POINTING.

All masonry in cement or lime will be finished with a good pointing of

cement, without extra charge.

BRICKWORK.

When bricks are required, or allowed to be used, they shall consist of

sound, hard-burned brick, laid in cement, or common mortar, as directed,

and no soft or salmon brick will be admitted; and none but regular

bricklayers must be employed.

CENTERING AND BACKING.

The whole top of all arches, whether brick or stone, shall be finished

by plastering with a good coat of cement, so as to prevent the

percolation of water, and turn it away from the arch. The centering

shall be such as the engineer approves of in every respect, and shall

not be removed until he directs. The cost of backing to be included in

the price bid. For arches of more than twenty-five feet span,

compensation shall be made, at the engineer’s estimate, for the extra

value and cost of the centering proper for large arches.

GENERAL PROVISION.

79. The engineer reserves the right to require the whole or any part of

the above described work of masonry to be laid in cement, lime, mortar,

or dry, at his discretion. First and second class masonry, and

brickwork, will be bid for at prices for laying in cement, from which

will be deducted fifty cents per yard if laid in lime mortar, and one

dollar if laid dry. Third and fourth class masonry at prices for laying

dry, to which will be added fifty cents per yard if laid in lime mortar,

and one dollar if laid in cement.

SCAFFOLDING.

80. Nothing shall be allowed for workmanship or timber of any

scaffolding used in the construction of timber bridges, or in carrying

up abutments, piers, coffer-dams, or otherwise. Should the timber used

in any coffer-dam be carried away by floods, the renewal of it shall

fall upon the first party.

FOUNDATIONS.

81. The foundations for all structures shall be executed by the

contractor for masonry in such manner and to such depth as to secure a

safe and secure foundation, of which the engineer will judge. If a

natural foundation cannot be procured at a reasonable depth, then the

contractor shall prepare such artificial foundation as the engineer may

direct. The stuff moved from the foundations, if of the proper quality,

shall be deposited in the adjoining embankment, provided the site for

said embankment has been cleared of all perishable material. So much of

the stuff as shall not be fit for the embankment, and all roots, stumps,

etc., shall be deposited beyond the limits of the clearing, so as not to

obstruct roads, watercourses, or ditches.

For the earth moved from such foundations, and for all earth used

according to direction, in the construction of coffer-dams, there shall

be paid —— cents per cubic yard.

Whenever it may be necessary to pump or bale water in the foundations,

the contractor shall furnish the pumps or buckets, and all scaffolding

and apparatus necessary to work them. He shall be allowed the net cost

of all labor employed in the operations of pumping or baling water, and

shall make a monthly return to the engineer of the value of such labor,

provided that these operations are conducted in an economical manner,

with efficient men, pumps, and tools, under the direction and to the

satisfaction of the engineer. He shall also be allowed such compensation

for the use of the pumps and apparatus, and for superintendence, as the

engineer shall judge to be fair and reasonable.

TRESTLE WORK.

82. Includes all wooden structures commonly used as substitutes for

abutments and piers, and for farm passes, etc., etc. These shall be

built according to the plans furnished, and directions given by the

engineer, of sound, durable material, to be approved by him. The price

bid shall be by the thousand feet board measure, and will be considered

as in full for all material except iron, and for the labor of building

and erecting complete. The iron used will be of the best American, and

the workmanship of approved quality. The bids will be by the pound, and

will cover all cost of material and the labor incident to its use.

Spikes and nails when used will be furnished by the contractor at cost.

BRIDGING.

83. Contractors may submit plans for bridging in connection with, or

separate from their bids; but the engineer of the company may reject

such plans if he choose, and substitute others, which if the contractor

decline building at the approved prices, may be let to other parties. In

every case, the exact manner of building, erecting, adjusting, and

finishing bridges, and the determination of the nature and amount of

material, will be specified by the engineer. The price bid must be by

the running foot of the whole _length_ of bridge, as erected and

finished complete.

84. _Specifications for Superstructure._

SUBSILLS.

To maintain the track in good adjustment until embankments are settled,

subsills will be laid on certain banks, and likewise in cuts where the

imperfect nature of the bottoming may, in the opinion of the engineer,

render them expedient. These subsills to be fairly bedded in the earth

or ballasting, and carefully adjusted and rammed so as to correspond

with the grade lines given by the engineer. An additional piece of sill,

four feet long, shall be laid at each joint of the subsill, either under

the sill, or alongside, as may be directed. The sills will be of 3 × 9

plank, in length of twelve, fifteen, eighteen, and twenty-one feet; of

which one fourth may be below fifteen, one fourth below eighteen, and

one fourth below twenty-one feet. The plank must be square at the ends,

and of sound, durable material, and not have more than two inches wane

on one end only. There will be about 25,000 feet, board measure, laid

per mile where it may be required, and 660 joint sills, 3 × 9 inches,

and four feet long. When the depth of stuff to be moved to admit the

subsills exceeds six inches, an allowance shall be made for extra labor,

the amount of which shall be noted by the assistants on their receiving

notice of such extra labor from the contractor or his agent.

CROSS TIES.

The cross ties shall be of white, black, or yellow oak, burr oak,

chestnut, red elm, black walnut, or other sound timber of suitable

character in the opinion of the engineer. Eight feet long, and not more

than three inches out of straight, hewn to a smooth surface on two

parallel plane faces six inches apart, the faces being not less than

seven inches wide for at least half of the number, and the remainder not

less than six inches wide. The ties shall be carefully and solidly laid

on the subsills, or ballasting, or earth previously properly prepared,

so as to give the true planes required by the rails, whether on straight

or curved lines. They shall be laid at the rate of eight ties to each

eighteen feet rail. All imperfect ties shall be excluded by the

tracklaying party. The surface of the ties to be faithfully adjusted to

the grades given, and to the web of the rail; and the rail to be truly

laid and firmly spiked so as to correspond neatly to the alignment of

the road. There will be about 2,500 ties required per mile of road.

CHAIRS AND JOINTS.

When chairs are used, they shall be such as directed by the engineer,

and furnished by the company, and shall be well and accurately placed

and spiked in such manner and position as required. When chairs are

used, the largest ties shall be selected for the joints. When the joint

is made by fishing, there will be no tie directly under the joint.

RAILS.

The rails will weigh about sixty pounds per lineal yard. No rail shall

be laid on the tangents which is in any way twisted or bent. It shall be

the duty of the first party to correct and make true any crooked rails

received by him, also to bend to the proper curve, and in such a manner

as not to affect the strength of the bar, all rails laid in curves.

Punching of rails, and cutting, will also be done by the contractor.

TRACK LAYING.

The materials composing the track will be furnished by the company, and

it will be laid in the best manner according to the conditions

following. The track will be laid on cross-ties, and the ties at the

proper places on subsills. Where the sills are used, they will be laid

with four feet blocks at the joints, and with six feet blocks at the

rail joints, the whole being set to their places by stakes, and by the

engineer’s directions, and mauled down to a perfect bearing, being

settled at least half an inch by mauling. The cross ties will be placed

uniformly distant, (twenty-eight inches from centre to centre). The iron

must be so cut or selected that the joints of the parallel rails shall

be within two inches of being opposite to each other; no joint tie being

allowed a greater amount of askew than this, whether on tangents or

curves. A slip of metal shall be inserted at the rail joints while

laying, to keep the rails apart sufficiently to allow for expansion,

which thickness, (depending upon the temperature,) shall be fixed by the

engineer. Notches to be cut at the centre of each bar, to correspond

with half a spike, to prevent longitudinal motion of the rails. Each

joint chair to be fastened with four spikes. Two spikes at each end of

each tie upon straight lines and upon curves of less than 1,500 feet

radius at the outer end of the tie two spikes outside and one inside,

and at the inner end two spikes outside and one inside of the rail. Upon

curves the outer rail to be raised by such an amount, depending on the

radius of curvature, as the engineer may direct.

TURNOUTS.

The contractor to put in such turnouts and sidings, with the necessary

frogs and switches, as may be required; the frogs and switches to be

firmly and truly placed in position so as to work easily.

FILLING AND DITCHING.

The stuff moved in bedding the sills and ties, to be placed between the

latter. The ditches to be properly cleaned out after the track is laid;

the filling never to rise higher than the top of the cross tie. Any

surplus stuff to be moved out of the cuts, or if on embankment, to be

thrown over the bank, leaving the track and road-bed in a neat and

workmanlike shape.

DELIVERY OF MATERIALS.

The ties and sills to be delivered at some point on the road as near as

possible to the places where they are to be used, in no case requiring

more than one thousand feet of haul; to be so piled as easily to be

counted and inspected. The bids for ties will be by the piece; the

proposal stating the number and conditions; the sills to be bid for by

the thousand, board measure. All material furnished in connection with

track laying to be delivered in such manner and time as to comply in

good season with the contract for laying the rails.

MEASUREMENT OF TRACK.

The measurement of track laid shall include the turnouts, measuring from

heel to heel of switch. No extra allowance being made for putting in

frogs or switch machinery.

85. _Specification for Fencing._

Bids for fencing will be by the running foot, or mile, including both

sides of the road. Where required, it will consist of posts placed eight

feet apart from centre to centre, set three feet into the ground, either

by digging or boring, and not by mauling. The posts shall be of oak,

elm, chestnut, or other durable wood, not less than eight inches in

diameter at the bottom, barked and charred where put into the ground.

The boards to be 6 × 1 inches, and to square sixteen feet long, to be

placed six inches apart vertically, and fastened to the posts with

tenpenny nails at each bearing, and breaking joint with each other.

There will be five bars in depth, the top of the uppermost being five

feet from the ground. In side hill and in ground liable to slide,

particular care shall be taken to place the posts firmly in the ground.

At cattle guards, the fence will be turned in to the proper distance,

and such arrangement made as to prevent the passage of animals.

86. _General Provisions._

CLASSIFICATION.

The classification of material excavated will be referred to the

engineer, in all cases where the nature of the material is questioned,

and his judgment taken thereon. Also all material used in structures

will be submitted to the inspection of the engineer or his assistants.

QUANTITIES AND QUALITIES APPROXIMATE.

The quantities and qualities of work presented in the schedule are

merely approximate, and the information given on the maps and profiles

in relation thereto is according to the best present knowledge. The

company retains the right to change at any time during the progress of

the work, the alignment, grades, and width of the road, or any part

thereof; and also the limits of the sections, or to alter the character,

vary the dimensions, or change the location of structures, or substitute

one kind of work or material for another, or to omit entirely, when

found necessary, or to require to be built where not now contemplated;

and the contractor shall carry into effect all such alterations when

required, without the contract prices being thereby affected, unless the

aggregate value of all work contemplated by the contract be changed full

twenty per cent., in which case a fair allowance, either for the company

or the contractor, shall be made by the engineer. In case, however, the

aggregate value of the work be changed by over twenty per cent. of the

original amount, and the contractor be not satisfied with the altered

compensation, then said contractor may throw up said contract, on

condition, that within ten days after receiving notice from the engineer

of such alteration, he give written notice to the engineer or the

company of his desire to do so. In which case, as in other cases of

throwing up the contract, he shall as soon as desired, give peaceable

possession to the company or their agents; leaving also in their

possession any tools or machinery upon which they have advanced any

thing; and the company may then settle with the contractor on the

measure of damages which either shall suffer.

BASIS FOR ESTIMATING EFFECT OF CHANGES.

The basis for estimating any changes as above mentioned is understood to

be the schedule exhibited at the letting.

NO LIQUOR, AND GOOD ORDER.

The contractor shall not sell, or allow to be sold or brought within the

limits of his work any spirituous liquors, and will in every way

discountenance their use by persons in his employ. He will do all in his

power by his own act, or by assisting the officers of the county, or of

the corporation, in maintaining the laws and such regulations as conduce

to good order and peaceable progress, and prevent encroachment on the

rights of persons or property; and he shall discharge from his service,

when required by the engineer, any disorderly, dangerous, insubordinate,

or incompetent person, and refuse to receive into his employ any who may

have been discharged for such cause from other parts of the work.

MONTHLY ESTIMATES.

Measurements and estimates shall be made by the engineer once in each

month, by means of which may be known approximately the amount of work

done, and the contractor shall be entitled to payment therefor at such

rates below his contract prices as the engineer or president of the

company deems expedient; it being understood that the contractor has no

claim on account of any material not laid in its place in the road-way,

or for labor bestowed thereon; and the quantities shall be estimated

from the dimensions when so laid, though on the advice of the engineer,

advances may be made on such material when delivered for use, in which

case it becomes the property of the company, in the contractor’s care

and keeping, and he becomes liable for its loss or injury.

EXTRA WORK.

No claim for extra work or for work not provided for in the contract

shall be allowed, unless a written order to perform such work shall have

been given by the engineer; or that the work be subsequently certified

by him, and the certificate produced at the time of demanding the

payment of the monthly estimate next after such work shall have been

performed.

SUB-CONTRACTS.

The contractor will be required to perform the work himself, and no

sub-contracts relieving him from the responsibility of a proper

performance of his contract will be permitted, unless by the written

consent of the president of the company. And no moneys shall be paid to

any such sub-contractor for work or materials, without sufficient

authority from the principal contractor.

WHEN WORK TO BE COMMENCED.

On the acceptance of a proposal, the chief engineer will give notice

thereof to the person proposing, by letter directed to his stated

address; and in twenty days from the date of such notice, provided there

be no impediment on the part of the company, or in twenty days after

such impediment is removed if there be, the work shall be begun with an

adequate force, and from that time be prosecuted vigorously until its

completion.

HOW TO PROGRESS.

It shall be understood that proper progress is not made, if the amount

of work done in each month is not in due proportion to the total amount

to be done up to the time fixed for completion by the contract; in which

case the engineer shall call the attention of the contractor (or whoever

may be in charge of the work if the contractor be absent,) to the fact,

and state to him what additional exertion is necessary to be made, and

what further force is required, in such reasonable time as may be

prescribed.

PUTTING ON MORE FORCE.

