EQE512-Week01-Lecture.ipynb

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   "source": [
    "<h1 align=\"center\">EQE512 MATRIX METHODS IN STRUCTURAL ANALYSIS \n",
    "<br>\n",
    "<br>\n",
    "Week 01\n",
    "<br>\n",
    "<br>\n",
    "Defining the solution methods in engineering calculations using matrices and development of algorithms</h1> \n",
    "\n",
    "<h3 align=\"center\">Dr. Ahmet Anıl Dindar (adindar@gtu.edu.tr)</h3> \n",
    "<h4 align=\"center\">2021 Fall  </h4> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "** What is \"Structural Analysis\"?**\n",
    "<table style=\"width:100%\">\n",
    "<tr>\n",
    "<th><img src=\"https://media-cdn.tripadvisor.com/media/photo-o/0d/fc/4c/03/burj-khalifa.jpg\" alt=\"Drawing\" style=\"width: 500px;\"/> </th>\n",
    "<th><img src=\"http://www.mooseyscountrygarden.com/willow-tree-garden/bridge-wood-willow.jpg\" alt=\"Drawing\" style=\"width: 500px;\"/></th>\n",
    "</tr>\n",
    "</table>\n",
    "- It is essential to do a system analysis before design and construction of the (engineering) structures. \n",
    "- Indeed, structural analysis is the first step in the determination of the internal forces occcuring due to the external forces acting on the structures. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   "source": [
    "** What are the methods in the Structural Analysis? **\n",
    "\n",
    "Structures are assumed that they are in the statically equilibrium under the external forces. \n",
    "<table style=\"width:100%\">\n",
    "<tr>\n",
    "<th><img src=\"./images/1-two_story_building.jpg\" alt=\"Drawing\" style=\"width: 500px;\"/></th>\n",
    "<th><img src=\"./images/2-tsunami_vehicle_on_top.jpg\" alt=\"Drawing\" style=\"width: 500px;\"/></th>\n",
    "</tr>\n",
    "<tr>\n",
    "<th>Static Forces</th><th>Dynamic Forces</th>\n",
    "</tr>\n",
    "</table>\n",
    "However, a structure may undergo dynamic forces due to sudden natural disasters such as earthquakes, tsunami, flood or man-made disasters blast, bomb, accident etc. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "** What are the methods in the Structural Analysis? **\n",
    "\n",
    "External forces are grouped in two classes; \n",
    "\n",
    "<img src=\"./images/3-loads.svg\" alt=\"Drawing\" style=\"width: 80%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "** What are the methods in the Structural Analysis? **\n",
    "\n",
    "Structural Analysis Methods are divided into two groups; \n",
    "\n",
    "<img src=\"./images/4-SA methods.svg\" alt=\"Drawing\" style=\"width: 80%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "** Now another question arises: What is the relation between computers and structural analysis?**\n",
    "\n",
    "To be more specific, do we need algorithms and programs running these algorithms?\n",
    "\n",
    "** Question: Can you solve the following problem?**\n",
    "\n",
    "<img src=\"./images/5-simple_beam.svg\" alt=\"Drawing\" align=\"middle\" style=\"width: 50%\"/>\n",
    "\n",
    "- Calculate the support reactions.\n",
    "- Calculate the max axial (N), shear (V) and bending moment (M) values on the beam. \n",
    "\n",
    "_Can you draw the flow chart of the steps you'll follow?_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "** Flow-chart for the simple beam with uniform loading problem **\n",
    "\n",
    "<img src=\"./images/5-simple_beam_flowchart.svg\" alt=\"Drawing\" align=\"middle\" style=\"width: 100%\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "** Flow-chart for the simple beam with uniform loading problem **\n",
    "\n",
    "<img src=\"./images/5-simple_beam_solution-Hand Calculation.png\" alt=\"Drawing\" align=\"middle\" style=\"height: 120%\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "** Why do we need computers for engineering works? **\n",
    "\n",
    "Think of the simple beam problem given above. What if the \"given\" values are found in a range i.e.: L is between 1 to 10m increasing at 25cm and q is between 1 to 100kN/m increasing at 1kN/m. Would you solve the problem easily?\n",
