Question

1. For the cross section shown in the accompanying illustration, compute the location of the controid (i.e., X, Y), moment of inertias 7, and I, and the radii of gyrations k, and ke about the centroidal axes for combine area shown below. You should first locate the centroid and then transfer your moment of inertia for the individual sub- sections you use to compute the centroid axes using the parallel axis theorem. 1-248-45, +4,8, +4,8, 24 4 + 4 + 4 4 45+ Aj+ Ajs. 4+4+A; 4 1, +1, +AR:

Answer 1

area a A Box4o mm- 6omm Coormak (enhoid Ppart omm 120 mm & oomm nmm 4omm omm- Coordmat of part D remm C Area f pat - Ro mm 200 XYo mm2 A2 Centroid a art 2 120 x o mm2 A2 Area (OCTdinate of Cenhvid of part 3 yot - 180 mm location afCenbroid a ComponHe section ArXItA2 t A3 X3 ArtA2 A3 8oxyo 200xyo 120x4o

AiyiA2 Y2 + Agy AI+A2 +As 8ox40x 20 + obx4oX|oD+ [20x40 x 12o goxy ot200*40 +120x40 08 mm moment anetca Dbouthonontal Cenbroidat Axij Ix tA (-y)+ Ix2t A2 (5-y2 A3 (-ys) x goxyo3+ Boxyox (lo8-20)2 T2 x 4ox200 + Uox200 X(108-100) (2 x 120x403120x4ox ((08-180) T77909933,33 mm Jnestra abuut vertical Cenbuidal Axe? moment TryA ( I2yA2 (-2 T3A x3)2 xyox ox80X(56-80) 1 x00xy03+ 200xyox(S6-20) (2 xwx20120x yo X(S6- 100) 2 / 2 Iy 30037333.33 mm 4

total Area A = AIt A2 + A2 11 Box 4o 00x40 120X40 11 16000 mm2 Yadius f gyrathon af honzontal Cenbroidal Axe 7790933333 16o00 69.78060 mm X kz 1 A adiui af gy saton vertical Centoidal Ae B0037333,33 43.32820y KJ mm 16000