EQE512-Week12-InClass.ipynb

{
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  {
   "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 12 - Construction of Response Spectrum</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": [
    "**This week : \"_Construction of Response Spectrum_\"**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Response Spectrum**\n",
    "\n",
    "<img src=\"./figures/17-EQE512-Week14-Chopra_ResponseSpectrum.PNG\" width = \"50%\">\n",
    "\n",
    "<img src=\"./figures/2020_1221-ResponseSpectrum.png\" width = \"70%\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Write the code of SDOF dynamic Solution in OpenSeesPy**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "import openseespy.opensees as ops\n",
    "\n",
    "ops.wipe()\n",
    "ops.model(\"basic\",\"-ndm\",2 , \"-ndf\", 3)\n",
    "ops.node( 1, 0 , 0 )\n",
    "ops.node( 2, 0 , 5000 ) # units in mm\n",
    "ops.fix(1 , 1 , 1 ,1)\n",
    "ops.mass( 2 , 2000 , 0 , 0 )\n",
    "ops.geomTransf( \"Linear\" , 1)\n",
    "ops.element( \"elasticBeamColumn\", 1 , 1 ,2 , 30_000 , 500*500 , (500 * 5000**3)/12 , 1)\n",
    "\n",
    "# Gravity\n",
    "ops.timeSeries(\"Linear\" , 1)\n",
    "ops.pattern( \"Plain\" , 1 ,1 )\n",
    "ops.load( 2 , 0 , -2000 , 0)\n",
    "ops.constraints('Plain')  \t\t\t\t# how it handles boundary conditions\n",
    "ops.numberer('Plain')\t\t\t    # renumber dof's to minimize band-width (optimization), if you want to\n",
    "ops.system('BandGeneral')\t\t    # how to store and solve the system of equations in the analysis\n",
    "ops.algorithm('Linear')                 # use Linear algorithm for linear analysis\n",
    "ops.integrator('LoadControl', 0.1)\t\t\t# determine the next time step for an analysis, # apply gravity in 10 steps\n",
    "ops.analysis('Static')\t\t\t\t\t    # define type of analysis static or transient\n",
    "ops.analyze(10)\t\t\t\t\t        # perform gravity analysis\n",
    "\n",
    "ops.loadConst('-time', 0.0)\t\t\t\t# hold gravity constant and restart time\n",
    "\n",
    "#Dynamic Analysis ( EQE Loading)\n",
    "G = 9.81 * 1000 # mm/s2\n",
    "ops.timeSeries( \"Path\",2,\"-dt\", 0.005 , \"-filePath\", \"A10000.dat\", \"-factor\", G)\n",
    "ops.pattern( \"UniformExcitation\",2, 1, \"-accel\", 2)\n",
    "freq = ops.eigen( \"-fullGenLapack\", 1)\n",
    "freq = freq[0]**.5\n",
    "dampRatio = 0.05\n",
    "ops.rayleigh( 0 , 0 ,0 , 2* dampRatio/freq)\n",
    "ops.recorder( \"Node\",\"-file\", \"temp.out\", \"-time\",\"-node\",2,\"-dof\",1,2,3, \"accel\")\n",
    "ops.wipeAnalysis()\n",
    "ops.constraints(\"Plain\")\n",
    "ops.numberer(\"Plain\")\n",
    "ops.system(\"BandGeneral\")\n",
    "ops.algorithm(\"Linear\")\n",
    "ops.integrator(\"Newmark\" , 0.5 , .25) \n",
    "ops.analysis(\"Transient\")\n",
    "ops.analyze( 3995 , 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt , pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_df = pd.read_csv( \"temp.out\", names=[\"Time\",\"Ax\", \"Ay\",\"Az\"] , delim_whitespace= True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time</th>\n",
       "      <th>Ax</th>\n",
       "      <th>Ay</th>\n",
