Chapter XXXVI.—Boilers for Stationary Steam Engines

The boiler for a steam engine requires the most careful usage and inspection, in the first case because a good boiler may be destroyed very rapidly by careless usage, and in the second case because the durability of a boiler depends to a great extent upon matters that are beyond ordinary control, and that in many cases do not make themselves known except in their results, which can only be discovered by careful and intelligent inspection. All that the working engineer is called upon to do is, to use the boiler properly, keep it clean, and examine it at such intervals as the nature of the conditions under which it is used may render necessary.

The periods at which a boiler should be cleaned and inspected depend upon the quality of the water, whether the feed water is purified or not, and to a certain extent upon the design of the boiler; hence these periods are variable under different circumstances.

The horse power of a boiler is estimated in various ways, and there is no uniform practice in this respect. Some makers estimate a boiler to have a horse power for every fifteen square feet of heating surface it possesses, while others allow but 12 square feet.

The heating surface of a boiler of any kind is the surface that is exposed to the action of the fire on one side, and has water on the other; hence the surface of the steam space is not reckoned as heating surface, even though it may be exposed to the action of the heat. The effectiveness of the heating surface of a boiler obviously, however, depends upon the efficiency of the fire, and this depends upon the amount of draught, hence the estimation of horse power from the amount of its heating surface, while affording to a certain extent a standard of measurement or comparison while the boiler is not in use, has no definite value when the boiler is erected and at work.

Thus whatever amount of steam a boiler may produce under a poor or moderate draught, it will obviously produce more under an increased draught; hence the efficiency of the same boiler depends to a certain extent upon the draught, or in other words upon the quantity of fuel that can be consumed upon its fire bars.

The amount of water required in steam boilers varies from 16 lbs. to 40 lbs., per horse power per hour, and it has been proposed to compute the horse power of boilers from the water evaporation, taking as a standard 30 lbs. of feed water at a temperature of 70 degrees, evaporated into steam at a temperature of 212 degrees, at which temperature the steam is assumed to equal the pressure of the atmosphere.

“The strength of the shell of a cylindrical boiler to resist a pressure within it, is inversely proportional to its diameter and directly, to the thickness of the plate of which it is formed.

“For instance, take three cylindrical boilers each made of ⁄2 inch plate, the first one 2 feet 6 inches in diameter; the second twice that, or 5 feet in diameter; and the third twice that again, or 10 feet in diameter; and if the 2 foot 6 inch boiler is fit for a safe working pressure of 180 lbs. per square inch, then the 5 foot boiler will be fit for exactly one-half that amount, or 90 lbs. per square inch; and the ten foot boiler will be fit for half the working pressure of the five foot boiler, hence we have:

Diameter of
boiler shell. Thickness
of plate. Relative
working pressure.

2 feet 6 inches. ⁄2 inch. 180 lbs. per square inch.

5 „ „ „ 90 „ „ „ „

10 „ „ „ 45 „ „ „ „

“The reverse applies to the thickness of the plate. For instance, if we take two cylindrical boiler shells, each 5 feet in diameter, the first one made of plate ⁄2 inch thick, and the second twice that, or 1 inch thick, and if the first is equal to a safe working pressure of 90 lbs. per square inch, then the second is equal to a safe working pressure of twice as much, or 180 lbs. per square inch, providing, of course, that the riveted seams are of equal strength in each case, and that both boilers are allowed the same margin for safety; hence we have:

Diameter
of boiler. Thickness
of shell. Safe working pressure.

5 feet. ⁄2 inch. 90 lbs. per square inch.

5 „ 1 „ 180 „ „ „ „

“These principles (namely, that the strength of a boiler is, all other things or elements being equal, inversely proportional to its diameter, and directly proportional to its thickness) afford us a groundwork upon which we may lay down rules for determining by calculation the strength of the solid part of any boiler shell, and the bases of these calculations are as follows:

“If the shell plate of a cylindrical boiler is ⁄2 inch thick, there is one inch section of metal to be broken before the boiler can be divided into two pieces, that is to say there is ⁄2 inch on each side of the shell, as shown in Fig. 3237, and the two together will make 1 inch. If we take a ring an inch broad, as, say, at a in Fig. 3238, we shall obviously have a section of 1 square inch of metal to break before the ring can be broken into two pieces.

