EQE512-Week11-Lecture.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "<h1 align=\"center\">EQE512 MATRIX METHODS IN STRUCTURAL ANALYSIS \n",
    "<br>\n",
    "<br>\n",
    "Week 11\n",
    "<br>\n",
    "<br>\n",
    "Dynamic characteristics of the systems and application in Earthquake Engineering (MDOF)</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": {
    "tags": []
   },
   "source": [
    "---\n",
    "**Today's Topics**\n",
    "\n",
    "This code is composed of three sections, namely \n",
    "\n",
    "A. Pre-process\n",
    "\n",
    "B. Process\n",
    "\n",
    "C. Post-Process\n",
    "\n",
    "---\n",
    "\n",
    "Problem: This is a multistory 2D Elastic RC frame under static loads\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A. Pre-Process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# from openseespy import *\n",
    "\n",
    "import openseespy.opensees as ops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "ops.wipe() # Clear all OS values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "ops.model( \"Basic\", \"-ndm\", 2 , \"-ndf\", 3) # This is a 2D Frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "numBay = 2\n",
    "numFloor = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "bayWidht = 3.0 # m\n",
    "storyHeight = 3.0 # m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "E = 295000000 # kN/m2\n",
    "massX = 1_000\n",
    "M = 0. \n",
    "coordTransfer = \"Linear\" # Linear Transformation\n",
    "massType = \"-lMass\" # Lumped mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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": 38,
   "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": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'C50X50': [0.25, 0.005208333333333333],\n",
       " 'B20X50': [0.1, 0.0020833333333333333]}"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Section"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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",
    "    \"\"\"\n",
    "    M = do your own calculation\n",
    "    \"\"\"\n",
    "    \n",
    "    ops.element( \"elasticBeamColumn\", eleTag ,iNode, jNode, Area, E , I , transfTag , \"-mass\", M, massType)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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": 42,
   "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",
    "        ops.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": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "for nodeNumber in floorNodes[0]:\n",
