Mechanics of Materials · The cantilever
One end, and nothing under the tip
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One end, and nothing under the tip

Take away one support and everything gets worse at once. A cantilever is built in rigidly at one end and free at the other — a balcony, a canopy, a diving board, the arm of a crane. It carries its whole load back to a single connection, and that connection has to resist a moment as well as a force.

Point load at the free end: δ=PL33EI\delta = \dfrac{P L^{3}}{3 E I}, read aloud delta equals P L cubed over three E I. Uniformly distributed along the whole projection: δ=wL48EI\delta = \dfrac{w L^{4}}{8 E I}, delta equals w L to the fourth over eight E I. The letters are the ones you already know, with one difference worth stating plainly: on a cantilever LL is the projection, measured from the built-in face to the free tip — not a span between two supports.

Now put the divisors side by side and the lesson lands. Propped at both ends a point load divides by 48; cantilevered it divides by 3. Same load, same span, same section — sixteen times the deflection. That single ratio is why balconies are the fussiest members on any drawing, why cantilever spans are kept short, and why the fixed end is detailed with such care: it is the only thing holding the whole arrangement up.

Compare the two cantilever cases too. The same total load spread along the length instead of hung at the tip gives three-eighths of the sag, because most of it now acts on a shorter lever. That is the general shape of the whole subject: WHERE a load sits matters as much as how big it is.