Calculate Principal Inertias - Exercise Hint

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The discussion focuses on calculating the principal inertias for a given painted area with respect to the x and y axes. Participants suggest using the superposition property of moment of inertia to break the shape into simpler components for easier calculation. Key formulas provided include I_x = (bh^3)/12 and I_{xy} = (b^2h^2)/24, specifically for triangles. There is a mention of needing equations for rectangles and the potential application of the parallel axis theorem. The conversation highlights the importance of understanding these concepts to solve the exercise effectively.
fabiancillo
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Hello I have problems with this exercise

For the painted area calculate inertias with respect to the x and y axes and the principal inertias

Hint:
$I_x = \displaystyle\frac{bh^3}{12}$
$I_{xy} = \displaystyle\frac{b^2h^2}{24}$

Thanks
 

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Keeping in mind the superposition property of the moment of inertia, can you split this shape up into pieces and evaluate ##I_x## and ##I_y## for them separately?
 
ergospherical said:
Keeping in mind the superposition property of the moment of inertia, can you split this shape up into pieces and evaluate ##I_x## and ##I_y## for them separately?
I am totally blocked
 
fabiancillo said:
I am totally blocked
That's also called a moment of inertia!
 
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Likes jbriggs444, haruspex and ergospherical
Ok I'll try
 
fabiancillo said:
$$I_x = \displaystyle\frac{bh^3}{12}$$
$$I_{xy} = \displaystyle\frac{b^2h^2}{24}$$
Fixed the LaTeX by doubling the dollar signs.
I note you only quote equations for a triangle. Do you have any for the rectangles? If not, you'll need to cut those into triangles.
Do you know the parallel axis theorem?
 
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