    "    ops.fix( nodeNumber , 1,1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: [1, 2, 3], 1: [4, 5, 6], 2: [7, 8, 9], 3: [10, 11, 12]}"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Rigid Diaphram Assignment\n",
    "floorNodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "for key, value in floorNodes.items():\n",
    "    for item in value[:]:\n",
    "        if item == value[0]:\n",
    "            ops.mass( item , massX , 0.000001 , 0.0000001 )\n",
    "        else: \n",
    "            ops.equalDOF( value[0] , item , 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adding columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "ops.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",
    "        eleTag += 1        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eleTag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "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\"  )\n",
    "    plt.text( node_dict[key][0] ,  node_dict[key][1] , str(key) ,  )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "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": 50,
   "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": 51,
   "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": 52,
   "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=\"gray\")\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",
    "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",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from math import asin, sqrt\n",
    "\n",
    "\n",
    "numEigen = numFloor\n",
    "eigenValues = ops.eigen( numEigen) \n",
    "\n",
    "PI = 3.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[124.4330712218822, 1488.2491250593762, 5362.067994282098]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenValues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5629784014360583\n",
      "0.16278778945291267\n",
      "0.08576172056847917\n"
     ]
    }
   ],
   "source": [
    "for i in eigenValues:\n",
    "    print( 2*3.14/(sqrt( i )))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No Model_ODB specified to plot modeshapes\n",
      "2D model\n"
     ]
    },
    {
     "data": {
