This is the boss. No calculator. Every draw is pinned so the arithmetic fits in your head, and every answer feeds the next: the load and the span give the moment, the section gives $I$, $I$ and the half depth give $S$, and the moment through $S$ gives the fibre stress. Write each line down as you go — one early slip rolls all the way to the bottom, and the finish will show you where it started.

Note what the last line asks for. It does not want another number; it wants a verdict, the way a real check does. Adequate, or not adequate. The four lines of arithmetic exist only to earn you the right to say which.

And keep the units honest with no calculator to hide behind: the section in millimetres, the moment in kN·m, $I$ in millions of mm⁴, $S$ in thousands of mm³, and the stress in MPa — one newton per square millimetre. Get the scales right and the numbers stay small enough to carry.

A bonus mark follows on the way out, and it comes in two flavours. One lays the joist flat and asks what that does to the section modulus. The other hands you a site-built tee and asks for its centroid: each area times its own height, summed, over the total area, with every height taken from the same datum.

Everything in the chapter rides in this one joist. 5★ under par here is the chapter crown. Clock in.