Question

strengths

Answer 1

So I need y_bar this would be before the pieces are transformed or after? Before I calculated y-bar = 0.2877 in

Answer 2

The transformed width of 8.25 is correct, i.e. b2=b*E2/E1. So now we treat everything like aluminium, and have a shape like this:

Note that I don't have the same y_bar as you, so we need to review from here.

Answer 3

For the transformed area moments, I usually calculate in one step as follows:
yb=centroidal axis with respect to bottom of section (I get 0.85054, please check).
b1,b2 are widths of transformed section
A1,A2 are areas of transformed section
d1,d2 are heights/depths of transformed section

I1=A1*(d1^2/12+(yb-d1/2)^2)
I2=A2*(d2^2/12+(d1+d2/2-yb)^2)
I composite=I1+I2
I get I=0.982 in^4

Answer 4

I get the same numbers as you except y_bar. It's Ay/total A = y_bar

Answer 5

Are you sure your y_bar is correct? I get y_bar = 0.4616

Answer 6

You are correct, but how???

Answer 7

We know that the section is top heavy, so the centroid must be in the steel section, namely y_bar > 0.625.
It turns out that you have swapped the areas A1 and A2.
A1 should be 1.71875 and A2=6.1875. You had them backwards.

Answer 8

oh okay. I will fix that hold on.

Answer 9

k got your y bar

Answer 10

now I need to find the moment of inertia about the horizontal centroidal axis?

Answer 11

btw when calculating A*y I actually miscalculated a number which threw everything off.

Answer 12

actually calculating Iz1 i need to find the centroidal from the right side?

Answer 13

What is |z| ?

Answer 14

basically need to find the areas again but finding the Zi starting from the right to the center of each shape?

Answer 15

This is how I calculate the moment of inertia about the neutral axis, it comes to the same way as you usually calculate it, but for me this is more compact.

I1=A1(d1^2/12+(yb-d1/2)^2
I2=A2(d2^2/12+(d1+d2/2-yb)^2
I=I1+I2
The first term in parentheses is the MI about local centroid, the second term moves it to the global centroid (neutral axis.