      "image/png": 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tW+Z3KuQgb5bF+qJg064tJxq8MYYzLFLDGTxp4Qy+EbwZ/OjRo/1OhRzE+iIt2rXlRIPndq6kifVFWrhdcCN4/8wZPHiw36mQg1hfpEW7tpxo8N5ZMCYmxu9UyEGsL9KiXVtONHjvLFhTU+N3KuQg1hdp0a4tJxo8t3MlTawv0sLtghvBOwvm5+f7nQo5iPVFWrRry4kGzxkWaWJ9kRbO4BuBqxxIE+uLtHAVTSN4Z8GpU6f6nQo5iPVFWrRry4kG750Fk5KS/E6FHMT6Ii3ateVEg/fOgoFAwO9UyEGsL9KiXVtONHjvLFhZWel3KuQg1hdp0a4tJxq8dxZ85pln/E6FHMT6Ii3ateVEg+cMizSxvkgLZ/CNwBkWaWJ9kRbO4BvBOwump6f7nQo5iPVFWrRry4kGzzsNSRPri7TwTtZG8M6CERERfqdCDmJ9kRbt2lJt8CLSRkQWiMh2ESkWkRs0xvHOgllZWRrhqZljfZEW7doKVYn6N78B8KG19nYRaQmglcYg3lmwpKREIzw1c6wv0qJdW2oNXkQiAdwEYBIAWGtPAjipMVZZWRm2bt2K2267DdnZ2RpDOMVa63cKV5SdO3fijTfewFNPPYXbbrvN73Que6yvxisoKMCePXswdepUlf1oNGfwXQEcAvAHEekDoADAg9barxp+kYhMATAFAK677romDVRRUYH9+/ejqqoKZWVlSE5OxtKlSzFo0CDU1tYiLy8PI0aMwMaNGxEeHo4ePXpg0aJFGDFiBI4ePYqioiLccsstyMvLQ3R0NBISEjB//nz84Ac/wMGDB1FaWorBgwdjzZo1iI2NRXx8PObMmYMJEyZg9+7dqKioQP/+/ZGTk4PExES0b98eixcvxg9/+EOUlZWhqqoKGRkZ+OSTT5CcnIzIyEgsX74ct912G4qLi3HixAn07dsXy5cvR0ZGBkJDQ/HZZ59h9OjRKCoqAoCgH1NZWRkGDx6M1atXIy4uDvHx8Zg9ezZ+9KMfYffu3SgvL8eAAQOQk5ODhIQEdOjQAYsWLcIdd9yB0tJSVFdXIyMjAx9//DFSUlIQGRmJDz74ANnZ2SguLsbx48eRnp6ODz74AJmZmQgNDUVOTg7GjBmDwsJCAEBKSgqWLFmCwYMHo7a2Frm5uRg5ciQKCgrQqlUr9OjRAwsXLsTIkSNx9OhRFBYWYtiwYcjLy8M111yDxMREvP3227jttttw4MABtWOqra3FkiVL8OWXX+KLL75ASkoK3nvvPQwZMgRff/018vLy6vMODw9Hz549sXDhQowYMQI1NTXYsmULhg8fjtzcXERHRyMxMRHz5s1DdnY2Dhw4gNLSUgwZMgSrV69GbGwsunTpglmzZmHixInYtWsXKioqMGDAAKxYsQKJiYno0KEDFi5ciPHjx6O0tBRVVVXIzMzERx99hD59+iAiIgLLly9HdnY2Pv/8c5w4caL+7yIjIwMtWrTAihUrMHbs2LP+LoJ9TEOHDsWqVasQFxeHLl264K233sJdd92FXbt2oby8HAMHDsSnn36KpKQkdOjQAQsWLMCdd96J0tJSHD58GDfccAM++uijs/4ubr/9dnz++ec4fvw4AoEA3n//fWRmZqJFixb49NNPMW7cOGzZsgUA0KdPH7z77rsYOnQovv76a+Tm5mLUqFHIz89Hq1at0LNnTyxYsOCs+ho+fDjWrVuHtm3bIjExEXPnzsXtt9+OAwcOoKSkJOjHtGTJErRqpXJhAwAgWmdbEQkAyAXQ31qbJyK/AXDUWvvE+b4nEAjYpmx8v2jRIsyaNQsvvPACn5tJQXfjjTdixowZiI+PZ31RUK1ZswY//elP8c477zS5tkSkwFp7zs1sNN9kLQdQbq3Nq/t4AYC+GgMZY3D69GluBkUqWF+kRbu21Bq8tfZPAPaJSLe6T90M4HONsbwfEm8lJw3GGJw6dYr1RUGnXVva6+D/DcBsESkEkApgusYg3g+Jt5KTBm8CwfqiYAsJCVGtLdVlktbazQDU/13r/ZA4wyINrC/Son31wYk7WTnDIk2sL9KiXVtONXhuBkUaWF+kRbu2nGrw3AyKNLC+SIt2bTnV4LkZFGlgfZEW7dpyqsFzMyjSwPoiLdq15VSD52ZQpIH1RVq0a8upBq+xWQ8R64u0aNeWUw2eSAPri7Ro15ZTDZ4zLNLA+iItnME3gvdDSkpK8jsVchDri7Ro15ZTDX7ZsmV+p0IOYn2RFu3acqrB19TU+J0KOYj1RVq0a8upBj9lyhS/UyEHsb5Ii3ZtOdXgCwoK/E6FHORtR836omDTri1nGvypU6fwyCOP+J0KOcibQLC+KNi8rai1asuJBu/9kPi8TNLA+iIt3uRBq7acaPCcYZEm1hdp0a4tpxo8Z1ikgfVFWjiDbwTvh5Sfn+93KuQg1hdp0a4tpxo8d/sjDawv0sLdJBuBe4WQJtYXaeFeNI3g/ZBycnL8ToUcxPoiLdq15VSD552GpIH1RVp4J2sjeD+kQCDgdyrkINYXadGuLacaPGdYpIH1RVpEBAAwefJklfjnbfAi8oGIxKuMGmR86j1pYn2RJmOMWm191wz+dQAficjPRaSFyuhB4v0CVlZW+p0KOYj1RZqMMdi7d69O7PO9YK2dDyANQCSAfBF5VEQe9v6oZNNEXOVAmlhfpMkY49sqmq8BfAUgDEDEN/5cNrxfwJkzZ/qdCjmI9UWajDF45ZVXVGKHnu8FEfk+gGcBLAHQ11p7XCWDIPC2C166dKnfqZCDWF+kyRiD+fPn68T+jtd+DuAfrbWPXc7NHfjbDGvChAl+p0IO8rYLZn2RhpCQENxzzz0qsc87g7fWDlQZUYH3C5iVleV3KuQgbwLB+iINxhgMHz5cJ7ZK1EuMM3jSxPoiTcYYZGdn68RWiXqJeb+A3k0DRMHE+iJNxhhER0frxFaJeol5v4DWWr9TIQexvkiTMQYHDhzQia0StQERCRGRTSKyTHEMAMDs2bO1hqBmzGvwc+bM8TsVcpAxBgsWLNCJrRL1bA8CKNYexBjDZWykwmvwy5apzVGoGTPG4KOPPtKJrRK1jojEARgFQGcVfwPGGLz11lvaw1AzxBk8aTLG4IUXXtCJrRL1b34N4KcATp/vC0Rkiojki0j+oUOHmjyQMQZjx45t8vcTnY/X4EePHu13KuQgYwwmTZqkE1slKgARyQJw0Fpb8F1fZ62daa0NWGsD7dq1a/J4xhj8+Mc/bvL3E50PtwsmTcYYjB8/Xie2StQz+gMYIyK7AcwDMFREZmkNZozBgAEDtMJTM+Y1+MGDB/udCjnIGIPrr79eJ7ZKVADW2p9Za+OstfEAxgP41Fo7UWs8YwwSEhK0wlMz5jX4mJgYv1MhBxljcMMNN+jEVonqA2MMKioq/E6DHOQ1+JqaGr9TIQcZY7Bp0yad2CpRv8Fam2OtVd3IwxiD1157TXMIaqa4XTBpMsZg3rx5OrFVovpA8yxIzZvX4PPz8/1OhRxkjEFRUZFK7PPuJnmlMcZgxowZfqdBDvL2g//DH/7gdyrkIGMM/uu//ksntkpUH4SEhGDcuHF+p0EO8raj5ioa0qC5H7wzDd4Yg4cfvqweFUuO8C7RTJ061e9UyEHGGNx33306sVWi+sAYg/j4eL/TIAd5DT4pKcnvVMhBxhh06tRJJ7ZKVB8YYzBq1Ci/0yAHeQ0+EAj4nQo5yBiDiRN1bhFyqsHn5eX5nQY5yGvwlZWVfqdCDjLG4P3339eJrRLVB8YYrlMmFV6Df+aZZ/xOhRxkjMGsWTq7uDjV4P/0pz/5nQY5iDN40mSMwcXspPudsVWi+sAYg8cee8zvNMhBnMGTJmMM7r//fp3YKlF9YIzBD37wA7/TIAd5DT49Pd3vVMhBxhj85Cc/0YmtEtUHxhiuUyYV3IuGNBlj8Mgjj+jEVonqA2MMwsPD/U6DHOQ1+IiICL9TIQcZY3DVVVfpxFaJ6gPN61jUvHkNPitLdUNUaqaMMXj88cd1YqtE9YExBu+9957faZCDvAZfUlLidyrkIM2tzp3ZTXLfvn2455578MMf/tDvVMgxa9euxYYNG3DzzTfj5ptv9jsdckxhYSF+9atf4dZbbw167JDL6Y3JmTNnTm3qg41/8Ytf4NixY6iursa1116L5557DrGxsTh48CBmzZqFnj174oMPPkBFRQXatm2LGTNmICEhAXv27MHChQvRrVs3vPvuu6iurkZUVBSmT5+O5ORkFBcXY/ny5UhISMD8+fNx/PhxXH311Zg2bRr69euHjRs3IicnB126dMGsWbNgrUXLli3xy1/+Eunp6cjLy0Nubi6uu+46vPbaawgPD0dtbS2ee+45pKamYtWqVdiyZQtiY2Px0ksv4ZprrkFNTQ1efvllJCcn45NPPkFpaSmPycdj6tChA3bu3IlDhw6hpqYGHTt2xHPPPYe4uDgcOnQIs2bNQq9evbB8+XJUVFSgffv29Xnv3bsXixYtQvfu3fHee++huroa0dHRmD59OlJSUrB9+3Z8+OGHSExMxDvvvIMTJ06gTZs2mDZtGjIyMrBp0yZ89tln6Nq1K2bPng0ACAsLwy9/+UsEAgHk5eVh/fr16Ny5c33ep06dwvPPP4+0tDSsWrUKRUVFiIuLw0svvYTo6GgcO3YML7/8MlJSUvDHP/4RZWVlPCYfj6lFixaIjo7GpEmTmtT7pk2btn/q1KnnXAEg1tomBdUQCARsUx+q0K9fP0ydOpX70VDQffbZZ3jiiScwb948PpeVgm706NHIzs5ucoMXkQJr7Tk3SnLmGryI4J/+6Z/8ToMcJCKw1nKzMVIhImpbnTvT4I0xWLZsmd9pkIOMMbDWcqsCUqH5JqszDV5E6q99EQWTiHCrAlIjInj33XdVYjvT4DU37KHmjTN40mSMQVVVlU5slag+EBHe6EQqOIMnTSKCu+++WyW2Mw1ec8Meat68N1m52RhpEBH8x3/8h0psZxq8iKht2EPNm3eJhpuNkQZjDCZPnqwTWyWqD0SEm42RCu8SDTcbIw0igrCwMJXYzjR4zQ17qHnzZvDcbIw0GGPwq1/9Sie2SlQfiAhef/11v9MgB3kzeG42RhpEBDNmzFCJ7UyDN8bgjTfe8DsNcpD3JuvltG8TuUNEsHDhQpXYzjR475eQKNi8SzREGozRa8NONfiJEyf6nQY5yLtEwxk