For this example we will take a case where the purlins rest on the chord of the truss, other than at the joints, as in Fig. 253. For a roof of this span the type of truss shown is the most economical one that can be used, but if the purlins were spaced at the joints the rafters should be 2"x6", while by spacing the purlins as shown 2" x 4" rafters will answer even with slate roofing, and on a large roof this will effect quite a saving in cost.
We will assume that the trusses are spaced 12 ft. apart on centres. The roof area supported by each of the purlins A, B, C, will therefore be equal to 8' x 12' = 96 sq. ft. The roof area sup8' ported by each of the purlins D, E = - + 2'4" x 12 = 76 sq. ft., hence the roof area directly supported at joint 5 = 152 sq. ft. As purlin A. comes at a joint its load is transmitted directly to the joint. The reaction of purlin B, coming at a point between two joints, will be supported in part by each joint, and the same is true of purlin C. We must therefore find the amount of the purlin loads that will be borne by each of the joints. When a beam sustains a concentrated load applied at some point other than the centre, as in Fig. 254, the portion of the load which is transmitted to each support may be found by the equations given for P1 and P2 in Fig. 254. If the load is applied 1/3 of the span from P1, then 2/3 of the load will be supported at P1 and 1/3 at P2. When the load is applied at the centre, then each support receives one half.
To return now to Fig. 253, it is evident from the above that joint 3 must support of the load on B, or 57.6 sq. ft. Joint 4 must support 4/10of the load on B, and also 8/10 of the load on C, which together equal 115.2 sq. ft. Joint 5, in addition to supporting purlins D and E, must also support 2/10 of the load on purlin C and on the corresponding purlin on the other side of the roof, hence the roof area supported at joint 5 = 152 + 4-10 of 96 = 190.4 sq. ft. It will be seen from the above computations that with the arrangement of joints and purlins shown, joint 5 receives more load than joints 3 and 4 combined. As a load at the apex, however, brings no stress on the rods, this is really a more economical arrangement than if the roof area was evenly distributed on the joints.