1292

THEORY AND PRACTICE OF ENGINEERING.

Book II.

he should study well the nature of every strain, and itsdirection in the timber he is .about to apply.

Suppose, for instance, an upright beam pushed in thedirection of its length by a load at B, and abutting onthe ends of two beams A C, A D, which are firmly sup-ported at C and D ; and as they cannot move, the pres-sures they sustain from the post B A are in the directionA C and AD: to ascertain what each of these timberssustain, we must produce A E to B, taking A E from ascale of equal parts, to represent the number of tons orpounds by which B A is pressed : draw E F and E Gparallel to A D and A C; then A F, measured on the samescale, will give the number of pounds by which A C isstrained, and A G will give the strain A 1).

Where two pieces of timber, » AC and A D. arcpressed or drawn down by a weight at B, the samerule will apply, and the nature of the strain producedmust always be observed ; in general, if the strainingpiece be within the angle formed by the pieces strained,the strains which they sustain are of the opposite kindto that which it exerts; if it be pushing, they aredrawing, but if it be within the angle formed bytheir directions, the strains which they sustain are ofthe same kind; all the three are either drawing orpressing.

Resistance of Timber to a transverse Strain. — Theweight that will break a piece of timber must beascertained before we can find the load that it will per-manently bear ; the stillness of a beam is the proportionthat exists between its deflection and its length, and the deflection, is what it sinks whenloaded below a horizontal line : the deflection of beams of the same timber similarlyloaded varies as the weight applied, and the cube of the length directly, and as the breadthand cube of the depth inversely, and this deflection should never be permitted to extendbeyond part of the length, or ^ part of an inch to the foot.

The lateral strength of a beam is less than its absolute longitudinal strength, eitheragainst extension or compression; timber will bear a considerable weight if suspended toit perpendicularly, or when pressing in the direction of its length, provided the timber isprevented from bending ; and in using timber, a lateral strain should always be avoided,where a longitudinal one can be substituted.

Rectangular pieces of timber have their centres of gravity in the centre of theirdimensions: a piece of timber 12 inches by 12 contains 144 square inches, and its centreof gravity will bo 6 inches from each side ; if the piece be broken by any load its fracturewill terminate at the upper surface, or 6 inches above the centre of gravity. The area 144multiplied by 6, gives 864 as the lateral strength, which may be applied in comparisonwith any other scantling of different dimensions on wood of the same quality : saw thispiece of timber down the middle; the centre of gravity remains the same; if the sides are inthe same vertical position, the area of the section of each is 72, and this multiplied by 6,the distance of the centre of gravity from the upper surface, makes half the productobtained before the timber was sawn; it is apparent, then, that, the depth remaining thesame, the strength varies as the thickness: should the position of these latter timbers bereversed, that is, placed flat instead of on edge, the centre of gravity then is only 3 inchesbelow the upper surface : the area of the end 72 being multiplied by 3, we obtain only 216as the product, which is only half the strength which it had placed edgeways. Thescantling which has the greatest strength is not all square, but that with the same area,which has its centre of gravity farthest from the top ; a piece of timber 14 by 10 inchessquares to 140 inches, and contains less than a piece 12 x 12, or 144 square inches : but thecentre of gravity of the first is 7 inches from the top, and 140 multiplied by 7 produces980, which exceeds 144 x6 = 864. This is further illustrated by a plank 10 inches indepth and 1 inch in thickness; the sectional area, 10 inches, multiplied by 5, the distance ininches of the centre of gravity from the upper edge, the product is 50: the same pieceplaced flatwise must only be multiplied by £ inch ; the product then is only 5, conse-quently the plank xvhen placed on edge is ten times stronger than when placed flatwdse.

A beam or piece of timber whose section is that of an equilateral triangle, whensubjected to lateral pressure, is twice as strong, when resting on its broad base, as whenplaced on edge, the centre of gravity of this figure being at ^ of its height measured fromthe base, or jj from its apex : the lateral strength of square beams is as the cubes of theirbreadth or depth; the lateral strength of any beams whose sections are similar are as thecubes of similar sides of the section. In cylindrical beams, the lateral strengths are as the

A

Hg 2065.

B