_Haulage._--The costs given comprise in mixing, the cost of delivering the materials to the mixer, and, in placing, the cost of hauling the concrete away. A Robins belt conveyor was used to deliver materials to the gravity mixer and this accounts, in a large measure, for the lower cost of mixing by gravity. The mixed concrete was hauled from both mixers in dump cars pushed by men.
_Form Work._--The labor cost of forms for 19,300 cu. yds. of concrete placed in 1903 was $16,800, or 87 cts. per cu. yd. of concrete. The total labor days consumed on form work was 6,340 at $2.70 per day. The total cost of concrete in place for mixing, placing and form work was $1.46 per cu. yd., not including lumber in forms, fuel, interest and depreciation.
CHAPTER XVII.
METHODS AND COST OF CONSTRUCTING ARCH AND GIRDER BRIDGES.
The construction problems in arch and girder bridges of moderate spans are simple, and with the exception of center construction and arrangement of plant for making and placing concrete, are best explained by citing specific examples of bridge work. This is the arrangement followed in this chapter.
~CENTERS.~--The construction of centers is no less important a task for concrete arches than for stone arches. This means that success in the construction of concrete arches depends quite as much upon the sufficiency of the center construction as it does upon any other portion of the work. The center must, in a word, remain as nearly as possible invariable in level and form from the time it is made ready for the concrete until the time it is removed from underneath the arch, and, when the time for removal comes, the construction must be such that that operation can be performed with ease and without shock or jar to the masonry. The problem of center construction is thus the two-fold one of building a structure which is immovable until movement is desired and then moves at will. Incidentally these requisites must be obtained with the least combined expenditure for materials, framing, erection and removal, and with the greatest salvage of useful material when the work is over. The factors to be taken count of are it, will be seen, numerous and may exist in innumerable combinations.
[Ill.u.s.tration: Fig. 148.--Center for 50 ft. Arch Span (Supported).]
[Ill.u.s.tration: Fig. 149.--Center for 50-ft. Arch Span (c.o.c.ket).]
Centers may be cla.s.sified into two types: (1). Centers whose supports must be arranged so as to leave a clear opening under the center for pa.s.sing craft or other purposes, and (2) centers whose supports can be arranged in any way that judgment and economy dictate. Centers of the first cla.s.s are commonly called c.o.c.ket centers. As examples of a c.o.c.ket and of a supported center and also as examples of well thought out center design we give the two centers shown by Figs. 148 and 149, both designed for a 50-ft. span segmental arch by the same engineer. The development of the center shown by Fig. 148 into the c.o.c.ket center shown by Fig. 149 is plainly traceable from the drawings. In respect to the center shown by Fig. 149 which was the construction actually adopted we are informed that 16,464 ft. B. M. were required for a center 36 ft.
long, that the framing cost about $12 per M. ft. B. M., with carpenters"
wages at $4 per day, and that the cost of bolts and nuts was about $1.50 per M. ft. B. M. With lumber at $20 per M. ft. B. M., this center framed and erected would cost about $35 per M. ft. B. M. As an example of framed centers for larger spans we show by Fig. 158 the centers for the Connecticut Avenue Bridge at Washington, D. C., with costs and quant.i.ties; other references to costs are contained in the index.
A center of very economical construction is shown by Fig. 159, and is described in detail in the accompanying text. The distinctive feature of this center is the use of lagging laid lengthwise of the arch and bent to curve. Another example of this form of construction may be found in a 3-span arch bridge built at Mechanicsville, N. Y., in 1903. The viaduct was 17 ft. wide over all, and consisted of two 100-ft. spans and one 50-ft. span. Pile bents were driven to bed rock, the piles being s.p.a.ced 6 ft. apart and the bents 10 ft. apart. Each bent was capped with 1012-in. timber. On these caps were laid four lines of 1012-in.
stringers, and 810-in. posts 3 ft. apart were erected on these stringers, and each set of four posts across the arch was capped with 810-in timbers the ends of which projected 3 ft. beyond the faces of the arch. The tops of these cross caps were beveled to receive the lagging which was put on parallel with the center line of the viaduct, sprung down and nailed to the caps. This lagging consisted of rough 1-in. boards for a lower course, on top of which was laid 1-in. boards dressed on the upper sides. Hardwood wedges were used under the posts for removing the centers. In the centers, forms and braces for the three arches there were used 140,000 ft. B. M. of lumber. The structure contained 2,500 cu. yds. of concrete.
