Steel roof trusses – effective length of a rafter between nodes for out-of-plane buckling A rafter member has lateral restraints (nodes) at a spacing of L measured perpendicular to the truss plane. Assuming simple (pin-like) restraint at nodes out of plane, the effective length for out-of-plane buckling should be taken as:

Introduction:
For slender truss members, out-of-plane buckling often governs design. Effective length captures boundary conditions provided by purlins, bracing, or panel nodes perpendicular to the truss plane. This question tests your ability to associate a realistic effective-length factor with lateral restraints at panel points.

Given Data / Assumptions:

• Rafter with lateral restraint at nodes spaced at L out of the truss plane.
• Out-of-plane restraint provides lateral support but negligible rotational fixity.
• Member is axially loaded in compression.

Concept / Approach:

When a compression member is braced laterally at points along its length, each unbraced segment buckles between adjacent points with end conditions approximating pin–pin about the out-of-plane axis. For pin–pin conditions, the effective length equals the clear segment length, so Le = 1.0 * L. Reductions below L (e.g., 0.85L or 0.7L) imply partial fixity; increases above L imply weaker restraint.

Step-by-Step Solution:

Verification / Alternative check:

Design guides for truss members commonly recommend K ≈ 1.0 for segments braced at panel points unless additional rotational restraint is demonstrated.

Why Other Options Are Wrong:

2.00L and 1.50L overstate unbraced length, unconservative if real bracing exists. 0.85L or 0.70L require partial fixity not specified in the problem.

Common Pitfalls:

Confusing in-plane and out-of-plane restraints; assuming rotational fixity at purlins without connection evidence; overlooking intermediate bracing provided by sheeting.

Final Answer:

1.00 L