diff --git a/book/week_13/session_1/intro.ipynb b/book/week_13/session_1/intro.ipynb index 578f8bc..974a0f6 100644 --- a/book/week_13/session_1/intro.ipynb +++ b/book/week_13/session_1/intro.ipynb @@ -2,10 +2,8 @@ "cells": [ { "cell_type": "markdown", - "id": "33b18457", - "metadata": { - "cell_marker": "r\"\"\"" - }, + "id": "b89c7e41", + "metadata": {}, "source": [ "```{index} Transformations; Class exercise using analytical formulas\n", "```\n", @@ -14,6 +12,10 @@ ":text: \".ipynb\"\n", "```\n", "\n", + "```{custom_download_link} intro.md\n", + ":text: \".md\"\n", + "```\n", + "\n", "(lesson13.1)=\n", "# Lesson November 25th\n", "\n", @@ -78,7 +80,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6c66e8e3", + "id": "41f3415c", "metadata": { "tags": [ "remove-cell" @@ -122,8 +124,7 @@ ], "metadata": { "jupytext": { - "cell_markers": "\"\"\"", - "formats": "ipynb,py:percent" + "cell_markers": "\"\"\"" }, "kernelspec": { "display_name": "base", diff --git a/book/week_13/session_1/intro.md b/book/week_13/session_1/intro.md new file mode 100644 index 0000000..f173611 --- /dev/null +++ b/book/week_13/session_1/intro.md @@ -0,0 +1,120 @@ +--- +jupytext: + cell_markers: '"""' + text_representation: + extension: .md + format_name: myst + format_version: 0.13 + jupytext_version: 1.16.1 +kernelspec: + display_name: base + language: python + name: python3 +--- + +```{index} Transformations; Class exercise using analytical formulas +``` + +```{custom_download_link} intro.ipynb +:text: ".ipynb" +``` + +```{custom_download_link} intro.md +:text: ".md" +``` + +(lesson13.1)= +# Lesson November 25th + +During today's lesson you'll work on a complex exercise on the topic of the Transforming tensors. Please ask your questions regarding the [homework](homework13.1) as well! + +## Exercise Transforming tensors + +Given is the following structure and cross-section: + +```{figure} intro_data/structure.svg +:align: center +``` + +1. Find the relevant cross-sectional properties. +2. Find the normal and shear stresses just below $\text{G}$, in $\text{H}$, in $\text{I}$ and just right of $\text{C}$ in cross-section $\text{A}$. +3. Find the principal values of the stresses in the points just below $\text{G}$, in $\text{H}$, in $\text{I}$ and just right of $\text{C}$ in cross-section $\text{A}$. + +````{admonition} Solution assignment 1 +:class: tip, dropdown + +Normal force centre is given by: +```{figure} intro_data/NC.svg +:align: center +``` + +- $A \approx 17500 \text{ mm}^2$ +- $I_{zz} \approx 655 \cdot 10^6 \text{ mm}^4$ + +```` + +````{admonition} Solution assignment 2 +:class: tip, dropdown + +- $\sigma_\text{just below G} = +6.73 \text{ MPa}$ +- $\tau_\text{just below G} = +0.164 \text{ MPa}$ +- $\sigma_\text{H} = +6.73 \text{ MPa}$ +- $\tau_\text{H} = 0 \text{ MPa}$ +- $\sigma_\text{I} = -2 \text{ MPa}$ +- $\tau_\text{I} = +0.35 \text{ MPa}$ +- $\sigma_\text{just right of C} = -8.53 \text{ MPa}$ +- $\tau_\text{just right of C} = -0.12 \text{ MPa}$ + +```` + +````{admonition} Solution assignment 3 +:class: tip, dropdown + +- $\sigma_\text{1, just below G} = +6.73 \text{ MPa}$ +- $\sigma_\text{2, just below G} = -0.0040 \text{ MPa}$ +- $\sigma_\text{1, H} = +6.73 \text{ MPa}$ +- $\sigma_\text{2, H} = 0 \text{ MPa}$ +- $\sigma_\text{1, I} = 0.59 \text{ MPa}$ +- $\sigma_\text{2, I} = -2.06 \text{ MPa}$ +- $\sigma_\text{1, just right of C} = 0.0018 \text{ MPa}$ +- $\sigma_\text{2, just right of C} = -8.5 \text{ MPa}$ + +```` + +Test of adding more text + +```{code-cell} +:tags: [remove-cell] + +Izz = 655e6 + +tau_G = -3e3 * -250*10*286 / 20 / Izz +print(tau_G) + +tau_C = -3e3 * -250*20*(286-500) / 40 / Izz +print(tau_C) + +sigma_G = +6.73 +tau_G = -tau_G +sigma_G_1 = 1/2 * (sigma_G + 0) + ((1/2 * (sigma_G + 0))**2 + tau_G**2)**0.5 +sigma_G_2 = 1/2 * (sigma_G + 0) - ((1/2 * (sigma_G + 0))**2 + tau_G**2)**0.5 +print(sigma_G_1, sigma_G_2) + +sigma_H = +6.73 +tau_G = 0 +sigma_H_1 = 1/2 * (sigma_H + 0) + ((1/2 * (sigma_H + 0))**2 + tau_G**2)**0.5 +sigma_H_2 = 1/2 * (sigma_H + 0) - ((1/2 * (sigma_H + 0))**2 + tau_G**2)**0.5 +print(sigma_H_1, sigma_H_2) + +sigma_I = -2 +tau_I = +0.35 +sigma_I_1 = 1/2 * (sigma_I + 0) + ((1/2 * (sigma_I + 0))**2 + tau_I**2)**0.5 +sigma_I_2 = 1/2 * (sigma_I + 0) - ((1/2 * (sigma_I + 0))**2 + tau_I**2)**0.5 +print(sigma_I_1, sigma_I_2) + +sigma_C = -8.53 +tau_C = -tau_C +sigma_C_1 = 1/2 * (sigma_C + 0) + ((1/2 * (sigma_C))**2 + tau_C**2)**0.5 +sigma_C_2 = 1/2 * (sigma_C + 0) - ((1/2 * (sigma_C))**2 + tau_C**2)**0.5 +print(sigma_C_1, sigma_C_2) +``` diff --git a/book/week_13/session_1/intro.py b/book/week_13/session_1/intro.py index 9d97da3..37d1126 100644 --- a/book/week_13/session_1/intro.py +++ b/book/week_13/session_1/intro.py @@ -2,7 +2,6 @@ # jupyter: # jupytext: # cell_markers: '"""' -# formats: ipynb,py:percent # text_representation: # extension: .py # format_name: percent @@ -23,6 +22,10 @@ :text: ".ipynb" ``` +```{custom_download_link} intro.md +:text: ".md" +``` + (lesson13.1)= # Lesson November 25th