Approximately the same result will be obtained if we assume the flange a rectangle and substitute 18,000 for fin Gordan's formula. Then = 12 18,000 = 12 1 + 3,000 and for 1= 20 b = 15,900.
Table IV gives values to use for fibre stress, and proportions of full tabular load to use for different ratios of length and width of flange.
Tables V, VI, VII, and VIII give the properties of the minimum and maximum sizes of the different shapes. These tables are for use in choosing sections to meet the requirements of design, and will be explained in detail in the pages that treat of design of members in which these shapes are used.
These different functions can all be calculated quite readily, and it is impor tant that the student should understand how these are obtained. For this pur pose the functions of a 24-inch 80-lb. beam will be worked out. The sec tion of the beam is here shown.
It will be noticed that the areas of fillets and the roundings of outer edges are disregarded. These closely offset each other.
Since a cubic foot of steel weighs 490 lbs., the weight per foot of a 24-inch beam should be : I of web (taken to outside of flanges) x x = 576. I' of flange about an axis through center of gravity of each component element.
Where A -= area of flanges, and d = distance from center of gravity of flange to axis 1 — 1, as in the above, the flanges being divided into two figures, the d in each case will be the distance from 1-1 to the center of gravity of that figure.
I= 3.25 x .60 X X 4= 1,067.752 3.25 X .271 X x 4 = 443.505 1,511.548 576.
2,087.548 For axis 2-2 = 3.25 X .60 X (1.623 + X 4 = 27.362 1 Flange axis B' 13' = 3-6 X .542 X X 4 = 2.060 For axis 2-2 = + .542 X 1.63:X (1.08 X 4 = 6.250 42.538 42.788 Other methods of computing the moments of inertia would perhaps bring a result even closer to the values given in the tables, which are taken from the Carnegie Handbook, although the values vary a little in the different books for identical sections.