Question

A hollow circular column of external diameter 200 mm and thickness 5 mm is 6 m long. For the material properties of the column, a column is considered short if the slenderness ratio is less than or equal to 70, and long if the ratio is more than 100. For intermediate columns, a linear variation in critical stress from a yield stress of 280 MPa to a proportional limit of 210 MPa may be used. Find the load capacity of the column.

Answer 1

The load capacity of the column is determined by calculating the slenderness ratio to assess if it is short, intermediate, or long, and then applying the appropriate stress value based on this categorization to the cross-sectional area of the column.

Step-by-step explanation:

To calculate the load capacity of a hollow circular column, we must first determine whether it is short, long, or intermediate based on its slenderness ratio. The slenderness ratio is calculated by dividing the effective length of the column by the radius of gyration. In this case, we're given that the external diameter is 200 mm (therefore the radius is 100 mm), and the thickness is 5 mm, which makes the internal diameter 190 mm (internal radius 95 mm). The area moment of inertia for a hollow circular section is given by (π/4) * (R^4 - r^4), where R and r are the external and internal radii, respectively. The radius of gyration (k) is found by taking the square root of the Area Moment of Inertia divided by the cross-sectional area of the column. Using these values, we can calculate the slenderness ratio (L/k).

If the column is in the intermediate range, we use the linear variation of the critical stress from the yield stress to the proportional limit. Finally, the load capacity of the column can be calculated by multiplying the critical stress by the cross-sectional area of the column.