Formulas: other I-shaped members with compact or noncompact webs bent about their major axis

Formula 1

These two factors can vary from unity to as high as $M_{p} / M_{y c} \leq 1.6$ and $M_{p} / M_{y t} \leq 1.6$.

Formula 2

Formula 3

Formula 4

$A$: Total cross-sectional area ($A = A_c + A_t + A_w$.

Formula 5

Defined by height $h_c = 2(y - t_{fc}$.

Formula 6

Applicable range: $t_{fc} \leq y \leq d - t_{ft}$.

Formula 7

Defined by height $h_p = \frac{A - 2A_c}{t_w}$.

Formula 8

Valid when $2A_c \leq A \leq (A_w + 2A_c$.

Formula 9

Formula 10

Formula 11

If $\lambda>\lambda_{r w}$, then the web is slender and the design is governed by Section F5.

Formula 12

The basic maximum nominal moment is $R_{p c} M_{y c}=R_{p c} F_{y} S_{x c}$ corresponding to the compression flange, and $R_{p t} M_{y t}=R_{p t} F_{y} S_{x t}$ corresponding to tension flange yielding, which is applicable only when $M_{y t}<M_{y c}$ or $S_{x t}<S_{x c}$ (beams with the larger flange in compression).

Formula 13

Formula 14

Formula 15

Equation C-F4-3

For a more accurate solution, especially when the loads are not applied at the centroid of the member, the designer is directed to Galambos (2001), White and Jung (2003), and Ziemian (2010). The following alternative equations in lieu of Equations F4-5 and F4-8 are provided by White and Jung:

Equation C-F4-4

where

the coefficient of monosymmetry, $\beta_{x}=0.9 h \alpha\left[\left(I_{y c} / I_{y t}\right)-1\right]$, the warping constant, $C_{w}=h^{2} I_{y c} \alpha$, where $\alpha=1 /\left[\left(I_{y c} / I_{y t}\right)+1\right]$, and $F_{L}$ is the magnitude of the flexural stress in compression at which the lateral-torsional buckling is influenced by yielding. In Equations F4-6a and F4-6b, this stress level is taken generally as the smaller of $0.7 F_{y}$ in the compression flange, or the compression flange stress when the tension flange reaches the yield strength, but not less than $0.5 F_{y}$.

Formula 18

where the coefficient of monosymmetry, $\beta_{x}=0.9 h \alpha\left[\left(I_{y c} / I_{y t}\right)-1\right]$, the warping constant, $C_{w}=h^{2} I_{y c} \alpha$, where $\alpha=1 /\left[\left(I_{y c} / I_{y t}\right)+1\right]$, and $F_{L}$ is the magnitude of the flexural stress in compression at which the lateral-torsional buckling is influenced by yielding.

Formula 19

Formula 20

Found in

• OTHER I-SHAPED MEMBERS WITH COMPACT OR NONCOMPACT WEBS BENT ABOUT THEIR MAJOR AXIS