16.6Temperature Increase with Time in Protected Members

16.6.1.1

For beams and for all members with a four-sided fire exposure condition, the limiting temperature $\left(T_{1}\right)$ shall be taken as the average of all of the temperatures measured at the thermocouple locations on all sides.

16.6.1.2

For columns with a three-sided fire exposure condition, the limiting temperature (T) shall be taken as the average of the temperatures measured at the thermocouple locations on the face farthest from the wall. Alternatively, the temperatures from members with a four-sided fire exposure condition and having the same surface area to mass ratio may be used.

16.6.2.1 Regression analysis

The relationship between temperature (T) and time (t) for a series of tests on a group shall be calculated by least-square regression as follows:

$t=k_{0}+k_{1} h_{i}+k_{2} \frac{h_{i}}{k_{\mathrm{sm}}}+k_{3} T+k_{4} h_{i} T+k_{5} \frac{h_{i} T}{k_{\mathrm{sm}}}+k_{6} \frac{T}{k_{\mathrm{sm}}}$

where

$t=$ time from the start of the test, in min;

$\begin{aligned} k_{0} \text { to } k_{6} & =\text { regression coefficients from test data } \\ & \text { (see 16.6.2.2.); }\end{aligned}$

$\begin{aligned} h_{\mathrm{i}} & =\text { thickness of fire protection material } \\ & \text { in mm; }\end{aligned}$

$\begin{aligned} T & =\text { steel temperature, in degrees celsius } \\ & \text { obtained from test as give } \\ & \text { in } 16.6 .1, T>250^{\circ} \mathrm{C} ; \text { and }\end{aligned}$

$\begin{aligned} k_{\mathrm{sm}} & =\text { exposed surface area to mass ratio, in } \\ & 10^{3} \mathrm{~mm}^{2} / \mathrm{kg} .\end{aligned}$

16.6.2.2

In lieu of test results, the values for coefficients in Table 30 may be used in the equation 16.6.2.1 when the test satisfies the conditions specified in 16.6.2.3.

16.6.2.3

Limitations and conditions on use of

regression analysis

Test data to be utilized in accordance with 16.6.2.1 shall satisfy the following:

• a) Steel members shall be protected with board sprayed blanket or similar insulation materials having a dry density less than 1 000 kg/m³;
• b) All tests shall incorporate the same fire protection system;
• c) All members shall have the same fire exposure condition;
• d) Test series shall include at least nine tests;
• e) Test series may include prototypes which have not been loaded provided that stickability has been demonstrated; and
• f) All members subject to a three-sided fire exposure condition shall be within a group in accordance with 16.9.

The regression equation obtained for one fire protection system may be applied to another system using the same fire protection material and the same fire exposure condition provided that stickability has been demonstrated for the second system.

A regression equation obtained using prototypes with a four-sided fire exposure condition may be applied to a member with a three-sided fire exposure condition provided that stickability has been demonstrated for the three-sided case.