Another type of center that merits consideration in many places is one developed by Mr. Daniel B. Luten and used by him in the construction of many arches of the Luten type of reinforced concrete arch. The particular feature of this type of arch is that in shallow streams for bridges of ordinary span the ends of the arch ring are tied together across stream by a slab of concrete reinforced to take tension. This slab is intended to serve the double purpose of a tie to keep the arch from spreading and thus reduce the weight of abutments and of a pavement preventing scour and its tendency to undermine the abutments.
Incidentally this concrete slab, which is built first, serves as a footing for the supports carrying the arch center.
As an ill.u.s.tration of the center we choose a specific structure. In building a 95-ft. span, 11-ft. 1-in. rise arch bridge at Yorktown, Ind., in 1905, the centers were designed so as to avoid the use of sand boxes or wedges. Ribs of 212-in. pieces cut to the arc of the arch soffit were supported on uprights standing on the concrete stream bed pavement.
The uprights were so proportioned by Gordon"s formula for columns that without bracing they would be too light to support the load of concrete and earth filling that was to come upon them, but when braced at two points dividing the uprights approximately into thirds they would support their loading rigidly and without buckling. The design in detail was as follows: The uprights near the middle of the span were about 15 ft. long and were s.p.a.ced 7 ft. apart across the stream and 3 ft. apart across the bridge. Each upright then was to support a loading of concrete of 7 ft.3 ft.26 ins. and an earth fill 1 ft.7 ft.3 ft., or a total load of about 9,000 lbs. Applying Gordon"s formula for struts with free ends,
f S P = ------------------- l I + -------- 125h
where P is the total load = 9,000 lbs., f is fibre stress for oak--1,600 lbs., l is length of strut in inches and h is least diameter of strut in inches, it was found that for a length of 15 ft. a 77-in. upright would be required to satisfy the formula, but for a length of 5 ft., which would result from bracing each strut at two points, a 44-in. timber satisfied the formula. Therefore, 44-in.
timbers braced at two points were used for the longest uprights. About 30 days after the completion of the arch the bracing was removed from the uprights, beginning at the ends of the span and working towards the middle. As the bracing was being removed the uprights gradually yielded, buckling from 4 to 6 ins. from the vertical and allowing the arch to settle about in. at the crown. This type of center has been successfully employed in a large number of bridges.
Figure 150 shows a center for a 125-ft. span parabolic arch with the amount and character of the stresses indicated and with a diagram of the actual deflections as measured during the work.
[Ill.u.s.tration: Fig. 150.--Center for 125-ft. Span Parabolic Arch with Diagram of Deflections.]
In calculating centers of moderate span there is seldom need of more than the simple formulas and tables given in Chapter IX. When the spans become larger, and particularly when they become very large--over 200 ft.--the problem of calculating centers becomes complex. None but an engineer familiar with statics and the strengths of materials and knowing the efficiency of structural details should be considered for such a task. Such computations are not within the intended scope of this book, and the design of large centers will be pa.s.sed with the presentation of a single example, the center for the Walnut Lane Bridge at Philadelphia, Pa.
The main arch span of the Walnut Lane Bridge consists of twin arches s.p.a.ced some 16 ft. apart at the crowns and connected across by the floor. Each of the twin arch rings has a span of 232 ft. and a rise of 70 ft., is 9 ft. thick and 21 ft. wide at the skewback and 5 ft.
thick and 18 ft. wide at the crown. The plan was to build a center complete for one arch ring and then to shift it along and re-use it for building the other arch ring. The centering used is shown in diagram by Fig. 151. It consists of five parts: (1) Six concrete piers running the full width of the bridge upon which the structure was moved; (2) a steel framework up to E G, called the "primary bent"; (3) a separate timber portion below the heavy lines E I and W" I"; (4) the "main staging"
included in the trapezoid E I W" I", and (5) the "upper trestle"
extending from I I" to the intrados.
