Let Fig. 255 represent (in the upper portion) the intersection of two pitched roofs with the ridges at right angles to each other, and also in the lower portion a cross section of the roof. In its horizontal dimensions this roof is the same as that shown in Fig. 162, but to facilitate the computations the pitch of the roof has been changed. As far as computing the roof loads is concerned, however, Fig. 255 will apply as well to a roof supported by triangular trusses as by scissors trusses, but if the ceiling below is to be level it will be simpler and generally cheaper to support the roof over the intersection or crossing as shown in Fig. 168. Where the ceiling is raised or vaulted it will generally be found necessary to use diagonal trusses. In this example only one of the diagonals is a full truss, the other diagonal being formed of two half trusses supported at the center of the full truss as shown by Fig. 164.
We will now proceed to compute the roof area supported at each of the joints of the three trusses.
The entire roof area supported by the diagonal trusses is that portion included within the heavy broken line. This area is supported at the eight points where the purlins intersect the diagonals, and also at the apex. The roof area supported at joint 2 of each truss is shown by the shaded portion in the lower right-hand corner.
Fig. 203. - Plan and Elevation of Roof.
This area is equal to twice the length at X multiplied by the slant height, r, which is 8 ft. X = 1/2 distance from the centre of the valley to the centre of the side truss, or 3'2", therefore the entire area = 6' 4" x8' = 50 2/3t. The roof area supported at joints 3, 3, is the portion included between the shaded portions and the boundary lines. To compute this area it is necessary to consider it as made up of two portions, one measured by Z and the other by Y. The entire area = 2Yx4 + 2Z x 4 = 104 sq. ft. The ridge purlins are supported at the points P, P, by braces extending to the tie beams of the trusses directly below joint 3, which we will designate as joint 4. As this joint (4) will support 1/2 the load at the points P, P, on each side of it, the area supported is equal to twice (6' 2" +5'8"/2) x 4 = 72 sq. ft. The remaining roof area, 5'8" x 8', should be considered as supported at the apex, or joint 5 of the full truss. We will now add together the joint areas that we have found, and check them by the total area. The sum of the joint areas is made up as follows:
4 times the area at joint 2.......................
4 times the area at joint 3.......................
4 times the area at joint 4.......................
area at joint 5.......................
To compute the area included within the heavy broken line, first find the area included within the square abcd, and then add the additional areas at the corners.
The area a b c d = 23' 8" multiplied by twice the slant height, which is about 16' 3", or 769 1/2 sq. ft. To this should be added 8 times the area included within the points d e f h. This area is equal to e f + d g/2 x 4 plus 1/2 d g x 8 = 22 1-6 sq. ft. Multiplying by 8, we have 177 1/3 sq. ft. Adding the area a b c d, we have for the total area 947 sq. ft. or 5 ft. less than the sum of the joint areas. This slight discrepancy is due to some inaccuracy in figuring the slant heights, and is not of sufficient amount to be considered as an error.
In figuring the loads on the full truss, the reactions of the half trusses must be added to the load at the center.
These four examples should be sufficient to explain the method of figuring roof areas contributory to joints.