    "\n",
    "Answer is yes because this is a simple system and the calculations are indeed based on analytical methods. \n",
    "\n",
    "When the system becomes more complex for example indeterminate structure and the loading cases are more than one, that is usual in case of the loading combinations are encountered, there is strong tool for the computation.\n",
    "<img src=\"./images/6-sdof+mdof+truss.svg\" alt=\"Drawing\" style=\"width: 100%;\"/>\n",
    "\n",
    "How can you effectively solve the above problems? Let's learn throughout EQE512. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "<img src=\"http://i2.cdn.cnn.com/cnnnext/dam/assets/140116120426-northridge-earthquake-09-horizontal-large-gallery.jpg\" alt=\"Drawing\" style=\"width: 100%;\"/>\n",
    "Source: http://www.cnn.com/2014/01/16/us/northridge-earthquake-things-learned/index.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Computer programming languages**\n",
    "\n",
    "<img src=\"http://www.digibarn.com/collections/posters/tongues/ComputerLanguagesChart.png\" alt=\"Drawing\" style=\"width: 100%;\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**MATLAB?**\n",
    "\n",
    "<img src=\"./images/week02_popularComputerLanguages.png\" alt=\"Drawing\" style=\"width: 80%;\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**What else?**\n",
    "\n",
    "<img src=\"./images/programs1965_2019.jpg\" alt=\"Drawing\" style=\"height: 60%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Future?**\n",
    "\n",
    "Source : https://insights.stackoverflow.com/survey/2019\n",
    "\n",
    "<img src=\"./images/wee02_salary_devtype-1.svg\" alt=\"Drawing\" style=\"height: 70%;\"/>\n",
    "\n",
    "<img src=\"./images/week02_salary_language-1.svg\" alt=\"Drawing\" style=\"height: 70%;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Let's see these programs**\n",
    "\n",
    "- Flowchart Drawing (Draw.io)\n",
    "- Spreadsheet programs (MS Excel, Google Spreadsheet)\n",
    "- Numerical programming (PYTHON)\n",
    "- Mathematical Calculations (SMATH)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Algorithm**\n",
    "\n",
    "An algorithm is a list of rules to follow in order to solve a problem.\n",
    "\n",
    "<img src=\"http://ichef.bbci.co.uk/images/ic/320x180/p0258tkq.jpg\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TASK 01- QUESTION\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/5-simple_beam.svg\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TASK 01- ALGORITHM\n",
    "\n",
    "Let's develop an algorithm in Engineering Problems: \n",
    "\n",
    "<img src=\"./images/5-simple_beam_flowchart.svg\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TASK 01- SOLUTION IN EXCEL\n",
    "\n",
    "<img src=\"./images/7-Excel-00.png\" width=\"60%\">\n",
    "\n",
    "Follow this part in the class video."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CODING PRACTICE IN MATLAB AND PYTHON \n",
    "\n",
    "Keywords in coding:\n",
    "\n",
    "- Variables (number, string, array)\n",
    "- Calculations (adding, subtracting, multiplying, dividing)\n",
    "- Flows\n",
    "    - for / (end)\n",
    "    - If / else / (end)\n",
    "    - While / (end)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MATLAB \n",
    "\n",
    "<img src=\"./images/8-MATLAB-00.png\" width=\"60%\">\n",
    "\n",
    "Let's watch this part in class video"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PYTHON\n",
    "\n",
    "It is right now :)\n",
    "\n",
    "---\n",
    "\n",
    "this is a code.\n",
    "\n",
