Flexibility
Collier's New Encyclopedia (1921)
in physics, the propperty which all bodies possess to a greater or less degree, and which is evinced in their disposition to yield or change their form in a direction at right angles to their length, through their own weight or by means of any pressure or strain applied to them. Pieces of the same material differ from each other in the degree of flexibility they exhibit, in proportion to their length and thickness. Thus it is evident that a cylindrical bar of iron an inch in diameter and 20 feet in length will exhibit a far greater degree of flexibility than another which is only half the length, and has a diameter of two inches. Materials also exhibit a greater degree of flexibility in one condition than in another; metals, for instance, yielding far more readily to pressure when heated than when cold. The degree of flexibility possessed by any material is denoted by the extent to which it will bend, or by the weight which it will support without breaking. This property must not be confounded with that of elasticity; elastic bodies will return to their former shape when they have been bent or altered by pressure in any way; but bodies which possess flexibility without elasticity do not return to their original form in all cases. The consideration of the deflection or flexibility of beams of wood and iron bars and girders, as well as of ropes and chains, and other materials, is an important point in the construction of buildings, bridges, and engineering works of various kinds.
What Has Changed in the Last Century
The physics in Collier's 1921 account is still sound: deflection under load does grow steeply with span and fall with thickness, and the writer was right to warn against confusing flexibility with elasticity. What has changed is the vocabulary and the arithmetic. Engineers now speak of flexural rigidity, the product of Young's modulus and the second moment of area, and they keep stiffness (how far a beam sags) strictly apart from strength (the load that breaks it), whereas Collier's measured flexibility by either indifferently; modern codes treat them as separate limit states. The hand calculation of "beams of wood and iron bars and girders" has also largely gone over to computers: matrix methods and finite element analysis, developed from the 1950s onward, now handle frames far too complex for the closed-form formulas of 1921, and the flexibility method that gave the property its structural name has been largely displaced by the stiffness method.
Written for this edition, 2026.