Buckling

Buckling is a sudden failure mode of slender compression members, characterized by lateral deflection due to instability. The Euler buckling formula (P_cr = π²EI / (KL)²) gives the critical load for a column. The effective length factor (K) depends on end conditions: pinned-pinned (K=1), fixed-fixed (K=0.5), fixed-pinned (K=0.7), and fixed-free (K=2).

Governing FormulaP_cr = π² E I / (K L)²

Knowledge Check

10 Questions

1.A steel column with E = 200 GPa, I = 20×10⁶ mm⁴, and length 4 m is pinned at both ends. What is the Euler buckling load?

2.If the effective length of a column is doubled, the buckling load decreases by a factor of:

3.For a column with one end fixed and the other free, the effective length factor (K) is:

4.The slenderness ratio of a column is defined as:

5.A column with a slenderness ratio below the critical value is classified as:

6.The Euler buckling formula is valid for:

7.A column with fixed-pinned end conditions has an effective length factor K of:

8.If the moment of inertia (I) of a column's cross-section is quadrupled, the buckling load:

9.Which cross-section shape is most resistant to buckling for a given cross-sectional area?

10.The critical buckling stress for a long column is: