W e shall consider this combination of pressures a little more particularly.
Figure 13.—Suppose an upright beam, pushed in the direction of its length by a load, 13, and abutting on the ends of two beams, A C, A D, which are firmly resisted at their extreme points, c and n, which rest on two blocks, but are now ise joined to them : these two beams can only resist in the directions c A, D A ; and therefore the pressures which they sustain from the beam, 13 A, are in the directions A C, A D. To know how touch each sustain:, produce B A to E, taking A E from a scale of equal parts, to represent the number of tons, or pounds, by w hich B A is pressed. Draw E F and E G parallel to A D and A C; then A F, measured on the same scale, will give the number of pounds by which A C is strained or crushed, and A G will give the strain on A D.
Here it deserves particular remark, that the length of A c or A I) has no influence on the strain arising from the thrust of B A, while the directions remain the same. The effects, however, of this strain are modified by the length of the piece on which it is exerted. Tins strain compresses the beam, and will therefore compress a beam of double the length twice as much ; though it may change the front of the assem blage. If A c, for example, be Very much shorter than A D, it will be much less compressed : the line c A will turn about the centre. while n A will har,Ily change its position ; and the guide c A n will grow more open, the point A sinking down. By thus changing shape, strains are often produced in places where there were none before, and frequently of the very worst kind, tending to break the beams across. The dotted lines of this figure show another position of the beam, A n', which makes a material change, not only in the strain on A n', but also in that on ,c c : both are much increased ; A o being almost doubled, and A F four times greater than before. This addition was made to the figure to show what enormous strains may be produced by a very moderate force, A E, when it is exerted on a very obtuse angle.
Figures 14, 15, will assist the most uninstructed reader in conceiving how the very same strains, A F, A 0, are laid on these beams, by a weight simply hanging from a billet rest ing on A, pressing hard on A D, and also leaning a little on A C; or by an upright piece, A E, joggled on two beams, A C, A D, and performing the office of an ordinary king-post.
Figure 15.—The proportion of these strains will be pre cisely the same, if everything be inverted, and each beam be drawn or pulled in the opposite direction. In the same way that we have substituted a rope and weight in Figure 14, or a king-post in Figure 15, for the loaded beam, a A, of Figure 13. the framing of Figure 16 might have been substi tuted, whieh is a very usual practice. In this framing, the batten, 1) A, is stretched by a force, A G. and the piece A C is compressed by a force. A F. ft is evident that it' a rope, or an iron rod, be fil-tened on at D, in place of the batten D A, the strains will be ON same as before.
Figure 17.—By changing the form of this framing, the same strains are produced as in the disposition represented by the dotted lines in Figure 13. The strains on both the battens A D, A C. are now greatly increased.
Figure 18.—The same consequences result from an im proper change of the position A C, the strains on both are vastly increased. In short, the rule is general, that the more open we make the angle against which the push is exerted, the greater w ill be the strains on the struts or ties forming the sides of the angle.
The reader may not readily conceive the piece A C, of Figure IS, as sustaining a compression ; for the weight appears to hang from A c as much as from A D. But his doubts will be removed by considering whether he could employ a rope in place of A C ; which Ire cannot ; hut A D may be exchanged for a rope. A c is thereflwe a strut, and not a tie.
Figure 19.—A D is again a strut, butting on the block D ; A c is a tie; and the batten A c may be replaced by a rope. While A D is compressed by the force A 0, A C is stretched by the force A F. Give A c the position represented by the dotted lines, the compression of A D will be A o' ; while the force stretching A c' will be A ; both much greater than before. This disposition is analogous to Figure IS, and to the (lotted lines in Figure 13. Nor will the young artist have any doubt of A being on the stretch, if he consider whether A D can be replaced by a rope, which it cannot, but A c, may ; and it is therefore not compressed, but stretched.