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diameter of the circle. Then find the decimal opposite this ratio in the column headed “Area.” Multiply this area by the square of the diameter. The result is the required area.

Example. Diameter of circle = 72 in. Height of segment = 25 in. 25 + 72 = .347, which will be found it: the column headed “Ratio," and the area opposite this

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in.

is .24212.

Then .24212 x 72 x 72 = 1,255 sq. in., area of segment.

A boiler is 66 in. in diameter, the working pressure is 100 lbs. per sq. in. The distance from the top row of tubes to the shell is 25 in. Required, the number of diagonal crow foot braces that will be needed to support the heads above the tubes, also the sectional area of each brace. The thickness of the heads is 5/8 in. and the T.S. = 55,000 lbs. per sq.

Assume the head to be sufficiently strengthened by the Aange for a distance of 2 in. from the shell, the diameter of the circle of which the segment above the tubes requires to be stayed is reduced by 2 + 2 = 4 in. and will therefore be 66 - 4 = 62 in. The rise or height of the segment above the tubes is 25 – 4 = 21 in. Required, the area.* 21 + 62 = .338. Looking down the column headed “Ratio" in Table 19, area opposite -338 is .23358. Area of segment = .23358 x 62 x 62 = 897.88 sq. in. The total pressure on this area will be 897.88 x 100 = 89,788 lbs.

Assume the braces to be made of 1/8 in. round steel having a T.S. of 50,000 lbs. per sq. in. and to be designed in such a manner as to allow for loss of material in drilling the rivet holes in the crow feet. Each brace will have a sectional area of .994 sq. in., and using 8 as a factor of safety, the strength or safe holding power of each stay may be found as follows: .994 x 50,000 = 8 = 6,212 lbs., and the number of stays required = 89,788 lbs. (total pressure) divided by 6,212 lbs. (strength of each stay) = 14.5, or in round numbers 15. If the stays are made of flat bars of steel the sectional area should equal that of the round stays, and the dimensions of the crow feet of all stays should

* See rule for Table 19.

be such as to retain the full sectional area of the body after the rivet holes are drilled.

Each stay is connected to the plate by two 76-in. rivets, having a T.S. of 55,000 lbs. per sq. in. and a shearing strength of 45,000 lbs. per sq. in. These rivets are capable of resisting a direct pull of 10,818 lbs., using 5 as a factor of safety; ascertained as follows: 2A 45,000 + 5 = 10,818 = strength of two rivets. They are also subjected to a crushing strain, and the resistance to this is DxC + 5, which expressed in figures is .875 x 90,000 + 5 = 15,750 lbs.

The proper spacing comes next, and is arrived at in the following manner:

Area to be stayed = 897.88 sq. in.
Number of stays = 15.
Area supported by each stay = 897.88 + 15 = 59.8

sq. in.

The square root of 59.8 = 7.75 nearly, which is ihe distance in inches each way that the stays should be spaced, center to center.

If through stay rods are used in place of diagonal braces for staying the boiler under consideration, the number and diameter of the rods may be ascertained by the following method:

Assuming the heads to be supported by channel bars, as previously described, and that the stays are pitched 14 in. apart horizontally and 13 in. vertically, each stay would be required to support an area of 14% 13 = 182 sq. in., and the number of stays would be 897.88 + 182 = 4.9, in round numbers 5. See Fig. 107. The pressure being 100 lbs. per sq. in., the total stress on each stay = 182 x 100 = 18,200 lbs. Assume the stay rods to be of soft steel having a T.S. of 50,000 lbs. per sq. in., and using a factor of safety of 8, the

sectional area required for each stay will be found as follows: 18,200 x 8 + 50,000 = 2.9 sq. in., and the diameter will be found as follows: 2.9+.7854 = 3.69, which is the square of the diameter, and the square root of 3.69 = 1.9 in., or practically 2 in. The same methods of calculation are applicable to the staying of the heads below the tubes, also for stay bolts in fire box boilers.

Strength of Unstayed Surfaces. A simple rule for finding the bursting pressure of unstayed flat surfaces is that of Mr. Nichols, published in the "Locomotive," February, 1890, and quoted by Prof. Kent in his “Pocket-book." The rule is as follows: "Multiply the thickness of the plate in inches by ten times the tensile strength of the material used, and divide the product by the area of the head in square inches.” Thus,

Diameter of head 66 in.
Thickness of head = 5/8 in.
Tensile strength = 55,000 lbs.

Area of head = 3,421 sq. in. 5/8 x 55,000 × 10 + 3,421 = 100, which is the number of pounds pressure per square inch under which the unstayed head would bulge.

If we use a factor of safety of 8, the safe working pressure would be 100 + 8 = 12.5 lbs. per sq. in., but as the strength of the unstayed head is at best an uncertain quantity it has not been considered in the foregoing calculations for bracing, except as regards that portion of it that is strengthened by the flange.

In all calculations for the strength of stayed surfaces, and especially where diagonal crow foot stays are used, the strength of the rivets connecting the stay to the flat plate must be carefully considered. A large factor of safety, never less than 8, should be used, and

the cross section of that portion of the foot of the stay through which the rivet holes are drilled should be large enough, after deducting the diameter of the hole, to equal the sectional area of the body of the stay.

Dished Heads. In boiler work where it is possible to use dished, or "bumped up" heads as they are sometimes called, this type of head is rapidly coming into use. Dished heads may be used in the construction of steam drums, also in many cases for dome-covers, thus obviating the necessity of bracing. The maximum depth of dish, as adopted by steel plate manufacturers April 4, 1901, is 78 of the diameter of the head when flanged, and if the tensile strength and quality of the plate from which the heads are made are the same as those of the shell plate, the dished head becomes as strong as the shell, provided the head has the same thickness or is slightly thicker than the shell plate.

Welded Seams. A few boiler manufacturers have succeeded in making welded seams, thus dispensing with the time-honored custom of riveting the plates together. A good welded joint approaches more nearly to the full strength of the material than can possibly be attained by rivets, no matter how correctly designed the riveted joint may be. The weld also dispenses with the necessity of caulking, and a boiler having a perfectly smooth surface inside, such as would be afforded by welded seams, would certainly be much less liable to collect scale and sediment than would one with riveted joints. But in order to make a success of welded seams the material used must be of the best possible quality, and great care and skill are required in the work.

The Continental Iron Works of Brooklyn, New York, exhibited at the St. Louis World's Fair in 1904

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