. The strength of materials; a text-book for engineers and architects. centroid parallel to x x = 117-9 in. units 1 ,, ,, ,, y Y = O 194: ,, ,, Distance of centroid from web = -933 in. .-. Total area of section= (4 x 12 x i) -f- (2 x 8-296)= 40-592 sq. ins. Moment of Inertia about X X. 2 channels, 117-9 each = 2358 2 pairs of 12 x | in. plates about centroid = ~ ^— = 2-0 K X d^ for two pairs of plates = 2 x 12 x 5-5^ =726-1 Total . . . = 963-9 in. units 7 / 963-9 . „. •*^==V4ir592==^^^- Moment of Inertia about Y Y. 4 X - X 12^4 plates 12 X J about centroid = ~~ := 288-0 2 channels about centro
. The strength of materials; a text-book for engineers and architects. centroid parallel to x x = 117-9 in. units 1 ,, ,, ,, y Y = O 194: ,, ,, Distance of centroid from web = -933 in. .-. Total area of section= (4 x 12 x i) -f- (2 x 8-296)= 40-592 sq. ins. Moment of Inertia about X X. 2 channels, 117-9 each = 2358 2 pairs of 12 x | in. plates about centroid = ~ ^— = 2-0 K X d^ for two pairs of plates = 2 x 12 x 5-5^ =726-1 Total . . . = 963-9 in. units 7 / 963-9 . „. •*^==V4ir592==^^^- Moment of Inertia about Y Y. 4 X - X 12^4 plates 12 X J about centroid = ~~ := 288-0 2 channels about centroid = 2x8194 =16-4 A X ^2 for each channel = 2 x 8-296 x 3-1832 = 168-5Total = 472-9 4729^^ ^ V 40-592 ^ ^^^ ^^* 190 THE STRENGTH OF ^UTERIALS (6) Built-up Beam Section.—Composed of two 14 in. x6 in. 46 lb. I beams and four 14 in, x f in. plates (Fig. 95).Required I^^. From the Standard Section Tables we obtain the followinginformation concerning the I beams— Area of each = 1353 ?•.XX 5 > 5 > = 440-5 Mean thickness of each flange = 698 a Fig. 95. I^^ OF WHOLE Section (not attow^no for Rivets).-Ivx of two I beams -= 2 x 440o = 881 ? X 14 /5\I of two pairs of plates about centroid ~ -—-— x (- ) 12 \4/ 4-8 A d^ for two pairs of plates = 4x 14x — x 7 62o- = 2035 Total 2020 8 AixowANCE FOR RivETS (ucglcct I of each rivet-hole aboutits centroid). Area of each hole = (2 x -^--f 698)4 = 1TU4 o o Dist. of centroid from xx = I,, = 4 X 1-704 ? 7-276- = 3608. ?. Xett I,, = 2920-8 - 3608 = 2560 GEOMETRICAL PROPERTIES OF SECTIONS 191 (7) Built-up Sections—Approximate Method.—The moment of inertia of built-up sections can be found approxim-ately by adding the moment of inertia of the I beams orchannels to A d? for the plates, d being taken as the distancefrom the centre of one set of plates to x x and the nett areaof the plates being taken for A. Taking the section of the previous example, we then getI^^ as follows— I„ of two I beams = 2 x 440-5 = 8
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