EQE512-Week11-Lecture.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "EQE512 MATRIX METHODS IN STRUCTURAL ANALYSIS \n",
    "\n",
    "---\n",
    "<h3 align=\"center\"><font color = red >Week 11 - Frame Systems - Dynamic Properties </font></h3> \n",
    "\n",
    "<h4 align=\"center\"><font color = blue >Dr. Ahmet Anıl Dindar (adindar@gtu.edu.tr)</font></h4> \n",
    "<h4 align=\"center\"><font color = green >2020 Fall</font></h4> \n",
    "\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Let's calculate the modal parameters of the given MDOF system**\n",
    "\n",
    "<center><img src=\"./figures/15-EQE512-Week12-MDOF_Frame-Generic.PNG\" width=25% , alignment = \"center\"> </img><\\center>\n",
    "\n",
    "This code is composed of two (2) main parts, namely \n",
    "\n",
    "1- Hand Calculation\n",
    "\n",
    "2- OpenSeesPy\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hand Calculations\n",
    "<center><img src=\"./figures/15-EQE512-Week12-MDOF_Frame-Values.PNG\" width=40% , alignment = \"center\"> </img><\\center>\n",
    "\n",
    "Material is C25 ($E = 32GPA$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "E = 32_000_000 # kN/m2\n",
    "\n",
    "conc_weight = 25 # kN/m\n",
    "\n",
    "UDL = 10 # kN/m\n",
    "\n",
    "g = 9.81 # m7s2\n",
    "\n",
    "# *********************** GEOMETRY\n",
    "L , H1 , H2 , h_beam , b_beam, h_col , b_col = 5 , 3 , 3, 0.5 , 0.2 , 0.5 , 0.5 # m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mass Matrix**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load on beam\n",
    "beam_load = UDL * L\n",
    "beam_sw = ( h_beam * b_beam * L) * conc_weight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load on columns\n",
    "column_sw = (h_col * b_col * H1) * conc_weight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Mass of stories\n",
    "M1 = ( 4 * column_sw / 2 + beam_load + beam_sw) / g\n",
    "M1 = round( M1 ,2)\n",
    "\n",
    "M2 = ( 2 * column_sw / 2 + beam_load + beam_sw) / g\n",
    "M2 = round( M2 ,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[10.19  0.  ]\n",
      " [ 0.    8.28]]\n"
     ]
    }
   ],
   "source": [
    "# CONSTRUCT THE MASS MATRIX\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "Mass_sys = np.array( [[ M1, 0] , [ 0, M2]])\n",
    "\n",
    "print( Mass_sys)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Stiffness Matrix**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "Mom_inertia = (b_col * h_col **3 ) / 12\n",
    "\n",
    "K1 = 2 * (( 12 * E * Mom_inertia)/ ( H1**3))\n",
    "K1 = round( K1 ,0)\n",
    "\n",
    "K2 = 2 * (( 12 * E * Mom_inertia)/ ( H2**3))\n",
    "K2 = round( K2 ,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 296296. -148148.]\n",
      " [-148148.  148148.]]\n"
     ]
    }
   ],
   "source": [
    "# CONSTRUCT THE SYSTEM STIFFNESS MATRIX\n",
    "K_sys = np.array( [[K1 + K2 , -K2],[-K2 , K2]])\n",
    "\n",
    "print( K_sys)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Calculation of the Natural Circular Frequencies**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<center><img src=\"./images/EQE512-Week11-NaturalFrequencies.png\" width=25% , alignment = \"center\"> </img><\\center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 29077.13444553 -14538.56722277]\n",
      " [-17892.2705314   17892.2705314 ]]\n"
     ]
    }
   ],
   "source": [
    "# Calculation of natural circular frequencies\n",
    "\n",
    "w2 = np.dot( np.linalg.inv( Mass_sys) , K_sys)\n",
    "\n",
    "print( w2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculaiton of mode shape vectors and values\n",
    "\n",
    "V , D = np.linalg.eigh( w2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4738.80587179, 42230.59910515])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.59231397, -0.80570724],\n",
       "       [-0.80570724,  0.59231397]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[68.83898511590421, 205.50084940249792]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = [ item**0.5 for item in V]\n",
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 Mode Period is 0.09sec.\n",
      "2 Mode Period is 0.03sec.\n"
     ]
    }
   ],
   "source": [
    "T = [ round( 2* (22/7) / item ,2)  for item in w]\n",
    "for count, item in enumerate( T ) :\n",
