Second moment of area of a hollow triangle

In summary, to calculate the second moment of area for a hollow isosceles triangle, you can use the subtractive method, but must also account for the centroid location and use the parallel axis theorem.
  • #1
Becky6
3
0
Greetings!
Can someone please help me figure out how to calculate the second moment of area for a hollow isosceles triangle? Is there an equation available somewhere? Or can I simply subtract a smaller triangle from a larger one, using the equation I=bh3/36? (so I= b1h13/36 -b2h23/36)

Also, is there any way to account for the base wall being thicker than the sides?

Thank you!
 
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  • #2
Presumably you are looking for the area moment of inertia about the centroid of the hollow triangle. The subtractive method is ok. But it's not as simple as you indicate, because the centroid of each triangle do not share a common axis. You must first determine the centroid location of the hollow shape, then calculate the inertia of that shape using parallel axis theorem.
 

1. What is the second moment of area of a hollow triangle?

The second moment of area, also known as the moment of inertia, is a measure of an object's resistance to changes in its rotational motion. For a hollow triangle, it is calculated by integrating the area of the triangle with respect to its distance from the axis of rotation.

2. How is the second moment of area of a hollow triangle calculated?

The second moment of area of a hollow triangle can be calculated using the formula I = (b*h^3)/36, where b is the base length of the triangle and h is the height of the triangle. This formula applies to both solid and hollow triangles.

3. Why is the second moment of area important?

The second moment of area is an important property in structural engineering and mechanics. It helps determine the strength and stiffness of an object, and is used in the design of beams, columns, and other structural elements.

4. How does the second moment of area differ for a solid and a hollow triangle?

The second moment of area for a solid triangle is greater than that of a hollow triangle with the same dimensions. This is because the material in a solid triangle is distributed farther from the axis of rotation, resulting in a larger moment of inertia.

5. Can the second moment of area be negative?

No, the second moment of area cannot be negative. It is always a positive value that represents the object's resistance to changes in its rotational motion. If the calculated value is negative, it means there was an error in the calculation or the axis of rotation was chosen incorrectly.

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