Comparison of `concreteproperties` with spColumn using CSA A23.3-19

concrete_properties_A23.3-19.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d51d10dc-4e08-4b71-9137-2bf8c9e4fdd2",
   "metadata": {},
   "source": [
    "# Comparing `concreteproperties` with spColumn using CSA A23.3-19"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69ffc4e6-7d42-4962-9e5b-438be2b158a9",
   "metadata": {},
   "source": [
    "## `concreteproperties` imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "601f9cfd-6e2f-459d-9614-be721b941eee",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "15b260b4-f79c-472d-8eb1-aaa370c2a99a",
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a163286-3ad6-47db-9fad-37a902c26878",
   "metadata": {},
   "source": [
    "## Build section"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "e41db56d-5036-4d35-8438-fafb10ff448c",
   "metadata": {},
   "outputs": [],
   "source": [
    "concrete = Concrete(\n",
    "    name=\"35 MPa Concrete\",\n",
    "    density=2.4e-6,\n",
    "    stress_strain_profile=ConcreteLinearNoTension(\n",
    "        elastic_modulus=28.1647e3, # These values conferred with values calculated with spColumn\n",
    "        ultimate_strain=0.0035,\n",
    "    ),\n",
    "    ultimate_stress_strain_profile=RectangularStressBlock(\n",
    "        compressive_strength=0.65*35, # phi_c factor added directly on to f'c\n",
    "        alpha=0.7975, # These values conferred with values calculated with spColumn\n",
    "        gamma=0.8825, # These values conferred with values calculated with spColumn\n",
    "        ultimate_strain=0.0035,\n",
    "    ),\n",
    "    alpha_squash=1.,\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, # phi_s factor added directly on to fy\n",
    "        elastic_modulus=200e3,\n",
    "        fracture_strain=0.05,\n",
    "    ),\n",
    "    colour=\"grey\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76d9b07d-87a4-404c-8ec4-aa5d23a1c7c9",
   "metadata": {},
   "source": [
    "## Generate reinforcing array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "cc4fcff2-7232-461e-a40d-1c5598de2490",
   "metadata": {},
   "outputs": [
    {
     "data": {
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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": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "geom = concrete_rectangular_section(\n",
    "    b=600,\n",
    "    d=400,\n",
    "    dia_top=30,\n",
    "    n_top=5,\n",
    "    dia_bot=30,\n",
    "    n_bot=5,\n",
    "    n_circle=4,\n",
    "    cover=51.32, # spColumn calculates a clear cover based on a provided center-to-edge spacing (40 mm); used the calculated value from spColumn here\n",
    "    area_top=700,\n",
    "    area_bot=700,\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": 41,
   "id": "b0173e1f-7247-4bb9-9cd6-bc6e6ebad24b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-style: italic\">         Ultimate Bending Results          </span>\n",
       "┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┓\n",
       "┃<span style=\"font-weight: bold\"> Property                    </span>┃<span style=\"font-weight: bold\">     Value </span>┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━┩\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Bending Angle - theta       </span>│<span style=\"color: #008000; text-decoration-color: #008000\">         0 </span>│\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Neutral Axis Depth - d_n    </span>│<span style=\"color: #008000; text-decoration-color: #008000\">     162.7 </span>│\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Neutral Axis Parameter- k_u </span>│<span style=\"color: #008000; text-decoration-color: #008000\">    0.4877 </span>│\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Axial Force                 </span>│<span style=\"color: #008000; text-decoration-color: #008000\">   1.5e+06 </span>│\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Bending Capacity - m_x      </span>│<span style=\"color: #008000; text-decoration-color: #008000\"> 5.101e+08 </span>│\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Bending Capacity - m_y      </span>│<span style=\"color: #008000; text-decoration-color: #008000\">         0 </span>│\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Bending Capacity - m_u      </span>│<span style=\"color: #008000; text-decoration-color: #008000\"> 5.101e+08 </span>│\n",
       "└─────────────────────────────┴───────────┘\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[3m         Ultimate Bending Results          \u001b[0m\n",
       "┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┓\n",
       "┃\u001b[1m \u001b[0m\u001b[1mProperty                   \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1m    Value\u001b[0m\u001b[1m \u001b[0m┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━┩\n",
       "│\u001b[36m \u001b[0m\u001b[36mBending Angle - theta      \u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m        0\u001b[0m\u001b[32m \u001b[0m│\n",
       "│\u001b[36m \u001b[0m\u001b[36mNeutral Axis Depth - d_n   \u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m    162.7\u001b[0m\u001b[32m \u001b[0m│\n",
