Area Moment of Inerita simple rectangle composite I'm lost

In summary, the conversation is about determining the moments of inertia of a Z-section about its centroidal x0 and y0 axes. The x0 axis is 80mm up from the bottom and the y0 axis is 90mm from the leftmost point, making it in the middle of the piece. The person is confused about whether or not to set up a chart and what values to use for dx and dy. The other person confirms that their values for dx and dy are correct but their chart is missing the Ix and Iy values for two areas and suggests using the parallel axis theorem to compute them.
  • #1
frozenguy
192
0

Homework Statement



Determine the moments of the inertia of the Z-section about its centroidal x0 and y0 axes.
I didn't draw them in, but the x0 axis is 80[mm] up from the bottom and the y0 axis is 90[mm] from the left most point. So it is in the middle of the piece.

The Attempt at a Solution



So I guess I'm confused as to whether or not I need to even set up this chart since its only asking for [tex]\bar{I}x[/tex] and [tex]\bar{I}y[/tex]. Its just the sum of each from the three different parts? If I do need the chart, what is dx a distance from/to? I don't think my numbers are right at all.

I have the answers in the book.
staticsprobA43.jpg
 
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  • #2
Your values for dx an dy appear correct (d = distance from centroid of area to centroid of shape). But your chart is missing the Ix and Iy values, of the areas you designate as 1 and 3, about their individual centroids. You need the parallel axis theorem to compute the Ix and Iy of the overall shape.
 

1. What is the formula for calculating the area moment of inertia for a simple rectangle?

The formula for calculating the area moment of inertia for a simple rectangle is I = (bh^3)/12, where b is the base of the rectangle and h is the height.

2. What is the difference between a simple rectangle and a composite rectangle for calculating area moment of inertia?

A simple rectangle is a geometric shape with a uniform cross-section, while a composite rectangle is made up of multiple simple rectangles with different dimensions. The calculation for area moment of inertia for a composite rectangle involves breaking it down into smaller simple rectangles and using the parallel axis theorem to find the total area moment of inertia.

3. How do I find the centroid of a composite rectangle for calculating area moment of inertia?

To find the centroid of a composite rectangle, you need to first find the centroid of each simple rectangle within it. Then, use the weighted average method to calculate the overall centroid of the composite rectangle based on the areas and distances of each simple rectangle from the reference axis.

4. Can area moment of inertia be negative?

No, area moment of inertia cannot be negative. It is a measure of an object's resistance to bending and is always positive or zero. A negative value would suggest that the object is bending in the opposite direction, which is not physically possible.

5. How is area moment of inertia used in engineering and design?

Area moment of inertia is an important factor in structural analysis and design. It helps engineers determine the strength and stiffness of a structure, as well as its resistance to bending and buckling. It is also used in calculating deflections and stresses in beams, columns, and other structural elements.

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