It should be observed, however, that long columns and struts tend to fail by bending outwards in the centre and then breaking across. This form of failure is called buckling.

Transverse strength is the resistance offered by a body to forces acting across it, tending to bend it, and eventually to make it break across. Thus a beam supported at both ends and loaded over any part of its length, bends downward and tends to break across.

When a body is subjected to transverse stress, some parts of it are in compression, some in tension, and others are exposed to a shearing stress, therefore transverse stress is a combination of these three stresses. A beam secured at the ends, and subject to pressure from below, bends upwards and also tends to break across.

Shearing strength is the resistance offered by a body to being shorn, that is, to being distorted by one part of it sliding on another part. Thus, if two lapped plates united by a rivet be drawn longitudinally in opposite directions, the rivet would tend to shear by the upper plate sliding upon the lower.

Torsional strength is the resistance offered by a body to being broken by torsion, i.e. twisting. This stress frequently occurs in machinery, but not in structures connected with buildings.

Strength to resist hearing is the resistance offered by a material to being indented, or partially crushed by another body pressing upon it. Thus, the shank of a rivet may be indented by the plate bearing upon it, or the edge of the hole in the plate may be indented by the rivet; again, a beam may be indented by the end of a post bearing upon it. Indentation by bearing is merely one form of crushing.

The ultimate strength of any material is the intensity of stress required to produce fracture in any specified way.

The proof strength is the intensity of stress required to produce the greatest strain of a specific kind without injuring the strength of the material.

Pliability is the tendency of a body to change its form temporarily under different stresses.

Stiffness or Rigidity is the reverse of pliability, and expresses the disinclination of some bodies to change their form under stresses.

Thus stones and bricks are rigid up to a certain point.

Elasticity1 is the property which all bodies have (in greater or less degree of perfection) of returning to their original figure after being distorted (i.e. strained) by any kind of stress.

When the original figure is completely and quickly recovered, the elasticity is said to be perfect.2

When the original figure is not completely recovered, but remains permanently distorted to a certain extent, the elasticity is said to be imperfect,3 and the distortion produced is called a permanent set, or set.

It has been found by experiment that the elasticity of most building materials is practically perfect up to a certain point. When stresses below this point are applied and removed, the strain, distortion, or change of figure is only temporary. There is no appreciable set. Stresses above this point, however, cause sets (see p. 330).

The Elastic limit of a material is the maximum intensity of stress that can be applied to it without causing an appreciable set.

A Modulus of Elasticity is a number representing the ratio of the intensity of stress (of any kind) to the intensity of strain (of any kind) produced by that stress, so long as the elastic limit is not passed.

The modulus of tensile elasticity is found by dividing the tensile stress in lbs. per square inch of sectional area by the elongation (produced by that stress) expressed as a traction of the length of the body.

Thus, if a weight of one ton hung from an iron bar produce an elongation of 1/12000 of the length of the bar, the modulus of elasticity of that bar will be 2240 lbs. 1/12000 = 26,880,000 lbs. This is rather lower than the modulus of average wrought iron.

Similarly the modulus of compressive elasticity is found by dividing the compressive stress in lbs. per square inch of section by the contraction (or rather shortening) produced by that stress, expressed as a fraction of the length.

In most building materials the modulus of tensile and that of compressive elasticity are practically equal to one another so long as the stresses do not exceed the elastic limit.

1 The elasticity here referred to is sometimes called elasticity of figure; there is also an elasticity of volume, which need not be considered in connection with building materials.

2 Mr. Eaton Hodgkinson's investigations seem to show that the elasticity of every solid is really imperfect, that the slightest strain produces a set. Up to a certain limit of stress, however, the sets produced are so small that they cannot be measured with ordinary instruments, and therefore within that limit the elasticity may be said to be sensibly perfect for all practical purposes (see p. 317).

3 Because the elongations and shortenings under equal stresses are practically equal up to the elastic limit; beyond that they are irregular.

The modulus is generally denoted by the letter E, and its value is given in the tables, because it is useful in calculating the stiffness of beams and girders.

In advanced works on applied mechanics several other moduli are used, which, however, are not required in ordinary calculations, and need not be referred to in these Notes.

Deflection is the bending caused by a transverse stress. If the intensity of stress be below the elastic limit the deflection will disappear when the stress is removed, but if the intensity of stress be in excess of the elastic limit a permanent set will remain.

Resilience is a term used to express the quantity of "work done" in deforming a piece of material (up to the elastic limit) by the application of any kind of stress. It is equal to the product of the alteration of figure into the mean load which acts to produce such alteration. Thus the resilience of a bar in tension is found by multiplying the proof load by half the corresponding elongation.1

Resilience may be tensile, compressive, transverse, shearing, etc., according to the nature of the stresses imposed.

Malleability is the property of being permanently extensible in all directions by hammering or rolling.

Ductility is the property of being permanently elongated or drawn out under a tensile stress higher than the elastic limit. The change of form remains after the force is removed. It is therefore the converse of elasticity.

Brittleness is the inclination to break suddenly under any stress.

Hardness is the property of resisting indentation, or wear by friction.

Softness is the converse of hardness.

Toughness is a term defined in several different ways.

Mr. Stoney defines it as the union of tenacity with ductility.

Ultimate toughness is defined by Professor Rankine as being the greatest strain which a body will bear without fracture; proof toughness the greatest strain it will bear without injury. He points out that malleable and ductile solids have ultimate toughness greatly exceeding their proof toughness, but that brittle solids have their ultimate and proof toughness equal, or nearly equal.2

Fusibility is the property of becoming fluid when subject to heat. The temperature at which this is effected differs in each metal, and is called its melting point.

Weldability is the power possessed by some metals of adhering firmly to portions of the same - or to other metals - when the two pieces are raised to a high temperature and hammered together.

Hardening is the property of becoming very hard when heated and quenched.

Tempering is lowering the degree of hardness after the process just mentioned, by reheating and cooling at different temperatures (see p. 307).

1 Rankine's Applied Mechanics.

2 Rankine's Useful Rules and Tables.