The criteria to select whether we should use the Euler formula or the J. B. Johnson formula to calculate for the critical load (Pcr) of the column is related to the value of the actual slenderness ratio or column constant, Cc. It is defined as
E = Modulus of elasticity of the material of the column
Sy = Yield strength of the column material
The use of the above column constant (Cc) is as follows,
- Determine the length and end fixity of the column
- Define the value of the constant (K) according to the type of end fixity
- Compute the effective length (Le) from Le = KL
- From the cross section shape and dimensions, compute the radius of gyration (r) from r = sqrt(I/A)
- Compute the slenderness ratio from Slenderness ratio = Le/r_min = KL/r_min
- From the material of the column, compute the column constant (Cc) as per the above formula
- Check whether KL/r > Cc?
- If yes, the column is Long: Use the Euler formula
- If no, the column is Short: Use the J. B. Johnson formula
In the next post, let's check the formulas of critical load (Pcr) of Euler and J. B. Johnson.