       "      <th>Az</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.100193</td>\n",
       "      <td>5.226980e-15</td>\n",
       "      <td>-0.000030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02</td>\n",
       "      <td>-3.059750</td>\n",
       "      <td>-1.943780e-14</td>\n",
       "      <td>0.000918</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.03</td>\n",
       "      <td>0.348596</td>\n",
       "      <td>3.364870e-14</td>\n",
       "      <td>-0.000105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.04</td>\n",
       "      <td>3.045960</td>\n",
       "      <td>-4.785950e-14</td>\n",
       "      <td>-0.000914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.05</td>\n",
       "      <td>2.224800</td>\n",
       "      <td>6.207040e-14</td>\n",
       "      <td>-0.000667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>3880</th>\n",
       "      <td>38.81</td>\n",
       "      <td>-1.348440</td>\n",
       "      <td>5.514330e-11</td>\n",
       "      <td>0.000405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3881</th>\n",
       "      <td>38.82</td>\n",
       "      <td>-0.316158</td>\n",
       "      <td>-5.515760e-11</td>\n",
       "      <td>0.000095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3882</th>\n",
       "      <td>38.83</td>\n",
       "      <td>0.798243</td>\n",
       "      <td>5.517180e-11</td>\n",
       "      <td>-0.000239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3883</th>\n",
       "      <td>38.84</td>\n",
       "      <td>1.180700</td>\n",
       "      <td>-5.518600e-11</td>\n",
       "      <td>-0.000354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3884</th>\n",
       "      <td>38.85</td>\n",
       "      <td>0.609773</td>\n",
       "      <td>5.520020e-11</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3885 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Time        Ax            Ay        Az\n",
       "0      0.01  0.100193  5.226980e-15 -0.000030\n",
       "1      0.02 -3.059750 -1.943780e-14  0.000918\n",
       "2      0.03  0.348596  3.364870e-14 -0.000105\n",
       "3      0.04  3.045960 -4.785950e-14 -0.000914\n",
       "4      0.05  2.224800  6.207040e-14 -0.000667\n",
       "...     ...       ...           ...       ...\n",
       "3880  38.81 -1.348440  5.514330e-11  0.000405\n",
       "3881  38.82 -0.316158 -5.515760e-11  0.000095\n",
       "3882  38.83  0.798243  5.517180e-11 -0.000239\n",
       "3883  38.84  1.180700 -5.518600e-11 -0.000354\n",
       "3884  38.85  0.609773  5.520020e-11       NaN\n",
       "\n",
       "[3885 rows x 4 columns]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbc7b1f2cf8>]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot( data_df.Ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbc7b108550>]"
      ]
     },
     "execution_count": 62,