       "│\u001b[36m \u001b[0m\u001b[36mNeutral Axis Parameter- k_u\u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m   0.4877\u001b[0m\u001b[32m \u001b[0m│\n",
       "│\u001b[36m \u001b[0m\u001b[36mAxial Force                \u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m  1.5e+06\u001b[0m\u001b[32m \u001b[0m│\n",
       "│\u001b[36m \u001b[0m\u001b[36mBending Capacity - m_x     \u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m5.101e+08\u001b[0m\u001b[32m \u001b[0m│\n",
       "│\u001b[36m \u001b[0m\u001b[36mBending Capacity - m_y     \u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m        0\u001b[0m\u001b[32m \u001b[0m│\n",
       "│\u001b[36m \u001b[0m\u001b[36mBending Capacity - m_u     \u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m5.101e+08\u001b[0m\u001b[32m \u001b[0m│\n",
       "└─────────────────────────────┴───────────┘\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-style: italic\">         Ultimate Bending Results          </span>\n",
       "┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┓\n",
       "┃<span style=\"font-weight: bold\"> Property                    </span>┃<span style=\"font-weight: bold\">     Value </span>┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━┩\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Bending Angle - theta       </span>│<span style=\"color: #008000; text-decoration-color: #008000\">         0 </span>│\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Neutral Axis Depth - d_n    </span>│<span style=\"color: #008000; text-decoration-color: #008000\">     263.2 </span>│\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Neutral Axis Parameter- k_u </span>│<span style=\"color: #008000; text-decoration-color: #008000\">    0.7889 </span>│\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Axial Force                 </span>│<span style=\"color: #008000; text-decoration-color: #008000\">     3e+06 </span>│\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Bending Capacity - m_x      </span>│<span style=\"color: #008000; text-decoration-color: #008000\"> 4.502e+08 </span>│\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Bending Capacity - m_y      </span>│<span style=\"color: #008000; text-decoration-color: #008000\">         0 </span>│\n",
       "│<span style=\"color: #008080; text-decoration-color: #008080\"> Bending Capacity - m_u      </span>│<span style=\"color: #008000; text-decoration-color: #008000\"> 4.502e+08 </span>│\n",
       "└─────────────────────────────┴───────────┘\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[3m         Ultimate Bending Results          \u001b[0m\n",
       "┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┓\n",
       "┃\u001b[1m \u001b[0m\u001b[1mProperty                   \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1m    Value\u001b[0m\u001b[1m \u001b[0m┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━┩\n",
       "│\u001b[36m \u001b[0m\u001b[36mBending Angle - theta      \u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m        0\u001b[0m\u001b[32m \u001b[0m│\n",
       "│\u001b[36m \u001b[0m\u001b[36mNeutral Axis Depth - d_n   \u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m    263.2\u001b[0m\u001b[32m \u001b[0m│\n",
       "│\u001b[36m \u001b[0m\u001b[36mNeutral Axis Parameter- k_u\u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m   0.7889\u001b[0m\u001b[32m \u001b[0m│\n",
       "│\u001b[36m \u001b[0m\u001b[36mAxial Force                \u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m    3e+06\u001b[0m\u001b[32m \u001b[0m│\n",
       "│\u001b[36m \u001b[0m\u001b[36mBending Capacity - m_x     \u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m4.502e+08\u001b[0m\u001b[32m \u001b[0m│\n",
       "│\u001b[36m \u001b[0m\u001b[36mBending Capacity - m_y     \u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m        0\u001b[0m\u001b[32m \u001b[0m│\n",
       "│\u001b[36m \u001b[0m\u001b[36mBending Capacity - m_u     \u001b[0m\u001b[36m \u001b[0m│\u001b[32m \u001b[0m\u001b[32m4.502e+08\u001b[0m\u001b[32m \u001b[0m│\n",
       "└─────────────────────────────┴───────────┘\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res_1500 = conc_sec.ultimate_bending_capacity(n=1500e3, theta=0)\n",
    "res_1500.print_results(fmt=\"8.4g\")\n",
    "\n",
    "res_3000 = conc_sec.ultimate_bending_capacity(n=3000e3, theta=0)\n",
    "res_3000.print_results(fmt=\"8.4g\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "6e8839f4-a32a-4e2b-ba38-0df65e875fe0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "331d96a3f5d64e54953e9d2293d45c09",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mn_dia = conc_sec.moment_interaction_diagram()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "9064ddc4-46c5-4a71-9614-125cb4fd0c0b",
   "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':'Moment Interaction Diagram'}, xlabel='Bending Moment', ylabel='Axial Force'>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mn_dia.plot_diagram()"
   ]
  },
  {
   "attachments": {
    "f26f3897-85bc-459a-a54e-66a4365d7f1a.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "5ccad043-b9b0-4045-8405-87239c23443a",
