Slenderness Limits to Control Vibrations in Axially Loaded Members with Doubly Symmetric Cross Sections

Present Canadian design standards for steel members prescribe a member slenderness limit of 200 for compression members and 300 for tension members to guard, in part, against excessive vibrations. The different threshold limits in both types of members reflect the fact that compressive forces tend to lower the natural frequency of members while tensile forces tend to increase it. The stepwise threshold slenderness limits presently provided in standards, while recognizing the influence of the type of axial force on the natural frequency of the member, do not reflect the effect of axial force magnitude within the member. Within this context, the present study aims to present slenderness limits for axially loaded members associated with a more consistent serviceability criterion based on the natural vibration, which reflects the level of axial loading. Toward this goal, a parametric study is conducted on compressive and tensile members with doubly symmetric cross sections by (a) developing a shell finite element model in Abaqus based on stressed eigenvalue natural vibration analysis and (b) closed-form analytical solutions. The study examines the effect of cross-sectional geometry, axial load level, and connection details on the natural frequencies of axially loaded members and proposes slenderness limits aimed to control excessive vibrations under human activity.