Calculation of the critical Euler force

For a VARH element (form node i to node j), we can define:

L	beam length
I_i, I_j	moment of inertia at end i and j
A_i, A_j	sectional area at end i and j
E	modulus of Young
N_cr	critical Euler force
R_i, R_j	beam stiffness at end i and j

The stiffness R and R' is given by:

The critical Euler force is given by

To calculate α, the next steps are followed :

1. Calculate L, I_i, I_j, R_i, R_j, R'_i, R'_j, ξ

2. We suppose that

3. Calculate a, b, c and d as follows

4.For a beam in non-sway system, we solve

For a beam in sway system, we solve

5. When a solution is found, we check if

6. If not, then recalculate a,b,c en d as follows :

and resolve the proper equation of 4.

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