    "    print( f\"{count+1} Mode Period is {item}sec.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "for mode_no , mode_shape in enumerate( D ):\n",
    "    \n",
    "    vector = list(D[:][mode_no])\n",
    "    vector.insert(0,0)\n",
    "    plt.subplot( 1,len(Mass_sys), mode_no + 1)\n",
    "    plt.plot( vector , range(len(Mass_sys)+1) , \"o-\" , MS = 10)\n",
    "    plt.plot( [0 for item in range( len(Mass_sys)+1) ], range(len(Mass_sys)+1) , \"o--\" , MS = 10 ,color=\"gray\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# OPENSEESPY"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "---\n",
    "\n",
    "### <center>2- OpenSeesPy Modeling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from openseespy import *\n",
    "\n",
    "import openseespy.opensees as os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "os.wipe() # Clear all OS values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "os.model( \"Basic\", \"-ndm\", 2 , \"-ndf\", 3) # This is a 2D Frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "numBay = 1\n",
    "numFloor = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "bayWidht = 5.0 # m\n",
    "storyHeight = 3.0 # m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "E = 32000000 # kN/m2\n",
    "massX = 5 * 2 # we'll discuss\n",
    "M = 0. \n",
    "coordTransfer = \"Linear\" # Linear Transformation\n",
    "massType = \"-lMass\" # Lumped mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "beams = [ \"B20X50\" for item in range( numFloor)]\n",
    "eColumn = [ \"C50X50\" for item in range( numFloor)]\n",
    "iColumn = [ \"C50X50\" for item in range( numFloor)]\n",
    "\n",
    "columns = [eColumn , iColumn , eColumn]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "Section = { \"C50X50\" : [ 0.5 * .5 , (0.5*0.5**3)/12],\n",
    "          \"B20X50\": [0.2*.5 , (.2*0.5**3)/12]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'C50X50': [0.25, 0.005208333333333333],\n",
       " 'B20X50': [0.1, 0.0020833333333333333]}"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Section"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ElasticBeamColum( eleTag, iNode, jNode, sectType, E, transfTag, M, massType) :\n",
    "    \n",
    "    prop = Section[sectType]\n",
    "    Area = prop[0]\n",
    "    I = prop[1]\n",
    "    \n",
    "    os.element( \"elasticBeamColumn\", eleTag ,iNode, jNode, Area, E , I , transfTag , \"-mass\", M, massType)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "axis_h = np.linspace( 0 , (numBay * bayWidht)  ,numBay+1)\n",
    "axis_v = np.linspace( 0 , (numFloor * storyHeight)  ,numFloor+1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "node_no =  1\n",
    "node_dict = {}\n",
    "floorNo = 0\n",
    "floorNodes = {}\n",
    "nodes = []\n",
    "for i in axis_v:\n",
    "    floorNodes[floorNo] = []\n",
    "    \n",
    "    for j in axis_h:\n",
    "        nodes.append(node_no)\n",
    "\n",
    "        # OPENSEES COMMAND\n",
    "        os.node( node_no , float(j) , float(i))\n",
    "        \n",
    "        node_dict[node_no] = [float(j) , float(i)]\n",
    "        floorNodes[floorNo].append(node_no)\n",
    "        \n",
    "        \n",
    "        node_no += 1\n",
    "    floorNo += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "for nodeNumber in floorNodes[0]:\n",
    "    os.fix( nodeNumber , 1,1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: [1, 2], 1: [3, 4], 2: [5, 6]}"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Rigid Diaphram Assignment\n",
    "floorNodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "for key, value in floorNodes.items():\n",
    "    for item in value[:]:\n",
    "        if item == value[0]:\n",
    "            os.mass( item , massX , 0.0000000001 , 0.0000000001 )\n",
    "        else: \n",
    "            os.equalDOF( value[0] , item , 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "os.geomTransf(coordTransfer, 1)\n",
    "column_dict = {}\n",
    "eleTag = 1 \n",
    "for  j in range(0 , numBay + 1):\n",
    "    end1 = j + 1\n",
    "    end2 = end1 + numBay + 1\n",
    "    thisColumn = columns[j]\n",
    "    \n",
    "    for i in range( 0 ,numFloor):\n",
    "        secType = thisColumn[ i]\n",