    "$\\alpha = \\beta^3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Variables; Some coding about variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "a  = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = [1 , 2 , 3 ,5 , a]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 5, 10]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = { \"d\" : \"Cimbom is the best team\", \"e\" : b}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type( c )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Cimbom is the best team'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[\"d\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 5, 10]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[\"e\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Numbers; Some coding about variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = 1 # this is an integer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = 1.4 # this is an float"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "list indices must be integers or slices, not float",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-16-70d4b65f33c0>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mb\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m: list indices must be integers or slices, not float"
     ]
    }
   ],
   "source": [
    "b[g]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# For loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 5, 10]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "5\n",
      "10\n",
      "This is the end of the for loop\n"
     ]
    }
   ],
   "source": [
    "for item in b :\n",
    "    print( item )\n",
    "  \n",
    "print( \"This is the end of the for loop\")    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is NOT TWO\n",
      "This is two\n",
      "This is NOT TWO\n",
      "This is NOT TWO\n",
      "This is NOT TWO\n"
     ]
    }
   ],
   "source": [
    "# If/Else loop\n",
    "\n",
    "for item in b :\n",
    "    if item == 2 :\n",
    "        print( \"This is two\")\n",
    "    else:\n",
    "        print( \"This is NOT TWO\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "counter is 0 and item is 0\n",
      "counter is 0 and item is 1\n",
      "counter is 1 and item is 2\n",
      "counter is 2 and item is 3\n",
      "counter is 3 and item is 4\n",
      "counter is 4 and item is 5\n"
     ]
    }
   ],
   "source": [
    "# While Loop\n",
    "item =  0 \n",
    "counter = 0 \n",
    "while counter < 5 :\n",
    "    #print( counter , item )\n",
    "    print( f\"counter is {counter } and item is {item}\")\n",
    "    counter = item\n",
    "    item += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### TASK 01- SOLUTION IN PYTHON\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/5-simple_beam.svg\" width=\"80%\"/>\n",
    "\n",
    "Let's do it rigth now!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# TASK 01- SOLUTION IN PYTHON"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "q , L = 10 , 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ax is equal to 0kN\n"
     ]
    }
   ],
   "source": [
    "Ax = 0 \n",
    "print( f\"Ax is equal to {Ax}kN\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ay is equal to 25.0kN\n"
     ]
    }
   ],
   "source": [
    "Ay = 0.5 * q * L\n",
    "print( f\"Ay is equal to {Ay}kN\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "By is equal to 25.0kN\n"
     ]
    }
   ],
   "source": [
    "By = q * L - Ay\n",
    "print( f\"By is equal to {By}kN\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "interimLength = [ 0,1,2,3,4,5] # distance from point A\n",
    "interimLength = range(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "range(0, 6)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interimLength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "for item in interimLength: print( item)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Why don't we use the given format for array creation. COMPREHENSION\n",
    "dx = .1\n",
    "interimLength =  [ item * dx for item in range( int( L/dx) + 1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.0,\n",
       " 0.1,\n",
       " 0.2,\n",
       " 0.30000000000000004,\n",
       " 0.4,\n",
       " 0.5,\n",
       " 0.6000000000000001,\n",
       " 0.7000000000000001,\n",
       " 0.8,\n",
       " 0.9,\n",
       " 1.0,\n",
       " 1.1,\n",
       " 1.2000000000000002,\n",
       " 1.3,\n",
