Lesson December 6th

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

Lesson December 6th#

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

Exercise Failure models#

Given is the following structure. It represents the Prinses Amaliabrug, a bicycle bridge near Dordrecht.

../../_images/structure6.svg

  1. Find the relevant cross-sectional properties.

  2. Find the bending- en torsional moment distribution.

  3. Find the shear- and normal forces in cross-section just right of \(\text{D}\) at point \(\text{E}\)

  4. Draw the stress state in cross-section just right of \(\text{D}\) at point \(\text{E}\) in the principal stress plane including Tresca’s failure criterium for unknown yield stress.

  5. What should be the minimum yield stress according to Tresca?

Solution assignment 1

\(A_m = 3.23 \text{ m}^2\)

Solution assignment 2

../../_images/Mline1.svg
../../_images/Mtline.svg

Solution assignment 3

  • \(\sigma_\text{E} = -0.0174 \text{ MPa}\)

  • \(\tau_\text{E} = 12.53 \text{ MPa}\)

../../_images/stress.svg

Solution assignment 4

../../_images/s1s2.svg

Solution assignment 5

  • \(f_y > 25.06 \text{ MPa}\)

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