In default of the contractor’s making such additional exertion, and

supplying such force, the chief engineer, or president of the company

may have such force sent to the work, and the necessary buildings may be

erected to receive them at the contractor’s charge and expense, who

shall receive the said force in his employ, and work it at whatever

price it may have been found necessary to employ it, without diminishing

the previous force of the work, and regarding always such extra force as

if employed by himself.

CAUSES FOR DETENTION.

There shall be no claim for detention on account of work not being laid

out, unless a written notice three days in advance, that it is required,

shall have been given to the engineer; and the damage for such detention

shall be estimated by the engineer. The right of way shall be furnished

by the company, but if it fail to do so for any particular place,

damages for detention shall not be claimed unless the contractor be

detained full twenty days after he shall have given written notice to

the engineer of his wish to commence work at such place. Then the

engineer may either estimate to him the amount of damage which he shall

take as satisfactory, or he may extend the time of the completion of

such work by as many days beyond the contract time, as the contractor is

detained beyond the twenty days following his notice to the engineer.

THE ENGINEER.

In all cases where the word “engineer” is used, the engineer in charge

of construction is meant; but the directions of any subordinate engineer

shall be obeyed when given in regard to any of the ordinary operations,

or where they are evidently in accordance with the specifications, or

when transmitting the orders of his superiors. In other cases they may

be referred to the resident engineer, and finally to the chief engineer,

he being the authorized officer, at the time acting in that capacity.

CONTRACTOR.

The word “contractor” applies to and includes all persons contracting

jointly, any one of whom shall be considered the authorized agent for

and in behalf of his associates, and empowered to receipt payment of

moneys, receive and act upon orders.

THE CONTRACT.

87. This is the mutually binding legal article of agreement between the

contractor and the company, specifying the times of completing, manner

of payment, and describing the work which is to be done. Thus:—

A AND B RAILROAD COMPANY.

_Contract._

Graduation on sections A C D,

Masonry on sections A C D,

Ballasting on sections A C D,

Bridging on sections A X T,

Fencing on sections O O O,

Sills and ties on sections O O O,

Track laying on sections O O O.

____________ }

____________ } _Contractors._

Articles of agreement made and concluded this first day of January, A.

D. 1857, between —— of the first part, and the A and B Railroad Company

of the second part, being a company duly incorporated by the State of ——

of the second part, whereby it is mutually agreed as follows, namely:

The said party/parties of the first part hereby agree to and with the

said party of the second part that he/they will perform in a substantial

and workmanlike manner the following work, namely:—

[_The work here described._]

The said work to be performed and completed agreeably to the directions

and to the approval of the chief engineer of said company for the time

being, and subject to all the general provisions of the specification

attached to and forming a part of this agreement, and also subject to

such of the special provisions of said specifications as are applicable

to the work hereby contracted for.

And in consideration of the full and faithful performance by the said

party/parties of the first part of this agreement on his/their part, the

said party of the second part hereby agrees to pay for the same in the

time and in the manner hereinafter mentioned, at the rates as follows,

namely:—

[_Here insert the items and corresponding prices._]

It is mutually agreed that this contract applies only to those items to

which prices are attached, and that where it embraces both labor and

materials introduced in the work, such prices are in full compensation

therefor when introduced in the manner required. When it embraces

materials only, such prices are in full compensation for the materials

and the labor necessary to deliver the same to the company, and when it

embraces labor only, such prices are in full compensation for such

labor, and every incident to its complete and proper performance. In

every case the estimate for ascertaining the amount of compensation

shall be made by the engineer from the actual work, from the material

furnished, or from that on which the labor contracted for is bestowed.

It is also agreed that partial payments shall be made from time to time

during the progress of the work as follows:—

[_Times and manner of payment._]

And that in thirty days after the contract is fully completed to the

satisfaction of the chief engineer of the company for the time being,

and the work is surrendered to and accepted by the company, a final

measurement and estimate thereof shall be made under the direction of

the chief engineer, and be duly certified by him, on the return of which

to the president of the company the whole amount then found to be due to

the said party/parties of the first part shall be paid to him/them on

demand as follows:—

[_Insert mode of payment._]

And it is also hereby further agreed, that bank-bills current in the

State of —— shall be accepted for cash in payment for all claims under

this contract.

And the said party/parties of the first part further agree/agrees that

in twenty days after he/they shall be notified to do so, as provided for

in said specifications, he/they will begin the work hereby contracted to

be performed, with a force of all kinds sufficient for its completion in

the time herein prescribed, and that he/they will finish and deliver the

same to the company fully completed in all its parts as follows:—

* * * * *

And the said specifications hereunto annexed are hereby made a component

part of this contract and (except so far as any provision therein may

not be pertinent to the subject-matter of the contract or may be

specially modified herein,) shall be looked to in ascertaining the

meaning, extent, and purport of this agreement, and in determining the

rights, powers, duties, privileges, and obligations of the contracting

parties as to any particular embraced therein.

In virtue whereof the said party/parties of the first part has/have

hereunto set his/their hand and seal, and the said party of the second

part have caused their president to subscribe his name and affix the

corporate seal of the company hereto, all done in triplicate the day and

year first above written.

_Contractor’s name_, [SEAL.]

_President’s name_, [SEAL.]

SOLICIT FOR BIDS.

88. The approximate estimates, plans, and profiles being made, and other

preliminaries settled, proposals for executing work are solicited by the

public papers. Thus:—

NEW YORK, January 1, 1857. }

Office of the A and B Railroad Company. }

Proposals for executing the graduation, bridging, masonry, and track

laying, and for the supply of materials upon the A and B railroad will

be received at this office until the 31st day of January, 1857.

Plans, profiles, and schedules of amounts of work may be seen, and blank

bids obtained by application at this office.

All proposals must be directed to the chief engineer of the A and B

Railroad Company.

No bids will be received after January 31st, at 12, M.

Per order,

C. D., _Secretary A and B R. R. Co._

FORM FOR A BID.

89. That proposers may make their bids in a convenient form for

comparison, a blank, somewhat like the following, is given them to fill

out.

┌─────────────────────────────────────────┬──────┬──────┬──────┬──────┐

│ Number of Section. │ Sec. │ Sec. │ Sec. │ Sec. │

│ │ 1. │ 2. │ 3. │ 4. │

├─────────────────────────────────────────┼──────┼──────┼──────┼──────┤

│ Length in miles. │ 1½ │ 1¼ │ 1¾ │ 1½ │

├──────────────┬──────────────────────────┼──────┼──────┼──────┼──────┤

│Graduation. │Clearing and grubbing, │ │ │ │ │

│ │Price per acre, │ │ │ │ │

│ │Cost on the section, │ │ │ │ │

│ │Earth excavation, │ │ │ │ │

│ │Price per yard, │ │ │ │ │

│ │Cost on the section, │ │ │ │ │

│ │Loose rock excavation, │ │ │ │ │

│ │Price per yard, │ │ │ │ │

│ │Cost on the section, │ │ │ │ │

│ │Solid rock excavation, │ │ │ │ │

│ │Price per yard, │ │ │ │ │

│ │Cost on the section, │ │ │ │ │

│ │Average haul on section, │ │ │ │ │

│ │Ballasting, │ │ │ │ │

│ │Price per yard, │ │ │ │ │

│ │Cost on the section, │ │ │ │ │

│ │Whole cost of graduation, │ │ │ │ │

├──────────────┼──────────────────────────┼──────┼──────┼──────┼──────┤

│Masonry. │First class masonry, │ │ │ │ │

│ │Price per yard, │ │ │ │ │

│ │Cost on the section, │ │ │ │ │

│ │Second class masonry, │ │ │ │ │

│ │Price per yard, │ │ │ │ │

│ │Cost on the section, │ │ │ │ │

│ │Third class masonry, │ │ │ │ │

│ │Price per yard, │ │ │ │ │

│ │Cost on the section, │ │ │ │ │

│ │Foundation timber, │ │ │ │ │

│ │Cost per M., b’d measure, │ │ │ │ │

│ │Cost on the section, │ │ │ │ │

│ │Excavation for foundation,│ │ │ │ │

│ │Price per yard, │ │ │ │ │

│ │Cost on the section, │ │ │ │ │

│ │Rip rap, │ │ │ │ │

│ │Price per yard, │ │ │ │ │

│ │Cost on the section, │ │ │ │ │

│ │Whole cost of masonry, │ │ │ │ │

├──────────────┼──────────────────────────┼──────┼──────┼──────┼──────┤

│Bridging. │Detailed as above, │ │ │ │ │

├──────────────┼──────────────────────────┼──────┼──────┼──────┼──────┤

│Track laying. │ │ │ │ │ │

├──────────────┼──────────────────────────┼──────┼──────┼──────┼──────┤

│Fencing. │ │ │ │ │ │

└──────────────┴──────────────────────────┴──────┴──────┴──────┴──────┘

This form being filled out, evidently gives the cost of each or all of

the items upon any one or all of the sections, the cost of all the items

upon any one section being at the foot of that section, and the whole

cost of any one item at the extreme right and on the line of that item.

On the bottom of the form is printed, “The undersigned having read the

specifications, and made due examination, hereby proposes to the A and B

Railroad Company, to perform the work in the above schedule, to which

he/they has/have set figures, at those prices and under the conditions

described, and upon acceptance of this proposal by the company,

binds/bind himself/themselves to enter into a written contract to that

effect, and to furnish the required security.

_Name_,

_Address_,

_Name of Surety_,

_Address of Surety_.”

COMPARISON OF BIDS.

90. The bids being received, are compared as follows:—

┌───────┬──────────────────────────────┬──────────────────────────────┐

│Name of│ Graduation. │ Masonry. │

│bidder.│ │ │

├───────┼─────┬─────┬─────┬─────┬──────┼─────┬─────┬─────┬─────┬──────┤

│ │Sec. │Sec. │Sec. │Sec. │Total.│Sec. │Sec. │Sec. │Sec. │Total.│

│ │ 1. │ 2. │ 3. │ 4. │ │ 1. │ 2. │ 3. │ 4. │ │

├───────┼─────┼─────┼─────┼─────┼──────┼─────┼─────┼─────┼─────┼──────┤

│ A │ │ │ │ │ │ │ │ │ │ │

│ B │ │ │ │ │ │ │ │ │ │ │

│ C │ │ │ │ │ │ │ │ │ │ │

└───────┴─────┴─────┴─────┴─────┴──────┴─────┴─────┴─────┴─────┴──────┘

┌───────┬──────────────────────────────┬──────────────────────────────┐

│Name of│ Bridging. │ Superstructure. │

│bidder.│ │ │

├───────┼─────┬─────┬─────┬─────┬──────┼─────┬─────┬─────┬─────┬──────┤

│ │Sec. │Sec. │Sec. │Sec. │Total.│Sec. │Sec. │Sec. │Sec. │Total.│

│ │ 1. │ 2. │ 3. │ 4. │ │ 1. │ 2. │ 3. │ 4. │ │

├───────┼─────┼─────┼─────┼─────┼──────┼─────┼─────┼─────┼─────┼──────┤

│ A │ │ │ │ │ │ │ │ │ │ │

│ B │ │ │ │ │ │ │ │ │ │ │

│ C │ │ │ │ │ │ │ │ │ │ │

└───────┴─────┴─────┴─────┴─────┴──────┴─────┴─────┴─────┴─────┴──────┘

┌───────┬──────────────────────────────┬──────┐

│Name of│ Fencing. │Grand │

│bidder.│ │Total.│

├───────┼─────┬─────┬─────┬─────┬──────┼──────┤

│ │Sec. │Sec. │Sec. │Sec. │Total.│ │

│ │ 1. │ 2. │ 3. │ 4. │ │ │

├───────┼─────┼─────┼─────┼─────┼──────┼──────┤

│ A │ │ │ │ │ │ │

│ B │ │ │ │ │ │ │

│ C │ │ │ │ │ │ │

└───────┴─────┴─────┴─────┴─────┴──────┴──────┘

From which the names may be easily selected either for one or more

sections, for any or all of the items, that shall give the least cost.

CHAPTER V.

LAYING OUT WORK.

91. The running of the line consists in placing a stake at every one

hundred feet upon tangents, and at every fifty feet distance upon sharp

curves; also a permanent post at each tangent point, and at points of

compound and reversed curvature. This is the centre line, the axis of

the road, and the base of all field operations. Wherever the work is

going on, the centre pins should be referred to fixed points outside of

the ground occupied by the road.

92. The first operation in preparing for excavation is to place side

stakes at one half the width of road-bed plus the ditch, on each side of

the centre line.

SLOPES.

93. Setting out slopes is a term applied to laying off upon the ground,

on each side of the centre, the distance to which the slope, commencing

at the outer edge of the ditch, will extend, depending upon the angle of

slope, width of road-bed and ditch, and depth of cutting. There are here

five distinct cases which may occur:—

In embankment when the natural surface is horizontal. In embankment when

the natural surface is inclined. In excavation when the natural surface

is horizontal. In excavation when the natural surface is inclined.

In mixed work (side hill,) when the road-bed is partly in cut and partly

in fill. In both excavation and embankment, when the natural surface is

horizontal, we have only to add the cut, in feet and decimals,

multiplied by the slope, to one half the width of road-bed plus ditch.

Thus suppose the cut is 20.55 feet,

half the road-bed, 10.25 feet,

ditch, 3.00 feet,

slope 1½ horizontal to 1 vertical,

and we have

(20.55 × 1½) + 10.25 + 3.0 = 44.075 feet.

When the ground is inclined transversely to the axis of the road, first

assume a point upon the ground, (apparently right) find its height above

grade with the level, multiply this by the slope and add one half the

distance between the outer edge of ditches, and see how near it comes to

the measured distance from the centre to the assumed point; if within a

foot, it will answer; if not, a second trial will fix the place.

CULVERTS.

94. The length of any structure passing under a railroad embankment is

_L_ – 2_Rh_, where _L_ is the distance between slope stakes, _R_

inclination of slopes, _h_ the height of structure from the natural

surface. Thus, suppose the distance between slope stakes to be 100 feet,

slope 1½ to 1, and _h_ 10 feet, we have

_L_ = 100 – (10 × 1½ × 2) = 100 – 30 = 70 feet.