“The next consideration is, what is the average strength of a plate of boiler iron? Now suppose we have a strip of boiler iron 2 inches wide and ⁄2 inch thick, or, what is the same thing, a bar of boiler iron 1 inch square, and that we lay it horizontally and pull its ends apart until it breaks, how many lbs. will it bear before breaking? Now for our present purpose we may assume this to be 47,040 lbs., and if this number of lbs. be divided by the diameter of the boiler in inches, it will give the bursting pressure in lbs. for any square inch in the ring, or any other square inch in the cylindrical shell of the boiler.

“The reason for dividing by the diameter of the boiler is as follows:

“Of course the steam pressure presses equally on all parts of the interior surface of the shell, and may be taken as radiating from the centre of the boiler, as in Fig. 3239, which represents an end view of a strip an inch wide, of one half of a boiler. Now leaving the riveted seam out of the question, and supposing the shell to be truly cylindrical, and the metal to be of equal quality throughout, it will take just as much pressure to burst the shell apart in one direction as it will in another, hence we may suppose that the boiler is to be burst in the direction of arrow a, and it is the section of metal at b b that is resisting rupture in that direction.

“Now suppose we divide the surface against which the steam presses into six divisions, by lines radiating from the centre c, and to find the amount of area acting on each division to burst the shell in the direction of arrow a, we drop perpendicular lines, as line e, from the lines of division to the line b b, and the length of the line divided off (by the perpendicular) on the diameter represents the effectiveness of the area of that division to burst the boiler in the direction of arrow a; thus for that part of the boiler surface situate in the first division, or from b to line e, the area acting to burst the boiler in the direction of a is represented by the length of the line k, while the general direction of the pressure on this part of the shell is represented by arrow m.

“Similarly, for that part of the shell situate between vertical line e and vertical line f, the general direction of the steam pressure is denoted by the arrow l, while the proportion of this part that is acting to sever the boiler in the direction of a is represented by the distance n, or from the line e to line f measured on the line b b.

“By carrying out this process we shall perceive that, although the pressure acts upon the whole circumference, yet its effectiveness in bursting the boiler in any one direction is equal to the boiler diameter. Thus in Fig. 3240, the pressure acting in the direction of the arrows a (and to burst the boiler apart at b b) is represented by the diametral line b b, while the pressure actually exerted upon the whole boiler shell is represented by the circumference of the boiler.

“To proceed, then, it will now be clear that the ultimate strength of the boiler material, multiplied by twice the thickness of the boiler shell plate in inches or decimal parts of an inch, and this sum divided by the internal diameter of the boiler, in inches, gives the pressure (in lbs. per square inch) at which the boiler shell will burst.”

We have here only considered the strength of the solid plate of the shell, and may now consider the strength of the riveted joints, because, as the boiler cannot be any stronger as a whole than its weakest part is, and as the riveted joints are the weakest parts of a cylindrical boiler, therefore the strength of the riveted joint determines the strength of the boiler.

“The strains to which a riveted joint is subjected are as follows: That acting to shear the rivet across its diameter is called the shearing strain. But the same strain acts to tear the plate apart; hence, when spoken of with reference to the action on the plate, it is called the tearing strain.

“The same strain also acts to crush and rupture the plate between the rivet hole and the edge of the plate, and in this connection it is called the crushing strain.

“Thus, Fig. 3241 represents a single riveted lap joint, in which the joint at rivets a, b, and c is intact, the metal outside of d has crushed, the rivets e, f have sheared, and the plate has torn at h, leaving a piece j on the rivets k l.

“It is obvious that, since it is the same strain that has caused these different kinds of rupture, the joint has, at each location, simply given way where it was the weakest.