8aRARjB07ViW2Mw2e6+BJizeDT0pK8jsVcpAxhuvg/x4RwZNPPul3GuQgbwbPzexIg4jggQceUIntTIM3xuD48eN+p0EO8t7fqamp8TsVcpCI4C9/+YtKbGcavIjg+eef9zsNcpB3iaapTxsj+i7GGLz55ps6sVWiAhCRTiKyQkSKRWSbiDyoNRZw5of07LPPag5BzZR3iaagoMDvVMhBIqJ2k6bmDL4WwCPW2h4AMgHcLyI9tQYTEbz66qta4akZ82bw3OuINBhj8M477+jEVokKwFq731q7se7/awAUA4jVGk9EcM0112iFp2bMm8HzeaykQUQQGRmpEvuSXIMXkXgAaQDyzvHaFBHJF5H8i3lghzEGo0ePbvL3E52P9yYrZ/CkQURw8803q8RWb/Ai8j0ACwE8ZK09+s3XrbUzrbUBa22gXbt2FzMO7r333ovIlOjcvEs0nMGTBs2NElUbvIi0wJnmPttau0hzLGMMnnrqKc0hqJnyLtHk5+f7nQo5SETw6KOPqsTWXEUjAF4FUGytVV/eIiJ8Ziap8Gbw3E2SNBhjcODAAZ3YKlHP6A/gLgBDRWRz3Z+RWoMZY7BgwQKt8NSMcS8a0iQi+PDDD1Vih6pEBWCtXQ1AtOJ/k4jg5z//+aUajpoRbwafk5PjdyrkIGMM/vVf/1UntkpUH4gIXnnlFb/TIAd5M3jeyUoaRATz589Xie1MgzfGoEuXLn6nQQ7ylkkGAgG/UyEHiQhiY3VuEXKmwYsIBg0a5Hca5CDuRUOajDHIyMjQia0S1QfGGNx3331+p0EO8i7RRERE+J0KOUhE8MQTT6jEdqbBiwg3GyMV3gyey3BJgzEGP/vZz3Riq0T1gYiguLjY7zTIQd4MnqtoSIOIYOfOnSqxnWnwxhisXLnS7zTIQd6brDNnzvQ7FXKQiB6Lf2YAAAh4SURBVGDDhg0qsZ1p8CKC+++/3+80yEHeJZqlS5f6nQo5yBiDH/3oRzqxVaL6wBjDdfCkwrtEM2HCBL9TIQdxHXwjiAh69+7tdxrkIG8Gn5WV5Xcq5CBjDJKSknRiq0T1gTGGN6KQCs7gSZOIoFevXiqxnWnwvAZPWrw3Wc9skEoUXCKC//7v/1aJ7VSDf+655/xOgxzkXaKx1vqdCjnIGKO2UaIzDd4Yo7bUiJo37xLNnDlz/E6FHCQiKCoqUontTIMXEWzdutXvNMhB3gx+2bJlfqdCDjLGoLS0VCe2SlQfGGNw1113+Z0GOYgzeNIkIhg9erRKbGcavIjg5Zdf9jsNcpD3JqvWLyE1byKi9jQ6pxp8Zmam32mQg7hdMGkyxqBPnz46sVWi+oAP/CAt3vJIPm+ANPCBH40gIvif//kfv9MgR4kIYmJi/E6DHGSMwe9//3ud2CpRfWCMwbRp0/xOgxwlIjhy5IjfaZCDRIQP3f57RAS5ubl+p0GO4pv4pIXr4BvBGIOKigq/0yBHGWOQn5/vdxrkIGMMDhw4oBNbJaoPRARjxozxOw1ylIjgxRdf9DsNcpCIYPDgwSqxnWrwr776qt9pkKOMMRg2bJjfaZCDjDFYvHixTmyVqD4wxmDIkCF+p0GOEhE8/vjjfqdBDhIRta3OnWnwIoKoqCi/0yBHiQgSEhL8ToMcJCKIjIxUie1MgzfGcJUDqTHGYODAgX6nQQ4yxmDRokU6sVWi+kBE8OCDD/qdBjlKRLBjxw6/0yAHiYja08KcafDGGK6DJzXGGDz//PN+p0EOMsagsLBQJ7ZKVB+ICI4ePep3GuQoEUFlZaXfaZCDRARfffWVSmynGvzQoUP9ToMcpfncTGreRAT9+vVTie1MgzfG4PXXX/c7DXKUMYYTCFJhjMGSJUt0YqtE9YGIYPjw4X6nQY4SEcyYMcPvNMhBms+ycKbBG2PQokULv9MgRxlj0Lp1a7/TIAcZYxAaGqoTWyVqHRH5vojsEJEyEXlMeSy1taREIoKJEyf6nQY5SESwYsUKldhqDV5EQgC8CGAEgJ4A7hSRnorjYdKkSVrhqZkzxmD16tV+p0EOMsYgKytLJ7ZK1DOuB1Bmrf3CWnsSwDwAY7UGM8Zg3bp1WuGpmeM1eNIiIlfkOvhYAPsafFxe97mziMgUEckXkfxDhw41ebChQ4eiR48eTf5+ou8yffp0XHXVVX6nQQ4KBAJIS0tTiS3WWp3AIv8I4FZr7b11H98F4Hpr7b+d73sCgYDlQxWIiBpPRAqstefcjlJzBl8OoFODj+MA8FZAIqJLRLPBbwCQKCJdRKQlgPEAdFbzExHRt+gsvgRgra0Vkf8D4P8BCAHwmrV2m9Z4RER0NrUGDwDW2g8AfKA5BhERnZszd7ISEdHZ2OCJiBzFBk9E5Cg2eCIiR6nd6NQUInIIwJ6LCNEWwOEgpeM3V47FleMA3DkWV44DcOdYLuY4Oltr253rhcuqwV8sEck/3x1dVxpXjsWV4wDcORZXjgNw51i0joOXaIiIHMUGT0TkKNca/Ey/EwgiV47FleMA3DkWV44DcOdYVI7DqWvwRET0N67N4ImIqA4bPBGRo5xp8JfyAd+aROQ1ETkoIlv9zuViiEgnEVkhIsUisk1EHvQ7p6YQkatEZL2IbKk7jml+53QxRCRERDaJyDK/c7kYIrJbRIpEZLOIXNFPCRKRNiKyQES21/2+3BC02C5cg697wHcJgGE486CRDQDutNZ+7mtiTSAiNwE4BuBNa21vv/NpKhHpCKCjtXajiEQAKAAw7kr7OxERAdDaWntMRFoAWA3gQWttrs+pNYmIPAwgACDSWqvzpOdLQER2AwhYa6/4m5xE5A0Aq6y1r9Q9O6OVtfZIMGK7MoO/pA/41mStXQmg2u88Lpa1dr+1dmPd/9cAKMY5nsl7ubNnHKv7sEXdnytyViQicQBGAXjF71zoDBGJBHATgFcBwFp7MljNHXCnwTfqAd/kDxGJB5AGIM/fTJqm7rLGZgAHAXxsrb0ijwPArwH8FMBpvxMJAgvgIxEpEJEpfidzEboCOATgD3WXzl4RkdbBCu5Kg5dzfO6KnGW5RkS+B2AhgIestUf9zqcprLWnrLWpOPNc4etF5Iq7dCYiWQAOWmsL/M4lSPpba/sCGAHg/rpLm1eiUAB9AfzOWpsG4CsAQXsP0ZUGzwd8X4bqrlkvBDDbWrvI73wuVt0/nXMAfN/nVJqiP4Axddeu5wEYKiKz/E2p6ay1lXX/PQhgMc5cpr0SlQMob/CvwgU40/CDwpUGzwd8X2bq3px8FUCxtfZZv/NpKhFpJyJt6v4/HMAtALb7m9WFs9b+zFobZ62Nx5nfj0+ttRN9TqtJRKR13Rv3qLucMRzAFbnqzFr7JwD7RKRb3aduBhC0hQiqz2S9VFx6wLeIzAUwGEBbESkH8KS19lV/s2qS/gDuAlBUd/0aAB6ve07vlaQjgDfqVmoZAPOttVf0EkMHdACw+MwcAqEA5lhrP/Q3pYvybwBm101OvwBwT7ACO7FMkoiIvs2VSzRERPQNbPBERI5igycichQbPBGRo9jgiYgcxQZPdB51O2LuEpFr6j6Oqvu4s9+5ETUGGzzReVhr9wH4HYBf1H3qFwBmWmv3+JcVUeNxHTzRd6jbbqEAwGsAJgNIq9uxlOiy58SdrERarLVfi8j/BfAhgOFs7nQl4SUaor9vBID9AK64XSSpeWODJ/oOIpKKM08KywTw73VPqiK6IrDBE51H3Y6Yv8OZvez3AngawAx/syJqPDZ4ovObDGCvtfbjuo9/C6C7iAzyMSeiRuMqGiIiR3EGT0TkKDZ4IiJHscETETmKDZ6IyFFs8EREjmKDJyJyFBs8EZGj/j8sEXvEVQsoCQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No Model_ODB specified to plot modeshapes\n",
      "2D model\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 432x288 with 1 Axes>,\n",
       " <matplotlib.axes._subplots.AxesSubplot at 0x180d084a850>)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import openseespy.postprocessing.Get_Rendering as opsplt\n",
    "\n",
    "opsplt.plot_modeshape(1, 1) # 1st Mode Shape\n",
    "opsplt.plot_modeshape(2, 1) # 2nd Mode Shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "**Now think of the eigenvector**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.0, -0.02036774434028256, -0.016687209756683582, 0.017512624617944637]\n"
     ]
    }
   ],
   "source": [
    "mode_shape = []\n",
    "for i in [1,4,7,10]:\n",
    "    value = ops.nodeEigenvector( i , 2 )[0]\n",
    "    mode_shape.append( value)\n",
    "print( mode_shape )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x180d19b8d60>]"
      ]
     },
     "execution_count": 58,
     "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(  mode_shape , range( len(mode_shape)) ,  marker = \"o\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem  : \n",
