This section is from the book "Safe Building", by Louis De Coppet Berg. Also available from Amazon: Code Check: An Illustrated Guide to Building a Safe House.
IN Figure 256 we have the design of one-half of an ordinary kingpost truss, with three bays to each principal rafter. Figure 257 gives the strain diagram and Figure 258 the design of the truss in detail. The length of principal rafter is 25 feet 6 inches, therefore length of each bay 8 feet 6 inches. The trusses in the building from which this example has been taken had to be spaced far apart-19 feet from centres - on account of ceiling and skylights; this, however, is not an economical arrangement, as it increases not only the sizes of the truss members, but of all the purlins as well. The weight assumed was 55 pounds per square foot of roof surface, being made up as follows:
Large spaces extravagant.
Boards and construction,
Wind and snow,
The slate was the ordinary roofing slate; if the slate used had been called for of even thickness and 1/4 inch thick the allowance would have been 10 pounds.
The weight of "Boards and construction" was estimated and not checked off, in this case. In important constructions and particularly in ironwork, this should be carefully weighed up.
The load on each joint of our truss was therefore: 19.8 1/2.55 = 8882 pounds, or say 9000 pounds on each joint, excepting, of course, the joints at reactions which carry only half-loads.
The loads on the truss being symmetrical, each reaction will be one-half the total load or 27000 pounds.
There is no difficulty in drawing the strain diagram, or in finding the stresses in each member, the latter are marked on Figure 256, the positive+sign denoting compression, and the negative-sign tension.
We now proceed to detail the truss. The principal rafter will evidently, though not necessarily, be made in one piece from foot to apex, the largest strain - at the bottom panel - will therefore determine its size. This is 58400 pounds compression. The rafter is evidently a series of columns each 8 feet 6 inches long, or comparatively short columns; for the struts brace the rafter against yielding downward;
Detailing wooden truss.
the loads and tie-rods keep it from yielding upwards ; and the purlins keep it from yielding sideways. The safe compression per square inch on Georgia pine (see Table IV) is 750 pounds. Without bothering with the complex Formula (3) for columns, we will assume that we can safely use
(c/f) = 700 pounds in our case, we require then in the main rafter an area of cross-section a = 58400/700 = 83,4 square inches, or say a timber 8 1/2 inches x 10 inches. This we increase to 10 inches x 10 inches to allow for cutting away at bolt-holes.
If the purlins had not been placed directly over the joints we should have to increase this size to provide for the transverse strain in each panel. In such a case we should have a beam 8 feet 6 inches long, supported at both ends. The transverse load on the beam would not be the full vertical load, but only its resultant normal to the rafter, as shown in
If C D were drawn at any scale equal to the vertical transverse load on rafter A B, draw ED parallel rafter, and E C normal to same, then will E C measured at same scale as D C represent the transverse load on the rafter A B, the latter being considered as a beam of length A B supported at A and B.
Returning to our truss; if it were not supported sideways by purlins we should have to greatly increase the size of rafter, to guard against lateral flexure, see Formula (5).
The stress in tie-beam is 54000 pounds tension, the safe (t/f) for
Georgia pine (Table IV) is 1200 pounds, therefore required area a = 54000/1200 = 45 square inches.
In a wooden truss the principal members are naturally of same thickness, therefore we should require 4 1/2 inches x 10 inches to resist tension. To this must be added the necessary area for bolt-holes, transverse strain due to ceiling hanging to tie-beam, etc. In our case the beam was pieced, as shown at centre, and it was therefore rather heavily increased and made 10 inches x 12 inches.
The struts were of spruce; their size will, as a rule, be determined by the area of their bearing against the principals - so as not to indent these - rather than by their length as columns, though both should be tried.
By making our larger strut 6 inches x 8 inches we get a bearing against the rafter of about 6 inches x 10 inches, or say 60 square inches, this would make a compressive stress across the grain on the
Georgia pine rafter of
14000/60 = 233 pounds per square inch.
Table IV gives 200 pounds as safe across the grain on Georgia pine, but we can pass the above as safe It should be remembered that the action of crushing stress in short blocks greatly resembles that of an explosion. A short block or cube of stone, if compressed, will fly off in the four directions normal to the four free sides, with sudden and great force, as if there hd been an internal explosion. If the block is large the central fibres will tend to explode outwardly, while, of course, the fibres nearer the edge will tend to explode inwardly and as a result the central fibres, meeting with the opposition of the external fibres, will resist more compression than they would if they were free. This is confirmed by actual experiment, where it is found that large blocks of the same material will resist crushing proportionately to a very much greater extent than will the small blocks.