“If a riveted joint was to give way by tearing only, the indication would be that the proportion of strength was greatest in the rivets, which might occur from the plate being of inferior metal to the rivets, or from the rivets being too closely spaced. If the rivets were to shear and the plate remain intact, it would indicate insufficient strength in the rivets, which might occur from faulty material in the rivets, from smallness of rivet diameter, or from the rivets being too widely spaced.

“The object then, in designing a riveted joint is to have its resistance to tearing and shearing proportionately equal, whatever form of joint be employed.”

The English Board of Trade recommends that the rivet section should always be in excess of the plate section, whereas, in ordinary American practice, for stationary engine boilers, the plate and rivet percentages are made equal.

The forms of riveted joints employed in boiler work are as follows:

Fig. 3242 represents a single riveted lap joint. Fig. 3243 represents a double riveted lap joint, chain riveted; and Fig. 3244, a double riveted lap joint, with the rivets arranged zigzag.

Fig. 3245 represents a single and Fig. 3246 a double riveted butt joint, so called because the ends of the boiler plate abut together. The plates on each side of joint are called butt straps.

The advantages of the butt joint are, first, that the boiler shell is kept more truly cylindrical, and the joint is not liable to bend as it does in the lap joints, in the attempt of the boiler (when under pressure) to assume the form of a true circle, and second that the rivets are placed in double shear. That is to say, if in a lap joint the rivet was to shear between the plates, the joint would come apart, whereas, in a butt joint, the rivet must shear on each side of the plate, and therefore in two places.

Fig. 3247 represents a form of joint much used in locomotive practice in the United States. It is a lap joint, with a covering plate on the inside of the joint; rivets e and f are in single and rivets d in double shear.

“When we have to deal with comparatively thin boiler plates, there is no difficulty in obtaining a sufficiently high percentage of strength in the joints, by using the ordinary double riveted joint, but when we have to deal with thick plates, as in the case of large marine boilers, as 1 inch or upwards, a more costly form of joint must be employed, in order to obtain the required percentage of strength at the joint; hence the ordinary double riveted joint is replaced by various other forms as follows:

“First, a triple zigzag riveted lap joint, such as shown in Fig. 3248, or a chain riveted joint as in Fig. 3249, in both of which the third row of rivets enables the rivet pitch to be increased, thus increasing the plate percentage, while the third row of rivets also increases the rivet percentage.

“Second, by employing butt joints with butt straps, either double or treble riveted.

“A double riveted butt joint with double straps is shown in Fig. 3250, and a treble with double straps in Figs. 3251 and 3252.

“Third. By various arrangements of the rivets in conjunction with butt joints and double straps, with which it is not necessary, at this point, to deal.

“One of the great advantages obtained by the use of the double strap is that of bringing the rivet into double shear (or in other words, the rivet must shear on each side of the plate, or in two places, instead of between the plates only, before the joint can give way by shearing), and thus obtaining an increased calculated strength of 1⁄4 times the ordinary or single shear, the rule being to find the rivet strength in the ordinary way (as before explained), and then multiply the result by 1.75.

“The Board of Trade rules for spacing the rivets of these joints are as follows:

“Dimension e is the distance from the edge of the plate to the centre of the rivet hole. Dimension v is the distance between the rows of rivets, dimension p is the pitch of the rivets, which is always measured from centre to centre of the rivets, and dimension pd is the diagonal pitch of the rivets.

“The rule for finding dimension e, whether the plates and rivets are either of steel or iron, is as follows:

“Multiply the diameter of the rivet by 3 and divide by 2, the formula being as follows:

3 × d = e.

2

“To find the distance v between the rows of rivets in chain riveted joints. This distance must not be less than twice the rivet diameter, and a more desirable rule is four times the rivet diameter plus 1 divided by 2, thus:

4d + 1 = v.

2

“To find the distance between the rows of zigzag riveted joints:

√ (11p + 4d) × (p + 4d) = v,

10

that is, multiply 11 times the pitch plus 4 times the rivet diameter, by the pitch plus 4 times the rivet diameter, then extract the square root and divide by 10.

“To find diagonal pitch pd, multiply the pitch p by 6, then add 4 and divide by 10, thus:

6p + 4 = pd.”

