Formulas: tees and double angles loaded in the plane of symmetry

Equation C-F9-1

F_{c r}=\frac{\pi^{2} E k}{12\left(1-\mathrm{v}^{2}\right)\left(\frac{b}{t}\right)^{2}}

where

$\begin{aligned} \mathrm{v} & =0.3 \text { (Poisson's ratio) } \\ b / t & =\text { plate width-to-thickness ratio } \\ k & =\text { plate buckling coefficient }\end{aligned}$

Equation C-F9-2

\bar{\lambda}=\frac{b}{t} \sqrt{\frac{F_{y}}{E}} \sqrt{\frac{12\left(1-\mathrm{v}^{2}\right)}{\pi^{2} k}}

Formula 3

In the traditional scheme, it is assumed the critical stress is the yield stress, $F_{y}$ , as long as $\bar{\lambda} \leq 0.7$ .

\bar{\lambda} \leq 0.7

Formula 4

Elastic buckling, governed by Equation C-F9-1, commences when $\bar{\lambda}=1.24$ and $F_{c r}=0.65 F_{y}$ .

F_{c r}=0.65 F_{y}

Formula 5

The limiting width-to-thickness ratio up to which $F_{c r}=F_{y}$ is (using $v=0.3$ and $k=1.61$ ),

F_{c r}=F_{y}

Formula 6

F_{c r}=\frac{0.70 E}{\left(\frac{d}{t_{w}}\right)^{2}}

Formula 7

F_{c r}=\frac{\pi^{2} E k}{12\left(1-\mathrm{v}^{2}\right)\left(\frac{b}{t}\right)^{2}}=\frac{1.52 E}{\left(\frac{d}{t_{w}}\right)^{2}}

Formula 8

\left(\frac{d}{t_{w}}\right)_{r}=\lambda_{r}=1.52 \sqrt{\frac{E}{F_{y}}}

Formula 9

Both standards maintain a plateau at 1.0 until the onset of buckling at $d/t_w = 0.84 \sqrt{E/F_y}$ .

d/t_w = 0.84 \sqrt{E/F_y}

Equation C-F9-3

M_{e}=\frac{\pi}{L_{b}} \sqrt{E I_{x} G J}

Found in

TEES AND DOUBLE ANGLES LOADED IN THE PLANE OF SYMMETRY