AISC LRFD 1.pdf

Comm. C3.] STABILITY BRACING 199The unbraced length, L b , in Equations C3-4 and C3-6 is assumed to be equal to thelength L q that enables the column to reach P u . When the actual bracing spacing isless than L q , the calculated required stiffness may become quite conservative sincethe stiffness equations are inversely proportional to L b . In such cases, L q can be substitutedfor L b . For example, a W1253 (W31079) with P u = 400 kips (1 780 kN)can have a maximum unbraced length of 14 ft (4.3 m) for A36 (A36M) steel. If theactual bracing spacing is 8 ft (2.4 m), then 14 ft (4.3 m) may be used in EquationsC3-4 and C3-6 to determine the required stiffness.Winter’s rigid model would derive a brace force of 0.8 percent P u which accountsonly for lateral displacement force effects. To account for the additional force dueto member curvature, this theoretical force has been increased to one percent P u .4. BeamsBeam bracing must prevent twist of the section, not lateral displacement. Both lateralbracing (for example, joists attached to the compression flange of a simply supportedbeam) and torsional bracing (for example, a cross frame or diaphragmbetween adjacent girders) can effectively control twist. Lateral bracing systems thatare attached near the beam centroid are ineffective. For beams with double curvature,the inflection point can not be considered a brace point because twist occurs atthat point (Galambos, 1998). A lateral brace on one flange near the inflection pointalso is ineffective. In double curvature cases the lateral brace near the inflectionpoint must be attached to both flanges to prevent twist, or torsional bracing must beused. The beam brace requirements are based on the recommendations by Yura(1993).4a. Lateral BracingFor lateral bracing, the following stiffness requirement was derived followingWinter’s approach: br = 2N i (C b P f ) C t C d / L b(C-C3-3)whereN i = 1.0 for relative bracing= (4-2/n) for discrete bracingn = number of intermediate bracesP f = beam compressive flange force= 2 2EI yc /L bI yc = out-of-plane moment of inertia of the compression flangeC b = moment modifier from Chapter FC t = accounts for top flange loading (use C t =1.0 for centroidal loading)= 1 + (1.2/n)C d = double curvature factor (compression in both flanges)=1+ (M S /M L ) 2M S = smallest moment causing compression in each flangeM L = largest moment causing compression in each flangeThe C d factor varies between 1.0 and 2.0 and is applied only to the brace closest tothe inflection point. The term (2N i C t ) can be conservatively approximated as 10 forany number of nodal braces and 4 for relative bracing and (C b P f ) can be approximatedby M u / h which simplifies Equation C-C3-3 to the stiffness requirementsLRFD Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION