## Example 373

Temperatures in unprotected steelwork

For the cross-section in Example 37.2, case 1, calculate the unprotected steel temperature under the natural fire condition evaluated in Example 37.1. For steel, assume a constant density of 7850 kg/m3 and a constant specific heat of 650J/(kgK). Also, assume a constant resultant emissivity of 0.5 and a convective heat transfer coefficient of 25 W/(m2K).

### Calculation results

The calculations are performed for intervals of 5 s and results of only the first time increment are shown. Equation 37.15 gives hr = 2.95 W/(m2K). The total heat transfer coefficient is 27.95 W/(m2K).

After a time increment of At = 5 s, Equation 37.3 in Example 37.1 gives a fire temperature of 41.74°C. The steel temperature is 20°C. The section factor from case 1 of Example 37.2 is 150 m-1. Equation 37.17 gives DTs = 0.0616°C. Thus, the steel temperature after 5 s is 20.0616°C.

Figure 37.5 plots the unprotected steel temperature development. The maximum steel temperature is 829.25° C, reached just after 30min.

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