Question

A composite shape is constructed by two angles and a plate to a W shape as shown. Determine the y-centroid the moment of inertia with respect to the x-axis ar thebase y and the y-axis (). Using the parallel-axis theorem -Ls (Similar to Problem 9.51 distance o-bar) for the composite shape shown. I+A ), compute the moment of inertia parallel with the x-axis at the centroid (.). Al units are in inches. The shape is symmetrical about the 5 in.- 5 in. The properties of the L3 x 3 x 4 are: Area 1.44 in I-bar- 1.23 in. y-bar = 0.836 in.4 L-bar 1.23 in. x-bar 0.836 in. W 8x31 Properties of the W8 x 31 Area 9.12 in. Depth 8.00 in. Width -8.00 in. I-bar- 110 in. o 0.5 in. 12.5 in. Plate -bar 37.1 in. Table for y-bar and I, at x-axis (at the base) computation Shape Area (A) y to baseA,x y, !, @ centroids A.* y; + 11 L3 × 3 × ¼ L3 x 3 x W8 x 31 Plate Table for l,e at the y-axis computation Area (A)lx,toy-axis | ?.*x;2 |Ly @ centroids! ?.*x;. +1y Shape L3 x 3 x W8 x 31 0.00 0.00 Plate 0.00 0.00 (10) y-centroid distance from the x-axis (-bar)- (9) Moment of inertia with respect to the x-axis at the base (U) (9) Moment of inertia with respect to the y-axis (y) Answers in (7) Moment of inertia parallel with the x-axis at the centroid ()-

Answer 1

y bar = sigma A;y;/sigma A: = 107.53268/18.25 = 5.8922 in \r\n