The length of an oblique structure will of course be greater than that

of one at right angles to the road; the length depending upon the

obliquity.

MASONRY.

95. There are eight general cases which may occur in laying out such

structures as bridge abutments with wings.

1. A right bridge on a level tangent.

2. A right bridge on a level curve.

3. A skew bridge on a level tangent.

4. A skew bridge on a level curve.

5. A right bridge on an inclined tangent.

6. A right bridge on an inclined curve.

7. A skew bridge on an inclined tangent.

8. A skew bridge on an inclined curve.

And these eight cases will vary again according to the natural surface

of the ground, whether horizontal, or inclined transversely.

96. The general position of wing walls and general form of the line

inclosing the base of the bridge, is shown from fig. 31 to fig. 38. Fig.

31 represents case one. The points A, B, C, D, are fixed by squares from

the centre line at E F, G H.

[Illustration: Fig. 31.]

Fig. 32 represents case two. The wings 3_c_, 4_d_, must evidently have a

different inclination from A1, B2. The points A, B, _c_, _d_, 1, 2, 3,

4, as before, are laid off by squares from a tangent to the curve.

[Illustration: Fig. 32.]

Fig. 33 explains itself.

[Illustration: Fig. 33.]

[Illustration: Fig. 34.]

Fig. 34, case five. Here the wings A1, C4, are the same, as also B2, D3,

the former being longer, on account of the greater depth of the fill.

[Illustration: Fig. 35.]

Fig. 35, case seven. Here each wing is peculiar; the figure being a

compound of figs. 33 and 34.

[Illustration: Figs. 36 and 37.]

Figs. 36 and 37, case 8. This is the most difficult of all. No two wings

have the same length or inclination on plan. The natural surface being

horizontal, the line inclosing the bridge is A″ B″ C″ D″. If the natural

surface descended from C″ to A, the position taken would be A, B, C, D.

Fig. 37 is the elevation of the position A B C D. The several points are

laid off from the line _n_, _n_.

The general manner of fixing the lines of figures 31 to 38, is to assume

the angle of some one wing, as A 1, in fig. 34, to draw A C parallel to

E F; and from C, the intersection of A C with the base of the

embankment, C 4 gives the other wing. Local circumstances will of course

often fix at once the length and angle of the wings. Upon simple curves,

as in fig. 32, the lines A _c_ and B _d_ are made radial.

97. In curving a viaduct, the axes of the piers are made radial to the

centre of the located curve, and the planes of the springing lines are

made parallel to the axes of the arches. The pier thus becomes a wedge,

and should be strengthened by a starling, upon the outside of the curve,

to resist the resultant of the thrusts of two adjoining arches.

98. We should never try to stake out the exact horizontal projection of

a complicated piece of work upon rough ground, but only the trenches,

which being cut, give a horizontal surface to work upon. In placing the

stakes, we must be careful to have them so far outside of the work that

they will remain undisturbed while operations are going on. The pegs for

cutting pits and trenches may be placed at the angles of the latter, but

the working pegs must be so placed that the lines stretched from one to

the other will define the masonry. All measurements made in laying out

work should be made by graduated rods, and carefully checked.

99. In founding piers, and in aquatic operations generally, two stakes

upon the shore, or a fixed transit, will define any line in the water.

Two transits will define points.

100. A permanent bench mark should be carefully fixed at each structure,

from which its levels may be obtained.

101. In adjusting oblique bridges, care must be taken so to place the

bridge seats that the floor beams shall lie in a correct plane, and not

be at all warped or winding.

[Illustration: Fig. 38.]

102. As an example of laying out work with regard to heights, take the

case of fig. 38. Let the grade of the centre line be one in 100, the

angle of obliquity 45°, the width of bridge twenty feet, and span on the

skew one hundred feet. Required the elevations of the points _a_, _b_,

_c_, _d_.

Assume the height of (2) as 100.00

That of (3) will be 99.00

_b_ being 10 ft. back of 2 is 0.1 ft. higher than 2, or 100.10

and _d_ 0.1 feet less than (2) or 99.90

also _a_ = 99.00 + 0.10, or 99.10

and _c_ = 99.00 – 0.10, or 98.90

TUNNELS.

103. The maintaining a correct centre line through tunnels is generally

considered difficult. The fixing of the line in deep shafts requires

great care, owing to the short distance between the only two fixed

points, that can be transferred from the surface to the bottom of the

pit. This is a matter of manual skill and of instrumental manipulation.

There is no difficulty in aligning the upper ends of two plumb-lines;

and the lower ones will certainly be governed by their position. The

following method has been found to answer every purpose.

Let the opening of the shaft be ten feet in diameter. Place two

horizontal bars at right angles to the road across the opening, upon

which slide blocks holding the upper end of the plumb-lines. Adjust

these lines, at the surface, with a transit; and when fixed, place iron

pins at the point marked by the plumbs at the bottom of the shaft. Upon

these pins fix the exact centres. For keeping the line in the shaft

headings, a straight rod, with steel points at each end, should be used,

which being placed upon the iron centre pins, fixes the centre line of

the tunnel. When the tunnel is curved, the line should be laid off by

offsets from the tangent to the curve at the shaft.

By this method points at ten feet distance may be fixed within 1/100 of

an inch, a difference of which would cause an error of ⅒ of an inch per

one hundred, or an inch per thousand feet.

CHAPTER VI.

EARTHWORK.

FORM OF RAILROAD SECTIONS.

104. The reader is presumed to be acquainted with the manner of finding

the areas and cubes of simple geometric figures and bodies. The

following fifteen figures show the forms which may be taken by the cross

section of a railroad in cutting; for embankment invert the same. They

are easily separable into simple figures.

[Illustration: Fig. 39.]

[Illustration: Fig. 40.]

[Illustration: Fig. 41.]

[Illustration: Fig. 42.]

[Illustration: Fig. 43.]

[Illustration: Fig. 44.]

[Illustration: Fig. 45.]

[Illustration: Fig. 46.]

[Illustration: Fig. 47.]

[Illustration: Fig. 48.]

[Illustration: Fig. 49.]

[Illustration: Fig. 50.]

[Illustration: Fig. 51.]

[Illustration: Fig. 52.]

[Illustration: Fig. 53.]

[Illustration: Fig. 54.]

105. The formation of tables for the amount of earth in level cutting is

very simple. The area of the following section, where B is the base, and

R the horizontal dimension of the slope, is

(_B_ + _B_ + 2_R_)/2 × _h_, or (2_B_ + 2_R_)/2 × _h_,

or finally

(_B_ + _R_) × _h_,

i. e., the base of a rectangle by its height. Multiply this by 100 and

divide the product by 27; or divide by 27/100, and we have the cubic

amount in a prism one hundred feet long. The road-bed being nineteen

feet wide, and slopes one and a half to one, the formula for the amount

of a prism one hundred feet long is

((19 + 1½_h_)_h_)/0.27,

and assuming the base of rock cutting as eighteen feet, and slope one

quarter to one, and embankment eighteen feet at subgrade, we have, rock,

((72 + _h_)_h_)/1.08,

and embankment,

((18 + 1½_h_)_h_)/0.27,

the figure being inverted for embankment. For a prism of ten or of one

thousand feet in length, we have only to move the decimal point. In

forming a table, proceed as follows:—

_h_ _B_ + 1½_h_ (_B_ + 1½_h_) × _h_ ((_B_ + 1½_h_) × _h_)/0.27

_a_ _b_ _c_ _d_

_a′_ _b′_ _c′_ _d′_

_a^n_ _b^n_ _c^n_ _d^n_.

[Illustration: Fig. 55.]

It is evident from inspection of fig. 55, that _c_ exceeds _c_^o by _h_

× 2_r_; and that _c″_ exceeds _c′_ by _h′_ × 2_r′_; and so on as far as

we go; this increase being constant, we have then to find the area of

_c_, and for the area _c_ + _c′_ double _c_, and add the increment;

whence the rule:—

Having found the increase (which varies with the angle of the slope) for

the _second_ section, add the increase to twice the first. For the

_third_, add twice the increase to three times the first; and for the

_n_th, add _n_ – 1 times the increment to _n_ times the first area, or

algebraically calling _a_ the first area, _a′_ the second, _a″_ the

third, _a^n_ the _n_th area, and we have

The first area _a_ = _a_;

The second area 2_a_ + _i_ = _a′_;

The third area 3_a_ + 2_i_ = _a″_;

The _n_th area _na_ + (_n_ – 1)_i_ = _a^n_.

We might operate at once upon the cubic contents, but for the length to

which some decimals run; some indeed circulating.

106. The table thus made may be of the following form:—

Cut (or fill), in feet. Cubic yards Earth. Cubic yards Rock.

Slopes 1½ to 1. Slopes ¼ to 1.

1 76 68

2 163 137

3 261 208

4 371 282

5 491 356

6 622 433

7 802 512

8 919 593

9 1083 675

10 1260 759

i. e., cut being eight feet, each one hundred feet length gives nine

hundred and nineteen cubic yards; one thousand feet, 9190 yards, and ten

feet of length 91.9 cubic yards.

107. The preceding system is intended only for approximate estimates.

Let one person read off the cuts or fills from the profile, a second

give the corresponding number of yards by the table made as above, while

a third sets the figures down; being careful to separate the cuts from

the fills.

For final measurements, none but the prismoidal formula should be used;

the length of the prismoids being taken at each one hundred feet, and

nearer when the ground is rough.

108. As an example of the comparative amounts given by the above

formula, and by the common method of averaging end areas, take the

following, the slopes being 1½ to 1.

Base. Distance. Cut. End Area. Mean Area. Middle Area.

20 0 0 000 000 000

20 50 5 137 069 059

20 50 10 350 244 236

20 50 15 637 493 483

20 50 00 000 318 236

By averaging end areas we have

50 × 69 = 3,450

50 × 244 = 12,200

50 × 493 = 24,650

50 × 318 = 15,900 Sum, 56,200.

And by the prismoidal formula,

50 × 305

50 × 1,257

50 × 2,669

50 × 1,755 Sum 299,300 ÷ 6 = 49,000,

and 56,200 – 49,000 = 7,200

cubic feet in favor of the method of end areas.

109. The prismoidal formula is algebraically

((_a_ + _a′_ + 4_a″_)/6)_L_ = _c_,

when _L_ = length,

_c_ = cubic contents,

_a_ = area of one end,

_a′_ = area of other end,

_a″_ = middle area;

or, verbally, _to the sum of the end areas add four times the middle

area, and multiply the result by one sixth of the length_; the _middle_

area being the area made upon the mean height of the two ends. Thus if

the length is one hundred feet, and one end ten feet high, the other

twenty feet high, and slopes one and a half to one, the cubic amount is,

(the base being twenty-two feet,)

[((22 + 22 + 30)/2 × 10) + ((22 + 22 + 60)/2 × 20) + ((22 + 22 + 45)/2 ×

15 × 4)] × 100./6

EXCAVATION AND EMBANKMENT.

110. Some writers have considered that the grades of a road should be so

adjusted as to equalize the cutting and the filling. The total rise and

fall might not be much affected by this, but the mechanical effect of

grades might. A perfect balance between the cuts and fills is not to be

desired. The whole cost of earthwork must be a minimum, and it is often

cheaper to waste and borrow, than to make very long hauls, and to form

the grade line by interchange of material on the profile only.

111. The transverse slopes depend upon the nature of the soil in which

the cut is made. Gravel will stand at a slope of one and a half

horizontal to one vertical, and in some cases one and a quarter, or even

one to one. Clay stands nearly vertical for some time, but finally

assumes a very flat slope, in some cases two, three, and even four

horizontal to one vertical. In places where a stratum of clay underlies

more reliable earth, to avoid a very long slope, it may be economical to

support the clay by a wall, and to slope the earth only.

112. Care should be taken in every case to secure good drainage and to

protect the slopes by surface drains at the top. The drains in long cuts

should be slightly inclined to insure the running off of the water. A

fall of ten feet per mile is enough; five will answer in many cases. On

side hill cuts a surface drain along the top of the upper slope will do

good service. On many high embankments, catchwater drains, commencing at

the road-bed and gradually sloping to the base, will prevent, in a great

degree, cutting of the bank.

113. Embankments, when made rapidly, should be finished to the full

width, somewhat above true grade, to allow for the after settlement.

(See specification.)

114. The following allowances have been made for the shrinkage of

material in some parts of America.

Light, sandy earth 0.12

Clayey earth 0.10

Gravelly earth 0.08

Gravel and sand 0.09

Loam 0.12

Clay 0.10

Clay puddled 0.25

Wet surface earth 0.15

The bulk of quarried rock on the contrary increases from twenty-five to

fifty per cent.

115. When embankments are carried up slowly, in layers of three or four

feet at a time, the after settling is very little; when carried up all

at once it will be more. The full width must be kept, even above the

required height. Fig. 56 shows the forms of a bank both before and after

settlement.

[Illustration: Fig. 56.]

The best method of forming a bank of bad material is to ram the layers

as in fig. 57; thus the tendency is to consolidate by settling, and not

to destroy the work by sliding.

[Illustration: Fig. 57.]

TRANSPORT OF MATERIAL.

116. In the formation of embankments it is not always advisable to make

the whole bank from an adjoining cut or cuts. The length of haul may be

too long. In this case it is customary to waste a part of the cut and to

borrow earth from some nearer point for the bank. That the transport

shall be effected in the most economical manner, the product of the cube

of earth, by the mean distance, (the distance between the centres of

gravity, of excavation and embankment) must be a minimum. To determine

the theoretical minimum expense, the problem becomes very complicated on

account of the great number of variable elements entering therein; and

the result obtained is applicable only to a particular case. Local

circumstances more than any other thing, determine the position of a

borrow pit, and the path over which the material is to be transported.

OF THE AVERAGE HAUL.