    "        ElasticBeamColum( eleTag, end1 , end2 , secType , E , 1, M , massType)\n",
    "        column_dict[eleTag] = [end1, end2]\n",
    "        end1 =end2\n",
    "        end2 += numBay + 1\n",
    "\n",
    "        \n",
    "        eleTag += 1\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "for key in node_dict.keys():\n",
    "    plt.plot( node_dict[key][0] ,  node_dict[key][1] , \"o\"  )"
   ]
  },
  {
   "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": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "for key in column_dict.keys():\n",
    "    plt.plot([ node_dict[column_dict[key][0]][0] ,node_dict[column_dict[key][1]][0]],\n",
    "              [ node_dict[column_dict[key][0]][1] ,node_dict[column_dict[key][1]][1]]  )\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "beam_dict = {}\n",
    "for j in range( 1 , numFloor +1):\n",
    "    end1 = (numBay + 1) * j + 1\n",
    "    end2 = end1+1\n",
    "    secType = beams[j -1 ]\n",
    "    for i in range(0, numBay):\n",
    "        ElasticBeamColum(eleTag, end1, end2, secType, E, 1, M, massType) \n",
    "        beam_dict[eleTag] = [end1, end2]\n",
    "        end1 = end2\n",
    "        end2 = end1 + 1\n",
    "        eleTag += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "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": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "for key in beam_dict.keys():\n",
    "    plt.plot([ node_dict[beam_dict[key][0]][0] ,node_dict[beam_dict[key][1]][0]],\n",
    "              [ node_dict[beam_dict[key][0]][1] ,node_dict[beam_dict[key][1]][1]]  )\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize= (5,5))\n",
    "\n",
    "\n",
    "for key in node_dict.keys():\n",
    "    plt.plot( node_dict[key][0] ,  node_dict[key][1] , \"o\" , MS = 10 , color=\"blue\")\n",
    "    plt.text(node_dict[key][0] ,  node_dict[key][1] , key , fontsize=20 , color=\"blue\" )\n",
    "    \n",
    "for key in column_dict.keys():\n",
    "    plt.plot([ node_dict[column_dict[key][0]][0] ,node_dict[column_dict[key][1]][0]],\n",
    "              [ node_dict[column_dict[key][0]][1] ,node_dict[column_dict[key][1]][1]]  \n",
    "            , color=\"red\")\n",
    "    plt.text(0.5*( node_dict[column_dict[key][0]][0] + node_dict[column_dict[key][1]][0]),\n",
    "             0.5*(node_dict[column_dict[key][0]][1] + node_dict[column_dict[key][1]][1]), key , fontsize=22 ,color=\"r\" , horizontalalignment=\"right\")\n",
    "    \n",
    "for key in beam_dict.keys():\n",
    "    plt.plot([ node_dict[beam_dict[key][0]][0] ,node_dict[beam_dict[key][1]][0]],\n",
    "              [ node_dict[beam_dict[key][0]][1] ,node_dict[beam_dict[key][1]][1]] \n",
    "            , color=\"k\")\n",
    "    plt.text(0.5*( node_dict[beam_dict[key][0]][0] + node_dict[beam_dict[key][1]][0]),\n",
    "             0.5*(node_dict[beam_dict[key][0]][1] + node_dict[beam_dict[key][1]][1]), key , fontsize=24 , color = \"k\" , verticalalignment=\"center\")\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "numEigen = 2 \n",
    "eigenValues = os.eigen( numEigen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1422.5997276161331, 23907.01437626409]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenValues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 Mode Period is 0.00442sec.\n",
      "2 Mode Period is 0.00026sec.\n"
     ]
    }
   ],
   "source": [
    "T_ospy = [ round( 2* (22/7) / item ,5)  for item in eigenValues]\n",
    "for count, item in enumerate( T_ospy ) :\n",
    "    print( f\"{count+1} Mode Period is {item}sec.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.00442, 0.00026]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T_ospy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**=> It seems the values are different. Why?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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=\"40%\">\n",
    "</td>\n",
    "<td align=\"left\"><strong style=\"font-size: 20px;\">\n",
    "The topics for the next week \n",
    "<br><br>\n",
    "\n",
    "1- Assignment : 4\n",
    "    \n",
    "2- System behavior\n",
    "<br><br>\n",
    "\n",
    "<br>\n",
    "</td>\n",
    "</tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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