APPENDIX B 

 APPROXIMATE FORMULA FOR /^ 



Considerable computation is required to determine the parameter I , which is a measure 

 of frame strength. To simplify this work, an approximate formula has been derived which is 

 applicable to frames of various cross-sectional shapes. 



As previously defined, /^ is the moment of inertia of the combination of a frame plus an 

 effective length of shell L^ about the centroid of the combined section. Figure 4 is a diagram 

 of the most general frame shape in practical use, i.e., the builtup H-section with unequal 

 flanges. Other shapes, such as T- or I-sections, are special cases of this shape. Referring 

 to Figure 4, the quantity e of Equation [1] on page 3 can be written: 



VL 



bt 



(t \ as 



(d + u-t) + 



2 



[3] 



where a, b, c, d, s, t, and u are defined in Figure 4. Using the relationship 



Af = as -y bt + cu 

 Equation [3] can be rearranged so that 

 1 



4 



{d 



I as\ uAi bt 



[4] 



+ ^ [5] 



If the small quantity t — u\s neglected. Equation [5] becomes 



bt - cu 



and AfC'^ is written 



H 



e-- i (d-t) 



A^e^ ^^id-tf 



1 + 



^ 



'} 



1 + 



bt - cu u + h 



^ 



d - t 



t6] 



[71 



The quantity h can also be simplified if a few small terms are neglected. The exact expres- 



sion for If is 



l( = ( bt^ + a^s + cu^) + bt 



12 



t h 



d — - e + — 

 2 2 



[81 



— [d — t + u + h) - e 

 2 



— (u + h) — e 

 2 



10 