    "\n",
    "Determine the base shear force due to seismic actions for each cases : \n",
    "\n",
    "1. Equivalent Seismic Load (ESL)\n",
    "\n",
    "2. Response Spectrum Loading (RSL)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Equivalent Seismic Load (ESL)\n",
    "\n",
    "You need the first mode period value & spectral shape & you need the mass of the system\n",
    "\n",
    "$$  V_{base} = S_{ae}(T_1) \\times Mass$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.\n",
    "\n",
    "$S_{ae}(T_1)$ comes from the spectrum.\n",
    "\n",
    "<img src=\"https://pbs.twimg.com/media/Elwb7NFWMAwRvin?format=jpg&name=medium\" width = 500>\n",
    "\n",
    "You need the values of the spectrum. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Mass\n",
    "\n",
    "How to calculate the mass?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming you have the base shear values: \n",
    "$$ F_i = V_{base} \\times \\frac{H_i}{\\sum H_i }$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the load "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "ops.timeSeries( \"Linear\" , 1 )\n",
    "\n",
    "ops.pattern( \"Plain\"  , 1 , 1)\n",
    "\n",
    "load_dict = { nodes_ : f_i }\n",
    "\n",
    "for key , value in load_dict.items():\n",
    "    ops.load( key , value , 0 ,0 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ops.integrator('LoadControl', 1.0)\n",
    "ops.algorithm('Linear')\n",
    "ops.analysis('Static')\n",
    "analysis_resut = ops.analyze(1)\n",
    "\n",
    "if analysis_resut == 0 : \n",
    "    print( \"Analysis complete\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "scale = 10\n",
    "node_deform_dict = {}\n",
    "for i in node_dict.keys():\n",
    "    node_deform_dict[i] = [node_dict[i][0] + scale*(ops.nodeDisp(i,1)) , node_dict[i][1]]\n",
    "#    print( f\"{i} node disp = {round( ops.nodeDisp(i,1),5)}\")\n",
    "\n",
    "plt.figure(figsize= (5,5))\n",
    "for key in node_dict.keys():\n",
    "    plt.plot( node_dict[key][0] ,  node_dict[key][1] , \"o\" , MS = 10 , color=\"gray\")\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=\"gray\")\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=\"gray\")\n",
    "\n",
    "for key in node_deform_dict.keys():\n",
    "    plt.plot( node_deform_dict[key][0] ,  node_deform_dict[key][1] , \"o\" , MS = 10 , color=\"b\")\n",
    "for key in column_dict.keys():\n",
    "    plt.plot([ node_deform_dict[column_dict[key][0]][0] ,node_deform_dict[column_dict[key][1]][0]],\n",
