Time for Object to Fall Based on Center of Gravity

[Dragon M.]

Homework Statement
This has a fairly long problem statement, so I'll condense it.

There are two gates with 81 vertical pickets and two horizontal support bars. These are holo rectangular tubes. The pickets are 2" x 2" x 3/16" box beams and support bars are 4"x6"x3/16" Box Beams.

One gate has an x-axis center of gravity 5 inches away from the instantaneous center (y is the center of the gate). The second gate has an x-axis center of gravity 7 inches away from the instantaneous center.

I am to find the time it takes for each of these gates to fall over assuming neither of the gates are held up by anything and will just fall over.

Given are the AREA moment of inertias of each individual holo beam as well as the weight/ft of each.


What I've Done

I planned to do a moment equation where:

Total Weight * (X Length of Center of Gravity to IC) = (Mass of Gate) * (Angular Acceleration) * (Magnitude of Length of Center of Gravity to IC)^2 + (Center Moment of Inertia) * (Angular Acceleration)

Then, I would solve for the angular acceleration and use kinematics for angular motion ( Theta_f^2 = Theta_i^2 + 2*(alpha)*(time) ). I came at an impasse when I tried to find the center moment of inertia for these beams, when I'm given the AREA moment of inertia, so I can't apply parallel axis theorem (I + mr^2).

I'd like to know if this is even the correct direction to go, or if I should be looking at something else completely? If it is the way to go, how do I move forward?

I've attached the picture for the full problem statement at these links:
http://img826.imageshack.us/img826/5915/img0196dm.jpg
http://imageshack.us/a/img546/4456/img0197mh.jpg

Any help will be massively appreciated.

 

[SteamKing]

You'll need to set up a spreadsheet so that you can calculate the mass properties of the gate (total mass, c.g., mass moments of inertia). You will have to go back to the derivation of the mass moment of inertia and derive a new formula for calculating the mass moment of inertia of the pickets and cross beams given the information you have from the cross section properties.

On the whole, a very interesting problem!