2. As part of a circus act, an elephant reclines on a special diving board, generating the loading shown
in the image on the right below. The diving board is a beam with a rectangular cross-section (shown
in the image on the left below) with base $b = 1.5$ m and height $h$; the length of the beam is $L = 6$ m.
Please note that the two images shown below are drawn to different scales.
3 kN/m
1.5 m
h
A
B
000
Cross-section
View
$L/4$
a) Draw the free body diagram of the beam and compute the reaction loads.
b) Sketch the shear diagram and label all relevant values of $V$ and $x$ (i.e. label all values/positions of
peaks and where the curve crosses zero).
c) Sketch the moment diagram and label all relevant values of $M$ and $x$.
d) Determine the minimum required height $h$ if, for the material used in making the diving board, the
allowable normal stress $\sigma_{all} = 13$ MPa and the allowable shear stress is $\tau_{all} = 900$ kPa.