    "              [ node_deform_dict[column_dict[key][0]][1] ,node_deform_dict[column_dict[key][1]][1]]  \n",
    "            , color=\"b\")\n",
    "for key in beam_dict.keys():\n",
    "    plt.plot([ node_deform_dict[beam_dict[key][0]][0] ,node_deform_dict[beam_dict[key][1]][0]],\n",
    "              [ node_deform_dict[beam_dict[key][0]][1] ,node_deform_dict[beam_dict[key][1]][1]] \n",
    "            , color=\"b\")\n",
    "plt.box(False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Response Spectrum Loading (RSL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.\n",
    "\n",
    "$S_{ae}(T_1)$ comes from the spectrum.\n",
    "\n",
    "<img src=\"https://pbs.twimg.com/media/Elwb7NFWMAwRvin?format=jpg&name=medium\" width = 500>\n",
    "\n",
    "You need the values of the spectrum. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Mass\n",
    "\n",
    "How to calculate the mass?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming you have the base shear values: \n",
    "\n",
    "For each mode case:\n",
    "\n",
    "Obtain the Base shear and multipyle with the  modal shape values\n",
    "$$ \\{F_i\\}_{m\\times 1} = \\{V_{base}(T_m)\\}_{1\\times1} \\times \\{\\phi_m\\}_{m\\times 1}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the loads for each modal values "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in mode_number : \n",
    "    ops.timeSeries( \"Linear\" , 1 )\n",
    "\n",
    "    ops.pattern( \"Plain\"  , 1 , 1)\n",
    "\n",
    "    load_dict = { nodes_ : f_i }\n",
    "\n",
    "    for key , value in load_dict.items():\n",
    "        ops.load( key , value , 0 ,0 )\n",
    "\n",
    "    ops.integrator('LoadControl', 1.0)\n",
    "    ops.algorithm('Linear')\n",
    "    ops.analysis('Static')\n",
    "    analysis_resut = ops.analyze(1)\n",
    "\n",
    "    if analysis_resut == 0 : \n",
    "        print( \"Analysis complete\")\n",
    "        \n",
    "    # end of every analysis, store the results in the dictionaries: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modal Superposition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CQC, SRSS ..."
   ]
  },
  {
   "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": [
    "---\n",
    "\n",
    "**NEXT WEEK**\n",
    "The topics for the next week \n",
    "\n",
    "- Loads and solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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