Foz SOME APPLICATIONS OF 
The usual aim of the engineer is that no part of the structure he is 
designing should ever be strained beyond the elastic limit, and this 
end he of course desires to obtain with the least possible expenditure 
of material. Thus ideally he might be expected to calculate the dimen- 
sions of each piece, so that for the maximum load it is to be subjected 
to it shall just not pass beyond the limit of perfect elasticity. There 
are however in general agencies, such as wind pressure, dynamical 
action of a moving load, ete., whose effects are not very fully under- 
stood and whose magnitude can not always be foreseen. Thus it is 
the custom to allow a wide margin for contingencies. Now the limit 
of perfect elasticity seems the natural quantity to employ in allowing 
for this margin, but the uncertainties attending its determination are 
such that it is customary to employ the breaking load instead. The 
breaking load for the particular kind of stress the member in question is 
to be exposed to is divided by some number, e. g., 4 or 5, called a factor 
of safety, and the dimensions of the member are calculated so that its 
estimated load shall not exceed the quotient of the breaking load by 
the factor of safety. The engineer varies the factor of safety accord- 
ing to the nature of the load, and according to the confidence he pos- 
sesses in the uniformity of the material and in the completeness of his 
knowledge as to the vicissitudes the structure is exposed to. It has 
thus come to pass that attention has been largely directed to the 
breaking loads, and theories have been constructed which aim profess- 
edly at supplying a law for the tendency to rupture, under the most 
general stress systems possible, of materials whose rupture points have 
been found under the ordinary simple stress systems employed in 
experiment. 
There are only two such theories of rupture for isotropic materials 
that at present possess any general repute. To understand them the 
reader requires to know that for any stress system there are at every 
point in an isotropic elastic material three principal stresses along three 
mutually orthogonal directions, and likewise three principal strains 
whose directions coincide with those of the principal stresses. If an 
imaginary small cube of the material be taken at the point considered 
with its faces perpendicular respectively to the three principal stresses, 
then no tangential stresses act over these faces. In a bar under a uni- 
formly distributed longitudinal stress L per unit ot cross section, two 
of the principal stresses are everywhere zero, and the third is parallel 
to the axis and equals L. If E be Young’s modulus, and 7 Poisson’s 
ratio for the material, supposed isotropic and elastic, the greatest prin- 
cipal strain is everywhere L/E and its direction is parallel to the axis. 
The two remaining principal strains are each —7L/E and they may be 
supposed to have for their directions any two mutually perpendicular 
linesin the cross section of the bar. 
One of the theories referred to above is, that when the algebraic dif- 
ference between the greatest and least of the principal stresses at any 
