WORLD FOR CIVIL

_{ALLOWABLE STRESS DESIGN FOR BUILDING BEAMS}

_{The maximum fiber stress in bending for laterally supported beams and girders is F b = 0.66F y if they are compact, except for hybrid girders and members with yield points exceeding 65 ksi (448.1 MPa). F b = 0.60F y for non-compact sections. F y is the minimum specified yield strength of the steel, ksi (MPa). Table lists values of F b for two grades of steel.}

Yield strength,ksi (MPa)	Compact0.66Fy (MPa)	Non-compact,0.60 Fy (MPa)
36 ( 248.2)	24 (165.5)	22 (151.7)
50 (344.7)	33 (227.5)	30 (206.8)

_{The allowable extreme-fiber stress of 0.60F y applies to laterally supported, unsymmetrical members, except channels, and to non-compact box sections. Compression on outer surfaces of channels bent about their major axis should not exceed 0.60F y}

_{The allowable stress of 0.66F y for compact members should be reduced to 0.60F y when the compression flange is unsupported for a length, in (mm), exceeding the smaller of}

_{l max =76.0b f / ( F y ) ^½}

_{l max =20,000 / F y d / A f}

_{where b f =width of compression flange, in (mm)}

_{d=beam depth, in (mm)}

_{A f =area of compression flange, in ² (mm) ²
The allowable stress should be reduced even more when l/r T exceeds certain limits, where l is the unbraced length, in (mm), of the compression flange, and r T is the radius of gyration, in (mm), of a portion of the beam consisting of the compression flange and one-third of the part of the web in compression.
For (102,000 C b / F y ) ^½ £ l / r T £ (510,000 C b / F y ) ^½ use
F b =[ 2 / 3 - F y (l / r T ) ² / 1,530,000C b ] F y
For l / r T > ( 510,000 C b / F y ) ^½ use
F b = 170,000 C b / ( l/r T ) ²
Where C b = modifier for moment gradient}

_{When, however, the compression flange is solid and nearly rectangular in cross section, and its area is not less than that of the tension flange, the allowable stress may be taken as}

_{F b = 12,00C b / ld/A f
When Eq. applies (except for channels), F b should be taken as the larger of the values computed from Eqs above, but not more than 0.60F y .
The moment-gradient factor C b in Eqs. above may be computed from
C b = 1.75 + 1.05 M 1 / M 2 + 0.3 ( M 1 / M 2 ) ² £ 2.3 (9.6)
Where M 1 = smaller beam end moment, and M 2 = larger beam end moment.
The algebraic sign of M 1 / M 2 is positive for double curvature bending and negative for single-curvature bending. When the bending moment at any point within an unbraced length is larger than that at both ends, the value of C b should be taken as unity. For braced frames, C b should be taken as unity for computation of F bx and F by .
Equations can be simplified by introducing a new term:
Q=(l / r T ) ² F y
Now, for 0.2 £ Q £ 1,
F b =( 2 – Q ) F y /3
For Q > 1:
F b =F y / 3 Q}