connorferster/concreteproperties-areas.ipynb

## concreteproperties-areas.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2c2d157c-57db-4e93-8921-5f7d1effe23f",
   "metadata": {},
   "source": [
    "# Demonstration of bar area provided by user"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "7860db4c-441a-4ed5-a7ff-0c4fdc5a36e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "702.1538120589527"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import pi\n",
    "area_30M = pi * 29.9**2 / 4\n",
    "area_30M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "764773fc-e509-4203-9de6-f72f5011c9fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "from concreteproperties.material import Concrete, Steel\n",
    "from concreteproperties.stress_strain_profile import (\n",
    "    ConcreteLinearNoTension,\n",
    "    RectangularStressBlock,\n",
    "    SteelElasticPlastic,\n",
    ")\n",
    "from sectionproperties.pre.library.concrete_sections import concrete_rectangular_section\n",
    "from concreteproperties.concrete_section import ConcreteSection\n",
    "from concreteproperties.pre import add_bar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "d18939a6-38f0-4342-adc8-ebf7f379a94f",
   "metadata": {},
   "outputs": [],
   "source": [
    "concrete = Concrete(\n",
    "    name=\"35 MPa Concrete\",\n",
    "    density=2.4e-6,\n",
    "    stress_strain_profile=ConcreteLinearNoTension(\n",
    "        elastic_modulus=26.8779e3,\n",
    "        ultimate_strain=0.0035,\n",
    "        compressive_strength=35*0.65\n",
    "    ),\n",
    "    ultimate_stress_strain_profile=RectangularStressBlock(\n",
    "        compressive_strength=0.65*35,\n",
    "        alpha=0.7975,\n",
    "        gamma=0.8825,\n",
    "        ultimate_strain=0.0035,\n",
    "    ),\n",
    "    flexural_tensile_strength=3.5,\n",
    "    colour=\"lightgrey\",\n",
    ")\n",
    "\n",
    "steel = Steel(\n",
    "    name=\"400 MPa Steel\",\n",
    "    density=7.85e-6,\n",
    "    stress_strain_profile=SteelElasticPlastic(\n",
    "        yield_strength=0.85*400,\n",
    "        elastic_modulus=200e3,\n",
    "        fracture_strain=0.05,\n",
    "    ),\n",
    "    colour=\"grey\",\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "1191135c-0115-4ff5-b5f7-c46b2b4c3817",
   "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"
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'Reinforced Concrete Section'}>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "geom = concrete_rectangular_section(\n",
    "    b=600,\n",
    "    d=400,\n",
    "    dia_top=29.9,\n",
    "    n_top=5,\n",
    "    dia_bot=29.9,\n",
    "    n_bot=5,\n",
    "    n_circle=4,\n",
    "    cover=40,\n",
    "    area_top=area_30M,\n",
    "    area_bot=area_30M,\n",
    "    conc_mat=concrete,\n",
    "    steel_mat=steel,\n",
    ")\n",
    "\n",
    "conc_sec = ConcreteSection(geom)\n",
    "conc_sec.plot_section()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "e6f61f94-0e2b-4342-a224-03f121b2886b",
   "metadata": {},
   "outputs": [],
   "source": [
    "area_provided_1 = geom.geoms[0].geom.area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "2f9a3ee1-4940-43f8-8c41-b3be19599e60",
   "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"
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'Reinforced Concrete Section'}>"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "geom = concrete_rectangular_section(\n",
    "    b=600,\n",
    "    d=400,\n",
    "    dia_top=29.9,\n",
    "    n_top=5,\n",
    "    dia_bot=29.9,\n",
    "    n_bot=5,\n",
    "    n_circle=4,\n",
    "    cover=40,\n",
    "    conc_mat=concrete,\n",
    "    steel_mat=steel,\n",
    ")\n",
    "\n",
    "conc_sec = ConcreteSection(geom)\n",
    "conc_sec.plot_section()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "0b1b5edc-ca84-4980-b397-6a1df3666703",
   "metadata": {},
   "outputs": [],
   "source": [
    "area_calculated_2 = geom.geoms[0].geom.area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "af4603ae-8aed-4f47-bfa8-7d0a39f941e9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.029256408835790393\n"
     ]
    }
   ],
   "source": [
    "rho_1 = 1 - area_provided_1 / (400*600)\n",
    "print(rho_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "1aa38101-6182-48cb-9ac7-4f678c34bc1f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.018625208333333476\n"
     ]
    }
   ],
   "source": [
    "rho_2 = 1 - area_calculated_2 / (400*600)\n",
    "print(rho_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "f7cb1833-130c-4fa7-9ac7-177941308b6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Difference in reinforcing ratio: 0.010631200502456917'"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f\"Difference in reinforcing ratio: {rho_1 - rho_2}\""
   ]
  }
 ],
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