Question

For the shape shown above, b has a value of 4

1. Calculate the location of the x centroid
2. Calculate the MOI of the shape about the y axis
3. Calculate the MOI of the shape about the y axis through the x centroid

| ------- | Ix=y2/ 67 6/2 | ------- -

Answer 1

Y = x - - - > 2 - - b=4 0 F © Calculation of x-centroid x - 4 y yo, 4x = [4 - 2 y = mc L 15 o distance dx) x - y dz) x 2 of centroid from y-axis (4-4₂) dx 14 (25x - 2) dx 25. 6 - 10.66 Ja = 2.2432 X - 2. 2432

③ MOI of the shape about y-axis Iy = 13, de 2² - J ada) 2² 73.1428 – 32 41.1428) Iy = h Moment of Inertia about y axis through X-centroid. Im = I centroid / 5 = 212432 (do distance between to timo parallel axis in parallel d axis theorem Area of Shaded portion A= 1 (2-4 dx = [(25&- £) dz I cenhoid = 7.63 = 6.66 Parallel axis 121 Theorem Ty = Icentoid + Ad² 41:1428 = Icenbord + 6.66X(2, 2432)