Formulas: Design by Critical Temperature Method

Equation A-4-21

The critical temperature of a tension member is permitted to be calculated as follows:

T_{c r}=816-306 \ln \left(\frac{R_{u}}{R_{n}}\right) \text { in }{ }^{\circ} \mathrm{F}

The critical temperature of a compression member for flexural buckling is permitted to be calculated as follows:

T_{c r}=1580-0.814\left(\frac{L_{c}}{r}\right)-1300\left(\frac{P_{u}}{P_{n}}\right) \text { in }{ }^{\circ} \mathrm{F}

T_{c r}=858-0.455\left(\frac{L_{c}}{r}\right)-722\left(\frac{P_{u}}{P_{n}}\right) \text { in }^{\circ} \mathrm{C}

The critical temperature of a continuously braced beam not supporting a concrete slab is permitted to be calculated as follows:

T_{c r}=816-306 \ln \left(\frac{M_{u}}{M_{n}}\right) \text { in }{ }^{\circ} \mathrm{F}

T_{c r}=435-170 \ln \left(\frac{M_{u}}{M_{n}}\right) \text { in }{ }^{\circ} \mathrm{C}

where

$\begin{aligned} M_{n} & =\text { nominal flexural strength due to yielding at ambient temperature } \\ & \text { determined in accordance with the provisions in Section F2.1, kip-in. } \\ & \text { (N-mm) }\end{aligned}$
$\begin{aligned} M_{u} & =\text { required flexural strength at elevated temperature, determined using the } \\ & \text { load combination in Equation A-4-1 and greater than } 0.01 M_{n}, \text { kip-in. } \\ & \text { (N-mm) }\end{aligned}$

$T_{c r}=$ critical temperature in ${ }^{\circ} \mathrm{F}\left({ }^{\circ} \mathrm{C}\right)$