Please refer to step 5 of the solution on Chegg to Chapter 9, Problem 39 below.

Question

Please refer to step 5 of the solution on Chegg to Chapter 9, Problem 39 below. My query as follows:

For moment of inertia (Ix) the distance required in the formula is the distance from the centroid of the area (C) to the centroidal x-axis (x-x). For area 1 (A1): the centroid is 30mm from the base of the area. The distance from the base of A1 to the centroidal x-axis should be = 140mm - h = 140 - 115.84 = 24.16mm. Therefore the distance from the centroid of the area (C1) to the centroidal x-axis = 30 + 24.16 = 54.16. The answer in the solution is 85.84. Why is this?

Same applies to distance from A2 centroid to the centroidal x-axis. My calculation: Distance from centroid of A2 to base = 70mm. The distance from the base of A1 to the centroidal = 24.16mm (see 1st paragraph above). Distance between centroid of A2 and centroidal x-axis = 70 - 24.16 = 45.84 (y=-45.84). The answer in the solution is = -14.16 Why is this?

A follow up question refers to the formula used: Is the sign of (h) and (h1) or (h2) dependent on position of h? If h is above the x axis then the formula is h=h1-h and if h is below the x axis then the formula is h=h-h1

Thank you!!

DO NOT ANSWER THE TEXT BOOK QUESTION BELOW (for reference only)

Chapter 9, Problem 39

Determine the radius of gyration of the area shown in Figure 1 with respect to the x-axis

STEP 4

STEP 5

Explanation / Answer

To determine the moment of inertia of a part of section about centroidal axis of the section, we need to determine the distance between the centroid of the part of the section and centroid of the section to use parallel axes theorem . For area A1 , the centroid of A1 is located 30mm below topmost face and centroid of entire section is located 115.849mm below topmost face. Therefore ,distance between centroids of area A1 and entire section = 115.849-30=85.849mm.

Similary, centroid of area A2 is 130mm below topmost face and centroid of entire section is located 115.849 below topmost face. Therefore, distance bewtwwen centroid of A2 and entire section = 130-115.849 = 14.151mm.

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