Second moment of area of a hollow triangle

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SUMMARY

The calculation of the second moment of area for a hollow isosceles triangle involves using the parallel axis theorem after determining the centroid of the hollow shape. The subtractive method of calculating the moment of inertia by subtracting the smaller triangle's moment from the larger triangle's moment is valid but requires careful consideration of the centroids, which do not share a common axis. The equation I=bh3/36 is applicable for individual triangles, but adjustments must be made to account for the thickness of the base wall compared to the sides.

PREREQUISITES
  • Understanding of the second moment of area and its significance in structural engineering.
  • Familiarity with the parallel axis theorem for calculating moments of inertia.
  • Knowledge of centroid calculation for composite shapes.
  • Basic principles of geometry related to triangles and their properties.
NEXT STEPS
  • Study the parallel axis theorem in detail for composite shapes.
  • Learn how to calculate centroids for hollow and composite geometries.
  • Explore the application of the second moment of area in structural analysis.
  • Investigate the effects of varying wall thickness on the moment of inertia calculations.
USEFUL FOR

Structural engineers, mechanical engineers, and students studying mechanics of materials who need to understand the calculation of the second moment of area for complex shapes.

Becky6
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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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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.
 

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