10

Fig. 3253 represents a form of high percentage joint, used upon marine boilers of 10 to 14 feet diameter, and carrying from 100 to 190 lbs. pressure of steam. The rivets are what are termed unevenly pitched, or, that is to say, on each side of the joint, there are three rows of rivets, of which the inner and outer rows are wider pitched than the middle row.

“The advantage gained by this spacing is that the shear of the outer row of rivets is added to the plate section at the narrow pitch, that is to say, if the plate section broke through the line of rivet holes at the narrow pitch, it has yet to shear the outer row of rivets before the plate can separate.”

Fig. 3254 represents a second example of joint with rivets unevenly pitched, this form finding much favor in recent practice. The four inner rows of rivets are spaced at narrow pitch and the two outer rows are wide pitched.

“The strength percentage of this joint is calculated from three points of view, as follows:

“First. The plate section at the wide pitched rivets.

“Second. The rivet section in one pitch.

“Third. The plate section at the narrow pitch plus half the double shear of the outer or wide pitched rivet.”

The steam pressures generally employed in the boilers of stationary engines range from about 60 to 100 lbs. per square inch, and as a result of these comparatively low pressures less perfect forms of construction are employed than would be permissible if higher pressures were used.

The strength of the shell plate of boilers of small diameter is always largely in excess of the requirements, and as a result the strength of the joints may bear a very low percentage to that of the solid plate, and yet give a sufficient factor of safety for the working pressure.

Take, for example, a boiler shell of 36 inches internal diameter with a shell plate ⁄4 inch thick, and allowing the strength of the material to be 48,000 lbs. per inch of section, and with a factor of safety of 4, the working pressure will be 166 lbs. per square inch, thus:

Strength
of the
material. Plate
thickness
× 2.

48000 × (.25 × 2) = 666⁄3 lbs. = bursting pressure.

36

Diameter
of boiler.

By dividing this 666 by the factor of safety 4 we get 166⁄3 lbs. as the working pressure of the shell plate independent of the riveted joint. Usually, however, such a boiler would not be used for a pressure above about 60 lbs. per inch, and this leaves a wide margin for the reduction of strength caused by the riveted joints.

Suppose, for example, that a single riveted lap joint is used, and the strength of this joint is but 50 per cent. of that of the solid plate, and we have as follows:

Strength
of
material. % strength
of
riveted
joint. Twice
the plate
thickness.

48000 × .50 × (.25 × 2) = 83⁄3 lbs. = W.P.

36 × 4

Internal
diam. of
boiler. Factor
of
safety.

Here then we find that the working pressure of the solid plate is double that of the riveted joint, and that the working pressure of the boiler is 83 lbs. per square inch, notwithstanding that the strength of the riveted joints is but 50 per cent. of that of the solid plate. Such a boiler would not, however, be used for a pressure of over 60 lbs. per square inch.

If the above-named boiler was double riveted so as to bring the percentage of joint strength up to say 70 per cent, of that of the solid plate, its working pressure would be 116 lbs. per square inch, thus:

Strength
of
material. % strength
of
riveted
joint. Twice
plate
thickness.

48000 × .70 × (.25 × 2) = 116⁄3 lbs. = W.P.

36 × 4

Internal
diam. of
boiler. Factor
of
safety.

But in practice such a boiler would not be used for pressures above about 75 lbs. per square inch, hence the shell plate thickness is still largely in excess of the requirements, and it may be remarked that plates less than ⁄4 inch thick are not used on account of the difficulty of caulking them and keeping them steam tight.

On account therefore of the excessive strength of the shell plates in boilers of small diameter, butt straps are rarely used in stationary boilers, while punching the rivet holes and other inferior modes of construction are employed. We may now consider the circumferential seams of the boilers for stationary engines, such boilers sometimes being of great length in proportion to the diameter.

In proportion as the length of a boiler (in proportion to its diameter) is increased, the construction of the circumferential or transverse seams, as they are sometimes called, becomes of more importance.

