Question

Find the Area Moment of Inertia about a y axis passing through the centroid (ly) of the composite shape below. Y 2-in.-diameter hole 16" 10" 5" X X 5" 5" Y T (c)

Answer 1

Ya 6" Az B 16" 2in-dia. hole of area'Az - T AL х o A 15"75" + For the above area, we need to calculate location of Centroid. # For area Allie a Square OABD) → A, = 10*x 10") = 100 in2 Centooid of A, is (Mon 9,) = (4.0", 12") - (5“,5") For area Az (ie a Right L triangle DBC)→ Az = {x10x6"= 30 in2 Centroide of Az is (12,72) =(( 13"), (10"+ e')) = (46", 12") # 2 و CS Scanned with CamScanner

# For Area Az (ie a Circle of diameter 2 in.) = A3= 2x2 = 7 in2 Az = 3.14 in2 Cenfoid of Az is (Mlz ,43 ) = (s", 5") Now, Centroid of the whole body is (t ,J). So, ña AX -> T = 100*5 + 30% - 3.14.45 = 4.6" ΣΑ: 100 +30 - 3.14 y- I aiyi ΣΑ: → J = 100*5+ 30X12 -3.14*5 6.65" 100 of 30 - 3014 Hence, Centroid of the giren area is (4:6" , 6.65") CS Scanned with CamScanner

NOW, Iy = 36 -h6² chi t 6" 21 Az b Y * 4 Td 2" dia. 10" Iy = 24 hole. .Xc TY Iy A, b K5"-*-5" 0.4" By parallelaxis + → Iva Iyi 4 10 12 + (100 x 0-4) theoremit I = ICM + Ada 2 I → Area MOI about 68103 required axis 36 + (30% (406-1993) - [1 ***2* + (** 0-t?)] Icm Årea MOI about Centroid of the area (A) d distance betwen the axis and Centroid. >> I. - 1062.845 in Ye Hence, the area moment of inertia about yo axis passing through the centroid of the Composite 1062.845 int -Ye = give shape is Iy CS Scanned with Camboanne