# Hip Roof Framing — draw, ab, equal, join, ad and common

## draw, ab, equal, join, ad and common

Contents

4th. The angle that the common rafter makes with the level of the plate; that is, the pitch of the roof.

5th. The length of the common rafter.

6th. The angle that the hip-rafter makes with the adjoining sides of the roof.

7th. The length of the hip-rafters.

8th. The distance from the corner of the building to the center line of the first jack, that is, the common difference.

## To Find the Backing of a Hip Rafter

Fig. 45 shows the method of obtaining the backing of the hip where the plan is not right angled.

Bisect AD in a, and from a describe the semi circle AbD; draw ab parallel to the sides AB, DC, and join Ab, Db, for the seat of the hip-rafters. From b set off on bA, bD the lengths bd, be, equal to the height of the roof bj, and join Ae, Dd, for the lengths of the hip-rafters. To find the backing of the rafter: In Ae, take any point k, and draw kh perpendicular to Ae. Through h draw fhg perpendicular to Ab, meeting AB, AD, in f and g. Make 1 equal to hk, and join fl, gl; then flg is the backing of the hip.

How to Find the Shoulder of Purlins.—Fig. 46 shows how to find the shoulder of purlins: First, where the purlin has one of its faecs in the plane of the roof, as at E. From c as a center, with any radius, describe the arc dg; and from the opposite extremities of the diameter, draw dh, gm perpendicular to BC. From e and f, where the upper adjacent sides of the purlin produced cut the curve, draw ei, fl parallel to dh, gm; also draw ck parallel to dh. From 1 and i

draw lm and ih parallel to BC, and join kh, km. Then ckm is the down bevel of the purlin, and ckh is its side bevel.

When the purlin has two of its sides parallel to the horizon. This simple case is worked out at F. It requires no explanation.

When the sides of the purlin make various angles with the horizon. Fig. 47 shows the ap plication of the method described in Fig. 46 to these cases. See also Fig. 49.

How to Pierce a Circular Roof With a Saddle Roof.—It somtimes happens, particularly in rail road buildings, that the carpenter is called upon to pierce a circular or conical roof with a saddle roof, and to accomplish this economically is often the result of much labor and perplexity if a cor rect method is not at hand.

The following method, shown in Fig. 48, is an excellent one, and will no doubt be found useful in cases such as mentioned.

Let DH, FH, be the common rafters of the conical roof, and EL, IL the common rafters of the smaller roof, both of the same pitch. On Gil set up Ge equal to ML, the height of the lesser roof, and draw ed parallel to DF, and from d draw cd perpendicular to DF. The triangle Ddc, will then by construction be equal to the triangle KLM, and will give the seat and the length and pitch of the common rafter of the smaller roof B. Divide the lines of the seats in both figures, Dc, KM, into the same number of equal parts; and through the points of division in E, from G as a center, describe the curves Ca, 2g, lf, and through those in B, draw the lines 3f, 4g, Ma, parallel to the sides of the roof, and intersecting the curves in fga. Through these points trace the curves Cfga, Afga, which will give the lines of intersection of the two roofs. Then to find the valley rafters, join Ca, Aa; and on a erect the lines ab, ab perpendicular to Ca and Aa, and make them respectively equal to ML ; then Cb, Ab is the length of the valley rafter.

## draw, ab, equal, join, ad and common

4th. The angle that the common rafter makes with the level of the plate; that is, the pitch of the roof.

5th. The length of the common rafter.

6th. The angle that the hip-rafter makes with the adjoining sides of the roof.

7th. The length of the hip-rafters.

8th. The distance from the corner of the building to the center line of the first jack, that is, the common difference.

## To Find the Backing of a Hip Rafter

Fig. 45 shows the method of obtaining the backing of the hip where the plan is not right angled.

Bisect AD in a, and from a describe the semi circle AbD; draw ab parallel to the sides AB, DC, and join Ab, Db, for the seat of the hip-rafters. From b set off on bA, bD the lengths bd, be, equal to the height of the roof bj, and join Ae, Dd, for the lengths of the hip-rafters. To find the backing of the rafter: In Ae, take any point k, and draw kh perpendicular to Ae. Through h draw fhg perpendicular to Ab, meeting AB, AD, in f and g. Make 1 equal to hk, and join fl, gl; then flg is the backing of the hip.

How to Find the Shoulder of Purlins.—Fig. 46 shows how to find the shoulder of purlins: First, where the purlin has one of its faecs in the plane of the roof, as at E. From c as a center, with any radius, describe the arc dg; and from the opposite extremities of the diameter, draw dh, gm perpendicular to BC. From e and f, where the upper adjacent sides of the purlin produced cut the curve, draw ei, fl parallel to dh, gm; also draw ck parallel to dh. From 1 and i

draw lm and ih parallel to BC, and join kh, km. Then ckm is the down bevel of the purlin, and ckh is its side bevel.

When the purlin has two of its sides parallel to the horizon. This simple case is worked out at F. It requires no explanation.

When the sides of the purlin make various angles with the horizon. Fig. 47 shows the ap plication of the method described in Fig. 46 to these cases. See also Fig. 49.

How to Pierce a Circular Roof With a Saddle Roof.—It somtimes happens, particularly in rail road buildings, that the carpenter is called upon to pierce a circular or conical roof with a saddle roof, and to accomplish this economically is often the result of much labor and perplexity if a cor rect method is not at hand.

The following method, shown in Fig. 48, is an excellent one, and will no doubt be found useful in cases such as mentioned.

Let DH, FH, be the common rafters of the conical roof, and EL, IL the common rafters of the smaller roof, both of the same pitch. On Gil set up Ge equal to ML, the height of the lesser roof, and draw ed parallel to DF, and from d draw cd perpendicular to DF. The triangle Ddc, will then by construction be equal to the triangle KLM, and will give the seat and the length and pitch of the common rafter of the smaller roof B. Divide the lines of the seats in both figures, Dc, KM, into the same number of equal parts; and through the points of division in E, from G as a center, describe the curves Ca, 2g, lf, and through those in B, draw the lines 3f, 4g, Ma, parallel to the sides of the roof, and intersecting the curves in fga. Through these points trace the curves Cfga, Afga, which will give the lines of intersection of the two roofs. Then to find the valley rafters, join Ca, Aa; and on a erect the lines ab, ab perpendicular to Ca and Aa, and make them respectively equal to ML ; then Cb, Ab is the length of the valley rafter.