These two strains of compression and extension must be equal in amount--and upon the relative strength of the material to resist these strains, as well as its form and position, the situation of this axis depends. If wood resists a compression of 1000 lbs. per square inch of section, and a tension of 2000 lbs. the axis will be twice as far from the top as from the bottom in a rectangular beam.
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.
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
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