40

Art. 31. Table of greatest center loads for horizontal rectangular beams of white or yellow pine, or
of spruce, 1 inch broad, supported at both ends, and required not to bend more than inch per foot
of clear span, or 43♂ part of the entire clear span. In practice, to allow for knots, &c, take only % rds.
This table was calculated with a constant .000325, instead of .00032 as on p 507. The loads in this table include the weight of the clear beam itself: .625 of which (or
of which) must be deducted from the tabular loads to get the neat load, when the beam is loaded at its center. When uniformly loaded, the loads will be 1.6 times as great as
those in this table; but in that case the weight of the entire clear beam must be deducted. In practice this deduction need rarely be made.

1538

984

684

502

384

20

40

On this side of the dark lines, the safe loads of table, Art 23, would not bend the wooden beams as much as of their clear span. Iron and Steel.

Average cast iron, with the same safe def will bear about 11% as much as common yellow or white pine, or spruce; and wrought iron 19 times as much. The same proportion of the weight of the beam itself must, however, be deducted as stated above for wood. Average steel 29 times as much as pine.

Art. 32. Table of greatest center loads of square beams of cast iron, supported at both ends, and reqd not to bend more than of an inch per foot of clear length, or part of the span. For W. Pine div by 12; or in practice by 18.

480

Wrought iron will bear about more than cast, with the same safe deflection. But .625 (or 5%) of the wt of the beam itself must be deducted from these center loads. If the load is equally distributed, it will be 1.6 times as great as these tabular center loads; but in this case the wt of the entire clear length of the beam is to be deducted. These deductions are rarely reqd in practice.

4.4 5.1 5.7 6.2
4.5 5.2 5.8 6.4
5.5 6.1 6.7
5.7 6.3 6.9
5.9 6.6 7.2
6.8 7.4
6.9 7.6

6.7 7.2

7.8

26,880

7.2 7.9

29,120

7.4 8.1

8.3

33,600

7.7 8.4

8,5

8.7

8.8

42,560

8.1 8.9

44,800

49,280

53,760

58,240

62,720

7.6 8.0
6,9 7.4 7.8 8.2 8.6 9.0
9.4
7.2 7.7 8.2 8.6 9.0 9.4 9.8
7.5 8.0 8.5 8.9 9.4 9.8 10.2
7.8 8.3 8.8 9.3 9.7 10.1 10.6
8,0 8.5 9.0 9.5 10.0 10.4 10.9
8.2 8.8 9.3 9.8 10.3 10.7 11.2
8.4 9.0 9.5 10.0 10.5 11.0 11.5
86 9.2 9.7 10.2 10.8 11.2 11.7
8,8 9.1
9.9 10.4 11.0 11.5 11.9
8.9 9.5 10.1 10.6 11.1 11.7 12.1
9.1 9.7 10.3 10.8 11.4 11.9 12.3
9.2 9.8 10.4 11.0 11.5 12.0 12.5
9.4 10.0 10.6 11.2 11.7 12.2 12.7
9.5 10.1 10.8 11.3 11.9 12.4 12.9
9.6 10.3 10.9 11.5 12.2 12.6 13.1
9.0 9.7 10.4 11.0 11.6 12.5 12.7 13.2
9.2 10.0 10.7 11.3 11.9 12.8 13.0 13.6
9.4 10.2 10.9 11.5 12.2 13.0 13.4 13.9
9.6 10.4 11.1 11.8 12.4 13.3 13.6 14.2
9.8 10.6 11.4 12.0 12.7 13.5 13.9 14 4

A single beam of wood under each rail, and firmly braced against lateral motion, will suffice for light railroad bridges of very small span. If single beams of sufficient depth cannot be procured, built-beams may be used; see g, and ij, Figs 62, p 613. Assuming the weight of entire bridge and load at two tons per foot, the following dimensions may be used:

The greatest dimension to be the depth. The ends should be well bolted down to

bolsters. These are long stout sticks of timber, from 10 to 15 ins square, (according to the span,) laid across the abuts at the bridge-seat, for the chords to rest on. Frequently two are used at each abut, even in small spans; and we have seen but one, under railroad spans of 150 feet. Large spans may require three or more. They are not necessarily placed in contact with each other; but may be some feet apart, if required.

Or for spans of about 15 to 30 ft, we may use somewhat lighter beams; and truss each of them as in Fig 52, by an iron bar e s e; and a center post p. In this case the following dimensions will answer; the total deflection of the rod being of the clear span. The screw-ends of the bars are supposed to be upset; but the areas are given for the body of the rods.

It is better to have two rods instead of one under each beam; each rod being of half the section here given; and the two placed several ins apart. This affords a better footing for the post. The ends of the beam should be at right angles to the direction of the rod; and be provided with ample washers e e, of wood or iron, for distributing the pressure from the rod, over the whole area of the ends. The ends of these washers may extend a few ins each way beyond the sides of the beam, as shown on a larger scale at g. This allows the rods to be outside of the beam; instead of requiring holes to be bored in the latter, for passing the rods through them.. They may be nearer together at the foot of the post.

