Formulas: Steel Columns

Formula 1

Equation: $R = 130 \left[ \frac{h \left( \frac{W'}{D} \right)}{2} \right]^{0.75}$

R = 130 \left[ \frac{h \left( \frac{W'}{D} \right)}{2} \right]^{0.75}

Formula 2

R=96\left[\frac{h\left(\frac{W^{\prime}}{D}\right)}{2}\right]^{0.75}

Equation A-4-26

The fire resistance of wide-flange columns protected with sprayed fire-resistant materials is permitted to be determined as follows:

R=\left[C_{1}\left(\frac{W}{D}\right)+C_{2}\right] h

Equation A-4-26M

R=\left|C_{3}\left(\frac{W}{D}\right)+C_{4}\right| h

Formula 5

R=R_{o}\left(1+0.03 m\right)

Equation A-4-28

R_{o}=10\left(\frac{W}{D}\right)^{0.7}+17 \frac{h^{1.6}}{K_{c}^{0.2}}\left\{1+26\left[\frac{H}{p_{c} c_{c} h(L+h)}\right]^{0.8}\right\}

Equation A-4-28M

R_{o}=73\left(\frac{W}{D}\right)^{0.7}+0.162 \frac{h^{1.6}}{K_{c}^{0.2}}\left\{1+31000\left[\frac{H}{p_{c} c_{c} h(L+h)}\right]^{-0.8}\right\}

Equation A-4-29

For wide-flange columns completely encased in concrete with all reentrant spaces filled, the thermal capacity of the concrete within the reentrant spaces is permitted to be added to the ambient thermal capacity of the steel column, as follows:

H=0.11 W+\left(\frac{p_{c} c_{c}}{144}\right)\left(b_{f} d-A_{s}\right)

Formula 9

H=0.46 W+\left(\frac{P_{c} c_{c}}{1000000}\right)\left(b_{f} d-A_{s}\right) \quad \text { (A-4-29M) }

Formula 10

For these and similar situations of uncertainty, it is conservative to not rely on this beneficial effect of the free moisture and to assume the concrete is completely dry with $m=0$ for fire resistance of $R=R_{o}$ .

R=R_{o}

Formula 11

$R=1.22\left(\frac{W}{D}\right)^{0.7}+\left[0.0027\left(\frac{T_{e}^{1.6}}{K_{c}^{0.2}}\right)\right]\left\{1.0+1249\left[\frac{\left(A_{s} / d_{m} T_{e}\right)}{\left(0.25 p+T_{e}\right)}\right]^{0.8}\right\}$ (A-4-30M)

R=1.22\left(\frac{W}{D}\right)^{0.7}+\left[0.0027\left(\frac{T_{e}^{1.6}}{K_{c}^{0.2}}\right)\right]\left\{1.0+1249\left[\frac{\left(A_{s} / d_{m} T_{e}\right)}{\left(0.25 p+T_{e}\right)}\right]^{0.8}\right\}

Formula 12

User Note: Equations A-4-30 and A-4-30M are derived from Equation A-4-27 assuming $m=0, c_{c}=0.2 \mathrm{Btu} / \mathrm{lb}$ -°F (840 J/kg-K), $h=T_{e}$ , and $L=p / 4$ .

h=T_{e}

Formula 13

L=p / 4

Formula 14

Equation: $D = 2(w + d + 2(w - t_w$

D = 2(w + d + 2(w - t_w

Formula 15

Equation: $D = \pi d$

D = \pi d

Formula 16

Equation: $D = 2w + 2d$

D = 2w + 2d

Found in

DESIGN BY QUALIFICATION TESTING