Designs such as are shown in Fig. 91 have the tie elevated for the accommodation of an arch in the ceiling. This and all similar designs are seriously objectionable, and should always be avoided; as the small height gained by the omission of the tie-beam can never compensate for the powerful lateral strains which are exerted by the oblique position of the supports, tending to separate the walls. Where an arch is required in the ceiling, the best plan is to carry up the walls as high as the top of the arch. Then, by using a horizontal tie-beam, the oblique strains will be entirely removed. It is well known that many a public building has been all but ruined by the settling of the roof, consequent upon a defective plan in the formation of the truss in this respect. It is very necessary, therefore, that the horizontal tie-beam be used, except where the walls are made so strong and firm by buttresses, or other support, as to prevent a possibility of their separating. (See Art. 212.)

Fig. 89.

Fig. 90.

Fig. 91.

Fig. 92.

233. - Hip-Roofs: Lines and Bevils. - The lines a b and be, in Fig. 92, represent the walls at the angle of a building; b e is the seat of the hip-rafter, and gf of a jack or cripple rafter. Draw e h at right angles to b e, and make it equal to the rise of the roof; join b and h, and h b will be the length of the hip-rafter. Through e draw di at right angles to be; upon b, with the radius bh, describe the arc hi, cutting di in i; join b and i, and extend g f to meet b i in j; then gj will be the length of the jack-rafter. The length of each jack-rafter is found in the same manner - by extending its seat to cut the line b i. From f draw fk at right angles to f g, also fl at right angles to be; make fk equal to f l by the arc lk, or make g k equal to gj by the arc j k; then the angle at j will be the top-bevil of the jack-rafters, and the one at k will be the down-bevil*