The construction shown in Fig. 3 is a true truss and the simplest form in which a truss can be constructed. It also contains all the pieces required to support the weight W.
If a vertical member, k, were added, it must be evident that it would not affect the strain in the other pieces, except as it increases by its own weight the load at W; consequently, when only a single load is to be supported, and that is at the apex, a vertical rod is of no use, except to prevent the tie from sagging under its own weight.
The tie T may be of steel, iron or wood, and of any shape, provided that it has sufficient tensile strength and can be properly secured to the ends of the struts. In wooden trusses, however, it is generally more convenient to make it of wood, as shown in Fig. 7, which shows the next development of this truss. We have here a load to be supported at the apex of the truss, and also a load (represented by w w) at the centre of the tie-beam. To prevent transverse strain in the tie-beam it is evident that we must use the tie k to suspend the load w w from the apex. The tie k will then be strained by the amount of the load w w, and the load at the apex will be increased by the same amount. This will consequently increase the compression in the struts and the tension in the tie-beam.
In practice the load w w is made up of the weight of the tie-beam from a to b and the loads supported by that portion of the beam.
Fig. 8 represents the next step in the development of this truss. Here we have three loads, which are supported in the following-manner:
The load W1 is supported by the struts a and c and the load W3 is supported by b and d.
[Note. - Although the rafter a e is usually of one piece of material, it really forms two different members of the truss, being separated by a joint; hence in theory a and e are two different pieces.] The horizontal components of the stresses in a and b are resisted by t, and those of the stresses in c and d neutralize each other. The vertical components of the stresses in c and d are taken up by the rod r and transmitted to the apex, where they are added to W2, and the sum supported by the full length of the rafters. The thrusts produced by the stresses in the full rafters are again resisted by the full length of the tie. The above explanation may be illustrated by the diagram, Fig. 9, in which each stress is represented (in direction, but not necessarily in magnitude) by a line. Thus, the sides of the triangle A represent the stresses produced by the load W1; B, the stresses produced by W3; the vertical tie, the stress required to support the inner ends of triangles A and B, and the large triangle represents the stresses produced by W2 and the tie r. It will thus be seen that the tie-beam and the lower portion of the rafters receive two stressesand the other parts but one.
If the load W2 is half way between the supports, and W1 and W3 are half way between the supports and the centre, then the tension in r will equal 1/2 W1 + 1/2 W3, plus half the weight of the tie-beam. If the tie-beam supports a ceiling over its full length, then one half of the load will also be supported by r.
In practice the weight of the members is generally neglected in determining the stress in the rods.
Trusses of the form shown in Figs. 7 and 8 are commonly designated as "king-rod" or "king-post" trusses, they being the modern form of the old king-post truss, in which a wooden post was used for the centre tie. King-rod trusses are sometimes seen with rods at k and 1. When the tie-beam supports a ceiling they may be used to advantage, but where there is no ceiling they are useless.
Fig. 8. - King Rod Truss.