(Solved): A steel cantilever beam is fixed at one end and free to move at the other. A load \( (F) \) of \( ...

A steel cantilever beam is fixed at one end and free to move at the other. A load \( (F) \) of \( 980 \mathrm{~N} \) with a systematic error \( (95 \%) \) of \( 10 \mathrm{~N} \) is applied at the free end. The beam geometry, as determined by a metric ruler having 1-mm increments, is \( 100 \mathrm{~mm} \) long \( (L), 30 \mathrm{~mm} \) wide \( (w) \), and \( 10 \mathrm{~mm} \) thick \( (t) \). Estimate the maximum stress at the fixed end and its uncertainty. The maximum stress is given by \[ \sigma=\frac{M c}{I}=\frac{F L(t / 2)}{w t^{3} / 12} \]