If w 36 mm find the moment of intertie about the z axis The

If w = 36 mm, find the moment of intertie about the z axis. The centroid of the section is locating 21.500 mm above the bottom surface of the beam. 288500 mm^4 313300 mm^4 226300 mm^4 240300 mm^4 186600 mm^4

Solution

by finding the moment of inertia of each parts using the formula bh³/12

we obtain the values as 83333.33 for brown rectangle parts and 853.33 for blue rectangle.

by parallel axis theorem these are transferred on to the z-y co-ordinate system which is at 3.5 mm below the origin and 17.5mm above the orgin of the co-ordinate system.

As the area of brown rectangle is 400 and blue rectangle is 160 mm² and radius of gyrations are 3.5 and 17.5mm respectively.

using the parallel axis theorem, Izz = I_{zz CG} + Ak² for all three parts

we obtain the result as 226300mm⁴.