Slenderness ratio limit for a tie member in a roof truss (Member may experience stress reversal under wind or seismic actions.)

Introduction:
Slenderness limits prevent excessive vibration, lateral deflection, and second-order effects. For tension members that may see load reversal (becoming compression under wind or earthquake), stricter limits apply.

Given Data / Assumptions:

• Member type: tie in a roof truss.
• Possible stress reversal due to wind/seismic actions.
• Slenderness ratio is L_e / r, where L_e is effective length and r is radius of gyration.

Concept / Approach:
Ties normally work in tension and can have higher slenderness limits. However, if reversal is possible, they must satisfy lower limits similar to compression members to avoid buckling during transient compression.

Step-by-Step Solution:
1) Classify the member as a tie with potential reversal.2) Adopt the slenderness cap recommended for such members.3) The standard cap in this case is 180.

Verification / Alternative check:
Compare with ties that never see reversal; those may adopt higher limits (e.g., 350). The reduction to 180 reflects the compression vulnerability.

Why Other Options Are Wrong:
210, 250, 350 are too high for members that may see compression; they risk instability under wind/seismic load cases.

Common Pitfalls:
Ignoring accidental compression in design combinations; using overall length instead of effective length; not checking r about the weak axis.

Final Answer:
180