mirror of
https://github.com/TeachBooks/template.git
synced 2026-11-13 06:35:52 +00:00
80 lines
2.4 KiB
Text
80 lines
2.4 KiB
Text
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"# Explanation cross sectional properties\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}} $"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.8.0"
|
|
},
|
|
"widgets": {
|
|
"application/vnd.jupyter.widget-state+json": {
|
|
"state": {},
|
|
"version_major": 2,
|
|
"version_minor": 0
|
|
}
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 4
|
|
}
|