This problem takes another approach to the column buckling application in Section 18.1.3. If the beam is hinged at both ends, we obtain the boundary value problem along with the boundary conditions,...

This problem takes another approach to the column buckling application in Section 18.1.3.

If the beam is hinged at both ends, we obtain the boundary value problem

along with the boundary conditions, to show that the result is a matrix eigenvalue problem of the form

where

is a symmetric tridiagonal matrix. What is the relationship between

and the critical loads?

For copper,

<sup>9

2</sup>

Assume

⁴
and that

Using

find the smallest three values of

compute the critical loads, and graph

<sub>i

i</sub>

for each value of
on the same axes. Relate the results to the discussion in Section 18.1.3.

Suppose that

is a

matrix containing the eigenvectors corresponding to

<sub>1

2</sub>

and

₃
as well as the zero values at the endpoints. Each row has the format

_{y2 y3 ... y24 y25}

^T

To create a good looking graph place these statements in your program.