     "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( data_df.Ay)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbc7b0f28d0>]"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fKhHOdkIIqT9XVTfppU0uaeQVlijfZujAyXycOFeIHq/PCan3lqcokR08lRes0jLjx9V7ccJCVaPVPv4/rt6Lq99boBucT+WFVwf+sHIP3p21Fb3/OQ9bD2h/Xmc1qhEfnrgKr+p8n5bsMNdmJU+5oqSsnlX2Qrzho9/xyfxAc6oI3iSEH1PZUUHP1DXul+SdwkGinFJmanoNeFr7xkLYSEzplzh5lbk+73puGbsY09aW/jgnr9qD6z5caPr94xfmBh8H0yhXN+lk/wk2egzM33oIO4+cxXUf/q67T6dXZqHrmNmmjrfzyBn89euVeGiiOz2Nlu44ir9+vRJr95zArzpjAbQuxyOTVuGLxTsB6E84maga6OPUUsJWZO88hlFTA2tU6539bEGRbo8qpae/X4vL/jELx84UOJhCd3CQKKdiNQ+S+jxmzqtXtfHGL9o9enIPn0G2id5Oi7YfwX2KNouHJ67CCo0FYPYeP4dzBeFtKfmK5WHlNAZHgxu0SajfZ8Y8qb7eqJuv1t25Fnl5W7fG/uw5XjomQOt/mVdYrNvGccQgs0xKCM2qft/m7Ky8yrYHMx+R3j7vzzY3CPXEuULsPZGH37bGbvaIaHGQKKfUN2JurTmt/DHtOX7O1B2geg+jHks935iLGz62VucfyWVjZuNPnwaqy5RVOcr/S7Dh2uBYdroeFzscyOUgZ/YG4c/SNTBLGRC1gmGr56Zj5sboRhurS2pOlySsdniQ06P+eOVqRbPiYUZYDhLllPo3HKlKQ7Z4+5GQBkFz51GXJIzfM3vjQfywsrRqyW7jc35RcVhVldEd/fKdgTYjZdfVSHebZkoIr03fFNL12Og96ikljkQI5A9PXGmYccrVTHkapSQtVldL1Aqiaq9N32zpmFqs9phTj1ExKkmZCT9GbVBlCQeJcmrX0dDpAv44Gj59gNrQsYtxxRtz0fLZaRF7oiidNZkhKT0yaZXuIk9W7yCFEHhz5pawtSommeyfr8zIlaUteatRdZPSh3O34fFvSyce/Nt/VwcbQo0cPJWHZRGq1Cav2ms4YG/7oUCALzA5ZkPJTKlG+Zktzz2GFyavs3we+TTDxi1F5oip+K/UUK88favnpocE0AUGwezmsYtDvu83q3qaGX2nfDyDUExwkCinNuv0ItFSUBya0ecXleDb5YGpuA+eysNHc7eF/JCUj50evd7s6Z8tv+eAxiSAKxSjas1mAhMVgUWuspEHhpmNXSsVbSDfrdiDUVM3InPEVMPeLtPX7Q8LREdj2OhpdjCgbFL2LkxYtNPyeZ76bi2EEJgndWV+XOryqz67crJIM7MVK2dwVs8+W2Qw2aa6MX3lH8eC3WrjobrILg4SzND1Hy3SzZAem7Qar07fhPV7T2LOpoO4aOQvOGeyOmCpyW6KZrV7cUZU7ysoLsGonzZYynSnrtmH37Ycwn+lYJmnM72E2ZtQuXePFV8bjMrWE82dcYkQKCgqwab97k4fr1cV9NZM/WlI1O0VVqsn1d2khRBYtK2066t6csxrP/wdV745D0CgFBJP3VmjwUGCmdL3rXkhz+V8Rm5Uvuq9BRj980YcO1uInRozX2p56cf1+HxRrmNp1Orl8/G8bZp3e8p8cvbGg/hkwQ48r1E9Eik7vX1c6UArvUFdZhnNCkwaadHL7A+fzg9mtgdP5aHXG3Pxh+IzidRwvW7PCbR8dlrI1BmBcwEvTFmH/m/Px74T7i55+8wP4Z/Dl0vMBdGDJ/PQ/iWDLt2q58oBmEDge3TLvxcr9hcR55h64KvoR/nHQzmEgwQz5fDp8Lvsj+dtC5liQc6LP1uUa+qY6/eexHOT1xvvaMOczYcMf4gJUh98rV5UdqujrSwwdeR0Pl6bod+wG95Yrr1f1qhf0XXMbOQVFmPyyr3YfviM6c/kqvcWIL+oJGxuqBKB4HTux12e9+urJeElJLNXcV8U64uoS75a7XNm58pyItN/ZOJKPODy9DJWcJBgYcyMyC0qLsGYadqjXZVrQ/iCwS83SQoShcUl+N9yZ5c9tdLOnr3zmKWGfvWxiRAyvkOZsSmrcfQmd8w5WFrtoq7KcquLtFmRgrWy2tLM5VZ/HYpMfEjqkpXTSkoEWjwzDZ8v3okfVu3F1LX+qcJK8joBzH/OFhoPzjoTRa8lqx6btAqFDvSHN1pwST4FgfDe7NA7RrczByWj0bfqUkn4lOqEC56fHnz+8bxteHbQBQCAaeu054JSUg4WjETdiF1UXIKTJgf0ueHXjQeNd1II+0apNqh7/gkBy12/zZJL34UlJSgoLsHIH90tWUeDSxIsxNQ1+3DgpPFdY5J6PVSEz9Nk13cr9+BHnSVPrTDqgBKpIXf4Z9mWz/ff7F3oOmY2hBCWGolHfLc24uvZqvm+zMRPK50DBr1rbp4mZTdeABj50wZ0fHmm6fP4jXoyxYmq7tHztx4K6ZXmpC8XB0psflg5Ug+XJFhQQVEJHvhqBSokJ3qdlJiSM1sBEZbxRrPuRrDbpnButtCCYqE5m6+RX1xYT1k9WeRnUXR1dUNBUQmu+cB4Li51dmzU0eLJ/0UO3kpWr/ei7Udw4GQeqqUnAwitVisuEWFzVnmBSxIqbk0tHQ9+kEYlm+nCGqu5n5ywWNVzSAgR7LoqbQk+imauKdkn87djvGIGUAHnJkcs0So2qA4e62nE/cbsbLhmq9WsmL3pAMb+ts3UoFS14Z8vD36UyvaROZusVaO5hUsSkrzCYggBDHxnvtdJ8cwTFjIZPzWsGVGvJzBb9eNTrnFhtgeRFnmGUNmqXcddq8sGwkspC3KcnfTOL8xk/juPnEHltOQYpEbbXeOtV0vKjp8t0Pye6Y29iTUOEpJ2L85AYRTTFZRXbneDdNO7s0Ibp+W1PRbmhJY45tucofP6j4znwzLrlZ83hm2zU0qZvekAKqUmo1OTGlG9f/uh06hbtQLene3+MqpmSkin8opM3cWfcXl522gcPVOg2VW6wIUSTzQ4SEg4QJQfKUnmalnHLdhhaZxDrEU74hoovfPdPnpgcJyIFb3+Oc94J4forTGhVFwicP8XxmML/hJFRwS3CaEd8P1So8ttEqzcMbsqYFFJeEO2nxitwWDG4h2B0pPTU6Q4KdHE/Eh5hcU4ZaKU8Pu2yCPbvXA6v0izWtIvXz0uSTAWQTw10EdDXmb2H9e18zgl+szMofeDiVUL3Z53yg6ry8TGEpckYH1+elZ+lPEYETTTha6yTjEzhsDM52R2HIhfFBvMThsrHCTgTl9yxuKJuseXn+w7aTyhoHoAnBYv1sW2w8r4DDdxkID2egOMWV2Zjblj11F3Z531uwVbD4fNVBtL5bpNQgiBmRsOaHYvZIwxr+UVFgfXW9/xj4GeLHJUrksSU1bvxfDPl3udDMYY06TsOOHVYMlyHSS2WFjCkzHGYk05fmu/R9Xi5SpI3DV+GTJHTEVxiUDmiKn4YI691cQYY8xNylX2Hvdobi5HggQR9SeizUSUQ0QjNF5PJaJJ0utLiChT8dpT0vbNRNTPifTokXtwvDZDe7Ecxhjzs2jWJ7fLdpAgokQAHwAYAKA1gFuIqLVqt7sBHBNCnA/gLQCvSu9tDWAogDYA+gP4UDqeq/41b7vbp2CMMcc1eernmJ/TiZJEJwA5QojtQogCABMBDFHtMwTABOnxtwB6U6CZfgiAiUKIfCHEDgA50vEYY4z5gBNBoj4A5UiW3dI2zX2EEEUATgCoafK9AAAiGk5E2USUfeiQd32GGWOsPHEiSGh13FVXnOntY+a9gY1CjBVCZAkhsjIyMiwmkTHGyobC4thO1+FEkNgNoKHieQMA6oWJg/sQURKAqgCOmnwvY4wxSaynF3EiSCwD0JyImhBRCgIN0VNU+0wBMEx6fAOA2SLQTD8FwFCp91MTAM0BLHUgTRH9585L3D4FY4w5LnfMIKTFeA1629NyCCGKiOhBADMAJAIYJ4RYT0QjAWQLIaYA+BTA50SUg0AJYqj03vVE9A2ADQCKADwghHBtStYfHuiKLftP4YqWtXFr50b4akn0i7YwxlgsXdSomifnJS/63dqVlZUlsrPtrzDV8/U5yD1ifeFyxhiLhYd7N8c70nK7PVpkYMJd9jp/EtFyIUSWlfeUqxHXauPv7IT7ejbzOhmMMabprq5Ngo//eVN7T9JQrmeBzaxVEU/2b4V7uzdD+5G/GL+BMcZiqGp6MkZd0xYFRSWoVSnVkzSU6yAhq5qe7HUSGGNM05+6NPb0/OW6uokxVn60qVfF6yRYkpQQ+7UjtHCQYCyC/+ve1OskMIc81Lu510mwpFlGJa+TAICDBGMRebESWCx8/KeLvU6CoxY8eYXhPjUqppg6Vlbj6naT4wi/fPU4SDAWQTx2ETejQ8NquKBuafXLo1e28DA19jWono6Hep0fcR+ztTexzpzv7JqpuT3BJ1GCgwRjOvR+vGVBQgIwYkAr1KiYggVPXoE7yvD/tRRh9t96mNgrtplzSmICGlSvELY9wSe5s0+S4R/tG3ozqpH5y/91b4oXrm6DzFoVY3bOV69vF7NzJRKhR4sMrHiuDxpUTw97/bwqaTFLi5G3bnZmfAAR0NQn9fxKHRpWw79vDx/f9vxVbTxITTgOEipf3dPZ6yR4rlYlc3W3flG1gntdmIde0tB4Jx2XNatpaf8bL47+XJEoq5Vk1dIjf8Zad7Zqo65pa/n/GI3KqeY+X6OKQTfLB1/cHX2+MaBd3eBnVK9qaXD2ahoONQ4Sksf7tUTVCslISeJLsuTpKw33yXllQAxSEnBFy8hTw5vJ0KJlp+H6q790sbR/gsUuj88MvCDkedfzwzPsEQNaYdrD3cJKBonqc6lyWKP68JSkBPypS2O8NNgfd7sAUGLQfhTtZ3nDxQ0M90lPtT/p3rbRAzH/yV7B59wm4TMPXHE+Vr/Q1zcfjJfCMhAA3ZrXCnmudZ0e79fSlfTclBX5Djsp0V9f4zb1qiCzZngVjtPUn1NRcXgm+ZdugS68s/9uXBevZPQzmPxAV0vHs+PChlVN7We0zIJeDK6UqhpTrNovPcU4ANStar96LjGBQj5Tv+RE/vp1+YBfPhi/6dI09C5VKxN54IrIvUuiZXQHWLty5OkKaprs+ggAd18uzZVj44sw9aFumPu4cZdMKy5sEJ5RqjM9rXUG5F3SUyJPrlClQhJu7dwID5r4DP/et0WweiQW91S1K6eF3aRoMeqJptX2AgA/P9TN8Ngf/6ljxNerp6dgxz8GGh5HLVJ1nV/uVzlIqPjlg/HC8O5NMctE7w/A3fED1aRpUlKkEoLyVOo+7C9f0xZv3BC5YdNKUmtK7THR9HAJuyN1UFpS+N2suiTRNCO8kd1sFRYRYfS17YLBKFJ2e1/P0kBSO0YN3N2bG69GadQmoTdOQl3FrHXFzq8ducE7gcjx34RfxuhwkFDxywfjhUub1fTNKE8A+O7+y/DeLReFbLsxq7R+uGJKIv7cpbGJubfCP9Nxd1iaLdmUnx/qho9ui3zHGa2hncKr3FqrpploXrsyBl1Y15kTRshxlcGpSloyljzdG785XHKKRolDK7YRQeNzjJwvyNfEavahtX/b+v6aPoSDBDOljkt3jOrGV6X61Srg6vb1dF+f94S5jOnft4ePLlbWTHRvEbhLfeXatqaOJ/v23ktDnjeqmY4B7exl0o112jKu69gAT/QPbfNpdV5oZkIUyLT13HFZpul0CMP78lJ1qqShkYNtMJ2b1Ag+nvv3ngDMZb5ZmeZGSr8ztEPIc63/q7Lk0PuCOobHlOPmt/deZioNskSNwRBf3t0F399v7Thu4iDBTOnRwri4H42/dG+Kv6pGyqqrlpVVDcrXzEyd3KNFBi5qFJp59G1dB8mKxu4qaYFqosppyWHnjiQrs4bxThZVjNB2IDdCy7Q6D7Soo18StDJ63MtefnIvpeHdm5oapyI3ovdvWxcdTXQbHay68RAivGeY8tL2aJGBCorG676tw4OGXAPR0GJPu/rVwm++qqYnh31nvcRThbMgryrahnZqhPdm5wSfy5mZ/ENV/kCtViioq882jOyH9JQk3aqJgqJAFxmzmWTFlEScKXBtxd0Q6s9HHSPa1KuKLk1roH3DalhvjCWIAAAWN0lEQVS7+wQusRHEKiR7lzUMbFcXq3edwE1Zxl1PAaDleZWDjzMMOjEAxlXKWu1R9auVZv5jb8/Ch3Nz8Nr0zQCA565qrXyzJSHv9SkOEsxzene4Wj9Wq1MpjRjQKuS53MsnIYHC7rqFEKhdJZDJNKnlfhfW6Y90Q5NaFdHy2emK9Ol3tzTK3C6Vesp0bFQdHTXuROOlva1h9XRssTAOR1mi0utw8PKQyOM5lO+zepmCPeKiYNTrzA+4uokF6WUi617q51ivL60eQOqMf9S17VCnSioqWhigdG+PZmiu0QMlUongl0d74JdHewQbgOtVq4BbLmmE8Xdegms61Nd8j7orplHMSokwhiM5MQGpSYmoXTk12F4QKb1GJQkjsZ6sMJouoQDQXKPKTP3dbKKohlJ24HphcGtcd1HoZ3db50b486WZuudLTUoo170ajXCQYIYqpSZFXRV1iaox8Z5upXddeo3Wg9vXw5Knr9QcJKfXoDpiQCvMfCy0+67ZKTXu7d4Mkx/oiksyayAhgdCzZW3H7rqfv1q/OkGeTmTpM1fiRWnksroxOhLl3e/l5xuPIzhXaKVaTOAeG3fIzWtXiuoaXpJZHY1rhrdDyO1GMuUIcmVJom7VCnjz5tCG6Uh6taqNmpVSQ25U7Hz0sZ4cMBY4SMSZUddY64FjRaSvt/IO90NV98APbu2ITS/313xfpJtXvZ48Wm7p1Mj0vrIx119oar+EBIp6Ykd5XYb7ezaz/F6thvenBrbS2DNAnXkpn39hYs6x2zpbWwazncYAPrMi/T+03HFZJtJTEvFoH+0py6/vGNo+obxZsDqdiVK/NoFGaKMpPdT0dk9NNpelvjO0A3LHDLJ0Tq9wkIgzRoN63FJZ0bVyoKqb56AL6yIt2f7cNZHIGaLflnfo3iID20cPdGxKkuTEBKx/qR9eu+FCzFd18SUivK24S7aaNZoJhBdLgxXvUfWkAownUhzUri5uvLgBtowagF6t9LuN1lNNYbFMKkltGNkflzXTLhEpA0FKYgJeu978zLB9NHojyeSu3crvVeBxdIGnSlqyqTaKeJr+x/+tJixm6lVzfqK8SL8FK9UR8p5GMWLkkDZ4fvL6sO1u9kKKdCcbTUyrmJoUMl+VsqpFOXBQvn5O5jc1K6UG73Dnbj4Y8tpvT1yBvAhVVh+YHEh4XtU07D2RBwCoUyXVVI8kpc/u7mRpXEbPlrUNX1OWJJTLnBqtM11f4zdjZi3tCi7fVDmJSxIMAPDb41dYLqUseqoXsp/VnjF2kIVBZWZKB/JI4i5NInfrvF2ngXLpM1di9Qt9TafJKeo++VZNebArflW0tSizrGDgtBCJBrWra7rU06NFRmiAqpBseVCluncZYL+XlROT6akpL6FynrJGNSIHo0iDPSO5NAZTrDuFSxI+0KZeFazfe9LTNEQzYrZuVfem6Fa7rFktW3W4FR2eV6m1xhoNWuyudXFhA+0qom7Na4EoUKdupb3G7N0+EMjMr25fD18u+SNilU0kVuv6PaNKpjwpZN8257lyOqe/j26Kn5SWYVaL2342/ZFuqFYhBSN/ClT5WO3tEU0Ddaxc2KBq8C5YPUVGrHRpWhOXn18Lz1/VGkSEf/3Z+TmolORMvqfBmh56lDFicPt6GNy+Hj6aty24LZpxAk5ksHP+3jOk6kwdzKpXTMHK5/qgikGQj6OmhahxdRNzVKvzquA8RXWA+senOUBO2VPFxI/ub31a4K6u0XfPjNboa0uXF43m/njCXZ1sDbwCgLTkRHxxT2c0r1PZeGcHlEhrNCRGmRsqx2a8e8tFuLJ1nZCqyM/u6mT5mGamYzHSpFbFkBX7bteY16p6xZSQyQyHXdo4GCzlaWquvCC8vaOsBQ4OEj7g5+/UCxH6+ZtRpJj+YkiHeri7W3gmqYwjZtZ++Gvv5hHHHzitpZQhJyXa+6R6tMiwPLeP1ypJbRIVTCy8o0Vr5PedXTODjxsa1PnHipm2o5eGtMX4OwNBrW39qsgdMwgXNw5vI5O/z1qN2vHIVpAgohpENJOItkr/as5KRUTDpH22EtEwxfZXiGgXEZ22kw6nWVmkJl79777Is0z2bhW4Q2qos1CLEfmHoixJdG5SE5VSk4LH1vJgr+a6r5n1ztAO+N99lxrvaJLcXuNEj5R4mRpD9re+LfD0wFa46sLoGmgv0xjkF4trYGUMjls4SASMADBLCNEcwCzpeQgiqgHgBQCdAXQC8IIimPwobfOVaY8Yr1QVT7RWG7u4ceRZJuXeF9FOAS3HBq3V0mRaWYUTs48O6VBf8w4vWm/e1B5j/3wxGtes6OtSnxvSU5IwvHszzSVt7WhTrwreutn8WAcAuK5jfTys6J46aXiXsLEksk9uD7TVNKwR+4xanrlWXsAp3oOF3RagIQB6So8nAJgL4EnVPv0AzBRCHAUAIpoJoD+Ar4UQi6VtNpPhrNqVS+vUB7Q9D9PW7Xf0+KlJCcgvKl2Ql4jQt3Ud/LLhgKPnsePuy5tgYLu6IWMnfnigKw6czDP1frkEMbBd3WDPLb2PWQ4jfrj701I5LTm8l0uUnXZ89lX3zFQTS4aqvXlT6HQbnZvqdyON5majaUZFbD90xvL71Do2qo7Zf+uB+tUr4JcNB/Di4Na4a3y27eN6xW6QqCOE2AcAQoh9RKRVj1AfwC7F893StrhQv1oFVEhOtDjvTWRaGUWr8yr7KkgQUdjgug4Wpq6Q81CtsRfq/LVGeqB6z+6YgljgTN66EQNaIdXD9SnM+vbey7DjsP0gAQBNpSnqfzO5MJafGQYJIvoVgFZn4WdMnkPrZ2X5PoyIhgMYDgCNGsWum6RyNO3MR7ujz1u/2T6mnUnAoul2PujCunh/To7xjg4KrglhYt+q6clY91I/pMfRKNRolccYc28P6/Na2RXNb6xGxRTddbDLM8PwLoS4UgjRVuNvMoADRFQXAKR/D2ocYjcA5XScDQDstZpQIcRYIUSWECIrI8OdVdK09GyZEeyi6dS0FUTA+7deZLyjQy6oWyXmdbNyMFPOUdNPqrKRq6KUKzdWSk2yNVEbY8wddsuAUwDIvZWGAZissc8MAH2JqLrUYN1X2hYXlBOOOVnV0N2l5UD1zHy0h/FODipRrS4HIHiXVqIRQOKNlTWglSql8fjV8u7ZQfrruvuR3SAxBkAfItoKoI/0HESURUSfAIDUYP0ygGXS30hFI/ZrRLQbQDoR7SaiF22mxxVad8V2EGJf7eD2LK1qchaqdcnkpUPjMUjIS4JaKVUufqo3lktzXA1pHzfNcWWCH2cF0Zph189s3dYIIY4A6K2xPRvAPYrn4wCM09jvCQBP2EmDW35+qBv2HD8HIOqOLLqIKKRHV7v6VU2vGhbpDrZ9w2pYveu4hXS49yOSj0tEGNy+XsiynHK3WKe7VcbCfT2aYWC7uiEroxlRjkDnKrXYSJPWdbDyOTFtXPbV0bpeleCylo5HCZWHejfHO79usX0cP2U/8p12lbRkvHtLaPtLsYjfkkRCAnHGEwdqV0nDuDuyHB0vU15xkDBBvnt3Kk9TVzclJlCZ61v5/FWt0a15Lc1BeyVxXJJwwoe3dUQ1m7PDMmORFj5i5vm/87KPuLp+rR8rT22okJIYtoKd7G99W6JWpZTSklo5M7BdXc3pKljZlR7l3Fd+wCUJE5zOvzs1qRF9waEMxJJLm9VE9rN9vE4GY8wELkmYMLRTYJiHU9Ujo69rF75RFTUWPdXL8nGtBh557Yabsxoa7MkYK6+4JGHCyMFt8czA1o4FiZTEhPCqK9O9m5wzakhbPNanBaqn8yhTxpg2DhImJCRQ1PPpa1He8SfbXKMg5LgW909IIEcWcGGMRRbPTY5c3eSizAizmoZVDak2RNNI7rfZdBlj8Y+DhItu5Lp+xlic4yDhgVjPAssY8we5s0g84SDhIjPzJckBo1lG6CjehCg+Ga5sYszf4m1yP4Abrl315y6N8fJPGzRfUzcfDG5fD01qVUTtymmYtelAyOp4StHOPqr0yJX215FmjJlXo2IK9hw/F5dT0XCQcJGVJRSJCBc2CKz8dlvnxm4lCQDwyJUtXD0+YyzUxOFdMH/rYUd7ScYKVzeVIXF4k8JYudCwRjpu7Rx/7REAlySitvzZK1FUItB59CyvkxJ0Qd0qWJZ7TPf13q1q8/KMjDFLOEhEqWYUg9CqpCXhZF6R6f0Ht6+HKatDV3qN1LupThXtdgzZp3dcYvrcjDEGcHWTZbcZFBnvvryJ4THMNj6r12GIRtv65XOmVcaYMzhIWDTqmrbY+soA3defu6q17mtOjIjmYRKMsVji6iaLiCjq+ZaUS5QmSgGjV6vajqRLj6trYDDGyjwuSbjss7s6aW5PSkzAgievwNtDOzh2LrPrZDPGmFlcknBZVmbp8p3q6qYG1fUnANTTsk5l22lijDGzuCThsvQUZ+PweVXTkDtmUMi2z+/uhB8fvNzR8zDGGMBBokzo1jwD7RpU9ToZjLEyiINEnOIlRxljscBBIk69esOFXieBMVYOcJCIIxN0ekoxxphbOEh4INqeql2a1nA2IYwxZoCDRBwxGhiXlclBhDHmLA4SHnBrSu8uTWu6c2DGWLnFQcID0VY3RRNceI0JxpgdtoIEEdUgoplEtFX6t7rOfsOkfbYS0TBpWzoRTSWiTUS0nojG2EmLn9zZNRNZjUsvxcd/6oj3brmIM2zGWNyxW5IYAWCWEKI5gFnS8xBEVAPACwA6A+gE4AVFMHlDCNEKwEUAuhKR/vSqceSFq9vg2/suCz7v37Yurm5fz/ZxOcYwxmLNbpAYAmCC9HgCgGs09ukHYKYQ4qgQ4hiAmQD6CyHOCiHmAIAQogDACgANbKaHMcaYg+wGiTpCiH0AIP2rNe91fQC7FM93S9uCiKgagKsRKI1oIqLhRJRNRNmHDh2ymez4ZHU9ivSURDwfYX0LxhgzYhgkiOhXIlqn8TfE5Dm0crZg0y0RJQH4GsC7QojtegcRQowVQmQJIbIyMjJMntpfBrQ9DwCQlpwYk/PNeKQ7d4tljNliOEWpEOJKvdeI6AAR1RVC7COiugAOauy2G0BPxfMGAOYqno8FsFUI8bapFMexl4e0xWN9WqJCSnRBQivatq4bujxp45rp2HnkbFTHZ4wxNbvVTVMADJMeDwMwWWOfGQD6ElF1qcG6r7QNRDQKQFUAj9hMR1xISkxARuVUx443/4kr8M29l4Zsm/f4FahfrYJj52CMlW92g8QYAH2IaCuAPtJzEFEWEX0CAEKIowBeBrBM+hsphDhKRA0APAOgNYAVRLSKiO6xmZ4yTd0k0bBGOiql8rpRjDH32MphhBBHAPTW2J4N4B7F83EAxqn22Q3u1Wno1s6N8NWSP7xOBmOsnOIR1z43+tp2wcdWezcxxphdHCQYY4zp4iDBGGNMFwcJxhhjujhI2PTDA12Dj2+42J1ZRdKS+WNijHmD+0/a1KFhteDjN25s78o5fvrr5Viw9bArx2aMsUg4SMSB82tXxvm1K3udDMZYOcT1GIwxxnRxScIB391/GQ6ezPM6GWF4WAVjzC4OEg7o2EhzQT7PyA3dPPiOMWYXB4kyaPydnfDDyj2oVzXN66QwxuIcB4kyqGGNdPy1d3Ovk8EYKwO44ZoxxpguDhKMMcZ0cZBgjDGmi4MEY4wxXRwkGGOM6eIgwRhjTBcHCcYYY7o4SDDGGNNFQgiv02AZER0CsDPKt9cC4Nd5tzlt0fFz2gB/p4/TFp14TVtjIUSGlYPFZZCwg4iyhRBZXqdDC6ctOn5OG+Dv9HHaolOe0sbVTYwxxnRxkGCMMaarPAaJsV4nIAJOW3T8nDbA3+njtEWn3KSt3LVJMMYYM688liQYY4yZVG6CBBH1J6LNRJRDRCM8SkMuEa0lolVElC1tq0FEM4loq/RvdWk7EdG7UnrXEFFHF9IzjogOEtE6xTbL6SGiYdL+W4lomItpe5GI9kjXbxURDVS89pSUts1E1E+x3fHPnYgaEtEcItpIROuJ6GFpu+fXLkLaPL92RJRGREuJaLWUtpek7U2IaIl0DSYRUYq0PVV6niO9nmmUZhfSNp6IdiiuWwdpe0x/D9JxE4loJRH9JD2PzXUTQpT5PwCJALYBaAogBcBqAK09SEcugFqqba8BGCE9HgHgVenxQADTABCALgCWuJCe7gA6AlgXbXoA1ACwXfq3uvS4uktpexHA3zX2bS19pqkAmkifdaJbnzuAugA6So8rA9gipcHzaxchbZ5fO+n/X0l6nAxgiXQ9vgEwVNr+MYD7pMf3A/hYejwUwKRIaXYpbeMB3KCxf0x/D9KxHwPwFYCfpOcxuW7lpSTRCUCOEGK7EKIAwEQAQzxOk2wIgAnS4wkArlFs/0wELAZQjYjqOnliIcRvAI7aTE8/ADOFEEeFEMcAzATQ36W06RkCYKIQIl8IsQNADgKfuSufuxBinxBihfT4FICNAOrDB9cuQtr0xOzaSf//09LTZOlPAOgF4Ftpu/q6ydfzWwC9iYgipNmNtOmJ6e+BiBoAGATgE+k5IUbXrbwEifoAdime70bkH45bBIBfiGg5EQ2XttURQuwDAj9wALWl7V6l2Wp6Yp3OB6Xi/Ti5OsfLtElF+YsQuPP01bVTpQ3wwbWTqkxWATiIQAa6DcBxIUSRxnmCaZBePwGgZqzSJoSQr9sr0nV7i4hS1WlTpcGtz/RtAE8AKJGe10SMrlt5CRKksc2Lbl1dhRAdAQwA8AARdY+wr1/SLNNLTyzT+RGAZgA6ANgH4J/Sdk/SRkSVAPwPwCNCiJORdtVJh2vp00ibL66dEKJYCNEBQAME7mIviHAeT9NGRG0BPAWgFYBLEKhCejLWaSOiqwAcFEIsV26OcB5H01ZegsRuAA0VzxsA2BvrRAgh9kr/HgTwPQI/kgNyNZL070Fpd6/SbDU9MUunEOKA9EMuAfBvlBaVY542IkpGIBP+UgjxnbTZF9dOK21+unZSeo4DmItAfX41IkrSOE8wDdLrVRGogoxV2vpL1XdCCJEP4D/w5rp1BTCYiHIRqPbrhUDJIjbXzYkGFb//AUhCoAGpCUob4drEOA0VAVRWPP4dgbrK1xHa2Pma9HgQQhvGlrqUrkyENg5bSg8Cd1c7EGikqy49ruFS2uoqHj+KQP0qALRBaIPcdgQaXl353KVr8BmAt1XbPb92EdLm+bUDkAGgmvS4AoD5AK4C8F+ENsDeLz1+AKENsN9ESrNLaauruK5vAxjj1e9BOn5PlDZcx+S6OZ7p+PUPgd4IWxCoA33Gg/M3lT6g1QDWy2lAoK5wFoCt0r81FF/KD6T0rgWQ5UKavkag6qEQgbuMu6NJD4C7EGgEywFwp4tp+1w69xoAUxCa8T0jpW0zgAFufu4ALkegmL4GwCrpb6Afrl2EtHl+7QBcCGCllIZ1AJ5X/DaWStfgvwBSpe1p0vMc6fWmRml2IW2zpeu2DsAXKO0BFdPfg+LYPVEaJGJy3XjENWOMMV3lpU2CMcZYFDhIMMYY08VBgjHGmC4OEowxxnRxkGCMMaaLgwRjjDFdHCQYY4zp4iDBGGNM1/8Dhuh/KKKAuVcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot( data_df.Az)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Time    1.000000e-02\n",
       "Ax     -9.088900e+01\n",
       "Ay     -5.518600e-11\n",
       "Az     -2.400300e-02\n",
       "dtype: float64"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_df.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Time    3.885000e+01\n",
       "Ax      8.000990e+01\n",
       "Ay      5.520020e-11\n",
       "Az      2.726670e-02\n",
       "dtype: float64"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_df.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "Sa = data_df[\"Ax\"].abs().max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.05s period and Sa=90.889mm/s2\n"
     ]
    }
   ],
   "source": [
    "print( f\"{round((44/7)/freq,3)}s period and Sa={Sa}mm/s2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Create a loop in order to obtain the peak values for every single Period**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt , pandas as pd\n",
    "import openseespy.opensees as ops\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def responseSpectrumCalculator( height):\n",
    "    ops.wipe()\n",
    "    ops.model(\"basic\",\"-ndm\",2 , \"-ndf\", 3)\n",
    "    ops.node( 1, 0 , 0 )\n",
    "    ops.node( 2, 0 , height ) # units in mm\n",
    "    ops.fix(1 , 1 , 1 ,1)\n",
    "    ops.mass( 2 , 2000 , 0 , 0 )\n",
    "    ops.geomTransf( \"Linear\" , 1)\n",
    "    ops.element( \"elasticBeamColumn\", 1 , 1 ,2 , 30_000 , 500*500 , (500 * 5000**3)/12 , 1)\n",
    "\n",
    "    # Gravity\n",
    "    ops.timeSeries(\"Linear\" , 1)\n",
    "    ops.pattern( \"Plain\" , 1 ,1 )\n",
    "    ops.load( 2 , 0 , -2000 , 0)\n",
    "    ops.constraints('Plain')  \t\t\t\t# how it handles boundary conditions\n",
    "    ops.numberer('Plain')\t\t\t    # renumber dof's to minimize band-width (optimization), if you want to\n",
    "    ops.system('BandGeneral')\t\t    # how to store and solve the system of equations in the analysis\n",
    "    ops.algorithm('Linear')                 # use Linear algorithm for linear analysis\n",
    "    ops.integrator('LoadControl', 0.1)\t\t\t# determine the next time step for an analysis, # apply gravity in 10 steps\n",
    "    ops.analysis('Static')\t\t\t\t\t    # define type of analysis static or transient\n",
