3. Assignments Beams
Course subject(s)
Beams
On this page the assignments of the chapter Beams can be found. Read the descriptions carefully and good luck.
Assignment 1
In general, it can be stated that the Timoshenko method to determine the critical load for a beam is more accurate than the Rayleigh method. Demonstrate that this is not always the case.
Assignment 2
Given is a beam with length L and bending stiffness EI which is hinged on its left hand side, and connected via a hinge to a vertical spring on the right hand side.
- Determine the minimum spring stiffness such that the beam has an Euler buckling load.
- Draw the relation between the spring stifness and the beam buckling load in a graph.
Assignment 3
A horizontal simply supported beam with bending stiffness EI and length L is loaded with a uniform distributed load q in axial direction. Calculate the critical distributed load q_critical.
Assignment 4
Given is a horizontal simply supported beam with bending stiffness EI and length L. The beam is supported by a continuous distribution of springs with stiffness kf over its entire length.
Calculate the buckling load and buckling mode of this system.
Hint: make use of potential energy for an inextensible beam (which means that EAε is zero, but then you need to consider the axial load to be an external load), the Euler-Lagrange equations to find the equilibrium equations and adjacent equilibrium for the stability equations.
Buckling of Structures by TU Delft OpenCourseWare is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Based on a work at https://ocw.tudelft.nl/courses/buckling-of-structures/.