Assignment_8

Assignment_8 - with wave length of the order of the side...

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1 MAE157 – Lightweight structures (Winter 08) Homework Assignment #8 Due in class on Thursday, Mar 20 th THIS ASSIGNMENT IS OPTIONAL. IF YOU TURN IT IN, THE LOWEST GRADE IN THE HOMEWORK WILL BE DISCARDED. The beam depicted in figure 1 has a square cross section, with side a and thickness t . The length of the beam is L. The beam is compressed axially with a uniform load P , and is simply supported (i.e. pin-jointed) at both ends. We are interested in finding the buckling load. Notice that the beam can buckle in two different ways: (a) Globally , i.e. with a wavelength of the order of its length, L (this is the traditional buckling mechanism for beams that we saw in class) (b) Locally , i.e. with each wall buckling as a plate, with two-dimensional sine waves
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Unformatted text preview: with wave length of the order of the side dimension, a . Whether the local or the global buckling mode will occur depends on the geometry of the beam, i.e. on the dimensions L, a and t . Figure 1: Geometry and loading condition 2 1. In a Cartesian plane with the ratio (t/a) on the x-axis and the ratio (a/L) on the y-axis, draw the curve that separates the regions where the local and the global modes are active (see figure). 2. Using ABAQUS, probe the accuracy of your curve, by tracing the transition between global and local modes (see figure). Figure 2: Buckling map for the square section beam of figure 1....
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Assignment_8 - with wave length of the order of the side...

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