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.
Number of rivets in web leg of angles.
Frequently many more rivets will have to be used than are required by calculation in order not to exceed the greatest pitch for rivets given in Formula (107).
To ascertain the number of rivets required (along either web edge) between any two points of girder, we will, of course, take the difference between the numbers required from each point to end of girder.
In the flange leg of angles usually fewer rivets can be placed than in the web leg, though many good engineers frequently make them equal in number. But this is really unnecessary, for even if the strains on the flange rivets were the same as those on the web rivets (which they are not) we should still have two rivets in the flange to one in the web on all single plate girders.
There seems to be considerable difference of opinion as to just how to Figure the strain on the flange rivets. The best course would seem to the writer to be, to assume that each flange cover plate must transfer at each of its ends, by rivets, to the angle iron and parts of flange plates between it and the angle iron, an amount equal to the safe stress the plate is capable of exerting (that is, net area of cross section of the plate multiplied by either the safe compression stress ( c/f )or by the safe tensional stress ( t/f ) as the case by be).
This amount should be transferred by sufficient rivets, between the end of each plate, and the point of girder at which the full thickness of the plate is required to make up the required moment of resistance. From this point to centre the rivets can be spaced according to the rule for greatest pitch, Formula (107), but when rivets are so spaced the pitch of the rivets immediately nearest the ends of any cover plate should be greatly decreased for a distance of three or four rivets at each end.
By the above method the amount of strain on rivets can be quite accurately computed.
The simplest method of locating rivets is to construct what might be called the curve of moments of resistance. This can be done as shown in Figure 161, Chapter VII (Graphical Analysis Of Transverse Strains) (where C D K F G C is the curve of moments of resistance), or we can calculate arithmetically the required moments of resistance at several points of girder, and layout the curve as shown in Figure 196, where A B represents the length of girder, and M C, ID and N E the calculated required moments of resistance at points M, I and N.
Numberof rivets in flange leg of angles.
Locating flange rivets.
The curve of moments of resistance is, of course, A C D E B, and its axis or base B A.
H D will now represent the total required thickness of flange plates, which we can find from Formulae (36) or (98).
We will decide to divide it into three layers H G, G F and F D. We draw the lines as shown and find that plate No. 1 can stop at K, though it would be better to run it full length, it is, however, needed of full thickness at J. Again plate No. 2, can stop at J, but is needed full thickness at L. The top plate, of course, will run from L to centre. The left half of girder, will of course be similar, the loads evidently being symmetrical each side of centre. In practice the plates rarely are stopped at the exact points calculated, but are usually extended beyond these points a distance equal to from once to twice the width of plate.
There must now be rivets enough between D and L to equal the efficiency of plate No. 3, between L and J to equal the efficiency of plate No. 2 and between J and K to equal the efficiency of plate No. 1. If there is not room to get them in the plates must be sufficiently extended to get them in, that is No. 3 must be lengthened beyond L and towards J; No. 2 must be lengthened beyond J towards K and No. 1 carried on towards end.
In laying out the rivets they should be as regular as possible, the best method is to lay out the total number of rivets required from centre to end, gradually decreasing the pitch towards ends, and then to make each of the plates No. 3, No. 2 and No. 1 of sufficient length beyond their respective point D (for No. 3) L (for No. 2) and J(for No. 1) to take in the number of rivets required. The length of plates may always be more than shown in Figure 196 without harm, but never less. We should have then for the bottom flange :
Regularity of spacing.
Number rivets in end of each flange plate.
Where x = the number of rivets required in each end of each flange plate between its ends and the nearer points to ends at which its full strength is required by the girder.
Where a = net area of cross-section of the flange plate, in square inches (less rivet holes), at its weakest section.
Where (t/f ) = the safe tensional stress, per square inch of the material. For top flange use (c/f) and look out that rivets are not so far apart as to cause bending or wrinkling of plates.
Where v = the safe stress, in pounds, or least value of each rivet. That is the bearing, shearing or cross-breaking value of the rivet, whichever is the smaller.
The rivets in the flanges will, of course, be cantilevers, loaded with their respective amounts of a. (t/f) or a.(c/f) respectively, a being the area as given in Formula (122). The free end of cantilever will be of a length equal to the thickness of the respective flange plate, or equal to the thickness of leg of angle iron, whichever is the smaller should be used.
The bearing area will be the diameter of the rivet multiplied by the same smaller thickness.
In single plate girders the shearing of rivets will rarely determine their number, this will generally be more than the bearing or bending value.