Question

Problem 5.1: Determine the centroid of the composite shape given below. (Use table 5.8 and show your calculations.) Parabola 200 mm 150 mrm 240 mm 240 mm

Answer 1

formulae: x^bar = 3/4 b y^bar = 3/10 h A = 1/3 bh from fig(1) x^bar_1 = 3/4 b_1 => x^bar_1 = 3/4 (480) = 360 mm y^bar_1 = 3/10 h_1 => y^bar_1 = 3/10 (200) = 60 mm A_1 = 1/3 b_1h_1 => A_1 = 1/3 (480)(200) = 32000 mm^2 x^bar_1 = 360 mm y^bar_1 = 60 mm A_1 = 32,000 mm^2 \r\n from fig(2) x^bar_2 = 3/4 b_2 => x^bar_2 = 3/4 (240) = 180 mm y^bar_2 = 3/10 h_2 => y^bar_2 = 3/10 (50) = 15 mm A_2 = 1/3 b_2 h_2 => A_2 = 1/3 (240)(5) = 4000 mm^2 x^bar_2 = 180 mm y^bar_2 = 15 mm A_2 = 4000 mm^2 X^bar = A_1x^bar_1 - A_2x^bar_2/A_1 - A_2 X^bar = 32,000 (360) - 4000 (180)/32,000 - 4000 = 385.714 mm y^bar = A_1y^bar_1 - A_2 y^bar_2/A_1 - A_2 y^bar = 32,000 (60) - 4000 (15)/32,000 - 4000 = 66.428 mm X^bar = 385.714 mm Y^bar = 66.428 mm