## Example 376

Plastic bending moment capacity of a composite cross-section

Figure 37.15 shows a composite cross-section exposed to fire underneath the slab. The steel section is unprotected and fire exposure is according to the temperature-time relationship in Example 37.1. At ambient temperature, the design strength of steel is 275 N/mm2 and the design compression strength of concrete is 20 N/mm2. Calculate the minimum sagging bending moment capacity of the composite cross-section in fire.

Calculation results

According to the dimensions in Figure 37.15, the section factor of the top flange is 80 m-1 and that of the web/bottom flange is 147m-1.

Following calculations in Example 37.2, the maximum top flange temperature is 802.8° C reached at 32.25 min and the maximum lower flange/web temperature is 847.2°C reached at 28.75 min. It is interesting to notice that under natural fire exposure, different parts of a structural member will reach their maximum temperatures at different times. Therefore, in theory, calculations of the plastic bending moment capacity of the cross-section should be performed as a function of time. For simplicity, in this example, the maximum temperatures of the top flange and bottom flange/web, attained at different times, are used.

From Table 37.5, the residual steel strengths and tensile capacity of the steel cross-section are

Top flange: fy = 0.1086 x 275 = 29.9 N/mm2, As = 2250 mm2, Nuf = 67.3 kN

Bottom flange/web: fy = 0.08639 x 275 = 23.76 N/mm2

The lower flange tension resistance: Nlf = 53.5 kN

The web area is 3700 mm2, giving the web tension resistance: Nwf = 87.9 kN

The total tensile resistance of the steel cross-section: Ns = Nuf + Nwf + Nf = 208.7

Assume the top of the concrete slab is cold. The depth of concrete in compression is 208.7 x 1000/ (20 x 2000) = 5.22 mm.

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