   "metadata": {},
   "source": [
    "## Comparison from spColumn\n",
    "\n",
    "**Uniaxial bending about the x-axis**\n",
    "\n",
    "![image.png](attachment:f26f3897-85bc-459a-a54e-66a4365d7f1a.png)\n",
    "\n"
   ]
  },
  {
   "attachments": {
    "1bffe241-b4df-4104-96c7-e737268ba847.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "6fbd879d-d348-4ca4-9bd5-058f645ae79b",
   "metadata": {},
   "source": [
    "![image.png](attachment:1bffe241-b4df-4104-96c7-e737268ba847.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fca33a47-908d-4b80-9968-09561e55316a",
   "metadata": {},
   "source": [
    "# Summary of differences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "a10cb29c-9a1a-42ca-a86d-19335c72598a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import rich"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "0076b685-2ad2-444a-8f94-f991df9018ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">Ultimate bending capacity - Moment about x\n",
       "\n",
       "</pre>\n"
      ],
      "text/plain": [
       "Ultimate bending capacity - Moment about x\n",
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">@ N = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1500</span> kN, cp_mx = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">510089345.7065717</span> vs. sp_mx = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">510250000.0</span> | % diff = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.03</span>%\n",
       "</pre>\n"
      ],
      "text/plain": [
       "@ N = \u001b[1;36m1500\u001b[0m kN, cp_mx = \u001b[1;36m510089345.7065717\u001b[0m vs. sp_mx = \u001b[1;36m510250000.0\u001b[0m | % diff = \u001b[1;36m0.03\u001b[0m%\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">@ N = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3000</span> kN, cp_mx = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">450247698.2955919</span> vs. sp_mx = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">445460000.0</span> | % diff = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-1.07</span>%\n",
       "\n",
       "\n",
       "</pre>\n"
      ],
      "text/plain": [
       "@ N = \u001b[1;36m3000\u001b[0m kN, cp_mx = \u001b[1;36m450247698.2955919\u001b[0m vs. sp_mx = \u001b[1;36m445460000.0\u001b[0m | % diff = \u001b[1;36m-1.07\u001b[0m%\n",
       "\n",
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">Ultimate bending capacity - Neutral axis depth\n",
       "\n",
       "</pre>\n"
      ],
      "text/plain": [
       "Ultimate bending capacity - Neutral axis depth\n",
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">@ N = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1500</span> kN, cp_dn = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">162.74911583694742</span> vs. sp_dn = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">163</span> | % diff = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.15</span>%\n",
       "</pre>\n"
      ],
      "text/plain": [
       "@ N = \u001b[1;36m1500\u001b[0m kN, cp_dn = \u001b[1;36m162.74911583694742\u001b[0m vs. sp_dn = \u001b[1;36m163\u001b[0m | % diff = \u001b[1;36m0.15\u001b[0m%\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">@ N = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3000</span> kN, cp_dn = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">263.2494745093849</span> vs. sp_dn = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">258</span> | % diff = <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2.03</span>%\n",
       "</pre>\n"
      ],
      "text/plain": [
       "@ N = \u001b[1;36m3000\u001b[0m kN, cp_dn = \u001b[1;36m263.2494745093849\u001b[0m vs. sp_dn = \u001b[1;36m258\u001b[0m | % diff = \u001b[1;36m-2.03\u001b[0m%\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "conc_prop_mx_1500 = res_1500.m_x\n",
    "conc_prop_dn_1500 = res_1500.d_n\n",
    "\n",
    "conc_prop_mx_3000 = res_3000.m_x\n",
    "conc_prop_dn_3000 = res_3000.d_n\n",
    "\n",
    "spcol_mx_1500 = 510.25e6\n",
    "spcol_dn_1500 = 163\n",
    "\n",
    "spcol_mx_3000 = 445.46e6\n",
    "spcol_dn_3000 = 258\n",
    "\n",
    "rich.print(\"Ultimate bending capacity - Moment about x\\n\")\n",
    "rich.print(f\"@ N = 1500 kN, cp_mx = {conc_prop_mx_1500} vs. sp_mx = {spcol_mx_1500} | % diff = {round((1 - conc_prop_mx_1500 / spcol_mx_1500) * 100, 2)}%\")\n",
    "rich.print(f\"@ N = 3000 kN, cp_mx = {conc_prop_mx_3000} vs. sp_mx = {spcol_mx_3000} | % diff = {round((1 - conc_prop_mx_3000 / spcol_mx_3000) * 100, 2)}%\\n\\n\")\n",
    "rich.print(\"Ultimate bending capacity - Neutral axis depth\\n\")           \n",
    "rich.print(f\"@ N = 1500 kN, cp_dn = {conc_prop_dn_1500} vs. sp_dn = {spcol_dn_1500} | % diff = {round((1 - conc_prop_dn_1500 / spcol_dn_1500) * 100, 2)}%\")\n",
    "rich.print(f\"@ N = 3000 kN, cp_dn = {conc_prop_dn_3000} vs. sp_dn = {spcol_dn_3000} | % diff = {round((1 - conc_prop_dn_3000 / spcol_dn_3000) * 100, 2)}%\")"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "fe228c2a-c17c-4d3b-b826-609d0da300b2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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