EQE512-Week02-Lecture.ipynb

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    "<h1 align=\"center\">EQE512 MATRIX METHODS IN STRUCTURAL ANALYSIS \n",
    "<br>\n",
    "<br>\n",
    "Week 02\n",
    "<br>\n",
    "<br>\n",
    "Computer Algorithms</h1> \n",
    "\n",
    "<h3 align=\"center\">Dr. Ahmet Anıl Dindar (adindar@gtu.edu.tr)</h3> \n",
    "<h4 align=\"center\">2021 Fall  </h4> "
   ]
  },
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   "source": [
    "Today we will cover the given concepts\n",
    "\n",
    "- Development of computer algorithms (Determinate Single Degree of Freedom systems) \n",
    "\n",
    "- Development of algorithms for parametric calculations and optimal solution approach (Design of the Determinate Single Degree Freedom Systems under Desing Load Combinations) \n",
    "\n",
    "---"
   ]
  },
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   "source": [
    "## ALGORITHM\n",
    "\n",
    "Calculate the followings;\n",
    "- Support reactions\n",
    "- Draw the internal force diagrams\n",
    "\n",
    "using ~~Excel~~ and Python.\n",
    "\n",
    "<img src=\"./images/9-simple_cantilever_beam.svg\" width=\"50%\" align=\"center\">"
   ]
  },
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   "source": [
    "### ALGORITHM = PLANNING + EXPERIENCE + KNOWLEDGE\n",
    "\n",
    "Let's develop an algorithm for this problem: \n",
    "\n",
    "<img src=\"./images/week03-task02-algorithm-00.svg\" width=\"50%\" >"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see a simple but effective tool for algorithm development :\n",
    "\n",
    "\n",
    "Clicking this link <a href=\"https://app.diagrams.net/\" target=\"_blank\">Draw.io = diagrams.net</a> will open a new tab where we will do the flowchart for the problem. We'll embed the flowchart to the cell below. \n",
    "\n"
   ]
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--- \n",
    "**Introduction**\n",
    "\n",
    "Having learned Python basics in terms of variables, loops and visualization, it is time to go for a simple but efficient structural analysis problem; Lateral drift limit of a cantilever column. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Relation between force and deformation\n",
    "\n",
    "Remember the spring under axial load. \n",
    "\n",
    "<img src=\"./images/week04-Spring.png\" width=\"20%\" align=\"center\">\n"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Axial Stiffness\n",
    "\n",
    "<img src=\"./images/Week04-1_axialStiffness.png\" width=\"50%\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Flexural Stiffness\n",
    "\n",
    "<img src=\"./images/Week04-2_shearStiffness.png\" width=\"50%\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Flexural Stiffness Example\n",
    "\n",
    "<img src= \"./images/week04-task01-lateral-stiffness-TASK03.png\" width=\"40%\">\n",
    "\n",
    "**TASK**\n",
    "\n",
    "Let's create the algorithm to determine the lateral flexural stiffness of the given cantilever column"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Draw an algorithm that calculates the flexural stiffness of a given cantilever column!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "H = 10_000 # mm\n",
    "b = 0.5 * 1_000  # mm\n",
    "h = 0.5 * 1_000 # mm\n",
    "E = 30_000 # N/mm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def moment_of_inertia( b , h) :\n",
    "    \"\"\"\n",
    "    b = width\n",
    "    h = depth\n",
    "    \"\"\"\n",
    "    mom_inertia = ( b  * h**3) / (12)\n",
    "    \n",
    "    return( mom_inertia)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def flexural_stiffness( E, H , b , h):\n",
    "    \"\"\"\n",
    "    Inputs: \n",
    "    E: Modulus of elasticity\n",
    "    H : Member length\n",
    "    b : width\n",
    "    h : depth  \n",
    "    \n",
    "    Returns: \n",
    "    k : flexural stiffness\n",
    "    \"\"\"\n",
    "    I = moment_of_inertia( b  , h)\n",
    "    print( f\"Moment of inertia is found as {round(I)} mm^4\" )\n",
    "    \n",
    "    k = 12 * (E * I) / ( H**3)\n",
    "    print( f\"Flexural stiffnes is found as {round(k)} N/mm\" )\n",
    "    return( k )\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Moment of inertia is found as 5208333333 mm^4\n",
      "Flexural stiffnes is found as 1875 N/mm\n"
     ]
    }
   ],
   "source": [
    "k = flexural_stiffness(E , H , b , h)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parametric Study\n",
