A rivet in single shear

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1 don't respond much to articles I have read in magazines and I am not sure why I am doing this one. I guess I just thought I had something to say. In the March-April issue of IMA, there was an article written in 'Soot in the Flues' about Lap Seam and Butt-Strap joints. First, I don't claim to be an expert! Working on Steam Tractors is a hobby to me. This hobby comes with some special rules so what I have learned I have had to learn by necessity, mostly to please the state so I could go on working and running steam tractors!

In the article it was stated that a rivet in single shear was only half as strong as a rivet in double shear. True enough. A rivet in single shear must be sheared through in one place, a rivet in double shear must be sheared through in two places, see fig #1. In practice the strength of the rivet in double shear is taken to be 1.75% stronger. With this in mind, a butt-strap joint should be twice as strong as a lap seam joint because a rivet in a butt-strap joint is in double shear as compared to a lap seam joint, right? Try as I might, I just could not make this work! Not with twice as many, half as many, or the same number of rivets! The only way I could make this happen would be to design a really poor lap-seam and compare it against a properly designed Butt-Strap joint. (I will show you some math in a moment.) Let me define some terms, the seam we are talking about is the seam on the barrel of a boiler that runs the length of the barrel, that is left to right in most steam tractors. A lap joint is where one plate overlaps the other, a butt-strap joint is where the ends are butted up against each other and straps are used to hold them together (see fig #2). Joints are also classified by the number of rows of rivets used to hold them together. The two joints we see most often on our steam tractors are the double riveted lap joint, and the double riveted, double butt-strap joint. Otherwise called a Butt and double Strap joint, because it has two straps holding the butt together. Figure 2 shows an example of both of these. For the rest of this article, a 'lap joint' will refer to a double riveted lap joint and a 'butt-strap joint' will refer to a double riveted butt and double strap joint. When we talk about joint efficiency, we are talking about the strength of the joint compared to the strength of the same metal if there were no joint at all. The strength of a joint is always less that the strength of the metal with no joint. On our steam tractors, a well designed lap joint will show an efficiency around 73%, a butt-strap joint will be around 82%. It is interesting to note that in the earlier boilers they used a lap joint with only one row of rivets holding it together; this had an efficiency of about 57% and modern boilers that are fusion welded together can have an efficiency of 100%, if the weld is ground flat to the plate, stressed relived and certain other criteria are met. OK, here are the math definitions. If you're not interested in this part just skip it and I will sum up what happen after its all done.

TS=tensile strength of the boiler plate (psi)
t=thickness of the boiler shell (inches)
b=thickness of the butt straps in inches (where used)
P=pitch of rivets (inches). See figure #2
d=diameter of rivet after driving (inches)
a=cross sectional area of rivet after driving (inches)
s=shear strength of rivet in single shear (psi)
S=shear strength of rivet in double shear (psi)
c=crushing strength of boiler plate (psi)
n=number of rivets in single shear
N=number of rivets in double shear

Note that the diameter of a rivet is the diameter after driving it in. This is because a rivet will expand when it is red hot, that is to say an 11/16 diameter rivet when heated red hot will not go into an 11/16 hole, so you would use a inch hole and the calculation will use '. Here is the math for a lap joint.

A = P*t*TS
B = (P-d)*t*TS
C = n*s*a (n = 2 for our lap joint)
D = n*d*t*c

Divide B,C, and D by A and the lowest number is the efficiency. This is how it is done by the ASME. The first thing to notice is that there are 3 ways that the joint can fail, B,C and D, that is that the plate can tear between rivets, the rivets can shear off or the rivets can cut the plate leaving something that looks like a zipper. To give you an example of the joints I will use the museum's 16 horse Advance. Advance said in their catalogue that they used Flange quality steel. Flange quality steel is well defined and its definition has not changed since at least 1900. We will assume that they used iron rivets. The catalog also said they used 60,000 psi tensile strength boiler plate, that the shell is 5/16 inch thick (.3125) and that the rivet has a diameter of 11/16, For this rivet we will use a (.75) inch hole. For an iron rivet, s = 38000 psi and for flange steel c = 95000 psi. These numbers are from the ASME code for Flange Steel, and the pitch I measured to be 2 inches. We can now plug in some numbers, so....

A = 2.5*0.3125*60000 =46875
B = (2.5-0.75)* 0.3125* 60000 = 32812.5
C = 2*38000*0.442 = 33592
D = 2*0.75*0.3125*95000 =44531.25
B is the smallest value so B/A = 32812.5 / 46875 = 0.7, The joint has an efficiency of 70%.

