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2. Assignments Discrete Structures

Course week(s) Week 3
Course subject(s) Discrete Structures

On this page the assignments of the chapter Discrete Structures can be found. Read the descriptions carefully and good luck.

Assignment 1

Study the examples in paragraphs 2.9 and 2.10 of the book of Pignataro. Which one of the two structures is the most sensitive to imperfections? Explain your answer.

Assignment 2

A vertical rigid bar of length 2L is hinged at its top and bottom. The top part is able to move up and down as well. The bar is loaded with a vertical force N which does not change direction when the top part of the bar moves down. The bar is connected to the ground using an axial spring with stiffness k in the middle of the beam, and at the same location, a torsional spring with stiffness ko is located.

  1. Find the critical ratio between k and kθ for which there is no more snap-through behaviour in the post-critical equilibrium path (i.e. find the value for the ratio for which the equilibrium path transitions from a snap-through equilibrium path to a stable post-critical path.
  2. Prove that at this value for the ratio between k and kθ the stability of the bifurcation point changes from unstable to stable.

Assignment 3

Given is a flexbile beam with length 3L. The beam is divided in three equal length rigid elements, which are connected with hinges. The beams are supported at the hinge points with vertical axial springs of stiffness k. The beam is loaded with an axial force N. The beam has two independent degrees-of-freedom theta and phi. The springs can be assumed to remain vertical even if the beam elements move horizontal.

  1. Why are there only two independent degrees-of-freedom although the beam has three elements?
  2. What are the critical loads of the structure?
  3. What are the critical modes of the structure?

Assignment 4

Given is a flexible beam with length L. The beam is divided in n equal length rigid elements, which are connected with springs of stiffness kθ, and all springs are equal.

  1. Show that the lowest critical load converges to a certain value if the number of elements increases (demonstrate this by assuming a certain set of numerical values for the beam properties).
  2. What is the value for the spring stiffness if the lowest critical load should be equal to:

Variable EI is the overall bending stiffness of the beam.

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Buckling of Structures by TU Delft OpenCourseWare is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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