This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
Choosing the Sections. The fiber stresses used here are tension,
15,000 lbs.; compression, 12,000 lbs., reduced by Gordon's formula.
Both top and bottom chords are subjected to bending stresses due to the roof and ceiling joists, which come on these chords between the panel points. The bending stresses must be added to the direct stresses.
It is necessary at first to assume approximately what the direct fiber stress can be without exceeding the allowable stress reduced for unsupported length and for the bending stress. Having selected a section on the basis of this assumed fiber stress, the moment of inertia and the actual stress must be determined. If these vary materially from the allowable, a new section must be chosen and the process repeated. In this case the process is illustrated below.
Top Chord. Fig. 275 shows the assumed section of top chord. The first step is to determine the position of neutral axis.
86.70 ÷ 20.71 = 4.20 = Distance of neutral axis from top of cover plate. Moment of Inertia of Top Chord.
lab = 5.25 X 42 = 84.0
3.96 X 2 =8.0
Radius of gyration r = 4.4
Radius of gyration r = 4.05
The top chord between panel points may be considered as a beam of span equal to panel length, and fixed at the ends as regards the bending moment caused by the direct load. Therefore, fc = 64,000x4.2/410 = 656 fsd = 212,000/20.7 = 10,250/10,906
= 64,000 inch-pounds.
Since the top chord is braced laterally only at the ends and at three points equally distant, the unsupported length is 18 feet 6 inches. From Cambria, the allowable fiber stress in compression for a length of 18 feet 6 inches, and least radius of gyration 4.05, is found to be 11,000 lbs. reduced from 12,000 lbs. The above combined stress is therefore within the limit and close enough not to require redesign.
Bottom Chord. The bending moment is
= 14,700 pounds
Fig. 276 shows the assumed section of bottom chord. The neutral axis is determined as follows:
2X14 X 5/16 X 7.38 = 64.6
2X 1.93 X 1.44 = 5.5
14 X 3/8 X .19 = 1.0
71.1 ÷ 17.86 = 4.00 = Distance of center of gravity from bottom of plate. Moment of Inertia of Bottom Chord.
2 X 2.33 = 4.7
ft = 14,700x4.0/310.7 = 189
207,000 = 14,650 fsd= 14.11 (net) 14,839
As the bottom chord is subject only to tension, it is not necessary to calculate the radius of gyration or moment of inertia about axis c d.
Diagonals are designed by using 15,000 lbs. tension, and choosing angles whose net section, taking one rivet hole out, will be sufficient for the stress in the member.
Verticals are designed by assuming an allowable fiber stress based on the reduction of 12,000 lbs. for ratio of length to radius of gyration. After the section is determined, using this assumed fiber stress, it is necessary to see that this fiber stress is within the actual allowable stress for the radius of gyration of the member.
Where two angles are used, spread the thickness of gusset plate, the least radius is employed, either parallel with the outstanding legs or through the axis of the gusset. Where side plates are used, as in this ease, the radius employed should be that parallel to the outstanding legs. These angles being spread and either laced or tied with plates, are weakest in the direction of the axis of the truss. The student should follow through the different sizes given for verticals and diagonals, fully understanding the above explanations.
Fig. 278 shows a detail of the connections at one top chord panel point; and Fig. 279, of one bottom chord panel point. It should be noted that the rivets are in single shear, and that the side plates are deep enough to allow connections to be made without the use of gussets.
In Fig. 267, a detail is shown of a connection suitable for a rod hanging, a balcony, or other member to the truss. Note that the center of rod comes at the intersection of the strain lines at the panel point. This should always be the case unless the chord is made specially strong to resist the bending due to a connection between panel points. Note also that the connection is applied directly to the gusset plate by a pin through the clevis nut. This brings only shearing and bearing strains on the connection, and avoids any direct pull on the heads of rivets or of bolts, which should be divided wherever possible in such cases.
The open holes in top chord are for securing the roof purlins to the truss. These purlins run directly across the top chord.
Fig. 284 shows a general view of the truss and monitor frame in position, and the roof beams framing to them. This truss was short enough to be riveted up at the shop and shipped whole. The monitor frame, however, was shipped separate from the truss, as indicated by the open holes for connection to truss. As this monitor frame, if shipped whole, would be likely to become bent and distorted, it had to be shipped in two parts, as indicated by the details.
Figs. 281 and 282 show the top and bottom chord splices in the center panel of the truss shown in Fig. 272. Note that the point in top chord is specified to be planed, and therefore the rivets provided are sufficient for only a portion of the stress, the balance being transferred by direct compression on the planed surfaces.