       " 1.4000000000000001,\n",
       " 1.5,\n",
       " 1.6,\n",
       " 1.7000000000000002,\n",
       " 1.8,\n",
       " 1.9000000000000001,\n",
       " 2.0,\n",
       " 2.1,\n",
       " 2.2,\n",
       " 2.3000000000000003,\n",
       " 2.4000000000000004,\n",
       " 2.5,\n",
       " 2.6,\n",
       " 2.7,\n",
       " 2.8000000000000003,\n",
       " 2.9000000000000004,\n",
       " 3.0,\n",
       " 3.1,\n",
       " 3.2,\n",
       " 3.3000000000000003,\n",
       " 3.4000000000000004,\n",
       " 3.5,\n",
       " 3.6,\n",
       " 3.7,\n",
       " 3.8000000000000003,\n",
       " 3.9000000000000004,\n",
       " 4.0,\n",
       " 4.1000000000000005,\n",
       " 4.2,\n",
       " 4.3,\n",
       " 4.4,\n",
       " 4.5,\n",
       " 4.6000000000000005,\n",
       " 4.7,\n",
       " 4.800000000000001,\n",
       " 4.9,\n",
       " 5.0]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interimLength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4.6000000000000005, 4.7, 4.800000000000001, 4.9, 5.0]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interimLength[-5:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "51"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(interimLength)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "distanceList , VList , MList= [] , [] , []\n",
    "\n",
    "for distance in interimLength :\n",
    "    V = Ay - distance * q\n",
    "    # ------------------------------------\n",
    "    M = - (q * distance) * distance / 2 + Ay * distance\n",
    "    # ------------------------------------\n",
    "    #print( f\"at {distance}m distance V is {V}kN and M is {M}kN.m\")\n",
    "    distanceList.append( distance)\n",
    "    VList.append( V )\n",
    "    MList.append( M )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.0,\n",
       " 2.45,\n",
       " 4.8,\n",
       " 7.050000000000001,\n",
       " 9.2,\n",
       " 11.25,\n",
       " 13.200000000000001,\n",
       " 15.049999999999999,\n",
       " 16.8,\n",
       " 18.45,\n",
       " 20.0,\n",
       " 21.450000000000003,\n",
       " 22.8,\n",
       " 24.049999999999997,\n",
       " 25.199999999999996,\n",
       " 26.25,\n",
       " 27.2,\n",
       " 28.050000000000004,\n",
       " 28.8,\n",
       " 29.45,\n",
       " 30.0,\n",
       " 30.45,\n",
       " 30.800000000000004,\n",
       " 31.05,\n",
       " 31.2,\n",
       " 31.25,\n",
       " 31.199999999999996,\n",
       " 31.049999999999997,\n",
       " 30.79999999999999,\n",
       " 30.450000000000003,\n",
       " 30.0,\n",
       " 29.449999999999996,\n",
       " 28.799999999999997,\n",
       " 28.049999999999997,\n",
       " 27.20000000000001,\n",
       " 26.25,\n",
       " 25.200000000000003,\n",
       " 24.049999999999997,\n",
       " 22.799999999999997,\n",
       " 21.450000000000003,\n",
       " 20.0,\n",
       " 18.44999999999999,\n",
       " 16.799999999999997,\n",
       " 15.049999999999997,\n",
       " 13.200000000000003,\n",
       " 11.25,\n",
       " 9.199999999999989,\n",
       " 7.049999999999997,\n",
       " 4.799999999999983,\n",
       " 2.450000000000003,\n",
       " 0.0]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MList"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualization in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5.0, -25.0)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance, V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([0.0,\n",
       "  0.1,\n",
       "  0.2,\n",
       "  0.30000000000000004,\n",
       "  0.4,\n",
       "  0.5,\n",
       "  0.6000000000000001,\n",
       "  0.7000000000000001,\n",
       "  0.8,\n",
       "  0.9,\n",
       "  1.0,\n",
       "  1.1,\n",
       "  1.2000000000000002,\n",
       "  1.3,\n",
       "  1.4000000000000001,\n",
       "  1.5,\n",
       "  1.6,\n",
       "  1.7000000000000002,\n",
       "  1.8,\n",
       "  1.9000000000000001,\n",
       "  2.0,\n",
       "  2.1,\n",
       "  2.2,\n",
       "  2.3000000000000003,\n",
       "  2.4000000000000004,\n",
