EQE512-Week10-InClass.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 10 - OpenSeesPy - Frame Systems - InClass </font></h3> \n",
    "\n",
    "<h4 align=\"center\">Dr. Ahmet Anıl Dindar (adindar@gtu.edu.tr)</h3> \n",
    "<h4 align=\"center\">2020 Fall  </h4> \n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A. Pre-Process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "metadata": {},
   "outputs": [],
   "source": [
    "import openseespy.opensees as ops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Clear all variables inthe domain\n",
    "ops.wipe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the degree of freedom and model\n",
    "ops.model(\"Basic\",\"-ndm\",2 , \"-ndf\" , 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 381,
   "metadata": {},
   "outputs": [],
   "source": [
    "numBay = 1 # Two beams at each floor \n",
    "numFloor = 3 # Seven stories building"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 382,
   "metadata": {},
   "outputs": [],
   "source": [
    "bayWidth = 3.0 # m\n",
    "storyHeight = 3.0 # m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 383,
   "metadata": {},
   "outputs": [],
   "source": [
    "E = 29_500_500 # kN/m2\n",
    "massX = 0.49 # units must be consistent\n",
    "M = 0. # Lookout for the value below !!!!!!\n",
    "massType = \"-lmass\" # Lumped Mass required in OpenSees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 384,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Members in the system\n",
    "beams = [ \"B20X50\" for item in range( numFloor)] # List \n",
    "eColumn = [ \"C50X50\" for item in range( numFloor)]\n",
    "icolumn = [ \"C50X50\" for item in range( numFloor)]\n",
    "\n",
    "columns = [ eColumn, iColumn, eColumn]\n",
    "columns = [ eColumn, eColumn]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 385,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sections of the members\n",
    "Section = { \"C50X50\": [ 0.5*0.5 , round( (0.5 * 0.5**3)/12, 5) ],\n",
    "          \"B20X50\" : [0.2*.5 , round( (0.2* 0.5**3)/12,5)]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 386,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'C50X50': [0.25, 0.00521], 'B20X50': [0.1, 0.00208]}"
      ]
     },
     "execution_count": 386,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Section"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 387,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a Function in Definition of the Members\n",
    "\n",
    "def ElasticBeamColumn( eleTag, iNode, jNode, secType, E , transfTag , M , MassType):\n",
    "    prop = Section[ secType]\n",
    "    Area = prop[0]\n",
    "    I = prop[1]\n",
    "    \n",
    "    # OpenSees command in creation of the member\n",
    "    ops.element( \"elasticBeamColumn\" , eleTag, iNode, jNode, secType, E , transfTag , \"-mass\" , M , MassType)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Geometry**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "axis_h = np.linspace( 0 , (numBay * bayWidth) , numBay + 1 )\n",
    "axis_v = np.linspace( 0 , (numFloor * storyHeight) , numFloor + 1 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 389,
   "metadata": {},
   "outputs": [],
   "source": [
    "node_no =  1 \n",
    "node_dict={}\n",
    "floorNo = 0\n",
    "floorNodes = {}\n",
    "nodes = []\n",
    "\n",
    "for i in axis_v:\n",
    "    floorNodes[ floorNo] = []\n",
    "    \n",
    "    for j in axis_h:\n",
    "        nodes.append( node_no)\n",
    "        \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",
    "        node_no += 1\n",
    "    floorNo += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 390,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: [0.0, 0.0],\n",
       " 2: [3.0, 0.0],\n",
       " 3: [0.0, 3.0],\n",
       " 4: [3.0, 3.0],\n",
       " 5: [0.0, 6.0],\n",
       " 6: [3.0, 6.0],\n",
       " 7: [0.0, 9.0],\n",
       " 8: [3.0, 9.0]}"
      ]
     },
     "execution_count": 390,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "node_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 391,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: [1, 2], 1: [3, 4], 2: [5, 6], 3: [7, 8]}"
      ]
     },
     "execution_count": 391,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "floorNodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Boundary Conditions\n",
    "for nodeNumber in floorNodes[0]:\n",
    "    ops.fix( nodeNumber , 1 , 1 , 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 393,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Rigid Diaphram Assignments\n",
    "for key , value in floorNodes.items():\n",
    "    for item in value[:] :\n",
    "        if item == value[0]:\n",
    "            ops.mass( item , massX , 0.0000001 , 0.000001)\n",
    "        else:\n",
    "            ops.equalDOF( value[0] , item , 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 394,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Place the columns\n",
    "\n",
    "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",
    "\n",
    "        column_dict[eleTag] = [end1 , end2]\n",
    "        \n",
    "        end1 = end2\n",
    "        \n",
    "        end2 += numBay + 1\n",
    "         \n",
    "        eleTag += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 395,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 395,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eleTag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 396,
   "metadata": {},
   "outputs": [
