Moment of inertia of a composite shape: U or T

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Question 1

A composite shape is drawn to scale below. Grid units are [in].

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Determine the total area of the shape.

$A$ = Expected answer:

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Determine the moment of inertia of the shape with respect to the x-axis.

$I_\var{axis} =$ Expected answer:

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Determine the radius of gyration of the shape with respect to the x-axis.

$k_\var{axis} =$ Expected answer:

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Dimensions:

$b_1 = \var{b1} \qquad h_1 = \var{h1}\\b_2 = \var{b2}\qquad h_2 = \var{h2}$

Area:

$A_1 = b_1 h_1 = \var{A1}$

$A_2 = b_2 h_2 = \var{A2}$

$A_t = A_1 + A_2 = \var{A1} + \var{if(B[1]<A[1],'–','')} \var{A2} = \var{A_t}$

For the x-axis:

$I_{1x} = \frac{1}{3}b_1 h_1^3 = \var{siground(I1x,4)}$

$I_{2x} = \bar{I} + A d^2 = \frac{1}{12} (\var{B2}) (\var{H2})^3 +(\var{A2}) (\var{dx})^2 = \var{siground(I2x,4)}$

$I_x = I_{1x} + I_{2x} = \var{siground(I1x,4)} + \var{if(B[1]<A[1],'–','')} \var{siground(I2x,4)} = \var{siground(I_tx,4)}$

$k_x = \sqrt{\frac{I_x}{A}} = \var{siground(kx,4)}$

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