{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Beam2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pysketcher import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"A more sophisticated beam than in beam1.py.\"\"\"\n",
    "def beam():\n",
    "    L = 8.0\n",
    "    a = 3*L/4\n",
    "    b = L - a\n",
    "    H = 1.0\n",
    "    xpos = 0.0\n",
    "    ypos = 3.0\n",
    "\n",
    "    drawing_tool.set_coordinate_system(\n",
    "        xmin=-3, xmax=xpos+1.5*L,\n",
    "        ymin=0, ymax=ypos+5*H,\n",
    "        axis=False)\n",
    "    drawing_tool.set_linecolor('blue')\n",
    "    #drawing_tool.set_grid(True)\n",
    "    drawing_tool.set_fontsize(16)\n",
    "\n",
    "    A = point(xpos,ypos)\n",
    "\n",
    "    beam = Rectangle(A, L, H)\n",
    "\n",
    "    h = L/16  # size of support, clamped wall etc\n",
    "\n",
    "    clamped = Rectangle(A - point(h,0) - point(0,2*h), h,\n",
    "                        6*h).set_filled_curves(pattern='/')\n",
    "\n",
    "    load = ConstantBeamLoad(A + point(0,H), L, H)\n",
    "    load.set_linewidth(1).set_linecolor('black')\n",
    "    load_text = Text('$w$',\n",
    "                     load.geometric_features()['mid_top'] +\n",
    "                     point(0,h/2.))\n",
    "\n",
    "    B = A + point(a, 0)\n",
    "    C = B + point(b, 0)\n",
    "\n",
    "    support = SimplySupportedBeam(B, h)  # pt B is simply supported\n",
    "\n",
    "\n",
    "    R1 = Force(A-point(0,2*H), A, '$R_1$', text_spacing=1./50)\n",
    "    R1.set_linewidth(3).set_linecolor('black')\n",
    "    R2 = Force(B-point(0,2*H),\n",
    "               support.geometric_features()['mid_support'],\n",
    "               '$R_2$', text_spacing=1./50)\n",
    "    R2.set_linewidth(3).set_linecolor('black')\n",
    "    M1 = Moment('$M_1$', center=A + point(-H, H/2), radius=H/2,\n",
    "                left=True, text_spacing=1/30.)\n",
    "    M1.set_linecolor('black')\n",
    "\n",
    "    ab_level = point(0, 3*h)\n",
    "    a_dim = Distance_wText(A - ab_level, B - ab_level, '$a$')\n",
    "    b_dim = Distance_wText(B - ab_level, C - ab_level, '$b$')\n",
    "    dims = Composition({'a': a_dim, 'b': b_dim})\n",
    "    symbols = Composition(\n",
    "        {'R1': R1, 'R2': R2, 'M1': M1,\n",
    "         'w': load, 'w text': load_text,\n",
    "         'A': Text('$A$', A+point(0.7*h,-0.9*h)),\n",
    "         'B': Text('$B$',\n",
    "                   support.geometric_features()['mid_support']-\n",
    "                   point(1.25*h,0)),\n",
    "         'C': Text('$C$', C+point(h/2,-h/2))})\n",
    "\n",
    "    x_axis = Axis(A + point(L+h, H/2), 2*H, '$x$',).\\\n",
    "             set_linecolor('black')\n",
    "    y_axis = Axis(A + point(0,H/2), 3.5*H, '$y$',\n",
    "                  label_alignment='left',\n",
    "                  rotation_angle=90).set_linecolor('black')\n",
    "    axes = Composition({'x axis': x_axis, 'y axis': y_axis})\n",
    "\n",
    "    annotations = Composition({'dims': dims, 'symbols': symbols,\n",
    "                               'axes': axes})\n",
    "    beam = Composition({'beam': beam, 'support': support,\n",
    "                        'clamped end': clamped, 'load': load})\n",
    "\n",
    "    def deflection(x, a, b, w):\n",
    "        import numpy as np\n",
    "        R1 = 5./8*w*a - 3*w*b**2/(4*a)\n",
    "        R2 = 3./8*w*a + w*b + 3*w*b**2/(4*a)\n",
    "        M1 = R1*a/3 - w*a**2/12\n",
    "        y = -(M1/2.)*x**2 + 1./6*R1*x**3 - w/24.*x**4 + \\\n",
    "            1./6*R2*np.where(x > a, 1, 0)*(x-a)**3\n",
    "        return y\n",
    "\n",
    "    x = linspace(0, L, 101)\n",
    "    y = deflection(x, a, b, w=1.0)\n",
    "    y /= abs(y.max() - y.min())\n",
    "    y += ypos + H/2\n",
    "\n",
    "    elastic_line = Curve(x, y).\\\n",
    "                   set_linecolor('red').\\\n",
    "                   set_linestyle('dashed').\\\n",
    "                   set_linewidth(3)\n",
    "\n",
    "    beam.draw()\n",
    "    beam.draw_dimensions()\n",
    "    annotations.draw()\n",
    "    elastic_line.draw()\n",
    "    drawing_tool.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "80c268fe8be04b52b488fdeb4bcb8c58",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "drawing_tool.mpl.gcf().canvas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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