117. To find the cost of the movement of earth on any section, we must

have, the total amount of earth to be moved, and the _average haul_; the

latter being the distance through which, if the whole amount were moved,

the cost would be the same as the sum of the costs of moving the partial

amounts their respective distances. To find the average haul proceed as

follows: _First_, find the distance between the centres of gravity of

each mass both before and after moving, which may be done with

sufficient accuracy for practice by inspection of the profile. _Next_,

118. _Divide the sum of the products of the partial amounts by their

respective hauls, by the total amount_; the result is the average haul

in feet. Or algebraically, representing the partial amounts by _m_,

_m′_, _m″_, _m‴_, the respective hauls by _d_, _d′_, _d″_, _d‴_, the

total amount by _S_, and the average haul by _D_, we have

(_md_ + _m′d′_ + _m″d″_ + _m‴d‴_)/_S_ = _D_.

_Example._—Let column 1 show the partial amounts in cubic yards. Column

2 the corresponding hauls.

1,000 × 200 = 200,000

2,000 × 300 = 600,000

5,000 × 400 = 2,000,000

8,000 × 600 = 4,800,000

—————— —————————

16,000 7,600,000

and 7,600,000/16,000 = 475 feet _average haul_.

_Proof._—Assume the cost of moving 1,000 yards one foot as ten cents,

the costs of the separate masses are

1,000 yards 200 feet is $20.00

2,000 yards 300 feet is 60.00

5,000 yards 400 feet is 200.00

8,000 yards 600 feet is 480.00

———————

Sum, $760.00

also the cost of moving 16,000 yards 475 feet is

16 × 475 × 10 = $760.00.

119. The movement of earth is effected by shovels, barrows, horses and

carts, or by cars. In round numbers we can move earth

By shovels alone 10 to 20 feet,

By barrows alone 20 to 100 feet,

By carts 100 to 500 feet,

By cars 500 to 5,000 feet,

As the haul increases, the number of vehicles of transport remaining the

same, the number of excavators must decrease. Earths easily removed do

not admit of so large a haul, with a given number of excavators, as hard

earths. The nature of the ground, form of carts, kind of horses, season

of the year, and price of labor are some of the elements entering the

problem of transport. The best illustration of the matter will be found

among the very able writings of Ellwood Morris, Esq., C. E., in the

Journal of the Franklin Institute. Knowing the value of wages, the

nature of the earth and length of haul, it is easy to see what mode of

transport must have the preference.

CONTRACTOR’S MEASUREMENTS.

120. The price of executing any piece of work is paid to the contractor

at stated intervals, generally once each month. The amount of work done

at these partial payments is obtained by instrumental reference to the

ground. Towards the completion of operations the most correct and

easiest method of finding the rate of progress is to deduct the amount

already done from the total as given by primary measurement. The full

price is not paid to the contractor, but a percentage is kept back,

which insures a faithful performance of work. It is impossible to

establish a _pro rata_ price at first, owing to the uncertain nature of

the work; what appears to be earth may be rock. By deducting a maximum

price estimate for all but one of the items, an approximate _pro rata_

value for that one may be determined. An analysis of cost will define

the minimum limit for advantage to the contractor; and the _pro rata_

value less the percentage, the maximum for the company’s benefit.

DRAINING.

121. When a level is to be drained, or the water carried off from the

surface of a swamp, the first point to be ascertained is the location of

the lowest outfall. The direction in which aquatic plants lie show the

natural fall of the water, these always pointing down stream. When the

most available outlet has been decided upon, a main drain should be set

out, from which oblique branches are to be cut, pointing in the

direction of the current; into these all minor cuts are to be collected

so that the whole district may be equally drained. The fall should be

greatest at the most remote points, decreasing as the amount of water

increases. Large and deep rivers run sufficiently fast when the fall is

one foot per mile. For small rivers, double that is necessary. Ditches

and ordinary drains require eight feet per mile. When the water is made

to pass away from the surface, it should flow very gradually, that the

sides and bottom of the ditches may not be worn away by friction; it

should be in constant motion that the channel may be kept clean and

increase in velocity as it proceeds. When the surface is a perfect

level, the drains should of course be made straight.

After the quantity of water has been determined by careful observation,

the section of the main and branches must be fixed, so that regarding

both their areas and velocities, the main drain will not be overcharged.

To facilitate the current, the sides should be inclined about one and a

quarter to one; and the breadth of base should be two thirds of the

depth of water. These results are obtained from the practice of English

engineers, who have given a great deal of attention to the subject.

Drains cut through bogs, may have sides nearly, if not quite vertical,

as the fibres of plants forming the soil resist the action of the water.

SUBSOIL DRAINING.

Geology has assisted this operation very materially by rendering us

acquainted with the quality and nature, as well as of the succession of

strata. The soils which are impervious are usually the heaviest, and the

porous are those of lighter quality. Clays, when they receive water,

will only part with it by evaporation, when left in a natural state; and

therefore to make such a surface fit for a useful end requires

considerable ingenuity, and often great expense. Such a soil is not

rendered unstable by underground springs, and may be effectually drained

by boring through, and letting the water off into an under stratum, when

this is of a porous nature.

When land abounds with springs, or is subject to the oozing out of

subterraneous water, draining is effected in a different manner. Springs

have their origin in the accumulation of rain water, which falling upon

the earth, after passing the porous strata, lodges upon the impervious,

and glides along the sloping surface until it crops out, generally in

some valley where it forms a watercourse.

Descending streams are easily taken care of by collecting them into a

body before they reach the low lands.

When a morass is to be drained, the strata upon which it reposes should

be examined, and if, as is often the case, a layer of clay intervenes

between the substratum and the mossy covering, which holds the water, by

tapping this in well chosen places, the whole will sink away.

A fine example of embankment upon a bad bottom was performed by Mr.

Stephenson, on the Great Western Railroad, England, at the crossing of

Chatmoss. This moss was so soft that cattle could not walk upon it, and

an iron bar sank into it by its own weight. The moss was first

thoroughly drained by a system of longitudinal and cross drains, and the

embankment made of the lightest material possible—the dried moss itself.

Without this treatment, the moss would have sank beneath the bank alone;

it now supports the passage of the heaviest railroad trains.

METHOD OF CONDUCTING OPERATIONS.

122. The organization of the engineer corps upon a railroad is as

follows, differing somewhat in different parts of the country.

_The Chief Engineer_ has entire charge of all the work, of all

assistants, appointing and dismissing members of the corps, designing of

all structures, making of specifications, and of all mechanical

operations incident to the thorough, correct, and timely construction of

the road; and should be able also to specify, generally, the amount and

character of the equipment needed.

_The Resident Engineer_ has charge of the detailed construction of from

twenty-five to fifty miles of road, according to the nature of the work,

being responsible to the chief engineer for the proper execution of the

orders from headquarters; he returns to the chief engineer a monthly

account of the exact condition of his work, both as to the amount

executed, and also that remaining to be done.

The assistants of the resident engineer are a leveller and transit man;

to whom, under his supervision, is the duty of laying out, measuring,

and estimating the work. The leveller has with him one or more rodmen.

The transit man, two chainmen, and one or more axemen.

In some cases, added to the above are inspectors of masonry, bridging,

and superstructure. These are necessary only when the road embraces a

great number of mechanical structures; too many to leave the proper time

to the resident engineer for his other duties. Once each month the exact

amount of graduation, bridging, and masonry _executed_ is obtained by

the resident and his assistants. The chief engineer applies the prices

to these amounts, and the percentage deduction being made, the estimate

is ready for the treasurer.

123. The abstract prepared from the monthly estimate should show

clearly, without unnecessary figures, the amount of work completed, and

also that remaining to be done.

For convenience, the various blanks used on railroads should fold to the

same form and size. The blanks are,

The Contract,

The Specification,

The Resident Engineer’s Monthly Return,

The Assistant’s Weekly and Monthly Returns,

The Force Return,

The Pay Roll,

Vouchers.

The contract and specification are given in chapter IV. The resident’s

monthly return to the chief engineer is somewhat as follows:—

Monthly return of work done on the _first_ division of the A and B

Railroad, for the month ending ——, showing also the whole amount of work

up to ——; also the present estimate for completion.

┌─────────────────┬─────────────────┐

│ Section. │ Contractor. │

├─────────────────┼─────────────────┤

│ 1 │ │

└─────────────────┴─────────────────┘

┌──────────────────────────────────────────────────────────────────────┐

│ GRADUATION. │

├────────────────────────────────────┬─────────────────────────────────┤

│ Clearing and Grubbing. │ Excavation. │

├───────────────────┬────────────────┼────────────────┬────────────────┤

│ In July. │ Total to date. │ In July. │ Total to date. │

├──────┬──────┬─────┼──────┬───┬─────┼──────┬───┬─────┼──────┬───┬─────┤

│Acres.│Price.│Am’t.│Acres.│Pr.│Am’t.│Yards.│Pr.│Am’t.│Yards.│Pr.│Am’t.│

├──────┼──────┼─────┼──────┼───┼─────┼──────┼───┼─────┼──────┼───┼─────┤

│ 15 │ 100 │1500 │ 300 │100│30000│44000 │10 │4400 │100000│10 │10000│

└──────┴──────┴─────┴──────┴───┴─────┴──────┴───┴─────┴──────┴───┴─────┘

┌─────────────────────────────────────────────────────────────────────┐

│ MASONRY. │

├─────────────────────────────┬─────────┬─────────┬─────────┬─────────┤

│ │ │ │ Foun- │ Foun- │

│ First Class. │ Second │ Third │dation in│ dation │

│ │ Class. │ Class. │ Excava- │ Timber. │

│ │ │ │ tion. │ │

├──────────────┬──────────────┼───┬─────┼───┬─────┼───┬─────┼───┬─────┤

│ │ │In │Tot. │In │Tot. │In │Tot. │In │Tot. │

│ In July. │Total to date.│Ju-│ to │Ju-│ to │Ju-│ to │Ju-│ to │

│ │ │ly.│date.│ly.│date.│ly.│date.│ly.│date.│

├────┬───┬─────┼────┬───┬─────┼───┼─────┼───┼─────┼───┼─────┼───┼─────┤

│Yds.│Pr.│Am’t.│Yds.│Pr.│Am’t.│ │ │ │ │ │ │ │ │

│ │ │ │ │ │ │ │ │ │ │ │ │ │ │

│ │ │ │ │ │ │ │ │ │ │ │ │ │ │

│ │ │ │ │ │ │ │ │ │ │ │ │ │ │

└────┴───┴─────┴────┴───┴─────┴───┴─────┴───┴─────┴───┴─────┴───┴─────┘

┌────────────────────────────────────────────────────────────────────┐

│ BRIDGING AND TIMBERWORK. │

├───────────────────────────────────┬──────────┬──────────┬──────────┤

│ Truss Bridges. │ Pile │ Stringer │Trestling.│

│ │ Bridges. │ Bridges. │ │

├─────────────────┬─────────────────┼──────────┼──────────┼──────────┤

│ In July. │ Total to date. │ │ │ │

├─────┬─────┬─────┼─────┬─────┬─────┼──────────┼──────────┼──────────┤

│Feet.│ C. │Am’t.│Feet.│ C. │Am’t.│ │ │ │

│ │ │ │ │ │ │ │ │ │

│ │ │ │ │ │ │ │ │ │

│ │ │ │ │ │ │ │ │ │

└─────┴─────┴─────┴─────┴─────┴─────┴──────────┴──────────┴──────────┘

┌─────────────────────────────────────────────────────────────────────┐

│ SUPERSTRUCTURE AND FENCING. │

├─────────────────────────────────────────────────────┬───────────────┤

│ Superstructure. │ Fencing. │

├──────────────────────────┬──────────────────────────┼───────┬───────┤

│ │ │ In │ Total │

│ In July. │ Total to date. │ July. │ to │

│ │ │ │ date. │

├────────┬────────┬────────┼────────┬────────┬────────┼───────┼───────┤

│ Miles. │ Price. │ Am’t. │ Miles. │ Price. │ Am’t. │ │ │

│ │ │ │ │ │ │ │ │

│ │ │ │ │ │ │ │ │

│ │ │ │ │ │ │ │ │

└────────┴────────┴────────┴────────┴────────┴────────┴───────┴───────┘

┌─────────────────────────────────────────────────────────────────────┐

│ VALUE OF WORK AND PAYMENTS MADE. │

├─────────────┬─────────────┬─────────────┬─────────────┬─────────────┤

│Value of Work│ Amount paid │ Whole value │Whole amount │ Amount left │

│ in July. │ in July. │ to date. │ paid. │ due. │

├─────────────┼─────────────┼─────────────┼─────────────┼─────────────┤

│ │ │ │ │ │

│ │ │ │ │ │

│ │ │ │ │ │

└─────────────┴─────────────┴─────────────┴─────────────┴─────────────┘

┌─────────────────────────────────────────────────────────────────────┐

│ VALUE OF LABOR. │

├─────────────┬─────────────┬─────────────┬─────────────┬─────────────┤

│ Foreman and │ Laborers. │ Carts with │ Carts with │Whole value. │

│ Mechanics. │ │ Horses. │ Oxen. │ │

├─────────────┼─────────────┼─────────────┼─────────────┼─────────────┤

│ │ │ │ │ │

│ │ │ │ │ │

│ │ │ │ │ │

└─────────────┴─────────────┴─────────────┴─────────────┴─────────────┘

┌────────────────────────────────────────────────────────────────────┐

│ RECAPITULATION. │

├──────────────────────┬──────────────────────┬──────────────────────┤

│Value of work done in │ Value of work up to │ Remaining Value. │

│ July. │ date. │ │

├──────────────────────┼──────────────────────┼──────────────────────┤

│ │ │ │

│ │ │ │

│ │ │ │

└──────────────────────┴──────────────────────┴──────────────────────┘

The resident engineer’s assistants return to him weekly a statement of

the amount and value of the force employed upon the several sections,

and monthly the exact amount of work done on the same, for each of which

there should be a blank. The above forms may be printed and folded in

8vo., or may be the continuous headings of a large sheet.

CHAPTER VII.

ROCKWORK.

ROCK EXCAVATION.