       "  2.5,\n",
       "  2.6,\n",
       "  2.7,\n",
       "  2.8000000000000003,\n",
       "  2.9000000000000004,\n",
       "  3.0,\n",
       "  3.1,\n",
       "  3.2,\n",
       "  3.3000000000000003,\n",
       "  3.4000000000000004,\n",
       "  3.5,\n",
       "  3.6,\n",
       "  3.7,\n",
       "  3.8000000000000003,\n",
       "  3.9000000000000004,\n",
       "  4.0,\n",
       "  4.1000000000000005,\n",
       "  4.2,\n",
       "  4.3,\n",
       "  4.4,\n",
       "  4.5,\n",
       "  4.6000000000000005,\n",
       "  4.7,\n",
       "  4.800000000000001,\n",
       "  4.9,\n",
       "  5.0],\n",
       " [25.0,\n",
       "  24.0,\n",
       "  23.0,\n",
       "  22.0,\n",
       "  21.0,\n",
       "  20.0,\n",
       "  19.0,\n",
       "  18.0,\n",
       "  17.0,\n",
       "  16.0,\n",
       "  15.0,\n",
       "  14.0,\n",
       "  12.999999999999998,\n",
       "  12.0,\n",
       "  10.999999999999998,\n",
       "  10.0,\n",
       "  9.0,\n",
       "  8.0,\n",
       "  7.0,\n",
       "  6.0,\n",
       "  5.0,\n",
       "  4.0,\n",
       "  3.0,\n",
       "  1.9999999999999964,\n",
       "  0.9999999999999964,\n",
       "  0.0,\n",
       "  -1.0,\n",
       "  -2.0,\n",
       "  -3.0000000000000036,\n",
       "  -4.0000000000000036,\n",
       "  -5.0,\n",
       "  -6.0,\n",
       "  -7.0,\n",
       "  -8.0,\n",
       "  -9.0,\n",
       "  -10.0,\n",
       "  -11.0,\n",
       "  -12.0,\n",
       "  -13.0,\n",
       "  -14.0,\n",
       "  -15.0,\n",
       "  -16.000000000000007,\n",
       "  -17.0,\n",
       "  -18.0,\n",
       "  -19.0,\n",
       "  -20.0,\n",
       "  -21.000000000000007,\n",
       "  -22.0,\n",
       "  -23.000000000000007,\n",
       "  -24.0,\n",
       "  -25.0],\n",
       " [0.0,\n",
       "  2.45,\n",
       "  4.8,\n",
       "  7.050000000000001,\n",
       "  9.2,\n",
       "  11.25,\n",
       "  13.200000000000001,\n",
       "  15.049999999999999,\n",
       "  16.8,\n",
       "  18.45,\n",
       "  20.0,\n",
       "  21.450000000000003,\n",
       "  22.8,\n",
       "  24.049999999999997,\n",
       "  25.199999999999996,\n",
       "  26.25,\n",
       "  27.2,\n",
       "  28.050000000000004,\n",
       "  28.8,\n",
       "  29.45,\n",
       "  30.0,\n",
       "  30.45,\n",
       "  30.800000000000004,\n",
       "  31.05,\n",
       "  31.2,\n",
       "  31.25,\n",
       "  31.199999999999996,\n",
       "  31.049999999999997,\n",
       "  30.79999999999999,\n",
       "  30.450000000000003,\n",
       "  30.0,\n",
       "  29.449999999999996,\n",
       "  28.799999999999997,\n",
       "  28.049999999999997,\n",
       "  27.20000000000001,\n",
       "  26.25,\n",
       "  25.200000000000003,\n",
       "  24.049999999999997,\n",
       "  22.799999999999997,\n",
       "  21.450000000000003,\n",
       "  20.0,\n",
       "  18.44999999999999,\n",
       "  16.799999999999997,\n",
       "  15.049999999999997,\n",
       "  13.200000000000003,\n",
       "  11.25,\n",
       "  9.199999999999989,\n",
       "  7.049999999999997,\n",
       "  4.799999999999983,\n",
       "  2.450000000000003,\n",
       "  0.0])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distanceList  , VList , MList"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "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(distanceList , VList , \".\")\n",
    "plt.axhline(c=\"k\")\n",
    "plt.box(False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "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(distanceList , MList, \". \")\n",
    "plt.axhline(c=\"k\")\n",
    "plt.box(False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## TASK 02- QUESTION\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=\"80%\" align=\"center\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### TASK 02- ALGORITHM\n",
    "\n",
    "Let's develop an algorithm for this problem: \n",
    "\n",
    "<img src=\"./images/week03-task02-algorithm-00.svg\"/>"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}