[Ill.u.s.tration: Fig. 151.--Center for 232-ft. Span Arch at Philadelphia, Pa.]
The primary bent consists of four I-beam post bents having channel chords, the whole braced together rigidly by angles. Each bent is carried on 1 ft.6 in. steel rollers running on a track of 19 in.
plate on top of the concrete piers. Between the primary bents and the main staging, and also between the main staging and the upper trestles are lifting devices. The mode of operation planned is as follows: When the center has been erected as shown and the arch ring concreted the separate stagings under K I and K" I" are taken down. Next the portions under the lines I E and I" W" will be taken down and erected under the second arch. Finally the remainder of the center will be shifted sidewise on the rollers to position under the second arch.
~MIXING AND TRANSPORTING CONCRETE.~--The nature of the plant for mixing and handling the concrete in bridge work will vary not only with varying local conditions but with the size and length of the bridge. For single span structures of moderate size the concrete can be handled directly by derricks or on runways by carts and wheelbarrows. For bridges of several spans the accepted methods of transport are cableways, cars and cars and derricks. Typical examples of each type of plant are given in the following paragraphs, and also in the succeeding descriptions of the Connecticut Avenue Bridge at Washington, D. C., and of a five-span arch bridge.
~Cableway Plants.~--The bridge was 710 ft. long between abutments and 62 ft. wide; it had a center span of 110 ft., flanked on each side by a 100-ft., a 90-ft. and an 80-ft. span. The mixing plant was located at one end of the bridge and consisted of a Drake continuous mixer, discharging one-half at the mixer and one-half by belt conveyor to a point 50 ft. away, so as to supply the buckets of two parallel cableways. The mixer output per 10-hour day was 400 cu. yds. and the mixing plant was operated at a cost of $27 per day, making the cost of mixing alone 6 cts. per cu. yd. The sand and gravel were excavated from a pit 4 miles away and delivered by electric cars to the bridge site at a cost of 50 cts. per cu. yd. Two 930-ft. span Lambert cableways set parallel with the bridge, one 25 ft. each side of the center axis, were used to deliver the concrete from mixer to forms. The cableway towers were 70 ft. high and the cables had a deflection of 35 ft.; they were designed for a load of 7 tons, but the average load carried was only 3 or 4 tons. These cableways handled practically all the materials used in the construction of the bridge. They delivered from mixer to the work 400 cu. yds. of concrete 450 ft. in 10 hours at a cost of 2 cts. per cu.
yd. for operation.
[Ill.u.s.tration: Fig. 151a.--Cableway for Concreting Bridge Piers.]
Another example of cableway arrangement for concreting bridge piers is shown by Fig. 151a. The river was about 800 ft. wide, about 3 ft. deep and had banks about 20 ft. high. The piers were about 21 ft. high. The towers for the cableway consisted of a 55-ft. derrick without boom, placed near the bank on the center line of the piers and well guyed and a two-leg bent placed in the middle of the river and held in place by four cable guys anch.o.r.ed to the river bottom. A -in. steel hoisting cable was stretched from a deadman on sh.o.r.e, about 150 ft. back of the derrick, and followed along the center line of the piers, past the derrick just clearing it, to the bent in the middle of the river. At the top of this bent was a 16-in. cable block. Through this block the cable pa.s.sed down and was made fast to a weight, consisting of a skip loaded with concrete until the cable had the required tension, and a pitch of 18 to 20 ft. from center of river to anchor on sh.o.r.e. In order to secure the required pitch from the sh.o.r.e to the river bent the boom fall of the derrick was hooked onto the cable at the foot of the mast, and then, by going ahead on the single drum hoisting engine, was raised to the mast head. This gave the cable a pitch of 18 to 20 ft. from mast head to top of bent in river. The carriage vised on the cableway consisted of two 16-in. cable sheaves with iron straps, forming a triangle, with a chain hanging from the bottom point, to which was attached the 5 cu. ft.
