Product Second Moment of Area Ixy - Help

[Quadrophenia]

hi, I've been tryign to work out the stress at a point for a T X-section area of a beam. However, the T-shape IS NOT symmetrical.
The general formula is Ixy = Ixy g + AXY (X = X bar and Y = Y bar)
I have X bar and Y bar and Area of course too.
i Dont know how to calculate the first term of this equation which is the Ixy g bit.
Could someone please help. this is driving me nuts.

 

[radou]

What does "g" represent? I assume Ixy g meant the centrifugal moment of area through the centroid axis? I don't know why it wouldn't work. Apply Steiner's rule (the one you wrote down) a few times, and you should be able to calculate it.

 

[ravenprp]

Hello, I understand your frustration with trying to calculate the second moment of area, specifically the Ixy term, for a non-symmetrical T-section beam. This can definitely be a challenging task, but with the right approach and some patience, it can be solved.

First, let's break down the formula for Ixy that you mentioned. The first term, Ixy g, represents the moment of inertia about the centroidal axis of the section. This can be calculated using the parallel axis theorem, which states that the moment of inertia about any axis parallel to the centroidal axis is equal to the moment of inertia about the centroidal axis plus the product of the area and the square of the distance between the two axes. In this case, the centroidal axis will be the axis passing through the centroid of the T-section, and the parallel axis will be the axis passing through the point you are trying to calculate the stress at.

The second term, AXY, represents the product of the area and the distance between the centroidal axes in the x and y directions. This can be calculated by multiplying the area of the T-section by the distances between the centroid of the section and the centroidal axes in the x and y directions.

Now, to calculate the first term, Ixy g, you will need to determine the moment of inertia about the centroidal axis of the T-section. This can be done by dividing the T-section into simpler shapes, such as rectangles and triangles, and calculating their individual moments of inertia. Then, you can use the parallel axis theorem to calculate the moment of inertia about the centroidal axis of the T-section.

I understand that this may seem like a lot of steps, but with some practice and understanding of the parallel axis theorem, you will be able to solve for Ixy g and successfully calculate the stress at the desired point. I suggest looking up examples and tutorials online to help guide you through the process. Don't get discouraged, just keep practicing and you will get the hang of it. Best of luck!