Add bending-moment.ipynb as example

examples/bending-moment.ipynb

@@ -0,0 +1,93 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "dotnet_interactive": {
+     "language": "fsharp"
+    },
+    "polyglot_notebook": {
+     "kernelName": "fsharp"
+    },
+    "vscode": {
+     "languageId": "polyglot-notebook"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "z_bal: 123.00 mm\n"
+     ]
+    }
+   ],
+   "source": [
+    "open FSharp.Data.UnitSystems.SI.UnitSymbols\n",
+    "\n",
+    "[<Measure>]\n",
+    "type mm\n",
+    "\n",
+    "// 1. Define partial safety factors.\n",
+    "let γ_c = 1.5\n",
+    "let γ_s = 1.15\n",
+    "\n",
+    "// 2. Factors to account for long-term effects on concrete.\n",
+    "let α_cc = 0.85\n",
+    "let α_ct = 1.0\n",
+    "\n",
+    "// 3. Selected concrete strength.\n",
+    "let fck = 25.0<N / mm^2>\n",
+    "\n",
+    "// 4. Ultimate concrete design stress.\n",
+    "let fcd = α_cc * fck / 1.5\n",
+    "\n",
+    "// 5. Concrete strain limits.\n",
+    "let εc2 = 0.002\n",
+    "let εcu2 = 0.0035\n",
+    "\n",
+    "// 6. Rebar steel strength.\n",
+    "let fyk = 500.0<N / mm^2>\n",
+    "\n",
+    "// 7. Rebar steel modulus.\n",
+    "let Es = 200_000.0<N / mm^2>\n",
+    "\n",
+    "// 8. Rebar design yield strain.\n",
+    "let εy = fyk / (γ_s * Es)\n",
+    "\n",
+    "// 9. Equation to calculate neutral axis, x.\n",
+    "let x εst εcu2 (d: float<mm>) = d / (1.0 + (εst / εcu2))\n",
+    "let x_partial = x 0.00217 0.0035\n",
+    "\n",
+    "// 10. Stress block reduced to 0.8x depth.\n",
+    "let s d = (x_partial d) * 0.8\n",
+    "\n",
+    "// 11. Calculate concrete compressive force.\n",
+    "let Fcc d (b: float<mm>) = fcd * (s d) * b\n",
+    "\n",
+    "// 12. Calculate moment.\n",
+    "let z d = d - (s d / 2.0)\n",
+    "let M d b = (Fcc d b) * (z d)\n",
+    "\n",
+    "// 13. Calculate area of steel.\n",
+    "let As d b = (M d b) / (0.87 * fyk * (z d))\n",
+    "\n",
+    "M 440.0<mm> 260.0<mm> / 10E6\n",
+    "As 440.0<mm> 260.0<mm>\n",
+    "\n",
+    "let x_limit = 0.45\n",
+    "let z_bal (d: float<mm>) = d - (0.8 * x_limit * d) / 2.0\n",
+    "\n",
+    "printfn $\"z_bal: %.2f{z_bal 150.0<mm>} mm\""
+   ]
+  }
+ ],
+ "metadata": {
+  "language_info": {
+   "name": "csharp"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}