Lesson November 25th

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

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 as well!

Exercise Transforming tensors#

Given is the following structure and cross-section:

../../_images/structure3.svg

  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 \(\text{A}\).

Solution assignment 1

Normal force centre is given by:

../../_images/NC2.svg

  • \(A \approx 17500 \text{ mm}^2\)

  • \(I_{zz} \approx 655 \cdot 10^6 \text{ mm}^4\)

Solution assignment 2

  • \(\sigma_\text{just below G} = +6.73 \text{ MPa}\)

  • \(\tau_\text{just below G} = +0.164 \text{ MPa}\)

  • \(\sigma_\text{H} = +6.73 \text{ MPa}\)

  • \(\tau_\text{H} = 0 \text{ MPa}\)

  • \(\sigma_\text{I} = -2 \text{ MPa}\)

  • \(\tau_\text{I} = +0.35 \text{ MPa}\)

  • \(\sigma_\text{just right of C} = -8.53 \text{ MPa}\)

  • \(\tau_\text{just right of C} = -0.12 \text{ MPa}\)

Solution assignment 3

  • \(\sigma_\text{1, just below G} = +6.73 \text{ MPa}\)

  • \(\sigma_\text{2, just below G} = -0.0040 \text{ MPa}\)

  • \(\sigma_\text{1, H} = +6.73 \text{ MPa}\)

  • \(\sigma_\text{2, H} = 0 \text{ MPa}\)

  • \(\sigma_\text{1, I} = 0.59 \text{ MPa}\)

  • \(\sigma_\text{2, I} = -2.06 \text{ MPa}\)

  • \(\sigma_\text{1, just right of C} = 0.0018 \text{ MPa}\)

  • \(\sigma_\text{2, just right of C} = -8.5 \text{ MPa}\)

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