Built-up compression members – spacing of connectors: Two channels placed back-to-back form a built-up compression member. When connected by rivets, the spacing between the connections should be such that the slenderness ratio of each individual component between adjacent connectors does not exceed which limit?

Introduction / Context:
Built-up compression members (e.g., two channels back-to-back) need adequate interconnection to force the components to act together and to prevent local buckling of individual elements between connectors. Codes limit the slenderness ratio of each component between connections.

Given Data / Assumptions:

• Two channels back-to-back.
• Connections by rivets (similar guidance for bolts/welds).
• We seek the maximum allowable component slenderness between connectors.

Concept / Approach:

For laced systems, a commonly used rule is that the slenderness ratio of each component (measured between adjacent lacing or batten points) should not exceed about 50. This ensures sufficient stiffness of the built-up member and prevents excessive out-of-plane buckling of individual elements. Battened members sometimes adopt an even more stringent limit near 40, but for lacing or closely spaced connectors, 50 is a standard exam reference.

Step-by-Step Solution:

Verification / Alternative check:

Classical steel design texts for built-up members provide limits in the 40–50 range; 50 is widely used for laced systems to prevent local instability.

Why Other Options Are Wrong:

• 40: conservative, more typical for batten-type spacing.
• 60, 70: too lenient; may allow local buckling between connectors.

Common Pitfalls:

• Calculating slenderness with the wrong radius of gyration.
• Over-spacing connectors to save fasteners at the expense of stability.

Final Answer:

50.