Discussion
A section has \( I_{xx} = 8 \times 10^6 \), \( I_{yy} = 4 \times 10^6 \) and \( I_{xy} = 2 \times 10^6 \) mm\( ^4 \). The principal axes are inclined at
Answer: C
Correct answer: 22.5 degrees
\[ \tan 2\theta = \frac{2I_{xy}}{I_{xx}-I_{yy}} = \frac{4\times10^6}{4\times10^6} = 1, \] so \( 2\theta = 45^\circ \) and \( \theta = 22.5^\circ \). The factor of two is the trap: forgetting to halve the angle gives 45 degrees, which is offered here.
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