) -- ++(0, -1) node[below] {$V_A$};
      \draw[force, red] (B) -- ++(0, -1) node[below] {$V_B$};
      \draw[force', red] (C) -- ++(0, -1) node[below] {$V_C$};
      \draw[force', red] (D) -- ++(0, -1) node[below] {$V_D$};
      \draw[red, line width=1pt] (A) to[curve through={($(A)!0.5!(B) - (0, 0.5)$) .. (B) .. (C)}] (D);
      % \draw[purple, line width=1pt] (A) to[curve through={($(A)!0.5!(B) - (0, 0.5)$)}] (B);
      % \draw[red, line width=0.5pt] ($(A)!0.5!(B)$) -- ++(0, -1.5);
      % \draw ($(A)!0.5!(B) - (0, 0.5)$) circle[radius=0.1];
    \end{tikzpicture}
  \end{center}
\end{solution}

\begin{exercise}
  Draw the deflection of the following beam:
  \begin{center}
    \tikzsetnextfilename{week3-3}
    \begin{tikzpicture}
      \coordinate (A) at (0, 0);
      \coordinate (D) at ($(A) + (8, 0)$);
      \coordinate (B) at ($(A)!0.3!(D)$);
      \coordinate (C) at ($(A)!0.7!(D)$);
      \path pic at (B) {roller support};
      \path pic at (C) {roller support};
      \draw[line width=3pt, blue!75] (A) -- (D);
      \path pic at (A) {pin support};
      \path pic at (D) {pin support} ;
      \node[above=1mm] at (A) {A};
      \node[above=1mm] at (B) {B};
      \node[above=1mm] at (C) {C};
      \node[above=1mm] at (D) {D};
      \draw[force] ($(A)!0.5!(B)$) -- ++(0, 1) node[above] {$\textbf{P}_1$};
      \draw[force] ($(C)!0.5!(D)$) -- ++(0, 1) node[above] {$\textbf{P}_2$};
    \end{tikzpicture}
  \end{center}
\end{exercise}

\begin{solution}
  \begin{center}
    \tikzsetnextfilename{week3-1c}
    \begin{tikzpicture}
      \coordinate (A) at (0, 0);
      \coordinate (D) at ($(A) + (8, 0)$);
      \coordinate (B) at ($(A)!0.3!(D)$);
      \coordinate (C) at ($(A)!0.7!(D)$);
      \path pic at (B) {roller support};
      \path pic at (C) {roller support};
      \draw[line width=3pt, blue!75] (A) -- (D);
      \path pic at (A) {pin support};
      \path pic at (D) {pin support} ;
      \node[above=1mm] at (A) {A};
      \node[above=1mm] at (B) {B};
      \node[above=1mm] at (C) {C};
      \node[above=1mm] at (D) {D};
      \draw[force] ($(A)!0.5!(B)$) -- ++(0, 1) node[above] {$\textbf{P}_1$};
      \draw[force] ($(C)!0.5!(D)$) -- ++(0, 1) node[above] {$\textbf{P}_2$};

      \draw[force, red] (A) -- ++(0, -1) node[below] {$V_A$};
      \draw[force, red] (B) -- ++(0, -1) node[below] {$V_B$};
      \draw[force, red] (C) -- ++(0, -1) node[below] {$V_C$};
      \draw[force, red] (D) -- ++(0, -1) node[below] {$V_D$};
      \draw[red, line width=1pt] (A) to[curve through={($(A)!0.5!(B) - (0, 0.5)$) .. (B) .. (C) .. ($(C)!0.5!(D) - (0, 0.5)$)}] (D);
    \end{tikzpicture}
  \end{center}
\end{solution}

\begin{exercise}
  Using the \emph{force method} to determine the deflection at $C$ of the
  following portal frame. The cross sections of the truss members is given by
  $C_1$, that of the horizontal beam members by $C_2$, and that of the vertical
  members by $C_3$.
  \begin{center}
    \tikzsetnextfilename{week5-portal-frame}
    % \tikzexternaldisable
    \begin{tikzpicture}
      \draw[line width=3pt, blue!75] (0, 0) coordinate (node-A) node[left, text=black] {$A$}
      -- ++(0, 6) coordinate (node-B) node[above left, text=black] {$B$}
      -- ++(2.75, 0) coordinate (node-D) node[above right, text=black] {$D$}
      -- ++(2.75, 0) coordinate (node-F) node[above right, text=black] {$F$}
      -- ++(0, -6) coordinate (node-G) node[left, text=black] {$G$};

      \draw[line width=2pt, blue!75] (node-B)
      -- ($(node-B)!0.5!(node-D) - (0, 2)$) coordinate (node-C) node[below, text=black] {$C$}
      -- (node-D) 
      -- ($(node-D)!0.5!(node-F) - (0, 2)$) coordinate (node-E) node[below, text=black] {$E$}
      -- (node-F) 
      (node-C) -- (node-E); 

      \draw pic[draw, line width=1.5pt, blue!75] at ($(node-B)!0.07!(node-C)$) {pin connection};
      \draw pic[draw, line width=1.5pt, blue!75] at (node-C) {pin connection};
      \draw pic[draw, line width=1.5pt, blue!75] at ($(node-C)!0.5!(node-E)!0.95!(node-D)$) {pin connection};
      \draw pic[draw, line width=1.5pt, blue!75] at (node-E) {pin connection};
      \draw pic[draw, line width=1.5pt, blue!75] at ($(node-F)!0.07!(node-E)$) {pin connection};

