Lesson November 18th

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

Lesson November 18th#

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

Exercise normal stresses#

Given is the following structure and cross-section:

../../_images/structure2.svg

  1. Find the relevant cross-sectional properties.

  2. Find the normal stresses at cross-section \(\text{A}\) and draw the normal stress distribution in this cross-section.

  3. Find the normal stresses in the cross-section just below \(\text{B}\) and draw the normal stress distribution in this cross-section.

Solution assignment 1

  • \(A = 3000 \text{ mm}^2\)

  • \(I_\text{zz} = 2.32 \cdot 10^6 \text{ mm}^4\)

Solution assignment 2

../../_images/stresses1.svg

Solution assignment 3

../../_images/stresses2.svg

Given is the following structure and cross-section:

../../_images/structure21.svg

  1. Find the relevant cross-sectional properties.

  2. Find the normal stresses at cross-section \(\text{B}\) in beam \(\text{AB}\) in points \(\text{E}\), \(\text{F}\), \(\text{G}\), \(\text{H}\).

Solution assignment 1

  • \( A = 36000 \text{ mm}^2\)

  • \( W_\text{z} = 1.8 \cdot 10^6 \text{ mm}^3\)

  • \( W_\text{y} = 0.72 \cdot 10^6 \text{ mm}^3\)

Solution assignment 2

  • \(\sigma_\text{E} = 2.5 \text{ MPa}\)

  • \(\sigma_\text{G} = -7.5 \text{ MPa}\)

  • \(\sigma_\text{H} = -12.5 \text{ MPa}\)

  • \(\sigma_\text{I} = -2.5 \text{ MPa}\)

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