The head of the post may be tenoned into the bottom of the beam; and be further united to it by iron straps. To prevent the foot from being worn by the rods, it should be shod with iron. A castiron shoe, as at s, may be bolted to it; having ribs for keeping the bars in place. Or a stout wroughtiron shoe may be well secured to it. In either case the rod at s should be so united to the shoe as to check any tendency in the foot to slide toward r or r, under the vibration of passing loads. Perhaps this can be most conveniently done by making each rod es e, in two separate lengths, r, r; and by uniting their lower ends to the shoe at s by hooks and eyes; or by eyes and bolts, &c. Various methods are in use for the heads and feet of the posts of large spans; but we cannot here treat upon details which pertain more to the professional bridge-builder.

This mode of trussing is also well adapted to long floor beams; and has been used in long oblique web members; as well as in long stretches of chords from one point of support to another.

Continuous beams. When a single beam, as a b, Fig 40, is supported not only at its two ends, but at one or more intermediate points, it is said to be continuous. It is stronger than if it were cut into two parts, a c, b c, each supported

Fig 40

b

at both ends; because the tensile strength of the particles at o (lower Fig) assists in counteracting the bendg or breakg tendency of loads on the intermediate parts om, on, of the lower Fig. These particles at o must be torn asunder before the beam (if properly proportioned) can fail. Such a beam, mn, if very long and flexible, will, under its own wt, assume the shape of the reversed curve m sosn; or if it be stiff, and heavily loaded, the same effect will follow. The points ss, at which the curves reverse, are called the points of contrary flexure; and the spans are virtually reduced from mo and no, to ms and ns. When the beam is supported at only 3 points, as in the Fig, and uniformly loaded, the point of contrary flexure is dist from the central support 1/4 of the span; so that each span, om, on, becomes virtually reduced about 4 part; and the defs will be but about as great as if there were two separate beams. The sections of the beam at s and 8 will then experience no hor strain; but merely the vert one arising from half the wt between m and s, and n and s. The position of the point of contrary flexure varies with the number of intermediate supports, and with the manner of loading; and in bridges, &c, where the load moves along the beam, it changes its place during the transit, so as to bring the points ss considerably nearer to the central support o; thus reducing materially the advantage commonly supposed to arise from connecting together the ends of adjacent bridge-trusses; if indeed there is any advantage in so doing, which is doubtful. The principle, however, becomes very useful in the case of long rafters or girders, stretching over several points of support, especially when uniformly loaded. Each interval, except the two end ones, will have two points of contrary flexure; and will then have nearly twice as much strength, under an equally distributed load, as a single beam no longer than said interval.

Beams.

During the preliminary investigations relative to the construction of the Menai tubular bridge, a few experiments were made on the strength of hollow cast-iron beams of circular, oval, square, and rectangular cross-sections, supported at both ends, and loaded at the center. The clear span between the supports was in every case 6 ft, the thickness of metal in each beam, 3 inch; area of solid cross-section of each, 4.12 sq ins. The mean depth o o, Fig 12, of the circular tube, 311⁄2 ins; of the square one, Fig 13, 234; of the oval, 4; breadth, 23; and of the rectangular one, mean depth, 33; breadth, 1.833 ins. From these experiments Mr. Edwin Clark, assistant engineer in charge, deduced the following constants, and rules for center breakg loads:

Fig. 12.

Fig. 13.

Const for circ tubes, .95; oval, 1; square, 1.14; rectangle, .91. Then, first finding the area of the solid part of the cross-section in sq ins,

Mean depth, o 0, Corresponding
X
in ins
Clear span in feet.

Ex. Circular beam, mean depth o o, 31⁄2 ins; area of solid ring, 4.12 sq ins; clear span, 6 ft. Here,

Area. Mean depth. Const.

4.12 X 35 X .95

=

2.28 tons, or 5107 lbs, breakg load.

6 (length.)

The thickness of the cylinder or tube is about of the diam; and as a mean of 3 trials, it broke with a center load of 2.287 tons, or 5122 lbs; span 6 ft. Hence we derive for similar tubes, the constant 530, to be used in the rule, Art 12; that is, center breakg load in lbs, of circular cast-iron tubes with a thickness of one-tenth of the Cube of outer diam (in ins)X 530

outer diam="

of average quality.

Clear span in feet

; supposing Mr. Clark's iron to have been

The average breakg load of 3 square beams was 2.152 tons, or 4820 lbs; of the rectangular ones, 2.3 tons, or 5152 lbs; and of the 6 elliptic ones, 3.207 tons, or 7183 lbs. To all the foregoing extraneous loads must be added half the wt of the beam itself. See Art 9.

Our rule of thumb, p 495, and rule, p 488, give breakg loads about one-third greater than Mr. Clark's results, except for the oval beam, where they agree closely. The discrepancy is probably due to difference of quality of material.

Hollow beams of thin wrought iron were experimented on at the same time; and for these Mr. Clark deduced the following constants, to be used with his foregoing rule for cast-iron ones:

Constants for thin riveted tubes, circular, 1.74; oval, 1.85; rectangular, 1.96. 1.09; 66 1.27;

66

welded tubes,

Art. 34. The following experiments on riveted sheet-iron cylindrical beams are by Fairbairn. 1st. Cylinder 18 ft long; 1 ft outer diam; clear span 17 ft; thickness of iron .037, or of an inch; wt of tube 107 lbs.

27