Lesson December 2nd

# Matplotlib compatibility patch for Pyodide
import matplotlib
if not hasattr(matplotlib.RcParams, "_get"):
    matplotlib.RcParams._get = dict.get

Lesson December 2nd#

During today’s lesson you’ll work on a complex exercise on the topic of the Stresses due to torsion. Please ask your questions regarding the homework as well!

Exercise Stresses due to torsion#

Given is the following structure:

../../_images/structure5.svg

  1. Find the relevant cross-sectional properties.

  2. Find the maximum shear stress and its location.

  3. Find the principal stresses at that point and their directions. Draw a square stress element to represent those stresses.

Solution assignment 1

../../_images/NC3.svg

  • \(A = 9020 \text{ mm}^2\)

  • \(I_{zz} = 37.2 \cdot 10^6 \text{ mm}^4 \)

  • \(I_t = 364 \cdot 10^3 \text{ mm}^4\)

Solution assignment 2

In segment \(\text{AD}\) in grey crosses:

../../_images/max.svg

\(\left| \tau_{\max} \right| = 477.6 \text{ MPa} \)

Solution assignment 3

../../_images/max2.svg
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