While compound beams may be advantageously used under certain conditions, it will generally be fully as economical and much better where there is sufficient height, to use a trussed girder of one of the types described below, and when the span exceeds 30 feet these are generally the only kind of wooden girders that will afford the necessary strength.
The most common method of trussing wooden girders is by the use of a "belly-rod," as shown in Figs. 490 and 491.
Such girders, however, are often very carelessly used and without any consideration of the manner in which the pieces are strained.
The most common fault found in such girders is that the rod is not large enough, and is not placed at a sufficient depth below the girder. The author has seen a pair of beams trussed with a belly-rod where the rod did not go below the bottom of the beams, and very often but a little below. Now all solid wooden beams, with the possible exception of oak beams, generally commence to fail by the crushing of the upper fibres, showing that the tensile strength of the wood is greater than its crushing strength, hence any addition to its tensile strength is superfluous unless the upper fibres are also strengthened. A truss rod, placed within the depth of a long beam, may make it stiffer, but cannot materially increase its strength.
The proper use of a belly-rod requires such a relation of depth, h.
to span that the beam will only have to resist the crushing stress on the girder, while the rod sustains all of the tensile stress.
Rules for determining the stresses in belly-rod trusses are given in the Architects' and Builders' Pocket Book and other handbooks. In general the strain on the tie-rod is in the proportion of the length t to the height h (Fig. 490). The nearer the distance h approaches that of t, the less will be the strain on the rod. The distances l, h and t should be measured from the centre lines of the pieces.
The best method of constructing a short belly-rod truss is that shown in Fig. 490. The beam is made of two timbers, spaced about a inches apart, or far enough to allow the rod to go between them. A cast iron plate, of which a larger view is shown at A, Fig. 49a, should be placed over the ends of the beams to hold the nut or head of the rod. The strut, if made of wood, should be cut out of a large timber and tapered as shown, and a tenon should be cut on the upper end to go between the beams. This tenon should be secured by bolts passing through the beams. Only oak or selected hard pine should be used for making this piece.
Iron struts look neater, as they may be made much lighter in appearance. If iron struts are used they should be made of the shape shown at B, Fig. 492. The rod should be bent to the correct angle before it is put in place, and should have a nut at each end, unless a sleeve nut is provided, so that the rod may be tightened without drawing over the end of the strut. At least one sleeve nut is desirable, although not absolutely necessary, to facilitate tightening the rod, should any settlement take place through shrinkage of the timber. If the stress in the rod is found to be greater than 24,000 pounds it will be better and more economical to use two rods instead of one. When two rods are used the beam should be divided into three pieces, so as to leave two spaces for the rods. For trusses of over 20 feet span two struts should be used, as shown in Fig. 491.
By using two struts the stress in both the beam and tie are materially reduced, provided the same depth is given to the truss.
In computing the size of the beam it should be remembered that this acts both as a strut and as a simple beam. The span for the beam, however, is only from the bearing to the strut, or between the struts if two are used, as the strut divides the beam into two or three beams and transmits the load to the rod.
When girders are trussed in this way the joists must either rest on top of the girder or be hung in stirrup irons or joist hangers. In the so-called " mill construction" the floor joists are sometimes made of a pair of beams placed from 6 to 8 feet on centres and trussed with a belly-rod, the flooring being made of 3-inch plank.
268. When it is desirable that the girder shall project as little as possible below the ceiling, the form of trussed girder shown in Fig. 493 may be used to advantage. A cross section through this girder, to a larger scale, is shown in Fig. 494. This is an economical method of trussing, as only short rods and bolts are used, which can be made in almost any village. The top of the truss may also b kept Rush with the floor joist, and a good bearing for the latter still be afforded.