125. The sides of rock excavation are sometimes cut to a small slope, as

one fourth or one fifth horizontal to one vertical, and sometimes cut

quite perpendicularly. The earth, when it occurs, which covers the rock,

is first taken out at the proper slope; a berm of one or two feet being

left between the foot of the earth and the crest of the rock.

126. Rock is taken out one or two feet below grade, as well as earth, to

allow the introduction of the necessary ballast.

BLASTING AND QUARRYING.

127. The most common mode of removing rock is by blasting; for this

holes are drilled by steel-edged jumpers, worked either by hand or by

steam. The first object in cutting a passage through rock, is to open a

working face, so as to get the necessary lines of least resistance,

(this line is that by which the powder finds the least opposition to a

vent at right angles to the length of the drill); these lines should, if

possible, be at right angles to the beds of stratification; the holes

should be drilled parallel to the seams of the rock, as the powder will

then lift off the strata. In working a vertical face, it may be best to

blast out the lower part first, and so undermine the overhanging mass.

128. The amount of powder in different charges to produce proportional

results should be as the cube of the line of least resistance; for

example:—

2^3 is to 4 oz. as 3^3 is 13½ oz.,

or

8 to 4 as 27 to 13½;

and generally,

_L^3_ : _w_ :: _L′^3_ : _w′_;

whence

_w′_ = (_wL′^3_)/_L^3_.

129. The following charges corresponding to lines of least resistance

are from the works of Sir John Burgoyne.

Line of least resistance. Charge of powder.

2 feet, 0 lbs. 4 oz.

4 feet, 2 lbs. 0 oz.

6 feet, 6 lbs. 12 oz.

8 feet, 16 lbs. 0 oz.

130. After the powdered stone is removed, the powder is placed in the

lower part of the hole; after which a wad of turf, or some other light

material, follows; next the tamping of powdered brick, dried clay, or

something similar, and finally a stopper of wet clay, or some other firm

substance. A hole is left through all, communicating with the powder by

ramming the tamping around a wire; through this hole a fuse is inserted

by which to light the charge. The most perfect tamping would offer a

resistance as great as that by the natural rock. A great improvement

upon the above method is the sand blast; the powder is put in, and the

hole filled with loose, dry sand, simply poured in and settled by a

gentle stirring, but not at all rammed; the explosion of the powder

spreads the sand as a wedge, and causes the power of the blast to be

exerted sideways. In some cases a small cone of wood has been placed

(base down) in the hole with the sand, which aids very much in stopping

the exit of the blast through the drill.

131. Of late years an admirable method of lighting large charges

simultaneously has been employed, namely, voltaic electricity.

132. A gigantic example of the application of this method has been

furnished by the English engineers in overthrowing a portion of Round

Down Cliff, about two miles from Dover, (England). Two chambers, 13 × 5½

× 4½, and one 10 × 5½ × 4 feet were cut in the rock. Within these were

placed fifty bags of powder, amounting in all to eight and one half

tons. The charges were lighted by the voltaic system, by which operation

a mass of rock (chalk) 380 × 360 × 80 feet, amounting to 400,000 cubic

yards, was thrown into the sea, and by which there was estimated to have

been saved nearly $40,000.

133. The following table from Colonel Pasley’s memoranda on mining,

shows the capacity of different drills for powder, by weight, and also

the depth of holes of different diameters, to contain one pound of

powder.

Diameter of hole Ounces of powder Powder in one Depth of hole in

in inches. in one inch foot deep. inches to contain

depth. one pound.

lbs. oz.

1 0.4 0 5.0 38.2

1½ 0.9 0 11.3 16.9

2 1.7 1 4.1 9.5

2½ 2.6 1 15.4 6.1

3 3.7 2 13.2 4.2

3½ 5.1 3 13.5 3.1

4 6.7 5 0.4 2.4

4½ 8.4 6 5.7 1.9

5 10.5 7 13.6 1.5

5½ 12.7 9 8.0 1.3

6 15.1 11 4.9 1.0

134. Blasting under water has been practised to some extent, and with

great success by Messrs. Maillefert and Raasloff, both in New York

harbor and in the St. Lawrence River. The method is merely to explode

bodies of powder _upon the surface of the rock_, the water itself being

a sufficient source of reaction to the blast.

TUNNELLING.

135. Tunnels are driven through hills to avoid very deep cutting. When

in rock of a solid nature, the roof supports itself; but when in earth

or in loose rock, an artificial arched lining becomes necessary. Figs.

58 and 59 show sections in both rock and earth; the invert _b b_ is

placed in a bed of concrete. In excavating earth, a temporary roof is

made use of while the work is in progress, which is afterwards replaced

by an arch of brick or stone. The back of the arch must be closely

wedged, grouted, and the earth well rammed in.

[Illustration: Fig. 58.]

[Illustration: Fig. 59.]

The great disadvantages attending the construction of tunnels are want

of air, light, room, and drainage. To facilitate the latter requirement,

a very light grade may be introduced; this may easily be done, as they

generally occur on summits, or on the approach to summits; 1/1000 or

five feet per mile is sufficient.

In working a tunnel which is upon a grade, one end naturally drains

itself if the approach is taken out; the other drains the wrong way, to

meet which obstacle we must resort to pumps which follow the work,

keeping always in the lowest place, or by sinking a well at the shaft

through which the water is raised to the surface.

The ventilation of tunnels is effected by drawing off the bad air when a

fresh supply must enter.

136. In taking out the rock, the expense will depend much upon the

nature and stratification of the rock encountered.

SHAFTS.

137. In tunnels of considerable length, a long time would be consumed in

working from the ends only. In such cases it is customary to sink shafts

at the most convenient places (the shallowest when at the proper

distance,) and to commence at the bottom of these to work both ways.

This operation involves considerable expense, as all draining,

ventilating, and removal of excavated materials must be effected through

the shaft.

In leaving openings for the exit of smoke and for admission of light in

artificial arches, regard must be had to their position. They should be

at the springing rather than at the crown of the arch, as they will thus

less affect the strength of the masonry.

The approaches of tunnels in cities and in other places where appearance

is of importance, are finished with face coping and wings.

138. Tunnels, when conducted in the most expeditious manner, require for

their completion a long time. The following table shows the rate of

progress upon some of the most important tunnels of America.

Name of Tunnel. Average daily

Length in advance, in

feet. Time in days. feet.

*Penn Railroad, 3,612 697 5.18

*Kingwood B. & O. R. R. 4,100 750 5.47

Board Tree B. & O. R. R. 2,250 675 3.32

*Welling, B. & O. R. R. 1,240 524 2.37

Pacific Railroad, 700 210 3.33

Pittsburgh and Connelsville,

(estimated) 4,500 810 5.56

—————

General average daily advance, in feet, 4.205

Those marked * being for a double track.

The following table also gives the time and cost of other tunnels in

different parts of the world.

┌────────────────┬──────────────┬──────┬─────┬───────┬─────────┬──────┐

│ Name and │ Material. │ │ │ Daily │ │ │

│ location of │ │Length│Time │average│ │ Cost │

│ tunnel. │ │ in │ in │ in │ │ per │

│ │ │feet. │days.│ feet. │Section. │foot. │

├────────────────┼──────────────┼──────┼─────┼───────┼─────────┼──────┤

│ │ │ │ │ │ │ $ │

│Nerthe, France, │Hard limestone│15,153│ ——│ │29½ × 26¼│ │

│Riqueral, │Chalk │ │ │ │ │ │

│ France, │ │18,623│2,139│ 8.7│26¼ × 26¼│ 39.89│

│Pouilly, France,│Chalk & clay │10,928│2,504│ 4.4│20⅓ × 20⅓│113.96│

│Arscherville, │—— │ │ │ │ │ │

│ France, │ │ 7,348│1,878│ 3.9│26¼ × 26¼│ 68.38│

│Maurage, France,│—— │15,752│2,085│ 7.5│25½ × 25½│ 94.43│

│Rolleboise, │Chalk │ │ │ │ │ │

│ France, │ │ 8,670│ 626│ 13.9│25 × 25 │ 62.98│

│Roule, France, │—— │ 5,645│ 522│ 10.8│25 × 25 │ 62.98│

│Lioran, France, │—— │ 4,548│2,087│ 2.2│21⅓ × 21⅓│ 56.98│

│Kilsby, England,│Clay and sand │ 7,233│1,252│ 5.8│27 × 23½│194.31│

│Belchingly, │Blue clay │ │ │ │ │ │

│ England, │ │ 3,972│ 626│ 6.3│24 × 25 │102.86│

│Thames & Medway,│Chalk │ │ │ │ │ │

│ Eng’d, │ │11,880│ 939│ 12.6│30 × 38⅔│ 45.59│

│Box, England, │Marble, │ │ │ │ │ │

│ │ freestone │ │ │ │ │ │

│ │ and marl │ 9,680│1,252│ 7.7│35 × 39 │148.15│

│Harecastle, │Rock and sand │ │ │ │ │ │

│ England, │ │ 8,778│ 939│ 9.3│14 × 16 │ 57.05│

│Nochistongo, │Clay and marl │ │ │ │ │ │

│ Mexico, │ │21,659│ 287│ 75.4│13¾ × 11½│ ——│

│Blisworth, │Rock and clay │ │ │ │ │ │

│ England, │ │ 9,240│2,191│ 4.2│16½ × 18 │ 23.18│

│Sapperton, │Rock │ │ │ │ │ │

│ England, │ │12,900│1,878│ 6.9│15 × 15 │ 12.44│

│Black Rock, U. │Greywacke │ │ │ │ │ │

│ S. │ slate │ 1,932│ ——│ ——│19 × 17¼│ 77.18│

│Blaisy, France, │Chalk and clay│13,455│1,043│ 12.9│26¼ × 26¼│136.06│

│Edge Hill, │Clay & │ │ │ │ │ │

│ England, │ freestone │ 6,600│ ——│ ——│22 × 16 │ 30.15│

│Littlebourg, │—— │ │ │ │ │ │

│ England, │ │ 8,607│ 590│ 14.6│27½ × 24 │129.61│

│Woodhead, │Millstone │ │ │ │ │ │

│ England, │ │15,840│1,800│ 8.8│ —— │ ——│

└────────────────┴──────────────┴──────┴─────┴───────┴─────────┴──────┘

The cost per cubic yard for excavating tunnels in some places has been

as follows:—

Name. Material. Cost per cubic yard.

Blackrock, U. S. hard greywacke slate, $6.60

Lehigh, U. S. very hard granite, 4.36

Schuylkill, U. S. slate, 2.00

Union, U. S. slate, 2.08½

Blue Ridge, U. S. ——, 4.00

The Blue Ridge tunnel on the Virginia Central Railroad is 4,280 feet

long, made for a single track, 21 × 15 feet. Lining about four feet

thick. Excavation where lining is used is 26 × 23.

The Hoosac tunnel (Massachusetts) is proposed to be four and one half

miles long, 23 × 22 feet section. To have two shafts eight hundred and

fifty and seven hundred and fifty feet deep, and ten feet in diameter.

Artificial ventilation becomes necessary in headings over four hundred

and fifty or five hundred feet in length.

The cost of the shafts of the Blechingly tunnel, (England,) ninety-seven

feet deep, and ten and one half feet in diameter, cut through blue clay,

and lined, was $68.44 per yard down.

The shafts of the Blaisy tunnel average five hundred feet deep, through

clay and chalk and loose earth, (being lined,) cost $139.11 per yard

down.

The shafts of the Black Rock tunnel, one hundred and thirty-nine feet

deep, in hard slate, cost $18.72 per cubic yard.

CHAPTER VIII.

WOODEN BRIDGES.

139. Wooden bridging, owing to its cheapness and fitness for universal

application, has been and is being adopted in all parts of the country.

Almost any variety of form may be seen upon our railroads, and though

less durable than stone or iron, it may with proper precaution be made

to last a long time.

OF THE FORCES AT WORK IN BRIDGES.

140. There are four distinct strains to which a piece of timber or a bar

of metal may be exposed, each of which tends to destroy the piece in a

different manner. The amount and character of these strains, depend upon

the position of the bar or beam, and upon the direction of the force.

A beam may be pulled apart by stretching,—_Tension_.

It may be destroyed by crushing,—_Compression_.

It may be broken transversely,—_Cross strain_.

It may be crushed across the grain,—_Detrusion_.

TENSION.

141. If one thousand pounds were hung from the end of a suspended

timber, so that the direction of the weight coincides with the axis of

the timber, then will the tension upon the beam be one thousand pounds.

If the direction of the force is vertical, and the beam is inclined,

then the strain is increased by as much as the diagonal of inclination

exceeds the vertical; for example, let one thousand pounds be suspended

from the lower end of a beam ten feet long, inclined at an angle of 45°.

The diagonal being ten, the vertical will be 7.07 feet, and the strain

is increased as follows:—

7.07 to 10 as 1,000 to 1,414 lbs.

As the angle of inclination, from the horizontal, increases, the strain

from a given load decreases, until the beam is vertical, when a weight

acts with its least power.

COMPRESSION.

142. If a vertical post is loaded with one thousand pounds, the

compressive strain upon that post will also be one thousand pounds. If a

post is inclined, the amount of strain is increased, as noticed in the

case of tension, and to the same amount, that is, depending upon the

inclination.

A piece of wood or metal acting as a post, or pillar, must not only be

able to resist crushing, but also bending or bulging laterally.

143. A cylinder of which the length is only seven or eight times the

diameter, will not bulge by any force that can be applied to it

longitudinally, but will split. When the length exceeds this, it will be

destroyed by a similar movement to that produced by a cross strain. When

the length of a cast-iron pillar is thirty diameters, the fracture is

produced by bending alone; when less, partly by bending and partly by

fracture. When the column is cast hollow, and enlarged towards the

middle, the strength is increased in a very great ratio.