The strength of the circumferential seams is so much greater than that of the longitudinal seams that it is often taken for granted that they are sufficiently strong if made with a lap joint and single riveted, but that such is not always the case will be shown presently.

In Fig. 3255 is represented a boiler composed of three strakes (i. e., three rings or sections), and it is clear that as the thickness of the shell is doubled at the circumferential seams where the ends of the middle strake pass within the end strakes, therefore the strength of the lapped joint of the shell to resist rupture in a transverse direction, as denoted by the arrows a, b, is actually increased by reason of the lap of the riveted joint. But suppose this boiler to be supported at the ends only, and the weight of the shell and of the water within it will be in a direction to cause the middle of the boiler to sag down, and therefore places a shearing strain on the rivets of the circumferential seams.

Moreover, the temperature of the outside of the boiler cannot be made or maintained uniform, because the fire passing beneath the bottom of the boiler first will keep it hotter, causing it to expand more, and this expansion acts to shear the rivets of the circumferential seams. In proportion as the heat of the fire varies in intensity, the amount of the expansion will vary, and the consequence is that the circumferential seams may get leaky or the joint may work, especially in boilers that are long in proportion to their diameters. It is clear, therefore, that for the very best construction at least a double riveted circumferential joint should be employed.

Leaving these considerations out of the question, however, we may find the amount of stress on the circumferential seams by multiplying the area of the end of the boiler by the working pressure, and dividing by the cross-sectional area of all the rivets in one circumferential seam.

Suppose, for example, that the diameter of the boiler is 36 inches, the working pressure 60 lbs. per square inch, and that there are in each circumferential seam 50 rivets, each ⁄4 inch in diameter, and we proceed as follows:

The area of a circle 36 inches in diameter = 1017.87 square inches.

The area of a rivet ⁄4 inches in diameter = .4417 square inch.

Then

Area of
boiler
end. Working
pressure.

1017.87 × 60 = 2765 lbs. per cross-sectional square inch of rivet.

50 × .4417

Number
of
rivets. Area of
each rivet.

By multiplying the area of the boiler end by the working pressure, we get the total steam pressure acting to shear the rivets, and by multiplying the number of rivets by the area of one rivet, we get the total area resisting the steam pressure, and then by dividing the one quantity into the other, we get the shearing stress per square inch of rivet section.

In the case of longitudinal seams, we have as follows, the pitch being say 2⁄8 and the rivets ⁄4.

Diameter
of boiler
in inches. Steam
pressure. Pitch.

36 × 60 × 2.125 = 5196 lbs. per square inch of rivet area.

2 × .4417

Rivets
in one
pitch. Area
of
rivet.

It is seen, therefore, that the stress placed by the steam pressure on the transverse seam is about one-half of that it places on the longitudinal seam. But, as before remarked, the transverse seam is subject to racking strains, from which the longitudinal seams are exempt; thus, for example, the expansion of the boiler diameter, whether uniform or not, does not strain the longitudinal seam, whereas it may severely strain the transverse seam.

The English Board of Trade rules, in assigning values to the various constructions and qualities of workmanship, assign a certain value, in the form of an addition to the factor of safety, which takes into account the difference in the stress upon the transverse and longitudinal seams, the quantities in each case having been determined both from experiment and from experience. A comparison of the different values may be made as follows:

The rules take a boiler shell made of the best material, with all the rivet holes drilled after the strakes are rolled into shape and put together, with all the seams (both longitudinal and transverse) fitted with double butt straps each at least five-eighths of the thickness of the shell plates they cover, and with all the seams at least double riveted, with rivets having an allowance of not more than 75 per cent. over the single shear, and provided that the boilers have been open to the inspection of their surveyors during the whole period of construction, and say that such a boiler shell shall be allowed a factor of safety (divisor of seam strength) of 5.

But for every departure from this, which they deem the best mode of construction, a penalty in the shape of an addition to the factor of safety is made. These additions to the factors of safety with reference to the longitudinal as compared to the transverse seams, are given in the following table:

Nature of the deviation in the construction or workmanship. Addition to
the factor 5
if the
deviation
is in the
longitudinal
seam. Addition to
the factor 5
if the
deviation
is in the
transverse
seam.

