Question

4. (30 pts) Locate the centroid (x,y) of the composite area and determine its moment of inertia about the x-axis. 6 in. 3 in. 3 in. 3 in. -3 in. --- 3 in.-

Answer 1

Solution is attached in the image posted below.

Hope it helps.

6in BIRI 03 Bin | bl3 Bin Bin Oricing the area in to various compone nts. 243 -243 -37.68 sm malo 37.68 -36 component Area, e s d sine 1-3 square coine 1-3 3 Circle 1-12.56 in? Triangle al 146×3 Ain 2 16 17 Triangle ? Ecueo= 104:44 89 Jeax6=27in2 2 162 EYA =430:32 ja 413 313 3=b13 2013 - 6+ + b = 25= 2x8 313 3 92113 ģ=29= 2x96 Centre sign shows over along left [Negative side of y axis) shows that area í Negative area has been removed from diagram]

NON Ž Centroid of whole composite Area 1.793 inch SRA. 187.32 EA louuu ū – 4.12 inches – Ega EA 432.32 104. u4 composite Area Hence Centroid of [As per (-1.793 inches; 4.2 inches coordinate system) Non moment of ineitia about x-axis Here we will use parallel axis. Theorem JxIx'taq? where Ix'= MOI about the axis of diagram A Area y Distance from ravis of cente Ix Ay? Area Intay? 412 bhf=100 | 1995 component 03 Bline 54575 square ū 412.52 -113.04 -125.61 Reet -12.56 uul cice 14.5 ain? Triangles 121.5 972 1093.5 27 in? Triangle 2 Inrules uus 5

JU hab3 > MOJ CH Centroid Je-bn3 Ty not cie b=6 2=3 Triangle a Je 6x38-4.5 in =121.5iny Triangle 2 bone = 120S iny 36 36 1 oveau moment of inestia along x- axis E27875 125.61 THESS HOSS = 2685tHint =837 - 125.61 tuu5.5 41093.5 2250.39 in 4. Hence moment ob inertia f composite section is 2250.39 in 4.