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

where:

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.

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