A beam on two supports beats a cantilever
How support conditions change stiffness by an order of magnitude.
A beam held up at both ends resists a load far more stiffly than the same beam held at only one end, because a cantilever has to carry the full leverage of the load all the way back to its single fixed support, while a beam on two supports can share that leverage between both ends and let the middle of the beam do comparatively little of the resisting work.
Where the leverage goes in each case
A cantilever, fixed rigidly at one end and free at the other, has to resist a load applied anywhere along its length entirely through that one fixed end, since there is nowhere else for the internal bending to go. The further the load sits from the fixed end, the greater the leverage, and because the whole length of a cantilever lies between its fixed end and the free end where loads usually act, that leverage tends to be large. A beam supported at both ends has two points able to push back. A load in the middle of the span produces bending that both supports share, with the largest bending confined to the middle of the beam instead of concentrated at one rigid joint.
Because deflection grows so steeply with the length any single support has to reach across, as covered elsewhere in this set, halving the effective length each support is responsible for does far more than halve the droop. Take one beam of a given length and hang a weight from its free tip as a cantilever, then lay the same beam across two supports at its ends and hang the same weight from its middle. The textbook formulas give the cantilever sixteen times the deflection of the supported beam, which is where the order of magnitude in the subtitle comes from.
Carrying a plank alone, then with a friend
Carrying a long plank alone, gripping only one end while the rest sticks out unsupported, makes a cantilever's weakness obvious through the arm holding it. The far end droops, and the arm has to fight the full leverage of the plank's own weight acting through its entire unsupported length. Have a second person hold the far end and the droop all but disappears, the plank now feeling close to rigid even though nothing about the plank itself has changed. The material is exactly as strong as before; the load simply has two places to be resisted, which cuts the leverage either support has to fight on its own. Moving the second person's grip in from the far end changes the balance again, since the stretch of plank beyond their hands behaves like a short cantilever of its own.
Soft supports, badly placed supports, and strength
The improvement only arrives if both supports are rigid and well located. A beam propped on one solid support and one soft, springy one behaves somewhere between a true two-support beam and a cantilever, depending on how much give the softer support has. A rigid support placed only a short distance from the fixed end also delivers little, since most of the beam's length still hangs off that one good support like a cantilever. None of this says how much load the beam can carry before the material fails, which is a separate question about strength; it describes only how much the beam deflects and how that deflection is spread along it.
Designing brackets with a second support
A wing mount, a seat mount, or any bracket that can plausibly be supported at two points is worth designing that way whenever the surrounding structure allows it, because the stiffness gained is far larger than the weight or effort a second support point usually costs. A part with no realistic second support needs a deeper or stiffer cross-section near its fixed end than a two-support beam carrying the identical load would need anywhere along its span. That is why a designer facing an unavoidable cantilever, a wing mounted from one side only or a sensor arm with nowhere else to attach, treats that single fixed joint as the most important feature on the whole part.