Some other lap seams I have done are:
1911 CASE 40=71.6%
1911 CASE 80=73.8%
1912 CASE 60=68.2%
1895 Russell 15=70%

Here is the math for a Butt-Strap joint,
A = P*t*TS
B = (P-d)*t*TS
C = (N*S*a) + (n*s*a)
D = (P-2d)*t*TS + (n*s*a)
E = (P-2d)*t*TS + (d*b*c)
F = (N*d*t*c) + (n*d*b*c)
G = (N*d*t*c) + (n*s*a)

Divide B,C,D,E,F,G by A and the lowest number is the joint efficiency, You will notice that there are a lot more ways this joint can fail. I am going to use the measurements from the museum's 60 horse Baker except that I will substitute values to be the same as the above lap seam. The biggest change will be to the rivet pitch so that the rivets on the two inside rows have twice the pitch as in the lap joint. The pitch of the rivets in a butt-strap joint are measured in a different place than the lap joint so if is a different value. The changes are P = 10, and the new values of b = 0.5 for the thickness of the straps , S = 2*s and N=2 for rivets in double shear.

A=10 * 0.3125 * 60000 = 187500
B=(10 - 0.75) * 0.3125 * 60000 = 173437.5
C=(2 * 72000 * 0.442) + (1 * 38000 * 0.442) = 80442
D=(10 - (2 * 0.75) * 0.3125 * 60000 + (1 * 38000 * 0.442) - 176162.9
E=(10 - (2 * 0.75) * 0.3125 * 60000 + (0.75 * 0.5 * 95000) = 195000
F=(2 * 0.75 * 0.3125 * 95000) + (1 * 0.75 * 0.5 * 95000) = 80156.25
G=(2 * 0.75 * 0.3125 * 95000) + (1 * 38000 * 0.442) = 61327.25

G is the smallest value so G/A = 61327.25 /187500 = 0.327, The joint has an efficiency of 32.7%.

This joint is not nearly as strong as the lap joint! If you set the pitch to 5 so that the rivets in the two inside rows have the same pitch as the lap seam, you will get an efficiency of 65.4% . To be fair, this is not quite the same as what was presented in the March-April article. A lap-seam has its rivets staggered while a butt-strap joint has them in columns. In the lap seam, we are testing one rivet plus two half rivets for a total of two rivets. In the butt-strap joint, we are testing four rivets in the inside two rows. The pitch is the same but the rivet area will be different. So, how would you build a butt-strap joint?? Plug these numbers in, d = .875 (larger rivet), P = 4.75, TS = 55000. This is what our Baker has in it, all the other numbers stay the same. You should get a joint efficiency of 81.6%. I realize that I have not explained what the various equations mean but I did not want to get to wrapped up in the math. Check your local technical book store for a good book on power plant operation etc. if you want more information. To sum it up, here is what happens. If you put the rivets in double shear, it takes more to break them, and in the Baker they also used a larger rivet to give it more strength yet. If the rivets are stronger, you need fewer rivets. Having fewer rivets in the shell means fewer holes are used to put it together and so it is a stronger joint! This is just what was said in the article in the March-April issue of IMA, except that a butt-strap joint is not 'twice' as strong, clearly you cannot build a butt-strap joint with an efficiency of 140%. You should know that the above calculations require that the center of the rivets are 1.5 to 1.75 times their diameter in distance from the edge of the joint. The boiler codes in your area may vary. Both the lap-joint and the butt-strap joint can be built to hold the pressure in our steam tractors, so why do some people, and inspectors in particular like the butt-Strap joint better? In the earliest lap joint, mostly the single rivet variety, they hammered down the outside plate to meet the inside plate and form the joint, as was said in the March-April article, This caused a crease and so a stress point on the inside of the outer plate and weakened the joint. This fault was discovered rather early in tractor boiler history and most, if not all our steam tractors have had there lap-seams handled in such a way as to prevent this crease. Also stated in the previous article, a lap-seam is not a perfect circle, it has a tendency to UN-roll instead of pull apart. Probably the most feared thing by an inspector is a lap seam crack, this would be on the inside plate going from rivet hole to rivet hole. He cannot see this crack because it is covered by the outer plate. You might detect it with x-rays. I do not know, but short of cutting the boiler open or cutting slots in the seam it can not be checked for! Maybe an expert can let me know here. If a lap seam crack separates, it goes all the way in a hurry! Very dangerous! I will say that I have not heard of a boiler exploding in this way but it is in your inspector's mind because he is the one who put his OK on the boiler. A butt-strap joint when built will have its inside strap caulked down to be steam tight. The outside strap will not be caulked down, in this way if the inside plate cracks or leaks, the steam will come through to the outside plate and make itself known or it will show up in the Hydro test. In any case there is a warning that something is amiss. In writing this I mean no disrespect to the author of the article in the March-April IMA and I hope none is taken. He is substantially correct. I hope this clears up some of the mystery about lap seams.