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Author: GeoCalcul

Newmark_Beta_SDOF_Load_Cases.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "d33bd728",
+   "metadata": {},
+   "source": [
+    "# Newmark-Beta Method for SDOF System"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3065bf3a",
+   "metadata": {},
+   "source": [
+    "This notebook demonstrates solving an SDOF system using the Newmark-Beta method under different load conditions: constant, variable (sinusoidal), and synthetic earthquake loads."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "44fc6fb7",
+   "metadata": {},
+   "source": [
+    "## Constant Load"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f24a7410",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "\n",
+    "df_constant_load = pd.DataFrame({'Time (s)': [0.0, 0.1, 0.2, 0.30000000000000004, 0.4, 0.5, 0.6000000000000001, 0.7000000000000001, 0.8, 0.9, 1.0], 'Displacement (m)': [0.0, 0.004950495049504951, 0.019654935790608768, 0.04372557145921435, 0.07659302120121562, 0.11751934725861855, 0.16561433647864884, 0.2198546359741512, 0.27910533575238816, 0.3421435467060408, 0.40768348731943865], 'Velocity (m/s)': [0.0, 0.09900990099009903, 0.19507891383197729, 0.2863337995401344, 0.37101519529989113, 0.44751132584816744, 0.5143884585524384, 0.5704175313576086, 0.6145964642071305, 0.6461677548659223, 0.6646310574020348], 'Acceleration (m/s^2)': [1.0, 0.9801980198019802, 0.9411822370355845, 0.8839154771275561, 0.8097124380675753, 0.7202101728979491, 0.6173324811874652, 0.5032489749159366, 0.3803296820745006, 0.2510961311013302, 0.11816991962091539]})\n",
+    "df_constant_load"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c32641cc",
+   "metadata": {},
+   "source": [
+    "## Variable Load"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "128f52e0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "\n",
+    "df_variable_load = pd.DataFrame({'Time (s)': [0.0, 0.1, 0.2, 0.30000000000000004, 0.4, 0.5, 0.6000000000000001, 0.7000000000000001, 0.8, 0.9, 1.0], 'Displacement (m)': [0.0, 0.0014549139908229532, 0.008130540984096959, 0.023096286703440428, 0.045973719365043894, 0.07297820038138335, 0.09827019741971187, 0.11610190587291387, 0.12294080026182365, 0.11876029667838651, 0.10700556690689637], 'Velocity (m/s)': [0.0, 0.029098279816459065, 0.10441426004902105, 0.19490065433784837, 0.26264799889422097, 0.2774416214325681, 0.22839831933400223, 0.12823584973003788, 0.008542038048157674, -0.09215210971690035, -0.14294248571290247], 'Acceleration (m/s^2)': [0.0, 0.5819655963291812, 0.9243540083220578, 0.8853738774544873, 0.4695730136729619, -0.17370056290602065, -0.8071654790652989, -1.1960839130139895, -1.197792320623615, -0.8160906346775456, -0.1997168852424962]})\n",
+    "df_variable_load"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f3ee4014",
+   "metadata": {},
+   "source": [
+    "## Earthquake Load"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2b211163",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "\n",
+    "df_earthquake_load = pd.DataFrame({'Time (s)': [0.0, 0.1, 0.2, 0.30000000000000004, 0.4, 0.5, 0.6000000000000001, 0.7000000000000001, 0.8, 0.9, 1.0], 'Displacement (m)': [0.0, 2.5187322852073553e-07, 9.246499069476067e-06, 0.00013521308329256105, 0.0009168912908176206, 0.003416532710327638, 0.008209707715151811, 0.01453671593546621, 0.021172861052939626, 0.02744128130107861, 0.033112996507467546], 'Velocity (m/s)': [0.0, 5.03746457041471e-06, 0.0001748550522486919, 0.002344476632213008, 0.013289087518288183, 0.036703740871912166, 0.059159759224571284, 0.0673804051817167, 0.06534249716775162, 0.06002590779502809, 0.0534083963327506], 'Acceleration (m/s^2)': [1.1179959516236032e-06, 9.96312954566706e-05, 0.0032967204581088733, 0.04009571114117743, 0.17879650658032603, 0.2894965604921534, 0.15962380656102865, 0.004789112581879362, -0.04554727286118149, -0.06078451459328987, -0.07156571465225997]})\n",
+    "df_earthquake_load"
+   ]
+  }
+ ],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 5
+}