Answer :
The moment of inertia of a composite section can be determined by summing the individual moments of inertia of each component. Let's calculate the moment of inertia of the given composite section with respect to centroidal axes (lx and ly).
1. We are given the details for the W16 x 50 section:
- x = 657 in (distance from centroid to edge)
- ly = 37.1 in^4 (moment of inertia about the y-axis)
- A = 14.7 in^2 (area of the section)
2. The moment of inertia about the lx axis can be calculated using the parallel axis theorem:
I_lx = I_w16 + A_w16 * (d_w16)^2
- I_w16 is the moment of inertia of the W16 x 50 section about its own centroidal lx axis
- A_w16 is the area of the W16 x 50 section
- d_w16 is the distance between the centroids of the W16 x 50 section and the composite section along the lx axis
3. The moment of inertia about the ly axis can be calculated using the parallel axis theorem as well:
I_ly = I_w16 + A_w16 * (d_w16)^2
- I_w16 is the moment of inertia of the W16 x 50 section about its own centroidal ly axis
- A_w16 is the area of the W16 x 50 section
- d_w16 is the distance between the centroids of the W16 x 50 section and the composite section along the ly axis
4. To calculate the moment of inertia about the lx axis, we need the moment of inertia of the W16 x 50 section about its own centroidal lx axis. This value can be obtained from standard tables or formulas.
5. Once you have the moment of inertia of the W16 x 50 section about its own centroidal lx axis, you can substitute the values into the formula from step 2 to calculate the moment of inertia of the composite section about the lx axis.
6. Similarly, to calculate the moment of inertia about the ly axis, you need the moment of inertia of the W16 x 50 section about its own centroidal ly axis. This value can also be obtained from standard tables or formulas.
7. Once you have the moment of inertia of the W16 x 50 section about its own centroidal ly axis, you can substitute the values into the formula from step 3 to calculate the moment of inertia of the composite section about the ly axis.
Remember to double-check your calculations and units to ensure accuracy.
Know more about moment of inertia here:
https://brainly.com/question/30051108
#SPJ11
