Statics - Problem 10.27

 Statics, Chapter 10 - Moments of Inertia

Consider the "Z" section in (Figure 1) with h = 7 in.

▼ PART A

Determine the moment of inertia of the "Z" section with respect to the x centroidal axis. Express your answer in inches to the fourth power to three significant figures.

▼ PART B

Determine the moment of inertia of the "Z" section with respect to the y centroidal axis. Express your answer in inches to the fourth power to three significant figures.

 STEP 1  

Firstly, Gather all the information you have on the object. Make a FBD if needed. This Z section - if taken apart - can be constructively made out of three individual rectangles. Let's get the area of all three.

A₁ = 7 x 1 = 7 in^2 ........ (longer piece) 

A₂ = 5 x 1 = 5 in^2 ........ (twin piece) 

A₃ = 5 x 1 = 5 in^2 ........ (twin piece) 

 STEP 2  

Next, we need to find the second moment of area, or the moment of inertia for all three plane areas. Every basic shape has a specific formula. This table from fxsolver.com has a great one for two dimensional objects here.

I_x & I_y calculation for piece A₁: since it is coinciding with both axises, no need to for usage of parallel axis theorem.

 STEP 3  

Now, for the twin pieces. We can find the I_x & I_y of just one piece and multiply the end result by two since both pieces are of the same length and width and also the same distance from both the x and y axises.

 STEP 4  

For Part A, combine all I_x

answ = 189 in^4

For Part B, combine all I_y

answ = 61.4 in^4

centroidal axiExpress your answer in inches to the fourth power to three significant figures.