STRAINS AND STRENGTHS.

325

Example 2.-What is the proper diameter of a single-riveted boiler composed of plates 4 inches thick, and intended to work with a pressure of 100 lbs. on the square inch?

Here 4 × 89003560, which divided by 100 = 35.6 inches, which is the proper diameter of the cylindrical shell of the boiler in this case.

TO FIND THE PRESSURE TO WHICH A SINGLE-RIVETED CYLINDRICAL BOILER MAY BE WORKED WHEN ITS DIAMETER AND THE THICKNESS OF ITS PLATING ARE KNOWN.

RULE.-Multiply the thickness of the plating in inches by the constant number 8900, and divide the product by the diameter of the boiler in inches. The quotient is the pressure of steam per square inch at which the boiler may be worked.

Example 1.-What is the highest safe-working pressure in a single-riveted boiler 42 inches diameter, and composed of plates •377 of an inch thick?

Here 377 × 8900

3355-3, which divided by 42=79.8 lbs. per square inch, which is the highest safe pressure of the steam.

Example 2.-What is the highest safe-working pressure in the case of a single-riveted boiler 36 inches diameter, and composed of plates 4 of an inch thick?

Here 4 x 8900= 3560, which divided by 36 square inch.

= 99 lbs. per

The rules for double-riveted boilers are in every case the same as those for single-riveted, only that the constant 11140 is used instead of the constant 8900. It will therefore be unnecessary to repeat the examples for the case of double-riveted boilers.

Mr. Fairbairn has given the following table as exhibiting the bursting and safe-working loads of single riveted cylindrical boilers. But I have already stated that I consider Mr. Fairbairn's margin of safety too small. The working pressure, however, which he gives for single-riveted boilers would not be too great for double-riveted boilers, as will appear by comparing those pressures with the pressures which the foregoing rules indicate may be safely employed.

TABLE SHOWING THE BURSTING AND SAFE-WORKING PRESSURE OF CYLINDRICAL BOILERS, ACCORDING TO MR. FAIRBAIRN.

It will be useful to compare some of the figures of this tablo with the results given by the rules just recited. For example, according to Mr Fairbairn, a single-riveted boiler, 5 feet diameter, and formed of 4-inch plates, may be habitually worked with safety to a pressure of 94 lbs. on the square inch. Now, by our rule, 5 x 8900 = 4450, which divided by 60, the diameter of the boiler in inches, gives 74 lbs. as the safe pressure at which the boiler may be worked. If the boiler be double-riveted, then we have 5 x 11140 = 5570, which, divided by 60, gives 93 lbs. as the pressure per square inch at which the boiler may be safely worked. This differs very little from Mr. Fairbairn's result of 941 lbs., and his table may therefore be used if the results be regarded as applicable to double-riveted boilers, but as applied to single-riveted boilers his proportions, I consider, are too weak. The following diameters of boilers with the corresponding thick

COLLAPSING PRESSURE OF FLUES.

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ness of plates, it will be seen, are all of equal strengths, their bursting pressure being 450 lbs. per square inch, which answers to 34,000 lbs. per square inch of section of the iron. Diameter 3 ft., thickness 250 inches; 3 ft., 291; 4 ft., 333; 4 ft., 376; 5 ft., 416; 5 ft., 458; 6 ft., 500; 6 ft., 541; 7 ft., 583; 7 ft., 625; and 8 ft., 666.

The collapsing pressure of cylindrical flues follows a different law from the bursting pressure, being dependent, not merely upon the diameter and thickness of the tube, but also upon its length; and Mr. Fairbairn gives the following formula for computing the collapsing pressure. If T the thickness of the iron, P= collapsing pressure in lbs. per square inch, L = length of tube in feet, and D = diameter of tube in inches; then

=

and as to multiply the logarithm of any number is equivalent to raising the natural number to the power which the logarithm represents, we may for T2-19 write 2.19 log. T. With this trans

formation the equation becomes

If now we take the thickness of the plate of the circular flue at 291 inches, and if we make the diameter of the flue 12 inches and its length 10 feet, the equation will become

Now 291 being a number less than unity, the index of its logarithm will be negative, and for such a number as 291 the index will be I, the minus being for the sake of convenience written on the top of the figure; whereas for such a number as '0291 the index will be 2; for 00291 the index will be 3, and so on. It does not signify, so far as the index is concerned, what the sig. nificant figures are, but only at what decimal place they begin; and 1 has the same index as 291, and '01 as 0291. Now the ogarithm of 291, as found in the logarithmic tables, is 463893, and the index being 1, the whole logarithm is 1.463893. In multi

plying a logarithm with a negative index, as it is the index alone that is negative, while the rest of the logarithm is positive, we must multiply the quantities separately, and then adding the positive and negative quantities together, as we would add a debt and a possession, we give the appropriate sign to that quantity which preponderates. Now 463893 multiplied by 2.19=1·01592567, and I multiplied by 2.19 gives 2.19, which is a negative quantity. Adding these products together, we in point of fact subtract the 2·19 from the 1·01592567, which leaves 2-82592567. Now if we turn to the logarithmic tables, we shall find that the number answering to the logarithm 82592567, or the number answering to the nearest logarithm thereto (which is 825945), is 6698; but as the index is negative, this quantity will be a fraction, and the index being 2, the number will begin in the second place of decimals—or, in other words, it will be 0.6698. Now 806300 multiplied by •06698 = 54004-974, which, divided by 120, gives 450 lbs. as the collapsing pressure. If we allow the same excess of strength to resist collapse that we allowed to resist bursting-namely, 7.6 times-a tube of the dimensions we have supposed will be safe in working at a pressure of 60 lbs. on the square inch. But the strength of tubes to resist collapse may easily be increased by encircling them with rings of T iron riveted to the tube. Cylindrical flues of different dimensions, but of equal strength to resist collapse, are specified in the following table:

CYLINDRICAL FLUES OF EQUIVALENT STRENGTH, THE COLLAPSING PRESSURE BEING 450 POUNDS PER SQUARE INCH.

=

450 lbs., L = 10

If now we put p the collapsing pressure feet, and D = 12 inches, the expression becomes

In like manner the quantities L and D can easily be derived from the formula, and in fact the equations representing them will be

It is unnecessary to put these equations into words, as the rule for finding the collapsing pressure of flues is not much required, seeing that in the case of all large internal flues they may be strengthened by hoops of T iron, so as to be as strong as the shell.

PRACTICAL EXAMPLE OF A LOCOMOTIVE BOILER.

It will be useful to compare the results given by these computations with the actual proportions of a locomotive boiler of good construction, and I shall select as the example one of the outside-cylinder tank engines constructed by Messrs. Sharp and Co. for the North-Western Railway. The diameter of cylinder in this locomotive is 15 inches, and the length of the stroke 20 inches. The pressure of the steam in the boiler is 80 lbs. per square inch. The barrel of the boiler is 3 feet 6 inches diameter, and 10 feet 3 inches long, and it is formed of iron plates 3ths thick. The junction of the plates is effected by a riveted jump-joint, which is equal in strength to a single riveted-joint. The rivets are