144. The formula for finding the weight which any beam acting as a post,

will support before bending, is, according to Barlow, who considers the

weight as varying inversely as the length, as follows:—

(_WL^2_)/(80_E_) = _bd^3_,

and the value of _W_ is

(_bd^3_ × 80_E_)/(_L^2_),

and the weight being given, and the sectional dimensions assumed, we

have

_d_ = ∛((_WL^2_)/(80_Eb_)),

and

_b_ = (_WL^2_)/(80_Ed^3_),

Where _W_ represents the weight in pounds,

_L_ represents the length in feet,

_E_ represents a constant,

_d_ represents the depth in inches,

_b_ represents the breadth in inches.

CROSS STRAIN.

145. The amount of strain caused by any weight applied in a transverse

direction, to a beam supported at both ends, is as the breadth, as the

length inversely, and as the square of the depth. Whatever depression

takes place, tends to shorten the upper, and to extend the under-side;

whence the fibres of the top part suffer compression, and those of the

bottom extension. The amounts of compression and extension must of

course be equal, and therefore if any material resists these two strains

in a different degree, the number of fibres opposing each will also be

different.

The top being compressed, while the bottom is extended, of course at

some point within the beam there exists a line which suffers neither

compression nor extension. The position of this line (the neutral axis)

depends upon the relative power of the material to oppose the strains,

upon its form and upon its position. Thus if wood resists two thousand

pounds per square inch of extension, and one thousand pounds of

compression, the axis will be twice as far from the top as from the

bottom.

In some materials the neutral axis changes its place while the bar is at

work; thus wrought iron, after being a little compressed, will bear a

great deal more compression than when in its original state; also the

lower fibres, after being extended, will resist less than at first; the

effect of which two actions is to move the neutral axis up.

146. The following table shows the relative resisting powers of wood,

wrought and cast-iron; with the corresponding positions of the axis,

with sufficient accuracy for practice.

Distance of axis

Material. Resistance to Resistance to Ratio. from top, in

extension. compression. fractions of the

depth.

Wrought iron, 90 66 90/66 90/156 or 0.58

Cast-iron, 20 111 20/111 20/131 or 0.15

Wood, 2 1 2/1 ⅔ or 0.66

Thus in beams subjected to a cross strain, as well as to a direct

extensile or compressive one, the resistance is effected by the

incompressibility and inextensibility of the material.

147. The formula for dimensioning any beam to support a given weight

transversely is

_S_ = (4_bd^2_)/_e_,

Where _S_ represents the ultimate strength in lbs.

_b_ represents the breadth in inches,

_d_ represents the depth in inches,

_e_ represents the length in inches,

DETRUSION.

148. Detrusion, or crushing across a fixed point, is such as occurs

wherever a brace abuts against a chord, or where a bridge bears upon a

bolster or wall plate; also the shearing of bolts, pins, and rivets.

GENERAL RESISTANCE OF MATERIALS.

149. The resistance to extension, to compression, (as regards simple

crushing,) and to detrusion, is as the area of cross section; i. e., if

we double the area, we double the strength. The resistance to a cross

strain is _as the breadth_, _as the length inversely_, and _as the

square of the depth_; i. e. if we double the breadth we double the

strength; if we double the length, we divide the strength by two; and if

we double the depth, we multiply the strength by four.

ACTUAL STRENGTH OF MATERIALS.

150. Any material will bear a much larger load for a short time than for

a long one. The weight that does not so injure materials as to render

them unsafe, is from one third to one fourth only of the ultimate

strength. Throughout the present work one fourth will be the most that

will in any case be used.

WROUGHT IRON.

151. _Extension._

lbs. per square inch.

Mean of 17 experiments by Barlow (p. 270) 62,720

Weisbach’s Mechanics (Vol. ii., p. 71) 60,500

Overman’s Mechanics, (p. 408, 409) 61,333

Brown, Rennie, and Telford, (mean) 65,251

——————

The mean 62,451

——————

Reducing by 4 for safety 15,613

Or in round numbers 15,000 lbs. per square inch, is the resistance of

wrought iron to extension, to be used in practice.

152. _Compression._—Great discrepancies appear among writers on the

strength of materials, as to the compressive strength of wrought iron.

Though all estimate the resistance to compression, as great as to

extension, yet no one in summing up the general result of experiment,

places the former at more than from 50 to 75 per cent. of the latter.

William Fairbairn gives, as the relative resistances to extension and

compression in bars applied as girders, 2 to 1.

We have by Weisbach 56,000

We have by Rondelet 70,000

We have by Hodgkinson 65,000

——————

The mean 63,667

——————

Reducing by 4 15,917

——————

In round numbers 16,000 lbs. per square inch.

As far as practice is any guide, from 8,000 to 12,000 pounds per inch is

the most to be used. The ratio of 90 to 66, seems to express very nearly

the action as in the most reliable structures; which will, therefore, be

adopted, or 11,000 pounds per square inch nearly. The resistance to

compression is very much greater after wrought iron has been somewhat

compressed.

CAST-IRON.

153. _Extension._—This material is seldom used to resist a tensile

force. That the tables may be complete, however, the following is

given:—

By Weisbach 20,000 pounds.

By Barlow 18,233 pounds.

By Overman 20,000 pounds.

By Rennie 18,000 pounds.

By Hodgkinson 16,577 pounds.

By the British Iron Commission 15,711 pounds.

——————

The mean 18,087 pounds.

——————

Reducing by 4 4,522 pounds.

——————

In round numbers 4,500 pounds.

154. _Compression._

By Weisbach 109,800 pounds.

By Hodgkinson 107,520 pounds.

By Iron Commission 100,000 pounds.

Stirling’s toughened 130,000 pounds.

———————

Mean of Common 105,773 pounds.

———————

Mean of Stirling’s 130,000 pounds.

———————

Reducing by 4 for safety (Common) 26,443 pounds.

———————

Reducing by 4 for safety (Stirling’s) 32,500 pounds.

———————

In round numbers (Common) 25,000 pounds.

———————

In round numbers (Stirling’s) 30,000 pounds.

155. Following are given the condensed results of the preceding figures,

which may be relied upon as giving perfectly safe dimensions in

practice.

Wrought Iron. Cast-Iron.

15,000 4,500 Tensile strength,

11,000 25,000 Compressive strength.

For additional remarks on iron, see chap. IX.

156. _Nature and Strength of American Woods._

Name of the Weight per Resistance Resistance Value of

wood. cubic foot. to to _S_. Elasticity.

Extension. Compression.

White Pine 26 12,000 6,000 1,229 ——

Yellow Pine 31 12,000 6,000 1,185 ——

Pitch Pine 46 12,000 6,000 1,727 4,900

Red Pine 35 12,000 6,000 1,527 7,359

Virginia Pine 37 12,000 6,000 1,456 ——

Spruce 48 12,000 6,000 1,036 ——

Larch 33 12,000 6,000 907 2,465

Tamarack 26 12,000 6,000 907 ——

White Cedar 22 8,000 4,000 766 ——

Canada Balsam 34 12,000 6,000 1,123 ——

White Oak 48 15,000 7,500 1,743 8,595

Red Oak 41 15,000 7,600 1,687 ——

Live Oak 72 15,000 7,200 1,862 ——

White Beech 44 18,000 9,100 1,380 5,417

Red Beech 48 18,000 9,000 1,739 ——

Birch 44 15,000 7,000 1,928 ——

Black Birch 41 15,000 7,200 2,061 ——

Yellow Birch 36 15,000 7,200 1,335 ——

Ash 38 16,000 8,100 1,795 6,581

Black Ash 35 16,000 8,000 861 ——

Swamp Ash 57 16,000 8,000 1,165 ——

Hickory 51 15,000 7,200 2,129 ——

Butternut 54 15,000 7,600 1,465 ——

Ironwood 54 16,000 8,100 1,800 ——

Rock Elm 45 16,000 8,011 1,970 2,799

The mean tensile strength of wood is 14,080 lbs.

Reducing by 4 for safety 3,520 lbs.

Reducing for want of seasoning 2,000 lbs.

The reduced mean compressive strength 1,000 lbs.

Reduced resistance to detrusion 150 lbs.

Ratio of tensile to compressive strength 2 to 1.

Mean value of _S_ in formula (_WL_ = 4_Sbd^2_) for the

woods most used in practice 1,250.

157. The lateral adhesion of fir was found, by Barlow, to be six hundred

pounds per square inch. (Lateral adhesion is the resistance which the

fibres offer to sliding past each other in the direction of the grain;

as, in pulling off the top of a post where it is halved on to the

chord.)

158. As regards the nature of timber, seasoning, time of cutting, etc.,

although these are important items, still, generally, commercial

considerations outbalance all else. The most complete treatise on the

nature of woods, is “Du Hamel, _L′exploitation des bois_;” from which it

appears that the best oaks, elms, and other large trees, are the product

of good lands, rather dry than moist. They have a fine, clear bark, the

sap is thinner in proportion to the diameter of the trunk, the layers

are less thick, but more adherent the one to another; and more uniform

than those of trees growing on moist places. The grain of the latter may

look very fine and compact, but microscopic examination shows the pores

to be full of gluten.

The density of the same species of timber, in the same climate, but on

different soils, will vary as 7 to 5; and the strength, both before and

after seasoning, as 5 to 4.

In trees not beyond their prime, the density of the butt is to that of

the top, as 4 to 3; and of centre to circumference, as 7 to 5. After

maturity, the reverse occurs in both cases.

Oak, in seasoning, loses from ¼ to ⅓ of its weight; but its strength is

increased from 30 to 40 per cent.

GENERAL TABLE OF THE NATURE OF MATERIALS.

159. _The tensile strength of wrought iron assumed as 1,000._

Weight Sum divided

Material. Tension. Compression. Cross Sum. per by weight

Strain. cubic per cub.

ft. ft.

Cast-Iron 300 1,666 31.68 1,997.68 450 4.4

Wrought Iron 1,000 733 55.40 1,788.40 480 3.7

Wood 133 66 5.60 204.60 30 6.8

The advantage possessed by iron over wood, is in durability only. The

above figures show how much more of the strength of the material is

consumed by its own weight in iron than in wood. In actual practice,

however, the method of making joints and other details often render iron

the lightest material.

RULES FOR PRACTICE.

TENSION.

160. The tensile strength of any material, is expressed by the formula

_T_ = _Sa_,

Where _T_ represents the whole strength,

_S_ represents the strength per square inch,

_a_ represents the area of section in inches.

whence the necessary area of section of any material to resist a tensile

strain, is found by the following rules:—

Wrought Iron

_a_ = _W_/15,000,

Cast-Iron

_a_ = _W_/4,500,

Wood

_a_ = _W_/2,000.

COMPRESSION.

161. Wrought Iron

_a_ = _W_/12,000,

Cast-Iron

_a_ = _W_/25,000,

Wood

_a_ = _W_/1,000.

CROSS STRAIN.

162. The power of any material to resist a cross strain, is shown by the

formula

_W_ = (4_sbd_^2)/_L_,

Where _W_ represents the breaking weight in pounds,

_s_ represents the constant in the table of woods,

_b_ represents the breadth in inches,

_d_ represents the depth in inches,

and _L_ represents the length in inches,

and to reduce the load to one fourth of the breaking weight

_W_ = (4_sbd_^2)/(4_L_),

and finally, by substituting for 4_s_, 4 × 1,250, (1,250 of the table of

woods,) we have

_W_ = (5000_bd_^2)/(4_L_).

Also, knowing the weight to be supported, and requiring the dimensions,

we take out the values of _d_ and _b_, and have

_d_ = √((_W_ × 4_L_)/(5000_b_)) = the depth,

_b_ = (_W_ × 4_L_)/(5000_d_^2) = the breadth.

As an example of the use of the formula, take the following:—

Let the span, or length, be 20 feet,

The breadth 12 inches, and depth 18,

required the load.

The formula

_W_ = (5000_bd_^2)/(4_L_)

becomes

_W_ = (5000 × 12 × 18^2)/4 × 240 = 20,250 lbs.

Again, the weight to be supported being 15,000 lbs., length 30 feet,

breadth 16 inches, the formula for the depth becomes

_d_ = √((15000 × 1440)/(5000 × 16)) = √(270) = 16 inches,

also,

_b_ = (15000 × 1440)/(5000 × 256) = 21600000/1280000 = 16 inches.

CAST-IRON.

163. The formula, expressive of the strength of a cast-iron beam, is

850_bd_^2 = _WL_,

from which we have

_b_ = (_LW_)/(850_d_^2) = the breadth,

and _d_ = √((_L_ × _W_)/(850_b_)) = the depth.

WROUGHT IRON.

164.

952_bd_^2 = _WL_,

whence

_b_ = (_WL_)/(700_d_^2) = the breadth,

and _d_ = √((_LW_)/(700_b_)) the depth.

[Illustration: Fig. 60.]

165. Mr. Hodgekinson found, that by arranging the material in a

cast-iron beam, as in fig. 60, that the resistance per unit of section

was increased over that of a simple rectangular beam, in the ratio of 40

to 23. He makes the general proportion of such girders as follows:—

Length 16

Height 1

Area of top flange 1.0

Area of lower flange 6.1

In this consummate disposition of material, the areas of top and bottom

flanges are made inversely proportional to the power of cast-iron to

resist compression and extension.

166. Mr. Fairbairn found, that in wrought iron flanged girders, (under

which come the various rails, chap. XIII.,) the top web should contain

double the area of the lower one. This agrees with the conclusion

adopted on page 129, as wrought iron resists more extension than

compression.

167. In cast-iron girders, on no account should there be introduced

webs, or openings of any kind, either from economic or ornamental

motives; as the uniformity of cooling is thereby very much opposed.

168. Mr. Hodgekinson gives, as the result of his experiments, the

following formula for dimensioning the cast-iron girder above referred

to.

_W_ = (26_ad_)/_L_,

Where _W_ is the breaking weight in tons,

_a_ the area of the bottom flange,

_d_ the depth of the girder in inches,

_L_ the length in inches.

As it is not considered safe to load a cast-iron beam with more than one

sixth of the breaking load, the formula may be expressed as follows:—

_W_ = (26_ad_)/6_L_,

for the weight in tons which may be safely borne, and transforming

_a_ = (6_WL_)/26_d_

for the area of the lower flange.

