Our illustrations and examples have been chiefly taken from roofs, because they are the most familiar instances, of the difficult problems of the art. . We could have wished for mere room, even on ject. The construction of dome roofs bas (we think) mistaken, and the difficulty is much less than is-imagined,. We moan in respect of strength; for We, grant that the obliquity of the, joints, mid a general, intricacy, increases trouble of work manship exceedingly. Wooden bridges form ano ther clam equally difficult and important, ; but our limits are already overposed, and will not ad mit, them,. The principle on which, they should all, be constructed, witheut exceetien, is. that of a Walk avoiding all lateral. bqarings. on any of the tint.; hers, In the application of this principle, we must farther rcolark, that the angles of our truss should us. acute as possible ; therefore. we sliquIdgmke it of as few, stud, of as long ,pieces aa wo . can, taking care to prevent the bending of the, tress bgantsbx bridles, which embrace them, but without pressing them to either side. When , the truss consists of wog piques. the Tar &ape t ;. anti the thrusts.locre.sse, to .the, dikeikeetg, prepectien4 the-number of angles.
With respect. to .thp grams of. careepri,.741;g1 ORgOK in 011&PPrikaP4 Nit0ii-PRP, the, itarmMep AA 440 thiA.ir, would ,re5nsee volutne. to tr,ea,t of thq The prkofipIes.are already lai4 49N14 if the reader be really interested in the study, hew' engage in it with sertotptaeaskand.casmakfmk.0 being instructed. We recommeed to, his es a specimen of what nmy. be done in this. way, the working beam of I-Iorahlewer's.steamengine. (See Sxxam...Natxa, in When the Oman must act by chaiaa hung from clip upper .e4.4 of arch heads, the framing there given seems scientifically constritcted; • at the same time, vo, 0,4 dui; a strap, of wrought, iron, r,lag whole. length of the upper her (see the figure), waul,d be vastly preferelge to those, partial which, the engineer has Wit, tileXe• . f9; ON .b9443 aeon work loose.
But when arches are net neceFPFYs the, fung eat-, 4:0 kx Mr Wat; is vasVy preferable, fagth , my and for strength. It CpPviata of a, simple (fig. 4“Iiite LUI.)„ hav,ing tbe,gudgeon Op, the, timr 84 The two pa Eon rods are attached,to wrought,i0P, i9i9PA. 4. aPci 10- Two, 84i9uS strati _ This rule may be somewhat more accurately expressed in these words : From the point at which any three forces meet and balance each other, draw a line in the actual direction of any one of them, and from the extremity of this line draw two others, parallel to the directions of the other two forces respectively ; then supposing the pieces affording these two forces to be prdduced in definitely at their remoter ends, either of them which is cut by one of the two lines will be compressed, and act as a brace, and either of them which is not cut will be stretched, and act as a tie.
BB. P. 680. It is however difficult to imagine how the beam DA can furnish a force iA, to prevent the force At from carrying the beam BA towards H, when DA only affords a repulsive abutment. The true resolution of the force AE is found by consider ing the intersection of GE with Ae, which are the direction's of the separate forces composing lt ; these lines meeting in a point a little above r, we may call their intersection ro; then in the triangle A Er*, the side M.* will represent the pressure on the mitred joint, and r*E the pressure on the beam HD; and the former being again resolved into AG and Gr*, we have ultimately AG and Gr* r*E = GE = AF, for the horizontal and vertical forces, however they may be modified by intermediate combinations.
CC. P. 631. The reasoning contained in this and some of the subsequent articles may serve as an approximation to the truth in many cases of com mon occurrence ; but the supposition, on which it is founded, is by no means generally admissible as af fording a result mathematically accurate: for in reality, the distribution of the weight of a roof over the whole extent of the rafters, or the concentration of the whole weight in the point where they meet, is far from being an indifferent alternative, either with respect to the magnitude of the thrusts, or to the proper directions of the abutments or joints. In the case here discussed, where there is no king post, It is clear that the centre of gravity of the whole roof must be much nearer to the middle of the figure than the angular point, and that consequently the weights; supported by the two walls, will be very different from those which would be supported, if the whole load were placed at the summit although, where there is a heavy king post, supporting also, as it ought to do, about half the weight of the tie beam, with its floors or cieling, the case will approach much nearer to the supposition here assumed.
For a common light roof, without a king post, the calculation or construction is very simple. When two rafters only meet at the summit, they must support each other by a horizontal thrust (see Art. BRIDGE, Prop. Y) : and this thrust, acting on each rafter as a lever, of which the lower end is the ful crum, must be equivalent to the weight, acting at the horizontal distance of the centre of gravity from the fulcrum, which is a quarter of the whole span ; consequently the thrust must be to the weight as a quarter of the span to the height, and the compound oblique thrust on the abutment will be represented by the hypotenuse of the triangle of which those lines are the sides : so that if we had a roof of the same height, and of half the breadth, the direction of its rafters would exactly represent the actual di rection of the compound thrust on the en4 of the tie beam, and would consequently indicate the per form for the abutment of the given structure.