      \draw[force] (node-D) -- ++(0, 1) node[above] {\SI{5}{\kN}};

      \path pic at (node-A) {pin support};
      \path pic at (node-G) {roller support};

      \draw[dim edge] (node-A) -- ++(0, -1) coordinate (node-A-dim-down);
      \draw[dim edge] (node-B) -- ++(0, 0.5) coordinate (node-B-dim-up);
      \coordinate (node-D-dim-up) at ($(node-D) + (0, 0.5)$);
      \draw[dim edge] (node-F) -- ++(0.5, 0) coordinate (node-F-dim-right);
      \draw[dim edge] (node-G) -- ++(0.5, 0) coordinate (node-G-dim-right);
      \draw[dim edge] (node-G) -- ++(0, -1) coordinate (node-G-dim-down);
      \draw[dim edge] (node-A) -- (node-C |- node-A) coordinate (node-A-dim-inner);
      \draw[dim edge] (node-C) -- (node-A |- node-C) coordinate (node-C-dim-inner);

      \draw[dim length] (node-A-dim-down) -- (node-G-dim-down) node[below] {\SI{550}{\mm}};
      \draw[dim length] (node-B-dim-up) -- (node-D-dim-up) node[above] {\SI{275}{\mm}};
      \draw[dim length] (node-F-dim-right) -- (node-G-dim-right) node[right] {\SI{600}{\mm}};
      \draw[dim length] ($(node-A)!0.5!(node-A-dim-inner)$) -- ($(node-C-dim-inner)!0.5!(node-C)$) node[right] {\SI{400}{\mm}};

      \coordinate (c1-top-left) at ($(node-F) + (3, 0)$);

      \draw[line width=1pt, blue, fill=blue!50] (c1-top-left) 
      -- ++(0.45, 0) coordinate (c1-top-right)
      -- ++(0, -0.45) coordinate (c1-bottom-right)
      -- ++(-0.45, 0) coordinate (c1-bottom-left)
      -- cycle;

      \node at ($(c1-top-left)!0.5!(c1-bottom-left) - (0.5, 0)$) {$C_1$};

      \draw[dim edge] (c1-top-left) -- ++(0, 0.25) coordinate (c1-left-edge);
      \draw[dim edge] (c1-top-right) -- ++(0, 0.25) coordinate (c1-right-edge);
      \draw[dim edge] (c1-top-right) -- ++(0.25, 0) coordinate (c1-top-edge);
      \draw[dim edge] (c1-bottom-right) -- ++(0.25, 0) coordinate (c1-bottom-edge);

      \draw[dim length] (c1-left-edge) -- (c1-right-edge) node[above=1mm] {\SI{15}{\mm}};
      \draw[dim length] (c1-top-edge) -- (c1-bottom-edge) node[right=1mm] {\SI{15}{\mm}};

      \coordinate (c2-bottom-left) at ($(node-F)!0.5!(node-G) + (3, 0)$);

      \draw[line width=1pt, blue, fill=blue!50] (c2-bottom-left)
      -- ++(0, 0.9) coordinate (c2-top-left)
      -- ++(0.9, 0) coordinate (c2-top-right)
      -- ++(0, -0.9) coordinate (c2-bottom-right)
      -- cycle;

      \node at ($(c2-top-left)!0.5!(c2-bottom-left) - (0.5, 0)$) {$C_2$};

      \draw[dim edge] (c2-top-left) -- ++(0, 0.25) coordinate (c2-left-edge);
      \draw[dim edge] (c2-top-right) -- ++(0, 0.25) coordinate (c2-right-edge);
      \draw[dim edge] (c2-top-right) -- ++(0.25, 0) coordinate (c2-top-edge);
      \draw[dim edge] (c2-bottom-right) -- ++(0.25, 0) coordinate (c2-bottom-edge);

      \draw[dim length] (c2-left-edge) -- (c2-right-edge) node[above=1mm] {\SI{30}{\mm}};
      \draw[dim length] (c2-top-edge) -- (c2-bottom-edge) node[right=1mm] {\SI{30}{\mm}};

      \coordinate (c3-bottom-left) at ($(node-G) + (3, 0)$);

      \draw[line width=1pt, blue, fill=blue!50] (c3-bottom-left)
      -- ++(0, 1.2) coordinate (c3-top-left)
      -- ++(1.2, 0) coordinate (c3-top-right)
      -- ++(0, -1.2) coordinate (c3-bottom-right)
      -- cycle;

      \node at ($(c3-top-left)!0.5!(c3-bottom-left) - (0.5, 0)$) {$C_3$};

      \draw[dim edge] (c3-top-left) -- ++(0, 0.25) coordinate (c3-left-edge);
      \draw[dim edge] (c3-top-right) -- ++(0, 0.25) coordinate (c3-right-edge);
      \draw[dim edge] (c3-top-right) -- ++(0.25, 0) coordinate (c3-top-edge);
      \draw[dim edge] (c3-bottom-right) -- ++(0.25, 0) coordinate (c3-bottom-edge);

      \draw[dim length] (c3-left-edge) -- (c3-right-edge) node[above=1mm] {\SI{40}{\mm}};
      \draw[dim length] (c3-top-edge) -- (c3-bottom-edge) node[right=1mm] {\SI{40}{\mm}};

    \end{tikzpicture}
  \end{center}
\end{exercise}

\begin{solution}
  This is a trick question, there is no solution to type out right now.
\end{solution}

\printsolutionstype{exercise}

\end{document}