_Example._—Required the dimensions of a cast-iron beam, of Mr.

Hodgekinson’s form, for a span of thirty feet, to support a load of ten

tons at the centre.

Span 30 feet, Whence—

Length 34 feet, Length 34 feet,

Load 10 tons at centre. Span 30 feet,

Depth 25½ inches,

Lower flange 32.58 square inches,

Upper flange 5.34 square inches,

_a_ = (6 × 10 × 12 × 30)/(26 × (34 × 12)/16) = 32.58

and 32.58/6.1 = 5.34.

and the area of the top flange will be

36/6 = 6,

whence the following dimensions:—

Length 30 feet,

Depth 23 inches,

Lower flange 36 square inches,

Upper flange 6 square inches,

OF POSTS.

169. A post may be very well able to resist the compressive strain

thrown upon it by any load, but may bulge, or bend, laterally.

The formula by which beams are dimensioned for this requirement, changes

with the material, and with the form of section. For rectangular posts

of wood, we have the formula below.

_W_ = (2240_bd_^3)/(_L_2),

Where _W_ represents the weight in lbs., which may be safely borne,

_b_ represents the breadth in inches,

_d_ represents the depth in inches,

and _L_ represents the length in feet.

170. The value of the formula for the strength of cast-iron posts, seems

to depend more upon the authority consulted than upon the nature of

iron. For example, assume the length of a post as twenty feet, and the

diameter as ten inches; the load which may be safely borne is, according

to six different authorities, as follows:—

_A_ 4,000,000

_B_ 181,100

_C_ 370,000

_D_ 940,000

_E_ 307,242

_F_ 300,000

and assuming the length as ten feet, and diameter as ten inches, we have

_A_ 8,007,500

_B_ 204,500

_C_ 1,442,500

_D_ 3,640,000

_E_ 1,170,000

_F_ 600,000

showing not only a great difference in the unit resistance taken, but

also in the effect of the ratio between the length and diameter.

Such being the discrepancy, there will be given no formula; but in place

of such, the table following, which is calculated from the rules least

opposed to experimental evidence.

┌─────────────────────────────────────────────────────────────────────┐

│ TABLE SHOWING THE LOAD IN POUNDS SAFELY BORNE BY CAST-IRON COLUMNS. │

├─────────────────────────────────────────────────────────────────────┤

│ HOLLOW CYLINDERS. │

├──────┬──────────────────────────────────────────────────────────────┤

│Diame-│ Length or height in feet. │

│ter in│ │

│inches│ │

├──────┼──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┤

│ │ 6 │ 8 │ 10 │ 12 │ 15 │ 18 │ 20 │ 22 │ 24 │

├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤

│ 2│ 6000│ 5000│ 4000│ 3000│ 2500│ 1800│ 1500│ 1300│ 1100│

│ 3│ 16000│ 14000│ 13000│ 11000│ 9000│ 7000│ 6000│ 5000│ 5000│

│ 4│ 30000│ 29000│ 26000│ 24000│ 22000│ 18000│ 16000│ 14000│ 13000│

│ 5│ 50000│ 37000│ 45000│ 42000│ 39000│ 37000│ 31000│ 28000│ 26000│

│ 6│ 59000│ 57000│ 55000│ 52000│ 49000│ 44000│ 41000│ 38000│ 36000│

│ 7│101000│ 99000│ 96000│ 92000│ 88000│ 81000│ 76000│ 72000│ 68000│

│ 8│131000│129000│126000│122000│118000│109000│105000│100000│ 96000│

│ 9│169000│167000│164000│160000│156000│146000│141000│136000│131000│

│ 10│210000│200000│200000│200000│190000│180000│180000│170000│170000│

│ 11│250000│250000│240000│240000│240000│230000│220000│220000│210000│

│ 12│300000│300000│290000│290000│290000│270000│270000│260000│260000│

│ 14│450000│430000│410000│380000│370000│350000│330000│320000│300000│

│ 16│520000│500000│480000│460000│440000│420000│400000│370000│350000│

│ 18│650000│630000│610000│590000│560000│520000│470000│430000│400000│

│ 20│800000│760000│740000│690000│650000│590000│540000│490000│450000│

├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤

│Diame-│ 6 │ 8 │ 10 │ 12 │ 15 │ 18 │ 20 │ 22 │ 24 │

│ter in│ │ │ │ │ │ │ │ │ │

│inches│ │ │ │ │ │ │ │ │ │

├──────┼──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┤

│ │ Length or height in feet. │

└──────┴──────────────────────────────────────────────────────────────┘

┌─────────────────────────────────────────────────────────────────────┐

│ TABLE SHOWING THE LOAD IN POUNDS SAFELY BORNE BY CAST-IRON COLUMNS. │

├─────────────────────────────────────────────────────────────────────┤

│ H AND + SECTIONS. │

├──────┬──────────────────────────────────────────────────────────────┤

│Metal │ Length or height in feet. │

│thick-│ │

│ness. │ │

├──────┼──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┤

│ │ 6 │ 8 │ 10 │ 12 │ 15 │ 18 │ 20 │ 22 │ 24 │

├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤

│ ¼│ 4000│ 3000│ 2400│ 1800│ 1400│ 1100│ 1000│ 900│ 800│

│ ⅜│ 12000│ 11000│ 10000│ 9000│ 8000│ 7000│ 5000│ 4000│ 3000│

│ ½│ 25000│ 23000│ 21000│ 18000│ 16000│ 13000│ 12000│ 9000│ 6000│

│ ⅝│ 36000│ 34000│ 31000│ 28000│ 25000│ 23000│ 21000│ 20000│ 18000│

│ ¾│ 40000│ 38000│ 37000│ 36000│ 35000│ 34000│ 32000│ 30000│ 28000│

│ 13/16│ 60000│ 59000│ 58000│ 57000│ 56000│ 54000│ 53000│ 51000│ 49000│

│ ⅞│100000│ 98000│ 96000│ 94000│ 91000│ 88000│ 83000│ 78000│ 70000│

│ 1│140000│130000│126000│120000│114000│110000│106000│100000│ 90000│

│ 1⅛│190000│180000│170000│160000│150000│140000│130000│125000│120000│

│ 1¼│230000│220000│210000│200000│190000│180000│170000│160000│150000│

│ 1½│280000│260000│250000│240000│230000│220000│200000│190000│180000│

│ 1¾│360000│320000│310000│300000│290000│280000│270000│260000│240000│

│ 2│460000│430000│400000│370000│350000│330000│310000│300000│280000│

│ 2½│560000│530000│510000│480000│440000│410000│380000│350000│330000│

│ 3│600000│580000│550000│520000│500000│460000│430000│400000│380000│

├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤

│Metal │ 6 │ 8 │ 10 │ 12 │ 15 │ 18 │ 20 │ 22 │ 24 │

│thick-│ │ │ │ │ │ │ │ │ │

│ness. │ │ │ │ │ │ │ │ │ │

├──────┼──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┤

│ │ Length or height in feet. │

└──────┴──────────────────────────────────────────────────────────────┘

OF THE TRUSS.

171. The most simple bridge that could be built, consists of a single

piece of timber placed across the opening to be spanned. This form is

applicable to spans under twenty feet. The proper dimensions are found

by the formula:—

_d_ = √((4_wL_)/(5000_b_)) = the depth.

_Example._—The depth of a beam of twenty feet span, and twelve inches

wide, to support a load of twenty thousand two hundred and fifty lbs. is

_d_ = √((4 × 20,250 × 20 × 12)/(5000 × 12)) = 18 inches.

A beam 12 × 18, and of 20 feet span, will therefore bear safely a load

of 20,250 lbs., applied at the centre.

In this manner is formed the following table, giving the scantling of

sticks for railroad stringer bridges, of twenty feet span and under.

Span. Breadth. Depth.

5 12 12

10 12 13

12 12 15

15 12 18

18 12 20

20 12 21 inches.

The first scantlings exceed the requirement of the rule, but are none

too large to resist the shocks to which such sticks are exposed.

Cross-ties of plank, 2 or 3 by 6 or 8 inches, and plank braces

underneath, (as shown in the fig. at the end of chapter VIII.,) should

be bolted to the main timbers; the same bolt passing through the tie

beam and plank. The longitudinal pieces should be firmly notched and

bolted to the wall-plates, and these latter either built in or scribed

on to the masonry.

[Illustration: Fig. 61.]

172. For a span of from 20 to 50 feet, we may use the combination shown

in fig. 61. The piece A B, must be so strong as not to yield between A

and D, or D and B. The pieces C E must be stiff enough to resist the

load coming upon them which is as follows. A locomotive engine of the

heaviest class will not exceed fifty tons weight, each pair of driving

wheels will support ten tons, and on each side five tons, 2240 × 5 =

11,200 lbs.; or to allow for shocks and extra strains, 15,000 lbs. Each

brace, then, must support seven thousand five hundred pounds, which for

compression simply would require only seven and one half square inches

of sectional area; but the brace being inclined, the strain is increased

as follows:—

A E to E C as 7,500 to X.

And A E being ten feet, and A D fifteen feet, E C becomes eighteen feet,

whence

10 to 18 as 7,500 to 13,500 lbs.;

which would require only thirteen and one half inches for compression,

or a piece 4 × 3½. But is this enough for flexure?

On page 124 the load which may be safely borne, by a rectangular post of

wood, is shown by the formula

_W_ = (2240_bd^3_)/(_L^2_).

Substituting for _b_ and _d_, the dimensions 4 × 4, we have

_W_ = (2240 × 4 × 4^3)/(18^2), or 573,440/324, = 1,770,

which is evidently too small.

Placing 6 × 7, for _b_ × _d_, we have

_W_ = (2240 × 6 × 7^3)/(18^2) = 14,227;

exceeding by a small amount the requirement.

[Illustration: Fig. 62.]

173. It is evidently immaterial whether we _support_ the point D _upon_

C, or _suspend_ it as in fig. 62, provided we prevent any motion in the

feet of the inclines A _c_ B _c_. Abutting them against A B, throws a

tension against A B, found as follows:—

Representing by _c_ D, the applied weight, draw D E parallel to _c_ B;

also E _f_ parallel to A B; E _f_ is the tension. The graphic

construction gives results near enough for practice. Rigorously we have

A _c_ D, similar to E _c_ _f_;

also,

A _c_, to E _c_, as A D, to E _f_;

and

E_f_ = (E_c_ × AD)/(A_c_).

When _a d_ and _c d_ are differently inclined, proceed as follows. See

fig. 102, p. 200 inverted.

[Illustration: Fig. 63.]

Let _d b_ represent the weight; _e h_ shows the tension. The triangles

_a c d_, and _a b e_, are similar; as also _e b h_ and _d b c_; whence

_b e_ = (_a b_, _c d_)/(_a c_), and _e h_ = (_c b_, _b e_)/(_d c_) =

tension.

In practice place _w_ for _b d_; i. e. the actual weight.

In this plan, if the chord is able to resist the cross strain between A

and D, it will also resist the tension. This cross strain is found by

the formula already given and illustrated.

174. From what precedes, we have the following dimensions for bridges

such as are shown in figs. 61 and 62. The details of 62, at _f_ and _c_,

and at E, 61, are shown in figs. 62 A, 62 B, and 61 C.

[Illustration: Fig. 62 A.]

[Illustration: Fig. 62 B.]

[Illustration: Fig. 62 C.]

Span. Rise. A B. C E. Rod _b_.

20 8 12 × 12 (5 × 8)—2 1¼ inches.

25 10 12 × 15 (5 × 9)—2 1⅜ inches.

30 12 12 × 18 (5 × 10)—2 1½ inches.

35 13 12 × 20 (5 × 10)—2 1⅝ inches.

40 14 14 × 21 (5 × 12)—2 1⅝ inches.

45 15 14 × 22 (6 × 12)—2 1¾ inches.

50 16 14 × 24 (6 × 12)—2 1¾ inches.

The braces, (column 4,) being in pairs and blocked together. In spans

exceeding twenty-five feet, the braces _d f_, and the rods _f g_, should

never be omitted. The size of the rod _g f_, is found by considering A,

_d_, _f_, as a small bridge.

175. In all light bridges, like the one under consideration, all parts

should be _fastened_ by bolts, to prevent springing by reaction. A

bridge with but little inertia, or dead weight, tends to jump up when

the engine has passed over it. _Fastening_ takes the place of _weight_

in a large span.

As soon as the rise admits, the points C, on each side of the bridge,

should be connected to resist lateral motion. When the height is not

enough for this, the same points may be joined to a floor beam extended

out beyond the truss.

Though the dimensions are given for this plan up to fifty feet span, it

is very seldom advisable to go beyond twenty-five or thirty feet; as

frames consisting of a few long timbers are not so rigid, and free from

vibration, as those made of a greater number of short pieces.

176. In extending this system one hundred or two hundred feet, we see at

once that the pieces A _c_, B _c_, would become very long and would need

to be made large and heavy. We should always so proportion any beam in a

bridge that it is at once able to resist all of the several strains to

which it may be exposed, without being unnecessarily large.

As to compression, the above system might be extended to almost any

amount; but the braces would yield by flexure.

Instead of producing the braces A _c_, A′ _c′_, fig. 64, to their

intersection, we stop at _c_ and _c′_, insert _c c′_; to prevent the

approach of these points, suspend the points B and B′ from _c_ and _c′_,

and commence again with the braces B D, B′ D; and so on as far as

necessary.

To prevent the backward motion of the points B, and B′, either the chord

A A′, or the counter-braces _m_, _m_, are necessary.

[Illustration: Fig. 64.]

The pieces A _c_, A′_c′_ must support all of the load, including the

weight of the bridge, lying within the rectangle B _c_, B′ _c′_. The

next set of braces must sustain that part of the load only which comes

over the centre of the bridge. Thus the braces should decrease in size

as the centre is approached. The rods _c_ B, _c′_ B′, must resist a

tension equal in amount to the pressure on the braces, only being

vertical they do not need the increase given to the braces on account of

their inclination.

