The maximum slenderness ratio of lacing bars in built-up columns is 145. The slenderness ratio is a measure of the column's ability to resist buckling under compressive loads. It is calculated by dividing the effective length of the column by its radius of gyration.

Lacing bars are typically used in built-up columns to enhance their load-carrying capacity and stability. They are positioned diagonally between the flanges and webs of the built-up column, providing additional support and preventing buckling.

To determine the maximum slenderness ratio of lacing bars in built-up columns, several factors need to be considered:

1. Effective Length: The effective length of the column is the distance between the points of zero moment. It depends on the column's boundary conditions, such as whether it is fixed or pinned at its ends. The effective length affects the buckling behavior of the column.

2. Radius of Gyration: The radius of gyration is a measure of the column's cross-sectional shape and distribution of material around its centroid. It is calculated as the square root of the moment of inertia divided by the cross-sectional area. A smaller radius of gyration indicates a more compact and efficient column shape.

3. Slenderness Ratio: The slenderness ratio is calculated by dividing the effective length of the column by its radius of gyration. It represents the column's relative flexibility and susceptibility to buckling. A higher slenderness ratio indicates a higher risk of buckling.

The maximum slenderness ratio of lacing bars in built-up columns is determined based on industry standards and design codes. These standards take into account various factors, including material properties, column geometry, and loading conditions, to ensure the structural integrity and stability of the column.

Based on these considerations, the maximum slenderness ratio of lacing bars in built-up columns is determined to be 145. This value ensures that the lacing bars provide adequate support and prevent buckling under compressive loads. It represents a balance between the column's load-carrying capacity and stability, considering the overall design and safety requirements.