16.7Temperature Increase with Time in Unprotected Members

The time (t) at which the limiting temperature (T_i) is attained shall be calculated using the following equations:

• a) Three-sided fire exposure condition

$t=5.2+0.0221 T+\frac{0.433 T_{\mathrm{i}}}{k_{\mathrm{sm}}}$

• b) Four-sided fire exposure conditio

$r=4.7+0.0263 T+\frac{0.213 T_{1}}{k_{\mathrm{sm}}}$

where

• $t \quad=$ time from the start of the test, in min,
• $\begin{aligned} T & =\text { steel temperature, in }{ }^{\circ} \mathrm{C}, 500^{\circ} \mathrm{C} \\ & \leq T \leq 750^{\circ} \mathrm{C} \text {, and }\end{aligned}$
• $\begin{aligned} k_{\mathrm{sm}} & =\text { exposed surface area to mass } \\ & \text { ratio, } 2 \times 10^{3} \mathrm{~mm}^{2} / \mathrm{kg} \leq k_{\mathrm{sm}} \leq 35 \\ & \times 10^{3} \mathrm{~mm}^{2} / \mathrm{kg} .\end{aligned}$

For temperatures below 500°C, linear interpolation shall be used, based on the time at 500”C and an initial temperature of 20”C at tequals O.