177. There is another method of stiffening a beam, as shown in figs. 65

and 66, by trussing rods, and a post. The dimensions being the same, the

forces in both cases will be equal. The second, fig. 66, leaves the

passage beneath the bridge clear.

[Illustration: Fig. 65.]

The tension on the rods A _c_, B _c_, fig. 66, tends to draw the points

A and B together, an effort which is resisted by the top chord A B.

In extending this system, as in art. 176, the rods become either very

long, or very large, from the small angle of inclination; evils which

remedied as before, by supporting the post _c_ B, fig. 64, from the foot

of the first rod, fig. 64, and commencing again from _c_.

[Illustration: Fig. 66.]

To prevent the motion of the triangle _c_ B G, fig. 64, about the angle

B, we must introduce either the upper chord _c c′_, or the counter rod

_c_ A. If the lower chord is omitted the rod D B must be of the same

size as E B. In this truss, either the top or the lower chord simply may

theoretically be omitted, due allowance being made in the size of the

rods. In practice it is never advisable to omit either, as both are

required for lateral bracing, and for support of the road-way.

Having said thus much of the general ideas that apply to all bridges,

let us now look at some of the plans most in use; and to become familiar

with the subject, work out the dimensions of an example of each kind.

178. As rods, nuts, and washers are used in all bridges, the following

table may not be out of place:—

Column 1 gives the diameter of rod.

Column 2 strength at 15,000 lbs. per square inch.

Column 3 the weight per lineal foot.

Column 4 side of the square nut.

Column 5 the thickness of the same.

Column 6 the dimensions of washers.

Column 7 the thickness of washers.

Column 8 breadth (side to side) six-sided nut.

Column 9 breadth (across angles) six-sided nut.

Column 10 thickness of six-sided nut.

Column 11 number of screw threads per inch.

Column 12 gives the diameter of rod.

┌─────────┬────────┬──────┬──────┬──────────┬───────┐

│ 1 │ 2 │ 3 │ 4 │ 5 │ 6 │

│Diameter.│Strength│Weight│Square│Thickness.│Square │

│ │of Rod. │ per │ Nut. │ │ of │

│ │ │Foot. │ │ │Washer.│

├─────────┼────────┼──────┼──────┼──────────┼───────┤

│ ½│ 2,940│ 0.66│ 1¼│ ¾│ 2½│

│ ¾│ 6,630│ 1.49│ 1½│ ⅞│ 3│

│ 1│ 11,775│ 2.65│ 2│ 1│ 4│

│ 1⅛│ 14,910│ 3.36│ 2│ 1⅛│ 4½│

│ 1¼│ 18,405│ 4.17│ 2¼│ 1¼│ 5│

│ 1⅜│ 22,260│ 5.02│ 2½│ 1⅜│ 5½│

│ 1½│ 26,505│ 5.97│ 2¾│ 1½│ 6│

│ 1⅝│ 31,095│ 7.01│ 2⅞│ 1⅝│ 6½│

│ 1¾│ 36,075│ 8.13│ 3│ 1¾│ 7│

│ 1⅞│ 41,415│ 9.33│ 3¼│ 1⅞│ 7½│

│ 2│ 47,130│ 10.62│ 3½│ 1⅞│ 8│

│ 2⅛│ 53,190│ 12.00│ 3¾│ 2│ 8½│

│ 2¼│ 59,640│ 13.40│ 4│ 2⅛│ 9│

│ 2⅜│ 66,450│ 15.00│ 4⅛│ 2¼│ 9½│

│ 2½│ 73,620│ 16.70│ 4¼│ 2½│ 10│

├─────────┼────────┼──────┼──────┼──────────┼───────┤

│ 1 │ 2 │ 3 │ 4 │ 5 │ 6 │

└─────────┴────────┴──────┴──────┴──────────┴───────┘

┌─────────┬───────┬─────┬──────┬──────┬──────┬─────────┐

│ 1 │ 7 │ 8 │ 9 │ 10 │ 11 │ 12 │

│Diameter.│ Top │Six- │ Six- │ Six- │Screw.│Diameter.│

│ │Washer.│Sided│Sided │Sided │ │ │

│ │ │Nut. │ Nut. │ Nut. │ │ │

├─────────┼───────┼─────┼──────┼──────┼──────┼─────────┤

│ ½│ ¼│ 1⅜│ 1½│ 9/16│ 12│ ½│

│ ¾│ ¼│ 1¾│ 2│ ⅞│ 10│ ¾│

│ 1│ ⅜│ 1⅞│ 2¼│ 1⅛│ 8│ 1│

│ 1⅛│ ⅜│ 2⅛│ 27/16│ 1¼│ 7│ 1⅛│

│ 1¼│ ½│ 2¼│211/16│ 17/12│ 7│ 1¼│

│ 1⅜│ ½│ 2½│ 2⅞│ 17/16│ 6│ 1⅜│

│ 1½│ ½│ 2⅝│ 3⅛│111/16│ 6│ 1½│

│ 1⅝│ ⅝│ 2⅞│ 35/16│113/16│ 5│ 1⅝│

│ 1¾│ ⅝│ 3│ 3½│ 2│ 5│ 1¾│

│ 1⅞│ ⅝│ 3¼│ 3¾│ 2⅛│ 4½│ 1⅞│

│ 2│ ⅝│ 3½│ 4│ 2¼│ 4½│ 2│

│ 2⅛│ ¾│ 3⅝│ 43/16│ 2⅜│ 4│ 2⅛│

│ 2¼│ ¾│ 3¾│ 46/16│ 2½│ 4│ 2¼│

│ 2⅜│ ¾│ 4│ 4⅝│ 2⅝│ 4│ 2⅜│

│ 2½│ ¾│ 4¼│ 4⅞│ 2¾│ 3½│ 2½│

├─────────┼───────┼─────┼──────┼──────┼──────┼─────────┤

│ 1 │ 7 │ 8 │ 9 │ 10 │ 11 │ 12 │

└─────────┴───────┴─────┴──────┴──────┴──────┴─────────┘

179. Let us now assume the following data:—

Span 200 feet,

Rise (centre to centre of chords) 25 feet,

Width 20 feet,

Length of panel 15 feet,

Weight (bridge and load) per lineal ft. 4,000 lbs.

HOWE’S BRIDGE.

Fig. 67.

[Illustration: Fig. 67.]

_Lower Chords._—The _tension_, at the centre of the lower chord, is

found _by dividing the product of the weight of the whole bridge and

load by the span_, by eight times the height, or

_T_ = (_W_ × _S_)/(8_h_),

which becomes, with the above data,

_T_ = (800000 × 200)/200 = 800,000 lbs.

Here the tension and the total weight are equal, a result which can

occur only when the rise is one eighth of the span. This is the best

ration between these dimensions, as then the horizontal and vertical

forces are equal.

As to the proportion of the _panel_, (or the rectangle inclosed by the

chords and any two adjacent posts,) the ratio of base to height should

be such as to make the inclination of diagonal about 50° from the

horizontal; if much less, the timbers become large and heavy; and if

more, the number of pieces is unnecessarily increased.

The braces at the end of a long span, may be nearer to the vertical than

those near the centre, as they have more work to do. If the end panel be

made twice as high as long, and the centre panel square, the

intermediates varying as their distance from the end, a good

architectural effect is produced.

To determine the size of the lower chords, to resist the above 800,000

pounds of tension, proceed as follows: Each side truss will support one

half of the whole load, or 400,000 pounds; which, at 2,000 pounds per

inch, will require 200 square inches of section. Four sticks of 8 × 12

inches, give an area of 384 square inches, which must be reduced as

follows: Deduct 72 square inches for the area cut out by the splicing

blocks, 40 inches for the bolts connecting the pieces, 28 inches for

inserting the foot blocks, and 10 inches for inserting the washer, and

we have remaining 234 square inches; which exceeds by a little the exact

demand. This excess (about one seventh) is a necessary allowance for

accidental strain, to which all bridges are subjected.

[Illustration: Fig. 67 A.]

The splices used in bridge framing are shown in fig. 67 A and fig. 67 B.

For the first, the depth of insertion and length of the block depend

upon the tension upon the chord. The following dimensions have been much

used and are perfectly reliable:—

Span of Bridge. A C B C C D

Feet. Feet. Inches. Feet.

50 1.00 1½ 1.50

100 1.25 2 2.00

150 1.75 2½ 2.25

200 2.00 3 2.75

There is no need of cutting more than one notch, as in the figure; the

resistance of the triangles is thereby lessened, and the work increased.

[Illustration: Fig. 67 B.]

In fig. 67 B, the rods must of course be able to resist the tension upon

the one piece which is cut.

_Upper Chord._—The upper chords of a bridge suffer compression, to the

same amount numerically, as the tension on the lower chord; as whatever

tension is thrown by any brace upon the lower chord, reacts as just so

much compression upon the upper. In the case at hand, 800,000 lbs. in

all, or 400,000 on each chord.

The resistance to compression being one thousand pounds per inch,

renders necessary four hundred inches of section to each chord; four

pieces 8 × 12 give in all three hundred and eighty-four inches of

section, which requires no reduction, as the whole chord pressing

together and being properly framed is not weakened by splicing. The

splicing blocks in the upper are merely plain pieces, inserted one half

inch, the only duty being to keep the sticks at the proper horizontal

distance.

The spaces between the pieces should be large enough to allow the rods

to pass without cutting the chords; (two inches answers every purpose).

The bolts for splicing, have no very great strain to bear. In small

spans from ½ to ⅝, and in large bridges from ⅝ to an inch is enough.

The object in framing a built beam for a bridge chord, is to make a

stick which shall be uniformly strong. This is done by cutting the

pieces in the centre of the panel, and by having no two joints in either

chord in one panel; though in long spans this cannot always be done.

Figs. 67 D and 67 E (page 153)

BRACES.

The whole load being 800,000 pounds,

Each truss supports 400,000 pounds,

Each set of braces 200,000 pounds,

Each brace (there being 4) 50,000 pounds,

which must be increased for inclination as follows: The length of

diagonal is twenty-nine feet, (the height being twenty-five and length

15,) whence

25 to 29 as 50,000 to 58,000 lbs.;

which would need fifty-eight square inches, or 7 × 8 for compression;

which, however, is quite too small for flexure. 12 × 12 placed in the

formula gives

_W_ = (2240 × _bd^3_)/(_L^2_),

or

_W_ = (2240 × 12 × 1728)/841 = 55,296 lbs.

In practice, smaller braces than 12 × 12 would answer, because the four

braces in a set may be fastened together, making a post of four pieces 8

× 12, or in all a built post of 44 × 12 inches; twelve being the depth,

whence

_W_ = (2240 × 44 × 1728)/841 = 202,511 lbs.;

the forty-four inches being made by blocking the braces four inches

apart. The second set of braces are to be treated in the same manner,

the weight to be supported being only the rectangle included by those

braces; i. e. the whole bridge and load less the two end panels.

As the centre of the span is approached, the pressure on the braces

becomes very small; and the scantling of the braces will be reduced to

about 6 × 7 inches.

RODS.

The weight upon the first set of rods is the same as that upon the end

sets of braces; in the present case 800000 ÷ 2 = 400000 on each side

truss, and 400000 ÷ 2 = 200000 on each end; and if there are five rods

in each set, each rod bears 40,000 lbs. Referring to the table on p.

146, opposite to 41,415 lbs., is the diameter 1⅞ inches; whence the

first set must contain five rods, of 1⅞ inches diameter. The second set

decrease in size as the weight is lessened by the two end panels. The

nut and washer for the rod are also found in the same table.

COUNTERBRACING.

180. When a load is placed on the point C′, fig. 64, the truss tends to

sink at that point, and a corresponding rise takes place at C. This

motion changes the figure A B C E, from a rectangle to an oblique angled

figure; the diagonal E B being shortened, and A C lengthened. This

motion is easily checked by the introduction of the counter brace E B.

[Illustration: Fig. 64.]

The action which this timber is called upon to resist, being caused by

the moving or variable load on one panel, the brace must resist the load

coming thereon, (say fifteen feet,) and is thus the same size as the

brace at the centre of the span.

The counter braces may be so confined between the braces, at the

intersection, as not to move laterally or vertically, but must not be

fastened to the braces; because the action of the separate timbers is

thus trammelled.

[Illustration: Fig. 67 C.]

The manner of adjusting the braces and counter braces to the chord is

shown in fig. 67 C. It was formerly the custom to abut the braces

against a block on one side of the chord, and to screw the rod against a

block on the opposite side; the whole strain acting to crush the chord

crosswise. This has been remedied by the arrangement shown in the

figure, the two blocks being cast in one piece and connected by a small

hollow cylinder passing between the chord sticks.

[Illustration: Fig. 67 D. Fig. 67 E.]

This system is known as Howe’s bridge, and may be seen in almost any

section of the country; and though in many cases badly proportioned, and

of bad material, if properly made answers a very good end.

The following table has been formed for the use of engineers and

builders, giving, together with the table of nuts and washers, all

dimensions required.

┌───────┬───────┬───────┬────────┬───────┬───────┬───────┬───────┐

│ Span. │ Rise. │Panel. │Chords. │ End │Centre │ End │Centre │

│ │ │ │ │braces.│braces.│ rod. │ rod. │

├───────┼───────┼───────┼────────┼───────┼───────┼───────┼───────┤

│ 50│ 10 │ 7│2—8 × 10│ 7^2│ 5 × 5 │2—1⅛ │ 2—1 │

│ 75│ 12 │ 9│2—8 × 10│ 8^2│ 5 × 5 │2—1½ │ 2—1 │

│ 100│ 15 │ 11│3—8 × 10│ 9^2│ 6 × 6 │2—1¾ │ 2—1 │

│ 150│ 20 │ 13│4—8 × 12│ 10^2│ 6 × 7 │3—2 │ 3—1 │

│ 200│ 25 │ 15│4—8 × 16│ 12^2│ 7 × 7 │5—2 │ 5—1 │

└───────┴───────┴───────┴────────┴───────┴───────┴───────┴───────┘