products2 and 3 steel basics added + explanation cross sectional quantities

book/basics/steel/explanation_cross_sectional_quantities.ipynb

@@ -5,7 +5,42 @@
    "metadata": {},
    "source": [
     "# Explanation cross sectional properties\n",
-    "\n"
+    "\n",
+    "## Castellated beams IPE/HEA/HEB\n",
+    "```{figure} Images/moment_of_inertia.png\n",
+    "---\n",
+    "align: left\n",
+    "---\n",
+    "```\n",
+    "\n",
+    "### The carthesian coordinate system\n",
+    "In this coordinate system the axes are defined as follows:  \n",
+    "x-axis: length axis of the element  \n",
+    "y-axis: cross product of x and z axis  \n",
+    "z-axis: downward axis\n",
+    "\n",
+    "| Name                                       | Structural Mechanics  | NEN-EN 1993                                      |\n",
+    "|--------------------------------------------|------------------------- | ----------------------------------------------|\n",
+    "| Moment of inertia around y-axis (Resistance against moments in x-z plane) | $I_{zz}$ | $I_{y}$ |\n",
+    "| Moment of inertia around z-axis (Resistance against moments in x-y plane ) | $I_{yy}$ | $I_{z}$ |\n",
+    "| Section modulus around y-axis (Resistance against moments in x-z plane) | $W_{zz}$ | $W_{y}$ |\n",
+    "| Section modulus around z-axis (Resistance against moments in x-y plane) | $W_{yy}$ | $W_{z}$ |\n",
+    "\n",
+    "\n",
+    "## Top hat beams\n",
+    "```{figure} Images/radius_of_gyration.png\n",
+    "---\n",
+    "align: left\n",
+    "---\n",
+    "```\n",
+    "\n",
+    "The radius of gyration is needed to determine the slenderness of a structure. When the radius of gyration and the buckling curve are known, the buckling force can be determined.\n",
+    "\n",
+    "Radius of gyration around strong axis (y-axis)  \n",
+    "$ i_y = \\sqrt{\\frac{I_y}{A}} $\n",
+    "\n",
+    "Radius of gyration around weak axis (z-axis)  \n",
+    "$ i_z = \\sqrt{\\frac{I_z}{A}} $"
    ]
   },
   {

book/basics/steel/products_2_cold_rolled_sections.ipynb

@@ -4,7 +4,40 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Products 2: cold-rolled sections"
+    "# Products 2: cold-rolled sections\n",
+    "\n",
+    "## U and C profiles\n",
+    "```{figure} Images/u_and_c_profiles.png\n",
+    "---\n",
+    "align: left\n",
+    "---\n",
+    "Cold formed sections with and without stiffeners are available with equal (eq) or unequal (ue) height and width.\n",
+    "```\n",
+    "\n",
+    "| Type  | Size     | $h$ (mm)   | $b$ (mm)   |\n",
+    "|-------|----------|----------|----------|\n",
+    "| $CFU_{eq}$ | 10 - 100 | 10 - 100 | 10 - 100 |\n",
+    "| $CFU_{ue}$ | 10 - 160 | 10 - 160 | 10 - 70  |\n",
+    "| $CFC$   | 25 - 100 | 25 - 100 | 25 - 50  |\n",
+    "\n",
+    "Applications: Are used in residential buildings, carcase work, storage systems and finishings. Also used as purlins, or floorbeams. Due to plastic strains during fabrication the material properties differ from hot rolled sections.\n",
+    "\n",
+    "## L and Z profiles\n",
+    "```{figure} Images/L_and_Z_sections.png\n",
+    "---\n",
+    "align: left\n",
+    "---\n",
+    "Cold formed L or Z sections with and without stiffeners with equal (eq) or unequal (eu) height and width.\n",
+    "```\n",
+    "\n",
+    "| Type  | Size      | $h$ (mm)   | $b$ (mm)   |\n",
+    "|-------|-----------|----------|----------|\n",
+    "| $CF_{Leq}$ | 15 - 80   | 15 - 80  | 15 - 80  |\n",
+    "| $CFL_{ue}$ | 20 - 100  | 20 - 100 | 15 - 50  |\n",
+    "| $CFZ$  | 30 - 50   | 30 - 50  | 38 - 57  |\n",
+    "\n",
+    "\n",
+    "Applications: Are used in residential buildings, carcase work, storage systems and finishings. Also used as purlins, or floorbeams. Due to plastic strains during fabrication the material properties differ from hot rolled sections."
    ]
   },
   {

book/basics/steel/products_3_welded_sections.ipynb

@@ -4,7 +4,34 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Products 3: welded sections"
+    "# Products 3: welded sections\n",
+    "\n",
+    "## Castellated beams IPE/HEA/HEB\n",
+    "```{figure} Images/castellated_beams.png\n",
+    "---\n",
+    "align: left\n",
+    "---\n",
+    "Non-residential buidlings. Castellated beams can be built by cutting a H or I section in one cut without loss of material. Round holes are also possible, but are less economical due to material losses and extra cutting.\n",
+    "```\n",
+    "\n",
+    "| Type | Size        | $h$ (mm)      | $b$ (mm)      |\n",
+    "|------|-------------|-------------|-------------|\n",
+    "| IPE  | 180 - 600   | 270 - 900   | 91 - 220    |\n",
+    "| HEA  | 180 - 1000  | 257 - 1485  | 180 - 300   |\n",
+    "| HEB  | 180 - 1000  | 270 - 1500  | 180 - 300   |\n",
+    "\n",
+    "Applications: Large, light spans with possibilities to incorporate building services in the structural height. Strength increases only slightly. Stiffness of the sections \n",
+    "increases despite the increased shear deformations. Castellated beams are very sensitive to lateral torsion buckling and have reduced shear capacity.\n",
+    "\n",
+    "## Top hat beams\n",
+    "```{figure} Images/welded_integrated_beams.png\n",
+    "---\n",
+    "align: left\n",
+    "---\n",
+    "Welded integrated beams (top hat beams)\n",
+    "```\n",
+    "\n",
+    "Applications: Top hat beams are very useful in combination with prefab concrete floors such as hollow core slabs or composite floors. (see cb 6 and cb 7). By integrating the beam in the floor, the total structural height is reduced and fire resistance increased."
    ]
   },
   {