# 722.5.1.4 Concrete-Protected Columns

The fire resistance of structural steel columns protected with concrete, as illustrated in Figure 722.5.1(6) (a) and (b), shall be permitted to be determined from the following expression:

**(Equation 7-14)**

where:

R_{o} | = | 10 (W/D)^{0.7} + 17 (h^{1.6}/k_{c}^{0.2}) × [1 + 26 {H/p_{c}c_{c}h (L + h)}^{0.8}] |

As used in these expressions:

*R* = Fire endurance at equilibrium moisture conditions (minutes).

*R _{o}* = Fire endurance at zero moisture content (minutes).

*m* = Equilibrium moisture content of the concrete by volume (percent).

*W* = Average weight of the structural steel column (pounds per linear foot).

*D* = Heated perimeter of the structural steel column (inches).

*h* = Thickness of the concrete cover (inches).

*k _{c}* = Ambient temperature thermal conductivity of the concrete (Btu/hr ft °F).

*H* = Ambient temperature thermal capacity of the steel column = 0.11W (Btu/ ft °F).

*p _{c}* = Concrete density (pounds per cubic foot).

*c _{c}* = Ambient temperature specific heat of concrete (Btu/lb °F).

*L* = Interior dimension of one side of a square concrete box protection (inches).

For wide-flange structural steel columns completely encased in concrete with all reentrant spaces filled [Figure 722.5.1(6)(c)], the thermal capacity of the concrete within the reentrant spaces shall be permitted to be added to the thermal capacity of the steel column, as follows:

**(Equation 7-15)**

where:

b_{f} | = | Flange width of the structural steel column (inches). |

d | = | Depth of the structural steel column (inches). |

A_{s} | = | Cross-sectional area of the steel column (square inches). |

The fire resistance of structural steel columns protected with concrete masonry units or clay masonry units as illustrated in Figure 722.5.1(7), shall be permitted to be determined from the following expression:

**(Equation 7-16)**

where:

R | = | Fire-resistance rating of column assembly (hours). |

W | = | Average weight of structural steel column (pounds per foot). |

D | = | Heated perimeter of structural steel column (inches) [see Figure 722.5.1(7)]. |

T_{e} | = | Equivalent thickness of concrete or clay masonry unit (inches) (see Table 722.3.2 Note a or Section 722.4.1). |

K | = | Thermal conductivity of concrete or clay masonry unit (Btu/hr • ft • °F) [see Table 722.5.1(3)]. |

A_{s} | = | Cross-sectional area of structural steel column (square inches). |

d_{m} | = | Density of the concrete or clay masonry unit (pounds per cubic foot). |

p | = | Inner perimeter of concrete or clay masonry protection (inches) [see Figure 722.5.1(7)]. |

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