    "\n",
    "Let's see the parameters affecting the lateral stiffness of a cantilever member with free end.\n",
    "\n",
    "<img src= \"./images/week04-task01-lateral-stiffness-TASK03.png\" width=\"30%\">\n",
    "\n",
    "Let's take two cases: \n",
    "\n",
    "1- Varying \"b\"\n",
    "\n",
    "2- Varying \"h\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Case 1- Varying \"b\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "H = 10_000 # mm\n",
    "b_range = [200 , 300 , 400 , 500]  # mm\n",
    "h = 0.5 * 1_000 # mm\n",
    "E = 30_000 # N/mm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Moment of inertia is found as 2083333333 mm^4\n",
      "Flexural stiffnes is found as 750 N/mm\n",
      "Moment of inertia is found as 3125000000 mm^4\n",
      "Flexural stiffnes is found as 1125 N/mm\n",
      "Moment of inertia is found as 4166666667 mm^4\n",
      "Flexural stiffnes is found as 1500 N/mm\n",
      "Moment of inertia is found as 5208333333 mm^4\n",
      "Flexural stiffnes is found as 1875 N/mm\n"
     ]
    }
   ],
   "source": [
    "k_all = []\n",
    "for b_step in b_range :\n",
    "    k_step = flexural_stiffness(E , H , b_step , h)\n",
    "    k_all.append( k_step )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[200, 300, 400, 500] [750.0, 1125.0, 1500.0, 1875.0]\n"
     ]
    }
   ],
   "source": [
    "print( b_range , k_all)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Stiffness k')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot( b_range , k_all , marker=\"*\" , ms = 10 )\n",
    "plt.xlabel( \"b values\")\n",
    "plt.ylabel(\"Stiffness k\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Case 2- Varying \"h\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "H = 10_000 # mm\n",
    "b = 0.5 * 1_000 # mm\n",
    "h_range = [200 , 300 , 400 , 500]   # mm\n",
    "E = 30_000 # N/mm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Moment of inertia is found as 333333333 mm^4\n",
      "Flexural stiffnes is found as 120 N/mm\n",
      "Moment of inertia is found as 1125000000 mm^4\n",
      "Flexural stiffnes is found as 405 N/mm\n",
      "Moment of inertia is found as 2666666667 mm^4\n",
      "Flexural stiffnes is found as 960 N/mm\n",
      "Moment of inertia is found as 5208333333 mm^4\n",
      "Flexural stiffnes is found as 1875 N/mm\n"
     ]
    }
   ],
   "source": [
    "k_all = []\n",
    "for h_step in h_range :\n",
    "    k_step = flexural_stiffness(E , H , b , h_step)\n",
    "    k_all.append( k_step )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[200, 300, 400, 500] [120.0, 405.0, 960.0, 1875.0]\n"
     ]
    }
   ],
   "source": [
    "print( h_range , k_all)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Stiffness k')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot( h_range , k_all , marker=\"*\" , ms = 10 )\n",
    "plt.xlabel( \"h values\")\n",
    "plt.ylabel(\"Stiffness k\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimal Solution for Top Drift\n",
    "\n",
    "<img src=\"./images/week04-task01-SDOF-drift.png\" width=\"20%\" >\n",
    "\n",
    "For the given ranges of section geometry, calculate the most optimum geometry if the lateral drift is limited **1%** with **0.1%** tolerance. \n",
    "\n",
    "Which cross-section ( $h$ and $b$ values) lead me to $ Drift (\\delta) = 1\\% \\pm 0.1\\% $. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nWhich b is leading the target drift?\\n'"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = 10_000 # mm\n",
    "h_range = [200 , 300 , 400 , 500]   # mm\n",
    "E = 30_000 # N/mm\n",
    "F = 1_000 # N\n",
    "#\n",
    "\"\"\"\n",
    "Which b is leading the target drift?\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img 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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "**NEXT WEEK**\n",
    "\n",
    "<table >\n",
    "<tr>\n",
    "<td>\n",
    "<img src=\"http://worshiphousemedia.s3.amazonaws.com/images/main/s/st/bnt/st/seeyounextweek1.jpg\" width=\"50%\" >\n",
    "</td>\n",
    "<td align=\"left\">\n",
    "The topics for the next week \n",
    "<br><br>\n",
    "\n",
    "1- Assignment #1 : Tonight 8pm\n",
    "<br><br>\n",
    "2- \"Truss Element & System - Stifness Matrix\"\n",
    "<br>\n",
    "</td>\n",
    "</tr>\n",
    "</table>"
   ]
  }
 ],
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