applications_elastic_response_spectrum.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "<div style=\"display: flex; align-items: center;\">\n",
    "    <img src=\"https://github.com/nagelt/Teaching_Scripts/raw/9d9e29ecca4b04eaf7397938eacbf116d37ddc93/Images/TUBAF_Logo_blau.png\" width=\"500\" height=\"auto\" height=\"auto\" style=\"margin-right: 100px;\" />\n",
    "    <div>\n",
    "        <p><strong>Prof. Dr. Thomas Nagel</strong></p>\n",
    "        <p>Chair of Soil Mechanics and Foundation Engineering<br>Geotechnical Institute<br>Technische Universität Bergakademie Freiberg.</p>\n",
    "        <p><a href=\"https://tu-freiberg.de/en/soilmechanics\">https://tu-freiberg.de/en/soilmechanics</a></p>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Erdbebensicheres Bauen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Module laden"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Erdbebenersatzkraft nach dem Bemessungsspektrum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "abschnittsweise definiert"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ers(T, p):\n",
    "    \n",
    "    if T < 0:\n",
    "        Sd = 0\n",
    "        print(\"Warning, unphysical period\")\n",
    "    elif T < p[\"TB\"]:\n",
    "        Sd = p[\"agR\"]*p[\"gl\"]*p[\"S\"]*(1+(T/p[\"TB\"])*(2.5/p[\"q\"] - 1))\n",
    "    elif T < p[\"TC\"]:\n",
    "        Sd = p[\"agR\"]*p[\"gl\"]*p[\"S\"]*2.5/p[\"q\"]\n",
    "    elif T < p[\"TD\"]:\n",
    "        Sd = p[\"agR\"]*p[\"gl\"]*p[\"S\"]*(2.5/p[\"q\"])*p[\"TC\"]/T\n",
    "    else:\n",
    "        Sd = p[\"agR\"]*p[\"gl\"]*p[\"S\"]*(2.5/p[\"q\"])*p[\"TC\"]*p[\"TD\"]/(T**2)\n",
    "    \n",
    "    if Sd < 0:\n",
    "        Sd = 0\n",
    "        print(\"Warning, negative Sd value encountered\")\n",
    "    \n",
    "    return Sd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameter des Bemessungsspektrums festlegen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "para = {\"agR\": 0.8, \"gl\": 1.2, \"q\": 1.5, \"S\": 1.25, \"TB\": 0.05, \"TC\": 0.25, \"TD\": 2.0}        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grafische Darstellung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": [
    "Tgrid = np.linspace(0, 5)\n",
    "Sgrid = [ers(TT, para) for TT in Tgrid]       \n",
    "Tgrid\n",
    "plt.plot(Tgrid, Sgrid)\n",
    "plt.xlabel(\"$T$ [s]\")\n",
    "plt.ylabel(\"$S_d$ [m/s$^2$]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eigenperiode des Gebäudes schätzen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T1=0.1917 s\n"
     ]
    }
   ],
   "source": [
    "h = 6.0\n",
    "Ct = 0.05\n",
    "T1 = Ct*h**(3/4) \n",
    "print(\"T1={:6.4f} s\".format(T1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Erdbebenersatzkraft berechnen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F1=160.0000 kN, q1max=53.3333 kN/m\n"
     ]
    }
   ],
   "source": [
    "Sd1 = ers(T1, para)\n",
    "m = 80e3\n",
    "gamma = 1.0\n",
    "F1 = Sd1*m*gamma\n",
    "print(\"F1={:6.4f} kN, q1max={:6.4f} kN/m\".format(F1/1e3, F1*2e-3/h)) "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.13"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}