Fig. 3253Fig. 3253.
Fig. 3253.
Fig. 3253represents 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, thereare three rows of rivets, of which the inner and outer rows are wider pitched than the middle row.
[54]“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.”
[54]From “Steam Boilers.”
[54]From “Steam Boilers.”
Fig. 3254Fig. 3254.
Fig. 3254.
Fig. 3254represents 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.
[55]“The strength percentage of this joint is calculated from three points of view, as follows:
[55]From “Steam Boilers.”
[55]From “Steam Boilers.”
“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 plate1⁄4inch 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:
By dividing this 666 by the factor of safety 4 we get 1662⁄3lbs. 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:
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:
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 than1⁄4inch 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.
Fig. 3255Fig. 3255.
Fig. 3255.
InFig. 3255is 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 arrowsa,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, each3⁄4inch in diameter, and we proceed as follows:
The area of a circle 36 inches in diameter = 1017.87 square inches.The area of a rivet3⁄4inches in diameter = .4417 square inch.
The area of a circle 36 inches in diameter = 1017.87 square inches.
The area of a rivet3⁄4inches in diameter = .4417 square inch.
Then
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 21⁄8and the rivets3⁄4.
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:
Fig. 3256Fig. 3256.
Fig. 3256.
An addition of .25 is also made to the factor of safety, when the strakes are not entirely under or over. InFig. 3256for example, strakebis within or under strakeaat one end and strakecat the other end, hencebis entirely under; strakecis overbandd, and therefore entirely over; while strakedis underc, and overe, 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:
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 be7⁄8inch = decimal equivalent .875, and its area will be .6013 square inch. Suppose the thickness of the plate to be9⁄16= decimal equivalent .5625, then by the rule:
To this 1.0689 we are to add the rivet diameter, thus:
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:
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:
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:
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 example9⁄16, decimal equivalent = .5625, and the rivet diameter be7⁄8inch = decimal equivalent .875, the area of one rivet being .6013 square inch, and the pitch is calculated as follows:
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.
Fig. 3257Fig. 3257.
Fig. 3257.
InFig. 3257the 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) 25⁄32inches, or 2.156, and if wemultiply 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 ofb, one-half ofc, and the whole off), 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 atais obviously the same as that ata, 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.
In this example the pitch has been found to be 3 inches, hence we have
The diagonal pitch, that is, the distancepd,Fig. 3257, is therefore found to be 2.15, or 21⁄8inch full.
The amount of metal left between the rivets, measured on the diagonal pitch, is twice the dimensionhmultiplied by the thickness of the plate, and as this (with the diagonal pitch determined as above) always exceeds the pitchaora, therefore if the plate fails, it will be along the linea, 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 distancee, added to the distancevbetween the rows of rivets.
The distancee,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 distancev, 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,drepresenting the rivet diameter, andpthe pitch.
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 distancev, 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.