Tables XXI and XXII can be used to assist in the design of the different members of the centers for arches.
364. Safe Stresses in Lumber for Wooden Forms. In Table XXI are given the safe loads which may be placed on beams of long leaf yellow pine, of various depths, on various spans.
The values given in Table XXI are the safe loads in pounds uniformly distributed, exclusive of the weight of the beam itself, for rectangular beams one inch thick. The safe load for a beam of any thickness may be found by multiplying the values given in the tables by the thickness of the beam in inches. From the last column, the deflection may be obtained, corresponding to the given span and safe load, by dividing the coefficient by the depth of the beam in inches, which will give approximately the deflection in inches.
365. Exampk. if a beam is required to support a uniformly dis tributed load of 4,000 pounds on a span of 10 feet, what would be the dimensions of the beam of long-leaf yellow pine, and what would be the deflection? Solution. Following the line for beams of 10-foot span, it is found that a beam S inches deep and 5 inches wide (853 X 5 = 4,265) would support the load of 4,000 pounds, and the deflection would be 1.24 = .16 inch. A second solution would be to use a beam 12 inches deep and 2 inches wide (1,920 X 2 = 3,840); but according to the table, this beam would not be quite strong enough, as it would only support a load of 3,840 pounds.
366. Safe Loads on Wooden Columns. The values given in Table XXII are based on the formula: Example. If a column 10 feet long is required to support a load of 20,000 pounds, what would be the size of the column required if short-leaf yellow pine was used? Solution. Dividing the length of the beam in inches by the as sumed least diameter, 6 inches, we have 120 6 = 20, which gives the ratio of the length to the diameter. By the table it is shown that 2,857 pounds is the ultimate strength for a column of short-leaf pine, when / d = 20. Assuming a factor of safety of 5, and dividing 2,857 by 5, the working load is found to be 571 per square inch. Dividing 20,000 by 571, it is found that a column whose area is 35 square inches is required to support the load. The square root of 35 is 5.9. Therefore a column of short-leaf yellow pine 6 inches square will support the load.
367. Form for Arch at 175th Street, New York. In constructing the 175th Street Arch in New York City, the forms were built so that they could be easily moved. The arch is elliptical and is built of hard-burned brick and faced with granite. The span of the arch is 66 feet; the rise is 20 feet; the thickness of the arch-ring is 40 inches and 4S inches at the crown and springing line, respectively; and the arch is built on a 9-degree skew. The total length of this arch is S00 feet.
This arch is constructed in sections, the centering being sup ported on 11 trusses placed perpendicular to the axis of the arch and having the form and dimensions shown in Fig. 170. The trusses are placed 5 feet on centers, and are supported at the ends and middle by three lines of 12 by 12-inch yellow pine caps. The caps are supported by 12 by 12-inch posts spaced five feet center to center, and rest on timber sills on concrete foundations. The upper and
lower chord members of the trusses are of long-leaf yellow pine, but the diagonals and verticals are of short-leaf yellow pine. The lagging is 24 by 6-inch long-leaf yellow pine plank. The connections of the timbers are made by means of -inch steel plates and bolts arranged as shown in the illustration. As it was absolutely necessary to have the forms alike, so that they could be moved along the arch and at all times fit the brickwork, they were built on the ground from the same pattern, and hoisted to their place by two guyed derricks with 70-foot booms.
On the 12 by 12-inch cap was a 3 by S-inch timber, on which the double wedges were placed. When it was necessary to move the forms, the wedges were removed, the forms rested on the rollers, and there was then a clearance of about 21 inches between the brick work and the lagging. The timber on which the rollers ran was faced with a steel plate 1 inch by 4 inches. The forms were moved forward by means of the derricks. The settlement of the form under the first section constructed was 1 inch; and the settlement of the arch-ring of that section after the removal of forms,was 1 inch.* 368. Forms for Bridge at Canal Dover, Ohio.* The details of the centering used in erecting one of the 106-foot S-inch spans of a reinforced-concrete bridge over the Tuscarawas River at Canal Dover, Ohio, are shown in Figs. 171a and 171b. Besides this span, the bridge consisted of two other spans of 106 feet S inches each, and a canal span of 70 feet. The centering for the canal span was built in six bents, each bent having seven piles. A clear waterway of 18 feet was required in the canal span by the State Canal Commissioner, and this passage was arranged under the center of the arch. The piles were driven by means of a scow. The cap for the piles was a 3 by 12-inch timber.
Plank 2 inches thick were sawed to the correct curvature, and nailed to the 2 by 12-inch joists, which were spaced about 12 inches apart. The lagging was one inch thick, and was nailed to the curved plank.
The wedges were made and used as shown. The centering was constantly checked; this was found important after a strong wind. The centering for the other two of the main arches was constructed similarly to that of the arch shown.
After some difficulty had been experienced in keeping the forms in place during the concreting of the first arch, the concrete for the other arches was placed as shown in Fig. 172, and no difficulty was encountered. Sections 1 and 1 were first placed, then 2 and 2, finishing with section 6.
The concreting on the canal span was begun November 1, and finished November 12; and the forms were lowered by means of the wedges five weeks later. The deflection at the crown was 0.5 inch, and after the spandrel walls were built and the fill made, there was an additional deflection of 0.4 inch. In building the forms, an allowance of s part of the span was made, to allow for this deflec tion. The deflections at the crown of the other three arches were 0.0 inch, 1.45 inches, and 1.34 inches.