## Irr2 rT y F

12,000 Cb

where I is the distance between cross-sections braced against twist or lateral displacement of the compression flange (in.), rT is the radius of gyration of a section comprising the compression flange plus 3 of the compression web area taken about an axis in the plane of the web (in.), Af is the compression flange area (in.2), d is the depth of cross-section (in.), Cb = 12.5Mmax/(2.5Mmax + 3MA + 4MB + 3MC), where Mmax, MA, MB, MC are absolute values of the maximum moment, quarter-point moment, midpoint moment, and three-quarter point moment along the unbraced length of the member, respectively. (For simplicity in design, Cb can conservatively be taken as unity.)

It should be cautioned that Equations 4.30 and 4.31 are applicable only to I and Channel shapes with an axis of symmetry in, and loaded in the plane of the web. In addition, Equation 4.31 is applicable only if the compression flange is solid and approximately rectangular in shape and its area is not less than the tension flange.

4.5.1.1.1.2 Compact Section Members Bent about Their Minor Axes — Since lateral torsional buckling will not occur for bending about the minor axes, regardless of the value of Lb, the allowable flexural stress is

4.5.1.1.1.3 Noncompact Section Members Bent about Their Major Axes — For Lb < Lc

where Lc is defined as in Equation 4.28. For Lb > Lc, Fb is given in Equations 4.29 to 4.31.

4.5.1.1.1.4 Noncompact Section Members Bent about Their Minor Axes — Regardless of the value of Lb,

4.5.1.1.1.5 Slender Element Sections — Refer to Section 4.10. 4.5.1.1.2 Shear Strength Criterion

For practically all structural shapes commonly used in constructions, the shear resistance from the flanges is small compared to the webs. As a result, the shear resistance for flexural members is normally determined on the basis of the webs only. The amount of web shear resistance is dependent on the width-thickness ratio h/tw of the webs. If h/tw is small, the failure mode is web yielding. If h/tw is large, the failure mode is web buckling. To avoid web shear failure, the computed shear stress, fv, shall not exceed the allowable shear stress, Fv, given by

tW sj Fy

CV h 380

—-Fy < 0.40Fy, if —> —ffiffi 2.89 7 - y tw ^/Fy

where

Cv = 45,000kv/[Fy(h/t„)2], if C < 0.8 = [190/(h/tw)]P(kv/Fy), if Cv > 0.8 kv = 4.00 + 5.34/(a/h)2, if a/h < 1.0 = 5.34 + 4.00/(a/h)2, if a/h > 1.0 tw = web thickness (in.)

a = clear distance between transverse stiffeners (in.) h = clear distance between flanges at section under investigation (in.)

### 4.5.1.1.3 Criteria for Concentrated Loads

4.5.1.1.3.1 Local Flange Bending — If the concentrated force that acts on the beam flange is tensile, the beam flange may experience excessively bending, leading to failure by fracture. To preclude this type of failure, transverse stiffeners are to be provided opposite the tension flange unless the length of the load when measured across the beam flange is less than 0.15 times the flange width, or if the flange thickness, tf, exceeds

Fy where Pbf is the computed tensile force multiplied by | if the force is due to live and dead loads only or by 3 if the force is due to live and dead loads in conjunction with wind or earthquake loads (kip) and Fy is the specified minimum yield stress (ksi).

4.5.1.1.3.2 Local Web Yielding — To prevent local web yielding, the concentrated compressive force, R, should not exceed 0.66Rn, where Rn is the web yielding resistance given in Equation 4.54 or 4.55, whichever applies.

4.5.1.1.3.3 Web Crippling — To prevent web crippling, the concentrated compressive force, R, should not exceed 0.50Rn, where Rn is the web crippling resistance given in Equations 4.56, 4.57, or 4.58, whichever applies.

4.5.1.1.3.4 Sideways Web Buckling — To prevent sideways web buckling, the concentrated compressive force, R, should not exceed Rn, where Rn is the sideways web buckling resistance given in Equation 4.59 or 4.60, whichever applies, except the term Crt^tfh2 is replaced by 6800t3./h.

4.5.1.1.3.5 Compression Buckling of the Web — When the web is subjected to a pair of concentrated force acting on both flanges, buckling of the web may occur if the web depth clear of fillet, dc, is greater than

4100 t^ypy

where tw is the web thickness, Fy is the minimum specified yield stress, and Pbf is as defined in Equation 4.36.

### 4.5.1.1.4 Deflection Criterion

Deflection is a serviceability consideration. Since most beams are fabricated with a camber that somewhat offsets the dead load deflection, consideration is often given to deflection due to live load only. For beams supporting plastered ceilings, the service live load deflection preferably should not exceed L/360 where L is the beam span. A larger deflection limit can be used if due considerations are given to ensure the proper functioning of the structure.

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