The holes not fair and good .75 .2

Holes drilled out of place after bending .15 .1

Holes drilled before bending .3 .15

Holes punched after bending .3 .15

Holes punched before bending .5 .2

Joints lapped and double riveted instead of having double butt straps .2 .1

Joints double riveted but have single butt straps .3 .1

Joints single riveted and have a single butt strap 1 .0 .2

Joints lapped and single riveted 1 .0 .2

An addition of .25 is also made to the factor of safety, when the strakes are not entirely under or over. In Fig. 3256 for example, strake b is within or under strake a at one end and strake c at the other end, hence b is entirely under; strake c is over b and d, and therefore entirely over; while strake d is under c, and over e, and therefore not entirely under nor entirely over.

When the rivet holes are punched they do not match properly, and unless the holes are punched somewhat smaller than the required size and reamed out afterwards, some rivets receive more stress than others, and may consequently shear in detail. It is customary, however, to punch the holes for ordinary stationary boilers, and it is with seams having punched holes therefore that we have at present to deal.

In the United States the rivet diameter and plate percentages are, in the boilers of stationary engines, usually made equal, and the reasons advanced both for and against this are as follows:

First, in favor of a greater plate percentage than rivet section, it is advanced that the plate gets thinner by wear, whereas the rivet does not, hence the wear reduces the plate section; that the plate is weakened by the punching process, and requires a greater percentage to make up its strength as compared to the rivet; that the rivets are usually of better material than the plates.

In favor of a greater rivet section than plate section, it is advanced that the shearing strength of iron is but about four-fifths of the tensile strength, and that with equal plate and rivet sections the rivet is therefore the weakest; that with punched holes the rivets may be sheared in detail, and that the rivets may be sheared gradually by the working of the joint from varying expansion and contraction.

From these premises the assumption is drawn that the weakening of the plate from being punched and from corrosion about offsets the excess of the tensile over the shearing strength, and that it is best therefore to employ such a pitch that the area of the rivet and of the metal left between the rivet holes shall be equal.

In order to do this the diameter of the rivet must be determined, and the following are the proportions given by the various authorities named:

Table of the Diameters of Rivets for Various Thicknesses of Plates with Single Riveted Lap Joint.

Thick-
ness
of
Plate. Diameter of Rivets.

Lloyds’
Rules. Liver-
pool
Rules. English
Dock-
yards. Fair-
bairn. Unwin. Wilson.

in. in. in. in. in. in. in.

⁄16 ⁄8 ⁄8 ⁄2 ⁄8 ⁄16 ⁄8

⁄8 ⁄8 ⁄8 ⁄8 ⁄4 ⁄4 ⁄16

⁄16 ⁄8 ⁄4 ⁄4 ⁄32 ⁄16 ⁄4

⁄2 ⁄4 ⁄16 ⁄4 ⁄4 ⁄8 ⁄4

⁄16 ⁄4 ⁄16 ⁄8 ⁄32 ⁄8 ⁄8

⁄8 ⁄4 ⁄8 ⁄8 ⁄16 ⁄16 ⁄8

⁄16 ⁄8 ⁄8 ⁄8 1 ⁄32 1 ⁄8

⁄4 ⁄8 ⁄16 1 1 ⁄8 1 ⁄16 1

⁄16 ⁄8 1 1 1 ⁄32 1 ⁄32 1

⁄8 1 1 ⁄8 1 ⁄8 ... 1 ⁄8 1

⁄16 1 1 ⁄16 1 ⁄8 ... 1 ⁄16 1 ⁄8

1 1 1 ⁄4 1 ⁄8 ... 1 ⁄4 1 ⁄8

From the above it is seen that with thin plates the diameter of rivet employed is about twice the thickness of the plate, whereas as the thickness of plate increases the proportion of rivet diameter decreases, and the reasons for this are, first, that with rivets twice the thickness of thick plates and pitched so as to equalize the rivet and plate sections the pitch would be too great to permit of the seams being caulked steam tight.

