Design of a Rectangular Column

To determine the appropriate design for a rectangular column with given dimensions and support conditions, we need to consider the column length, support conditions, and loading conditions. In this case, the column has a length of 4m and both ends are restrained against rotation and held in position. The correct design option is to consider the column as axially loaded with uniaxial bending moment (option C).

Short Column vs. Long Column

Short Column: A short column is one in which the ratio of its effective length to the smallest lateral dimension is less than a certain limit, typically 12-15. Short columns primarily resist the applied load through direct compression. In this case, the column dimensions are 600 x 450 mm, and the length is 4m. The ratio of length to width is 4m/0.45m = 8.88, which is less than the typical limit, indicating that the column can be considered as a short column.

Long Column: A long column is one in which the ratio of its effective length to the smallest lateral dimension is greater than the limit. Long columns are susceptible to buckling and require additional consideration to account for the bending moments induced by lateral displacement. Since the given column is a short column, the long column design option is not applicable.

Axially Loaded with Uniaxial Bending Moment

In the given design option (C), the column is considered as axially loaded with uniaxial bending moment. This means that the column will experience both axial compression and bending due to the applied load and the support conditions.

When a column is axially loaded with uniaxial bending moment, the design should consider the combined effects of compression and bending. The bending moment induces additional stresses in the column, which need to be accounted for in the design.

The design process for an axially loaded column with uniaxial bending moment includes the following steps:

1. Determine the axial load: Calculate the axial load on the column based on the applied load and the support conditions. In this case, the axial load is the compression force acting along the length of the column.

2. Determine the bending moment: Calculate the bending moment induced in the column due to the support conditions and the applied load. Since both ends of the column are restrained against rotation, the bending moment will be uniaxial.

3. Check for combined stresses: Calculate the combined stresses in the column due to axial compression and bending. The design should ensure that the resulting stresses do not exceed the allowable limits for the given material.

4. Select an appropriate column size: Based on the calculated axial load and bending moment, select a suitable column size that can resist the combined effects of compression and bending.

In summary, the given rectangular column with dimensions 600 x 450 mm and a length of 4m should be designed as an axially loaded column with uniaxial bending moment. This design option considers the combined effects of compression and bending due to the applied load and the support conditions.