capacity concrete bucket. The concrete was mixed on a platform at the foot of the mast. When ready for operation the chain on the carrier was hooked to the bucket of concrete, the engine started, and both bucket and cable raised, the former running by gravity to the pier. The speed of descent was governed by the height to which the cable was raised on the derrick, and as the bucket neared the dumping point the engine was slacked off and the cable leveled. The bucket was dumped by a man on a staging erected on the pier form. For the return of the bucket the engine was slacked off and the weight on the river bent would pull the cable tight so that the pitch would be toward the sh.o.r.e and the bucket could run down the grade to the mixing platform, the speed being governed as before by leveling the cable. When the piers were completed to the middle of the river the engine and derrick were taken over to opposite side of the river, the bent being left in the middle, and the work continued. By using the extreme grade of the cable it was found that the bucket would run from the platform to the bent (400 ft.) in less than 35 seconds.
[Ill.u.s.tration: Fig. 152.--Sketch Showing Car and Trestle Plant for Concreting an Arch Bridge.]
~Car Plant for 4-Span Arch Bridge.~--The bridge had four 110-ft. skew spans, and a total length of 554 ft. The mixing plant was located alongside one abutment on a side hill so that sand and stone could be stored on the slope above. The mixer was set on a platform high enough to clear cars below. Above it and to the rear a charging platform reached back to the stone and sand piles. Side dump cars running on a track on the charging platform took sand and stone to the mixer and cement was got from a cement house at charging platform level. The concrete for the abutment adjacent to the mixer was handled in buckets by a guy derrick. A trestle, Fig. 152, was then built out from the mixer to the first pier; this trestle was so located as to clear the future bridge about 20 ft. and was carried out from sh.o.r.e parallel to the bridge until nearly opposite the pier site, where it was swung toward and across the pier. The concrete was received from the mixer in bottom dump push cars; these cars were run out over the pier site and dumped.
When the first pier had been concreted to springing line level, the main trestle was extended to opposite the second pier and the branch track was removed from over the first pier and placed over the second pier.
This operation was repeated for the third pier. The last extension of the main track was to the far sh.o.r.e abutment, where the bodies of the cars were hoisted by derrick and dumped into the abutment forms. The derrick was the same one used for the first abutment having been moved and set up during the construction of the intermediate piers. To construct the arches a second trestle was built composed partly of new work and partly of the staging for the arch centers. This trestle rose on an incline from the mixer to the first pier across which it was carried at approximately crown level of the arch. The concrete for the portion of the pier above springing line and for the lower portions of the haunches was dumped direct from the cars. For the upper parts of the arch the concrete was brought to the pier track in two-wheel carts on push cars and thence these carts were taken along the arch toward sh.o.r.e on runways. When the first arch had been concreted the second trestle was extended to pier two and the operation repeated to concrete the second arch.
~Hoist and Car Plant for 21-Span Arch Viaduct.~--The double track concrete viaduct replaced a single track steel viaduct, being built around and embedding the original steel structure which was maintained in service.
The concrete viaduct consisted of 21 spans of 26 ft., 7 spans of 16 ft., and 2 spans of 22 ft. With piers it required about 15,000 cu. yds. of concrete. Two Ransome concrete hoists, one on each side of the original steel structure near one end, were supplied with concrete by a No. 4 Ransome mixer. The mixer discharged direct into the bucket of one hoist and by means of a shuttle car and chute into the bucket of the other hoist.
The shuttle car ran from the mixer up an incline laid with two tracks, one narrow gage and one wide gage, having the same center line. The car was open at the front end and its two rear wheels rode on the broad gage rails and its two forward wheels rode on the narrow gage rails. At the top of the incline the narrow gage rails pitched sharply below the grade of the broad gage rails so that the rear end of the car was tilted up enough to pour the concrete into a chute which led to the bucket of the hoist. The sand and gravel bins were elevated above the mixer and received their materials from cars which dumped directly from the steel viaduct.
The hoist buckets discharged into two hoppers mounted on platforms on the old viaduct. These platforms straddled two narrow gage tracks, one on each side of the old viaduct parallel to and clearing the main track.
These side tracks were carried on the cantilever ends of long timbers laid across the old viaduct between ties. At street crossings the overhanging ends of the long timbers were strutted diagonally down to the outside shelf of the bottom chords of the plate girder spans. Six cars were used and the concrete was dumped by them directly into the forms; the fall from the track above being in some cases 40 ft. The hoists and shuttle car were operated by an 812-in. Lambert derrick engine, the boiler of which also supplied steam to the mixer engine. The concrete cars were operated by cable haulage by two Lambert 710-in.
engines.