    "    ops.analyze(10)\t\t\t\t\t        # perform gravity analysis\n",
    "\n",
    "    ops.loadConst('-time', 0.0)\t\t\t\t# hold gravity constant and restart time\n",
    "\n",
    "    #Dynamic Analysis ( EQE Loading)\n",
    "    G = 9.81 * 1000 # mm/s2\n",
    "    ops.timeSeries( \"Path\",2,\"-dt\", 0.005 , \"-filePath\", \"A10000.dat\", \"-factor\", G)\n",
    "    ops.pattern( \"UniformExcitation\",2, 1, \"-accel\", 2)\n",
    "    freq = ops.eigen( \"-fullGenLapack\", 1)\n",
    "    freq = freq[0]**.5\n",
    "    dampRatio = 0.05\n",
    "    ops.rayleigh( 0 , 0 ,0 , 2* dampRatio/freq)\n",
    "    ops.recorder( \"Node\",\"-file\", \"temp.out\", \"-time\",\"-node\",2,\"-dof\",1,2,3, \"accel\")\n",
    "    ops.wipeAnalysis()\n",
    "    ops.constraints(\"Plain\")\n",
    "    ops.numberer(\"Plain\")\n",
    "    ops.system(\"BandGeneral\")\n",
    "    ops.algorithm(\"Linear\")\n",
    "    ops.integrator(\"Newmark\" , 0.5 , .25) \n",
    "    ops.analysis(\"Transient\")\n",
    "    ops.analyze( 3995 , 0.01)\n",
    "    \n",
    "    # post process\n",
    "    data_df = pd.read_csv( \"temp.out\", names=[\"Time\",\"Ax\", \"Ay\",\"Az\"] , delim_whitespace= True)    \n",
    "    Sa = round( data_df[\"Ax\"].abs().max() ,3 ) # Spectral acceleration \n",
    "    T = round((44/7)/freq,3) # Period\n",
    "    \n",
    "    # \n",
    "    return( T, Sa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.05s and Sa = 90.889 mm/s2\n",
      "0.142s and Sa = 515.277 mm/s2\n",
      "0.261s and Sa = 1639.25 mm/s2\n",
      "0.402s and Sa = 2397.48 mm/s2\n",
      "0.562s and Sa = 3082.6 mm/s2\n",
      "0.739s and Sa = 1984.9 mm/s2\n",
      "0.931s and Sa = 1694.75 mm/s2\n",
      "1.138s and Sa = 1723.57 mm/s2\n",
      "1.358s and Sa = 1395.93 mm/s2\n",
      "1.59s and Sa = 1636.9 mm/s2\n",
      "1.835s and Sa = 2329.34 mm/s2\n",
      "2.09s and Sa = 1462.73 mm/s2\n",
      "2.357s and Sa = 1497.69 mm/s2\n",
      "2.634s and Sa = 1557.77 mm/s2\n",
      "2.921s and Sa = 1517.21 mm/s2\n",
      "3.218s and Sa = 1436.27 mm/s2\n",
      "3.525s and Sa = 1348.39 mm/s2\n",
      "3.84s and Sa = 1268.96 mm/s2\n",
      "4.165s and Sa = 1203.21 mm/s2\n"
     ]
    }
   ],
   "source": [
    "T_list , Sa_list = [] , []\n",
    "for height in [ 5_000 * item for item in range( 1,  20)] :\n",
    "    T_value, Sa_value = responseSpectrumCalculator( height)\n",
    "    print( f\"{T_value}s and Sa = {Sa_value} mm/s2\")\n",
    "    T_list.append( T_value)\n",
    "    Sa_list.append( Sa_value /9810)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plot the T vs Sa**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Sa (g)')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize= [10,5])\n",
    "plt.plot( T_list , Sa_list)\n",
    "plt.box( False)\n",
    "plt.axhline(0)\n",
    "plt.axvline(0)\n",
    "\n",
    "plt.xlabel( \"Period (s)\")\n",
    "plt.ylabel( \"Sa (g)\")"
   ]
  },
  {
   "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 : 5\n",
    "    \n",
    "2- ?\n",
    "<br><br>\n",
    "\n",
    "<br>\n",
    "</td>\n",
    "</tr>\n",
    "</table>"
   ]
  },
  {
   "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
}