## Structural Behaviour

The simplest type of roof structure consists of two single rafters that rest on each other with a hinged joint at the top. In carrying vertical load such a structure creates both vertical and horizontal forces that act upon the supports. The horizontal forces need to be supported to avoid collapse of the structure. The early medieval roof structures have tie beams that provide such a support, see Figure 12. If the tie beam is missing or has been cut off the roof structure becomes dependent on an outer support provided by the walls to avoid large deformation and stress or even collapse.

With an increase in span the problem of deflecting rafters with high bending moments soon becomes evident, see Figure 12. The early solution was to put strut beams between the rafters and the tie beam to support them. Figure 12 and Table 2 presents the results from computations made on roof trusses with an outer span of nine metres and a roof angle of 47°, which is a typical size and shape of early medieval roof trusses. The support conditions are based on a one-metre-wide wall where the vertical support is given at the outside, 150 mm from the outermost part of the roof truss, and on the inside of the wall. The tie beam has 230 x 150 mm cross-section and the other parts has 150 x 100 mm cross section. The strut beams are connected to the tie beam 3.87 m from the joint between the rafters. The tie beam and the joint between the strut beams and the rafters are halfway to the ridge in the vertical direction from the tie beam. The centreline of the collar beam is 2.70 m above the centreline of the tie beam. The material is wood with an E-modulus of 10 GPa. The load is vertical and symmetrical and consists of the timber (density 500 kg/m3) and the weight of the outer roofing consisting of boarding and tiles which weigh 53kg/m2. The roof trusses stand one metre apart.

The moment diagram in Figure 12, case B, shows that the strut beams are successful in providing

Figure 12. Geometry and resulting moment diagrams from computations of roof trusses with tie beams and with or without strut beams and collar beam.