Strength of Materials

11.5 END CONDITIONS FOR LONG COLUMNS

In practice, the failure of long columns have been observed essentially due to buckling. The following four end conditions have to be adopted in practice (Figure 11.4).

 

 

Fig. 11.4 Sign conventions.

 

1. Both ends are hinged or pinned
2. One end is free and the other is fixed
3. Both ends are fixed
4. One end is fixed and the other end is pinned

The deflection is zero for hinged end.

The deflection and slope are zero for fixed end.

The following sign conventions for the bending of the columns will be adopted.

1. A moment causing the column to bend with its convexity towards its initial centre line (Figure 11.4(a)), ...