Colbert Shoals Canal. The average of the average thicknesses of these sections is found to be 36.6 per cent of the height for the land wall, and 33.8 per cent for the river wall. The Colbert Shoals Canal walls have been built up 42 feet higher with a thickness of 5 feet, which changes their average thickness from 42 per cent h to 34.3 per cent h. If we throw out the land section of Lock No. 2, Great Kanawha River, which is considerably heavier than any of the other sections taken, and take the new value for Colbert Shoals Canal, we have for the average thickness of land walls 35.4 per cent h.

If we average all the sections shown, we have for the land walls 36.4 per cent h, and for the river walls 36.3 per cent h, for the average thickness.

A rule for average thickness, however, should not be based on the average of a number of sections, but on the minimum, or average of the minimum sections. As the majority of the sections for both land and river walls have an average thickness of 35 per cent of their height, or less, we would be safe in making the average thickness for both land and river walls 35 per cent of their height.

In Rivieres Canalisees, by F. B. DeMas, it is found that the walls of two hundred locks of the Eastern Canal of France having battered backs, a height of 19 feet 614 inches, and an average thickness of nearly 35 per cent of the height above the floor, have given excellent results.

It may be of interest here to give the method employed by the writer for finding the stage of maximum pressure and moment on a wall subjected to varying stages of water on each side. In order to simplify the work the case of the dam for Lock B, Lower Cumberland River, will be taken.

It is assumed that there will be a fall of 3 feet over the dam at the epoch of submergence of the lock walls. Under this assumption, the lock having a guard of 15 feet, it is found that for each foot of rise on the dam there will be 1.84 feet rise in the lower pool above low water. Let h be the variable stage of the upper pool above the dam and H, equal to 1.84 h, the variable stage of the lower pool above low water. Taking a section of the dam 1 foot long, it is seen from Plate III that the areas of the trapezoids in square feet varying from ABE toward A C' D' E multiplied by 62.5 will give the varying pressures above the dam. Likewise, the varying areas to the right of A E multiplied by 62.5 will give

Plates I, II, and III were compiled by Mr. J. S. Walker, Assistant Engineer, under the direction of Maj. W. W. Harts, Corps of Engineers. The areas and mean thicknesses given are taken for the part of the wall above the footing, no deduction being made for openings.

the varying pressures below the dam. The areas A K L and A BE are constant.

Expressing the equation of the pressure in terms of the variables we have

After substituting H=1.84 h and reducing, we have

making the first derivitive equal to zero, we have

11.06-3.38 h=0.

Whence h=3.2 feet and H-5.89 feet, give the stages of upper and lower pools at the time of the maximum resultant pressure. Substituting these values in the above equation we find that pressure to be 14,000 pounds.

The maximum moment does not occur at the same stage as the maximum pressure and it is necessary to calculate this also. Expressing the equation for the moment in terms of the variables. we have

After substituting H-1.84 h and reducing, we have

1517.26+193.67 h-9.15 h2-1.04 h3—M.

Making the first derivitive equal to zero we have

3.12 +18.30-193.67=0,

which gives h-5.48 and H-10.08. Substituting these values in the equation of the moment above, we have 133,350 foot-pounds for the maximum overturning moment.

The maximum pressure for the river wall can be found by the same principle.

If the dam is not designed so that the sheet of water passing over it will hug the lower slope, it is thought advisable to increase the pressure and moment as found above to provide for rarification on the lower slope. Frizell says that this pressure can not be greater than that due to one-third the head on the crest of the dam, and this value would be taken.

COST OF FORMS AT LOCK NO. 21, CUMBERLAND

RIVER

BY

Mr. JOHN S. BUTLER
Junior Engineer

In order that this paper may be better understood, a brief description of the lock and some of the features of its construction will be here given.

Lock No. 21, Cumberland River, is 28.75 miles by water below Burnside, Ky., this place being the nearest railway station. The river here is generally navigable for steamboats during the winter and spring months, and practically all of the heavy material and supplies for the work must be purchased and delivered during this period. It is not uncommon, however, in the low-water or working season, to have quick rises which cause delay, and unless prepared for, do serious damage to the work.

The lock walls, guide wall, dam, abutment, and toe walls are of plain concrete, while the curtain wall and footway for the guard. wall are of reinforced concrete.

The lock is 386 feet long over all, with 280 feet by 52 feet as the effective size of the chamber. The top of the lock wall is 33 feet 8 inches above the concrete floor of the lock chamber. The guard is 12 feet and the maximum lift, with open river below, is 19.5 feet. The dam, which is of solid concrete, 340 feet long, has an ogee face on the lower side and a 20-foot concrete apron. This dam will give pool water up as far as Burnside, the head of navigation.

The guard wall, which presents some unusual features, is 160 feet long and is composed of seven concrete piers 10 feet long and 14 feet wide at the base, spaced 12 feet apart in the clear. These piers are joined on their face side with a vertical reinforced concrete curtain wall 3 feet thick and extending from 1 foot below the normal pool level to the top of the guard wall. There is a reinforced concrete walkway 1 foot thick extending over the piers and the curtain walls and joining the guard wall to the upper

end of the river wall of the lock, an 18-foot drift gap being left between the two structures. It will be seen that the guard wall, although resting on isolated piers, presents, to boats entering the lock, a smooth and continuous surface.

This work was carried on by contract for the first two seasons (1906-1907) during which time, it is said, the contractors lost $100,000. After the annulment of the contract, operations, by hired labor, were started June 1, 1908, under the direction of Maj. Wm. W. Harts, Corps of Engineers, U. S. Army, with the writer in local charge. The cost of the work by hired labor has been close to the contract prices.

The lock and guide wall were completed November 20, 1909. The abutment, toe walls, and guard wall were completed in December, 1910. Work on the concrete dam was not started in 1910 because of lack of funds.

During the present season of 1911, it is expected that the concrete dam will be built complete, thus making the lock operative.

LOCK WALL FORMS

While work on the lock was being done by contract, the style of form used for the construction of the concrete lock walls is shown on Plate I herewith. It will be seen that the trestle which was used for the delivery of the concrete was also used as a skeleton structure upon which the forms were built. The concrete for the lock walls was delivered from a central mixing plant over a 3-foot gage track on the trestle, in steel-bottom dump cars. From the bottom dump cars the concrete was delivered through a hopper car and chute to its place in the forms.

The forms were 6 by 15 foot panels, built of 15% inch ship-lap lagging nailed to a framework of 3 by 10 inch pine timbers. The panels were fastened to 10 by 12 inch posts with 3/4 inch lag screws. It was intended that the inside face of the panel be placed flush with the inside face of post, the post thus making part of the face of form; but it was soon found impracticable to keep the posts true to line, and to make a smooth joint between the panels, so the posts were set back 2 inches from the face line of the wall and the spaces between panels built in with a 7 inch dressed board. Neither the panels nor the posts were stiff enough to withstand the pressure from the green concrete, so heavy and expensive. bracing was required. There was no provision made for moving