    {
     "data": {
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by+hRSdc138FwqaTxiBjt9FAfhu2lU9cbbV+ixv8P3u7sVDNrzvltSSMR8Y0T7Nb156bIOrKcF9v9thc3P14o6XOSXpi2W6X9anmz4CrECW5AbPtOSfWIeFSNk/xvtl9R41+q1Z2Y9WQKruNG29dImlRjHdd3bOCTsP1dNV7VX2J7p6Tb1XjRRRHxTUk/UOPdC69I+j9JX+3MpK0VWMu1kv7c9qSkA5JWd+GTgimXS/qKpGea11Ql6W8l/bqU6twUWUeW87JM0n22e9T4x+WhiHhsNvvFT04CQDL85CQAJEO4ASAZwg0AyRBuAEiGcANAMoQbAJIh3ACQDOEGgGT+HxjJJLkicZhfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\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": 397,
   "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": [
    "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": 398,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Place the beams\n",
    "beam_dict = {}\n",
    "\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",
    "        \n",
    "        beam_dict[eleTag] = [end1, end2]\n",
    "        \n",
    "        end1 = end2\n",
    "        \n",
    "        end2 = end1 + 1\n",
    "        \n",
    "        eleTag += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 399,
   "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": [
    "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": 400,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 108x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scale_figure = 1.5\n",
    "plt.figure( figsize = (scale_figure * numBay , scale_figure * numFloor))\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",
    "    \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]] , color = \"black\" )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 401,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dynamic properties - Modal Analysis - Free Vibration Analysis\n",
    "from math import asin, sqrt\n",
    "\n",
    "numEigen = numFloor\n",
    "\n",
    "eigenValues = ops.eigen( numEigen)\n",
    "\n",
    "PI = 22 / 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 402,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[14169.844990005586, 183405.92995474653, 715415.9953641712]"
      ]
     },
     "execution_count": 402,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenValues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Loads**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 403,
   "metadata": {},
   "outputs": [],
   "source": [
    "ops.timeSeries( \"Linear\", 1)\n",
    "ops.pattern( \"Plain\" , 1 , 1)\n",
    "load_dict = { 4 : 20_000, 7: 20_000} # Change these values as you wish\n",
    "load_dict = { 4 : 40_000} # Change these values as you wish\n",
    "\n",
    "for key in load_dict.keys():\n",
    "    ops.load( key ,load_dict[key] , 0 ,0 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# B. Process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 404,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 404,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ops.integrator( \"LoadControl\", 1.0)\n",
    "ops.algorithm(\"Linear\")\n",
    "ops.analysis(\"Static\")\n",
    "ops.analyze(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# C. Post-Process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 405,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 405,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "node_dict[1][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 406,
   "metadata": {},
   "outputs": [],
   "source": [
    "node_deform_dict = {}\n",
    "\n",
    "for i in node_dict.keys():\n",
    "    node_deform_dict[i] = [node_dict[i][0] + ops.nodeDisp(i,1) , \n",
    "                           node_dict[i][1] + ops.nodeDisp(i,2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: [0.0, 0.0],\n",
       " 2: [3.0, 0.0],\n",
       " 3: [0.5092878347518897, 3.0061301366744746],\n",
       " 4: [3.5092878347518894, 2.9938698633255254],\n",
       " 5: [0.78438602424707, 6.007592753424022],\n",
       " 6: [3.78438602424707, 5.992407246575978],\n",
       " 7: [0.8658258520260309, 9.007923843455881],\n",
       " 8: [3.865825852026031, 8.992076156544119]}"
      ]
     },
     "execution_count": 407,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "node_deform_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 408,
   "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": [
    "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 node_dict.keys() :\n",
    "    plt.text( node_dict[key][0] , node_dict[key][1] , key)\n",
    "\n",
    "for key in node_dict.keys() :\n",
    "    plt.text( node_deform_dict[key][0] , 1.1 * node_deform_dict[key][1] , round( ops.nodeDisp(key,1),2) ,color=\"red\" )\n",
    "    \n",
    "    \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]] , 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 = \"red\")\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 = \"red\")\n",
    "    \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]] , color = \"red\" )   \n",
    "plt.box(False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Modal Analysis Results**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 410,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 mode number and period is 0.053sec\n",
      "2 mode number and period is 0.015sec\n",
      "3 mode number and period is 0.007sec\n"
     ]
    }
   ],
   "source": [
    "[ print(f\"{mode+1} mode number and period is {round(2*PI / sqrt(lamb),3)}sec\")  for mode , lamb in enumerate( eigenValues)];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.6.8"
  },
  "toc-autonumbering": false
 },
 "nbformat": 4,
 "nbformat_minor": 4
}