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.
Figure 197 shows clearly the way in which rivets are strained.
The web-rivet, No. 3, is bearing against web on the surface E F and against angles on the two surfaces (sum of) DE and FG
Value of rivets.
The rivet has two cross-shearing areas, at E and F. This rivet is a beam supported at D E and F G and loaded uniformity with its share of horizontal flange strain, which it is transferring to web.
The flange rivets, Nos. 1 and 2, we will suppose are connecting the flange plate A H to the angle iron. Their bearing then is against A H and in the opposite direction against B C, the lesser should be used. Their shearing area is either along the line H or the line B according to which end is considered the cantilever, so that they have only one shearing-area practically in the calculation, instead of two as with the web rivets.
Then rivets Nos. 1 and 2 are cantilevers and are built in either from H to C and loaded uniformity on the free end A H, or built in from A to B and loaded uniformly on the free end B C, whichever projection A H or B C is smaller should be used. The load on the cantilever being as already explained equal to each rivet's share of an amount equal to the net-area, of top plate A H multiplied by the safe tensional or compressive stress per square inch of the material.
There is, of course, a tendency of the plates HI, IB, etc., to slide past each other and past angles.
This tendency will exist particularly at the centre of girder and in those parts of rivets which simply tend to hold the plates together after the plates have once transferred their strength and become a permanent part of the flange. But this tendency rarely amounts to much, unless the plates are very thick ; and if the rivets are spaced according to rules given can be overlooked. If it is desired to calculate the strain on each rivet, due to this tendency of the flange plates to slide past each other, it can be done by the following formula, which assumes that at any right angled cross-section of flange through rivets there are always two rivet holes.
v = b/d. (x-y)2. (k/f) (123)
Where v = the safe value or stress on any flange rivet, in pound?, to resist the tendency of any two flange plates (or plate and angle leg) to slide past each other.
Plate tendency to slide.
Where b = the total breadth of flange plate, in inches.
Where d = the total depth of girder, in inches.
Where x= the distance, in inches, from the horizontal neutral axis of girder to centre of flange plate, further from neutral axis.
Where y = the distance, in inches, from the horizontal neutral axis of girder, to centre of flange plate (or centre of flange leg) immediately next to other plate, hut on the neutral axis side of same.
Where ( k/f) = the safe modulus of rupture, in pounds, of the material.
If any part of a girder, either web or flange, is spliced, made of two parts, the number of rivets each side of splice, and the amount of additional cover plates, etc., should be made sufficient to transfer the full strength of original plate across the joint.
In locating the rivets of a splice care should be taken not to weaken the original plate by holes not allowed for in the original calculation of moment of resistance of the section. There is no difficulty in splicing webs, as cover plates can be put on each side, and the strains in the web are comparatively small.
These (web-splice) plates and their rivets each side of joint should be of sufficient strength to transfer the amount of the vertical shearing strain at the joint from one side of (spliced) web joint to the other side of joint. In the flange, however, it is more troublesome.
In heavy girders, however, (the only ones usually, where it is necessary or where it pays to splice the flange plates), it is best to carry the upper or outside layers of flange plates a longer distance from the centre (or point of greatest bending-moment) than required by calculation, thus gaining extra material in the flange, and more than required there by calculation, and then using this extra material to offset the loss suffered by making the additional rivet holes and by cutting or joining one of the flange plates at the point. For instance. Figure 198 represents the side-view of part of the top flange of a plate girder. A B is the first flange plate running entire length of girder, A being towards end and B towards centre.
Splicing girder piates.
This plate has to be spliced. We have previously found that we can thin down our flange at the points F, E, D and C. We will decide to piece plate A B between D and E say at G. Of course the flange will thus be weakened at the point G by the entire loss of plate A B and if we attempt to regain this by cover plates it will lose the additional rivet holes. But by prolonging the upper plates as shown by dotted lines this loss can be made good and without any additional rivet holes.
For by the time the plate which originally ended at E has been ex. tended to G the girder is considerably stronger than needed, that is stronger by the amount of thickness of this extended plate, and the girder can therefore bear the loss suffered by the cutting of the lower plate. Providing, of course, the plates are of equal thickness. If there are not enough rivets between G and D to take up the strength of the spliced plate, the plate which ends at D will also have to be extended, as shown by dotted lines, till the number of rivets desired have been covered.
In many cases the extending of flange plates is sufficient to form the splice, but frequently an additional cover plate over the extended flange plate may simplify and cheapen the cost. The arrangement in each case will depend upon the number of rivets required, the respective thickness of plates and other local circumstances.