The diameter of the rivet having been determined, the rivet area and area of plate left between the rivet holes may be made equal by determining the pitch by the following rule:

Rule.—To the area of the rivet divided by the plate thickness add the diameter of the rivet, and the sum so obtained is the pitch. The correctness of this rule may be shown as follows:

Suppose the rivet diameter to be ⁄8 inch = decimal equivalent .875, and its area will be .6013 square inch. Suppose the thickness of the plate to be ⁄16 = decimal equivalent .5625, then by the rule:

Rivet
area.

Plate thickness = .5625 ) .6013 ( 1.0689

5625

388 00

337 50

50 500

45 000

5 5000

5 0625

To this 1.0689 we are to add the rivet diameter, thus:

1.0689

.8750 = rivet diameter.

1.9439 = pitch of the rivets.

We have thus found the required pitch to be 1.9439 inches, and as the joint is single riveted there are two half rivets or one whole one to one pitch, and if we subtract the diameter of the rivet from the pitch we shall get the width of the metal or plate left between the rivets, thus:

1.9439 = pitch of rivets.

.8750 = diameter of rivet.

1.0689 = distance in inches between the rivets.

If now we multiply this distance between the rivets by the thickness of the plate, we shall get the area of the plate that is left between the rivet holes, thus:

1.0689 = width of plate between rivets.

.5625 = thickness of plate.

53445

21378

64134

53445

Area of plate between rivets = .60125625

Here then we find the area of plate left between the rivet holes to be 6.01 square inches, and as the area of the rivet is 6.01 square inches, the two are shown to be equal.

We may now place the various rivet diameters and the pitches that will make the rivet area and plate area in a single riveted joint equal in a table as follows:

Table of Rivet Diameters and Pitches for Single Riveted Lap Joints.

Thick-
ness
of
Plate. Diameter
of
Rivet. Pitch.

⁄4 ⁄2 1 ⁄4

⁄16 ⁄8 1 ⁄8

⁄8 ⁄16 1 ⁄16

⁄16 ⁄4 1 ⁄4

⁄2 ⁄4 1 ⁄8

⁄16 ⁄8 2

⁄8 ⁄8 1 ⁄8

⁄16 ⁄8 1 ⁄4

⁄4 1 ..

⁄16 1 2

⁄8 1 1 ⁄8

⁄16 1 ⁄8 2 ⁄8

1 1 ⁄8 2 ⁄8

1 ⁄16 1 ⁄8 2 ⁄8

1 ⁄8 1 ⁄16 2 ⁄4

1 ⁄4 1 ⁄16 2 ⁄8

The rivets in double riveted lap joints, and in butt strap joints having a single cover, are spaced alike, because in both cases there are two rivets in one pitch, and the rivets are in single shear.

As there are two rivets in one pitch (instead of only one as in a single riveted joint), therefore the percentage of rivet section is doubled, and the plate section must therefore be doubled if the plate and rivet sections are to be made equal, and the rule for finding the required pitch is as follows:

Rule.—To the amount of rivet area in one pitch, divided by the thickness of the plate, add the diameter of the rivet.

Example.—Let the plate thickness be as in the last example ⁄16, decimal equivalent = .5625, and the rivet diameter be ⁄8 inch = decimal equivalent .875, the area of one rivet being .6013 square inch, and the pitch is calculated as follows:

.6013 = area of one rivet.

2 = the rivets in one pitch.

Plate thickness = .5625 ) 1.2026 ( 2.1377

1.1250

776 0 2.137

562 5 .875 = rivet diameter.

213 50 3.012 = pitch.

168 75

43 750

39 375

4 3750

3 9375

4375

We find, therefore, that the pitch is 3.012, or 3 inches (which is near enough for practical purposes), and we may now make it clear that this is correct.

In Fig. 3257 the joint is shown drawn one-half full size, and the length a of plate left between the rivet holes measures (as nearly as it is necessary to measure it) 2⁄32 inches, or 2.156, and if we multiply this by the thickness of the plate = .5625 inch, we get 1.2 square inches as the area of the plate left between the rivet holes.

