Question

(10 points) For the cross section shown below, find the centroid of the section y and the moment of inertia 1. 16 in 1.0 in L

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Answer #1

In this question we have to find the distance of the centroid and the moment of inertia of the given composite section.

In order to solve this question we have to divide this whole composite section into a number of sections and solve for them, then by adding them we get the answer for the whole section.

The step by step calculations are given below:-

16 in. 8 lin lin Z 10in K * ** 1 in 2 in lin 3 in zin zin. lin 3 in lin First we into have to divide this composite section.Now we have to find find the area. of all the individual sections 3 the componte. So. Area V section ① A 1 x2 2 in2 1 similarand. the distances of of the centroids the areas. from a-a. axis be calculated centroid distance of section in. as Y = 10 SimNow, from the principle of moments, the formula for the centroid of the section is given & Ay EA or y (AL Y + A2Z + Azt + A YNow all the Moment of Thertia the sections. about be calculated the centroid can. Moment inertia for section ④ I1 = 1 x (2)3So, the Mome ut of înentia of the whole section would be. Iz (12+ Izt Ist Ih) x2 + Ic I 2 = (0.667 + 0.167 + 210.917+ 0.25 )

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