Question

Section 8.5 Radius of Gyration 8.16 Compute the radii of gyration about both centroidal axes for the following structural steel shapes and compare your results with tabulated values: (a) W10 X 54 (b) C10 X 15.3 o TABLE 3 Properties of areas Polar S Moment of Inertia |Moment of Inertiaの|Radius of Gyration Area (A) Shape 4°、12 12 CG 12 13 CG 18 36 A- 12 Triangle CG e 64 0.7854d : 0.7854R Circle Shape Area (A) Moment of Lnertia Radius of Gyration Plar Moment of Inertia U ん·0.109u4 ● 0.5025A" 157L8 Hollow circle Ad-bid Hollow rectangle Xo '-. %-0.26448 な“0.5R 16

Answer 1

(a) for Structual Steel Wlo X54 A= 10-09 in 2 Area = 15-8 ïn2 a hollow rectonake ba-ba, | BA. Bi Ai2-10.030 (10.09)-466(9.35) 2 - 12(A») 12 C15-8) 0.965 recta Ygle O. 030 3- 464 12 = 2.8954-

(b) for Structural Steel Shape cOxl 5.3 A 1o in A A-2C. in B 2.6 in B B-C 23 n Area 4.48 n 12Area) 2-36 x (.128)7G 12 C4.48 53。70 Aleng 0WIS, the CIOXIS.3 SHI) acts as a holow rectangle AB A,b o (2-6)4.128 (23) I2( Avea) 12 X 4.48 Ry62.0304 53.76 Ry = 1。0741

Radius of gyration along Structure X-axis Y-axis 0.9651 in 2.8954 irn W10 x 54 C10 x 15.:3 1.8127 in 1.0741 irn