Problem 5-a Locate the centroid of the plane area shown. y x 20 mm

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Problem 5-a Locate the centroid of the plane area shown. y x 20 mm

Solving Problems on Your Own Problem 5-a 20 mm 30 mm Solving Problems on Your Own Locate the centroid of the plane area shown. 36 mm Several points should be emphasized when solving these types of problems. 24 mm x 1. Decide how to construct the given area from common shapes. 2. It is strongly recommended that you construct a table containing areas or length and the respective coordinates of the centroids. 3. When possible, use symmetry to help locate the centroid.

Decide how to construct the given area from common shapes. y Problem 5-a Solution 20 + 10 Decide how to construct the given area from common shapes. C1 C2 30 24 + 12 x 10 Dimensions in mm

y Problem 5-a Solution 20 + 10 Construct a table containing areas and respective coordinates of the centroids. C1 C2 30 24 + 12 x 10 Dimensions in mm A, mm2 x, mm y, mm xA, mm3 yA, mm3 1 20 x 60 =1200 10 30 12,000 36,000 2 (1/2) x 30 x 36 =540 30 36 16,200 19,440 S 1740 28,200 55,440

XS A = S xA X (1740) = 28,200 X = 16.21 mm YS A = S yA Problem 5-a Solution 20 + 10 Then XS A = S xA X (1740) = 28,200 X = 16.21 mm C1 or C2 and YS A = S yA 30 24 + 12 Y (1740) = 55,440 x 10 Y = 31.9 mm Dimensions in mm or A, mm2 x, mm y, mm xA, mm3 yA, mm3 1 20 x 60 =1200 10 30 12,000 36,000 2 (1/2) x 30 x 36 =540 30 36 16,200 19,440 S 1740 28,200 55,440