The following table by Mr. G.L.  Vose gives, with sufficient accuracy for practice, the relative resisting powers of wood, wrought, and cast iron, with the corresponding positions of the axis.

Dist. of axis
Resistance  Resistance            from top in
to          to                frac’s of
Material.     Extension.   Compression.   Ratio.  the depth.

Wrought Iron, 90 66 90/66 90/156, or 0.58.

Cast Iron, 20 111 20/111 20/131, or 0.15.

Wood, 2 1 2/1 2/3, or 0.66.

Thus we see that the resistance of a beam to a cross strain, as well as to tension and compression, is affected by the incompressibility and inextensibility of the material.

The formula for the dimensions of any beam to support a strain transversely is

      4 bd squared
  S = ——­
       l

[TeX:  $S = \frac{4 bd^2}{l}$]

S = the ultimate strength in lbs. b = the breadth in inches. d = the depth in inches. l = the length in inches.

=Detrusion.= Detrusion is the crushing against some fixed point, such as obtains where a brace abuts against a chord, or where a bridge rests on a bolster; and the shearing of pins, bolts and rivets, also comes under this head.

=General Abstract.= The resistance to the above mentioned strains varies as the area of the cross section; so that by doubling the area we double the strength.  Any material will bear a much greater strain for a short time than for a long one.  The working strength of materials, or the weight which does not injure them enough, to render them unsafe, is a mooted point, and varies, according to the authority, from 1-3 to 1-10 of the ultimate strength.  The ratio of the ultimate strength to the working strength is called the factor of safety.

The following is a table of ultimate and working strengths of materials, and factors of safety: 

Weight                Ult.     Ult.    Working Strengths Factor  Safety.
in lbs.   Materials.    Ext.     Comp.   Exten.     Comp.    Tension  Comp.

30    Wood.        14,000   7,000   2,000    1,000      7      7
480    Wrou’t Iron. 60,000  64,000  15,000   12,000      4      5.33
450    Cast Iron.   18,000 100,000   4,500   25,000      4      4

=Lateral Adhesion.= Lateral adhesion is the resistance offered by the fibres to sliding past each other in the direction of the grain, as when a brace is notched into a chord, or tie beam, at its foot, it is prevented by the lateral adhesion of the fibres from crowding off the piece, to the depth of the notch, against which it toes.  Barlow’s experiments give the lateral adhesion of fir as 600 lbs. per square inch, and the factor of safety employed varies in practice from 4 to 6, giving a working strength of from 150 to 100 lbs. per square inch.

=Table of compressive resistance of timber.=