The principal points to be kept in mind in designing such a truss are to get as much depth as possible and full strength in the joints. It should be remembered that the depth and length of the pieces of any truss are measured from the centre lines of the pieces. In order to get the full benefit from trussing, the pieces S and B must be joined in such a way that the full horizontal component of the thrust in the piece S shall be transmitted to the beam B, and neither timber be materially weakened. This is best accomplished by making the beam B in two pieces, as shown in Fig. 494, and letting the strut S pass between them. The three pieces should then be well bolted together.
The rods transmit only a direct load, and are not usually very large. They must be provided, however, with a heavy cast iron plate or washer at the bottom, to support the beams, and either a cast, or wrought, iron bent plate washer at the top.
The girder shown in Fig. 493 was drawn for a clear span of 18 feet. The total depth of the girder was limited to 28 inches - 12 inches for the joists, 14 inches for the beam B, and a 2x4 joist between them. The depth of D was taken at to inches, which gave 16 inches for the height R. The length of S and B by measurement (on centre lines) was found to be 68 and 66 inches, respectively.
To illustrate the method of calculating such a girder, we. will perform the calculations for the girder shown in Figs. 493 and 494. To start with we have the following data: A = 5 feet 6 inches, b = 7 feet, span = 18 feet. R = 16 inches, S = 68 inches, B = 66 inches. Distance between centres of girders, 16 feet. Total weight of floor and load, 125 pounds per square foot.
Total load on girder = W = 18x16x125 = 36,000 pounds. Load on each rod = 3/8* W - 13,500 pounds.
Compression in S = 3/8 W X length of S / length of R = 13,500 X 68/16 = 57,375 pounds.
Tension in B or compression in D = 3/8 W X length of B / length of R, = 13,.
500 X 66 / 16 = 55,687 pounds.
Timber, Georgia pine - safe crushing strength, 1,000 pounds per square inch; safe tensile strength = 2,000 pounds per square inch.
Sectional area of strut S = 57,375 ÷ 1,000 = 58 square inches. As the depth was taken at 10 inches, the breadth must be 6 inches.
Sectional area of beam B = 55,687 ÷ 2,000 = 28 square inches = 2x14 inches, or 1x14 for each side.
The beam B, however, also has to support the ends of the floor joists, and must therefore have sufficient transverse strength for this purpose, in addition to the 28 square inches of section above found.
In this case the greatest span of the tie-beam is at b = 7 feet. The load on each half of the beam for this span will be 7'x8'x125 pounds = 7,000 pounds.
From some handbook we find that a 1x14 inch Georgia pine beam, 7 feet span, will support 5,600 pounds, consequently a 2x14-inch beam on each side will be sufficient to support the transverse load, and a 3x14-inch beam will support both the transverse load and tension in truss.
As the load on each rod is 13,500, we find from a table that we must use a 1 3/8-inch rod. By having the screw end of the rod upset we might use a 1¼-inch rod, but the cost of upsetting would be greater than the additional cost of the larger rod, and only in the larger cities is there machinery for doing this class of work.
The outward thrust or kick of the piece S will be equal to the tension in B, = 55,687 pounds. If we connect the pieces by bolts they will be in double shear, and must be figured for a bearing of 6 inches X the diameter of the bolt. We may allow a pressure of the bolt against the wood of 1,600 pounds per square inch for Georgia pine or oak. This would give us a resistance of 14,400 pounds for a 1½-inch bolt. The resistance of the bolt to shearing (double shear) may be taken at 26,500 pounds, hence the number of bolts to be used will be determined by the bearing resistance. As the stress is 55,787 pounds and the bearing resistance 14,400 pounds per bolt, four 1½-inch bolts will be needed. The joints of all trusses should be carefully calculated in this way.
When designing buildings to be erected in small cities, at a distance from the centres of manufacture, the architect should always figure on using such material as can be readily obtained, if such can be made to answer. For this reason in figuring the size of rods, it is better not to allow more than 10,000 pounds to the square inch, as it will be difficult to get the class of rods that are used in engineering works, and for which greater strength may be allowed.