This section is from the book "Safe Building", by Louis De Coppet Berg. Also available from Amazon: Code Check: An Illustrated Guide to Building a Safe House.
For bending-moment we should have a 1" circular beam with a clear span of 1", uniformity loaded with 135000 pounds.
From Formula (21) we have the bending-moment m = 135000.1/8= 16875 pounds-inch
Moment of resistance will be as before r= 0,0982
Therefore the total strain on all the rivets s = 16875/0,0982 = 171843
This divided by(k/f), 1 = 18000 gives the required number of rivets as before x = 171843/1800 = 9,5
We now design the joint, as before, remembering to stagger the rivets and to place the required number each Bide of joint. The greatest number required was to resist breaking, viz ten.
Required number of rivets.
Advantage of Two Covers.
Designing the joint.
We can design as shown in Figure 175 or as shown in Figure 176; both require eleven rivets each side of joint, but cover-plates in Figure 176 need only aggregate 1 1/8" in thickness, that is, be 9/16" thick each; while those in Figure 175 would have to asrgrreate 1 5/16" in thickness, or be, say, 11/16" thick each.
Joint shown in Figure 175 looks a little better, but otherwise there is no preference.
If cover-plates are not equal in thickness each side of plate, it would require very many more rivets. Each rivet would become a double lever, with its central part built-in and a projecting free arm each side, the length of arms being equal to their respective thicknesses of cover-plates. The load on each arm would be the proportion of whole strain, that the thickness of its respective cover-plate would be of the whole required (aggregate) thicknesses of cover-plates.
There would be no sense in such an arrangement however. It would produce all sorts of unequal stresses, in shearing, bearing, cross-breaking, etc., and should be avoided. Riveted work at best is very theoretical, as the calculations depend entirely upon the accuracy and fit of each rivet. If a single rivet fails to do its share, it will at once disarrange all the strains and produce unequal stresses in different parts. Still if the above rules are followed, riveted work can be used with perfect safety. Where the result gives a fraction, a whole rivet should as a rule be used in place of the fraction. If the necessary spacing requires still more rivets, they can either be used, or, all the rivets can be reduced in size enough to bring them nearer to the allowable stresses.
No account has been taken of the loss due to punching, for this will affect the plate in tension mainly, and the safe stresses allowed for tension are very low. In compression the metal would not be strained as heavily as in tension, for the rivets will not weaken the plate so much if they entirely fill the holes, thus giving full bearing on the entire plate. Then, too, the butt joint if planed and carefully made and joined, will transfer directly more or less of the compression.
Covers of same thickness.
But in all good work it is customary to place no reliance whatever on the butt, and to calculate in compression the same as for tension, namely, sufficient net area in each plate, at its weakest section, to resist the whole compression strain.
Tallies XXXV to XL inclusive, have been calculated and laid out to save most of the wearisome Figuring necessary in riveted work and in connection with pins. The first three give the bearing value of pins and rivets against eye-bars or plates, and the latter three the values in tension, single and double shearing and in cross-breaking of pins and rivets. All the tables are laid out for both steel and wrought-iron.
The full heavy straight lines in Tables XXXV, XXXVI and XXXVII represent the thicknesses of plates or eye-bars against which the different sizes of rivets or pins bear. The thicknesses given are from 1/4" to 11 /2" in Table XXXV and from 1/4" to 2" in Tables XXXVI and XXXVII; all by 1/16". For thicker plates or eye-bars it will only be necessary to increase the bearing value found, in proportion to extra thickness.
The columns to the left give the diameters of pins and rivets, running in Table XXXV from 1/4 inch diameter (by 1/32 inch) to 1 inch diameter; in Table XXXVI from 1 inch diameter (by 1/16 inch) to 3 inches diameter ; and in Table XXXVII from 3 inches diameter (by 1/8 inch) to 6 inches diameter. The Figures at the tops of these tables give the bearing values in pounds for wrought-iron, and those along the bottoms, the bearing values in pounds for average steel.
The full heavy curved lines in Tables XXXVIII, XXXIX and XL give the single and double shearing values for the same sized pins and rivets as in the previous three tables.
The additional vertical columns to the left in these tables give the areas of cross sections in square inches, of the different sized pins and rivets, which multiplied by ten give their weights in pounds per yard of Length for wrought-iron, (for steel add 2 per cent to the weight of wrought-iron). There are also full heavy curve lines giving the strength, in tension, of tie-rods of same diameter as pins or rivets. The values selected for these curves are those always used by the writer in calculating pins, rivets or tie-rods.
No reliance on butt.
Explanation of Tables.
Tables xxxv, xxxvi, xxxvii.
Tables xxxviii, xxxix, xl.
It sometimes becomes desirable, in temporary work to use higher values, or in very important permanent structures with moving loads to use lower values. But even in such cases the tables can be used, for, as all of these curves are directly dependent on the area (or double area), of cross section of the rivet or pin, they can, of course, be used interchangeably. That is, any one who wishes to Figure the safe shearing