Now there are two rivets in a pitch (as one-half of b, one-half of c, and the whole of f), and as the area of each rivet is .6, therefore the area of the two will be 1.2, and the plate section and rivet section are shown to be equal.

The area at a is obviously the same as that at a, because the pitches of both rows of rivets are equal, this being an ordinary zigzag riveted joint.

We may now consider the diagonal pitch of the rivets, using the rule below.

The pitch × 6, + 4 times the rivet diameter = the diagonal pitch pd.

divided by 10

In this example the pitch has been found to be 3 inches, hence we have

.875 = diameter of rivet.

4 = constant.

3.500

3 = pitch of the rivets.

6 = constant.

18

3 .5 = rivet diameter multiplied by 4.

10 ) 21 .5 ( 2.15 = the diagonal pitch.

20

1 5

1 0

50

The diagonal pitch, that is, the distance pd, Fig. 3257, is therefore found to be 2.15, or 2⁄8 inch full.

The amount of metal left between the rivets, measured on the diagonal pitch, is twice the dimension h multiplied by the thickness of the plate, and as this (with the diagonal pitch determined as above) always exceeds the pitch a or a, therefore if the plate fails, it will be along the line a, and not through the diagonal pitch.

We may now consider the total amount that the plates overlap in a double riveted lap joint zigzag riveted, this amount being twice the distance e, added to the distance v between the rows of rivets.

The distance e, Fig. 3257, is usually made one and a half times the diameter of the rivet, this being found to give sufficient strength to prevent the edge of the plate from tearing out and to prevent the rivet from shearing the plate out to the edge, rupture not being found to occur in either of these directions.

The rule for finding the distance v, when the diagonal pitch has been determined by the rules already explained, is as follows:

Rule.—To the pitch multiplied by 11, add 4 times the rivet diameter, then multiply by the pitch, plus 4 times the rivet diameter. Then extract the square root and divide by 10.

Placed in formula, the rule appears as follows, d representing the rivet diameter, and p the pitch.

√(11p + 4d)(p + 4d) = distance v between the rows of rivets.

10

As this rule involves the extraction of the square root of the sum of quantities above the line, and as in determining the diagonal pitch, we have already determined the distance v, it is unnecessary to our purpose to carry out this latter calculation, as it is easier to find the diagonal pitch, and then, after drawing the joint, the distance between the rows of rivets can be measured if it is required, as it might be in finding the length of plate required to roll into a strake for a boiler of a given diameter and having a double riveted lap joint.

We may now consider chain riveted joints in comparison with zigzag riveted joints, which is especially necessary, because it has been assumed by some that the second row of rivets in a chain riveted joint added nothing to the strength of the joint.

Fig. 3258 represents a chain riveted joint, having the same thickness of plate, rivet diameter and pitch as the zigzag riveted joint in Fig. 3257, and it will be seen that the plate sections at a and at a are the same in the two figures, and as there are four half rivets, which are equal to two rivets, in one pitch, therefore the strength of the two joints is equal.

Each joint can be as efficiently caulked as the other, as the rivet spacing is the same and the edge of the plate is the same distance from the rivets in both cases.

The pitch of the rivets is obtained by the same rule as for zigzag riveted joints, and all we have now to consider is the distance apart of the two rows of rivets or distance v in the Fig. 3258, and for this there are two rules, the first being that it shall not be less than twice the diameter of the rivet, which would leave a dimension at h in the figure equal to the diameter of the rivet. The second rule is that a better proportion than the above is to multiply the diameter of the rivet by 3. This makes the dimension at h equal to twice the rivet diameter.

When the joints have double buttstraps, the rivets may be spaced as wide as the necessity for tight caulking will admit, because, on account of the rivets being in double shear, the rivet percentage exceeds the plate percentage.

The allowance for the rivets being in double shear is 75 per cent., or in other words, a rivet in double shear is allowed 1.75 times the area of the same size rivet in single shear.