The maximum slenderness ratio of lacing bars in a built-up column is 145.

Explanation:
The slenderness ratio is a measure of how slender or slender a member is. It is calculated by dividing the effective length of the member by its radius of gyration. The slenderness ratio is used to determine the stability of the member under compressive loads.

In the case of lacing bars in a built-up column, the slenderness ratio is calculated as the effective length of the lacing bar divided by its radius of gyration. The effective length of the lacing bar is the distance between the points of connection to the column flanges. The radius of gyration is a measure of how the material is distributed around the centroidal axis of the bar.

The maximum slenderness ratio of 145 is determined by considering the stability requirements of the lacing bars. Lacing bars are typically used to provide lateral stability to the built-up column and prevent it from buckling under compressive loads. To ensure the adequate stability of the lacing bars, a maximum slenderness ratio is specified. This maximum slenderness ratio is determined based on the material properties, column dimensions, and design standards.

The value of 145 is determined based on extensive research, testing, and analysis of different column configurations and loading conditions. It ensures that the lacing bars have sufficient stiffness and strength to resist buckling and provide the necessary lateral stability to the column.

By limiting the slenderness ratio to 145, the design ensures that the lacing bars are adequately sized and proportioned to effectively resist compressive loads and prevent buckling. This helps in maintaining the overall stability and integrity of the built-up column structure.

It is important to note that the maximum slenderness ratio may vary depending on the specific design standards and codes followed. Designers should always refer to the relevant design codes and standards to determine the appropriate maximum slenderness ratio for lacing bars in a built-up column.