Unbraced Lengths Research Articles

A General Solution for the Governing Bending Equation

The allowable bending stress Fb for most wide-flange sections is governed only by AISC Eq. 1.5-7, and Eq. 1.5-6 never need to be checked for these sections. Those wideflange sections for which Fb is determined by Eq. 1.5-6, and the unbraced lengths for which these forms govern, are easily identified by simultaneous solution of the bending equations for the common roots of length for any given yield stress Fy and bending coefficient Cb. Tables of these sections and a general solution for determining the governing bending equation are presented in this paper. The tables are useful supplements to Stockwells simplification of the bending equations and to Burgett and Tides extension of the use of the beam charts to designs with bending coefficients greater than unity. The tables and their use are presented in the body of this paper; simultaneous solutions of the bending equations for common roots of length are given in the appendix.

Nomograph for Design of Channel Section Beams

Channel sections are frequently used in the construction of operating platforms, passageways, stairs, etc. of industrial structures. They behave as beams and their moment of resistance for actual unbraced length must be calculated. The formulas used for channel sections are given in AISC Specification Sect. 1.5.1.4.6a. The value of d/Af (in these formulas) is available in manufacturers tables of properties for structural shapes as well as in the AISC Manual of Steel Construction. The value of Cb may be taken as unity for a simply supported system. For the convenience of designers, the AISC Manual of Steel Construction contains charts for determining the moment of resistance, MR, of wide flange beams when their unbraced lengths are known. However, no such charts are available for channel sections. A nomograph is presented herein for rapid determination of the values.

Allowable Loads on Beams without Lateral Support

Beams with unbraced lengths along the compression flange greater than Lc or Lu require the designer to consider factors other than section modulus alone, since torsional properties and the lateral bending strength of the compression flange influence the ability of the beam to resist lateral buckling. This paper presents tables developed to aid the designer in rapidly selecting the most economical WF or I section for laterally unsupported beams.