The labor force employed in mixing and placing concrete, including form work, was 45 men, and this force placed on an average 200 cu. yds. of concrete per day. a.s.suming wages we get the following costs of different parts of the work for labor above:
Item. Per day. Per cu. yd.
1 timekeeper at $2.50 $ 2.50 $0.0125 1 general foreman at $5 5.00 0.0250 3 enginemen at $5 15.00 0.0750 1 carpenter foreman at $4 4.00 0.0200 12 carpenters at $3.50 42.00 0.2100 1 foreman at $4 4.00 0.0200 8 men mixing and transporting at $1.75 14.00 0.0700 13 men placing concrete at $1.75 22.75 0.1137 1 foreman finishing at $4 4.00 0.0200 4 laborers finishing at $1.75 7.00 0.0350 ------ ------- 45 men at $2.70 $120.25 $0.6012
It is probable that the carpenter work includes merely shifting and erecting forms and not the first cost of framing centers. No materials, of course, are included. It should be kept in mind that while the output and labor force are exact the wages are a.s.sumed.
~Traveling Derrick Plant for 4-Span Arch Bridge.~--The bridge consisted of four 70-ft. arch spans and was built close alongside an old bridge which it was ultimately to replace. The approach from the west was across a wide flat; at the east the ground rose more abruptly from the stream.
Conditions prevented the use of a long spur track and also made it necessary to install all plant at and to handle all material from the west bank. A diagram sketch of the arrangement adopted is shown by Fig.
153.
[Ill.u.s.tration: Fig. 153.--Sketch Showing Traveling Derrick Plant for Concreting an Arch Bridge.]
The track from the west approached the existing bridge on an embankment 25 ft. high. A spur track 175 ft. long from clear post to end was built on trestle as shown. The cement house and mixer platform were placed at the foot of the embankment at opposite ends of the spur track. Between the two the slope of the embankment was sheeted with 1-in. boards and a timber bulkhead 4 ft. high was built along the toe of the sheeting.
Stone, sand and coal were stored behind the bulkhead on the sheeting. A runway close to the bulkhead connected the cement house with the mixer platform, all materials to the mixer being wheeled in barrows on this runway. A -cu. yd. Smith mixer was set on a platform 5 ft. above ground with its discharge end toward the stream. Beginning under this platform a service track was carried across the flat and stream to the extreme end of the east abutment. This track consisted of three rails, two rails 4 ft. apart next to the work and a third rail 25 ft. from the first. The 4-ft. gage provided for cars carrying concrete buckets from the mixer and the 25-ft. gage provided for a traveling derrick; 18-lb. rails were used and they proved to be too light, 40-lb. rails are suggested. The derrick consisted of a triangular platform carrying a stiff leg derrick with a 25-ft. mast and mounted on five wheels. The wheels were double f.l.a.n.g.e 16 ins. diameter and cost $30 each, being the most expensive part of the derrick. The derrick was made on the ground and took four carpenters between 3 and 4 days to build. Derrick and 350 ft. of service track, including pole trestle across the stream, cost between $600 and $800. The derrick was moved by means of a cable wrapped around one spool of the Flory double-drum hoisting engine and leading forward and back to deadmen set at opposite ends of the service track. Cars carrying concrete buckets were run out on the 4-ft. gage track and the buckets were hoisted by the derrick and dumped into a -cu. yd. car running on a movable transverse track across the bridge. This transverse track was necessary to handle the concrete to the far side of the work, the derrick being set too low and the boom being too short to reach. The derrick was used to handle material excavated from the pier foundations and also to tear down the centers and spandrel forms. Some rather general figures on the cost of this bridge are given by Mr. H. C.
Harrison, the contractor. They are:
Materials: Total.
6,000 bbls. cement at $2.05 $12,300 2,500 cu. yds. sand at $0.80 2,000 5,000 cu. yds. stone at $0.85 4,250 260 M. ft. B. M. lumber at $17 4,420 ------- Total $22,970