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.
Cover-plates, as in Figure 170, should each be the full width of original plates and at least one-half the thickness of same; in practice they too are each made about 1/16 inch (or more) thicker.
The plates A and B are themselves, of course, of the same thickness.
Now to prevent failure by the first method, compression, there must be area enough at both G H and C D, (if plates are in tension), not to crush the rivet or the plates at these points, (C D + E I and at G H in Figure 170). This area is considered equal to the thickness of either plate A or B (or of cover-plate or their sums) multiplied by the diameter of rivet-hole.
To resist failure by the second method, single-shearing of rivet, the area of cross-section of each rivet must be sufficient not to shear off under the total strain on either plate A or B. It will be readily seen that only the rivets in Figures 1G8 and 169 are subjected to single shearing, viz: at their sections G D. The rivets in Figure 170 have two areas resisting shearing, G D and H E, hence are subjected to double shearing ; therefore their area of cross-section need only be sufficient to resist a shearing strain equal to only one-half of the total strain on either plate A or B, in order to avoid failure by the third method.
To avoid failure by the fourth method, the rivet must be sufficiently strong to resist the load as a lever in Figures 168 and 169, and as a beam in Figure 170. In Figures 168 and 169 we can consider the part D C F G as the built-in part of a lever, with a free end D EH G which carries a uniform load equal to the whole strain on either plate A or B.
In Figure 170 we have a beam supported at CD G F and E I J H, with its span or central part G H E D loaded with a uniform load equal to the whole strain on either plate A or B.
To prevent failure by the fifth method the area of cross-section of either plate taken at right angles across same through the rivet-hole - (that is, deducting the rivet-hole from the area of cross-section) - should be sufficient to resist the tension or compression. To prevent failure by the sixth method the rivets must be far enough from the edges of plates (cover and original plates) not to shear out the metal ahead of them. The rule is shown in Figure 171. Make angle A 0 C=90° that is a right angle (0 being the centre of rivet-hole and C A part of its circumference), and so that the directions of O A and O C are at 45° with edge of plate D B. Then the sums of the areas A B+ CD- (that is, A B+ CD multiplied by thickness of plate) - must be sufficient to resist the longitudinal shearing strain, which in this case would be the strain on either plate A or B (Figures 168 to 170).
Failure by Compression.
Failure by Shearing.
Failure by bending.
To put the above in formulŠ we should have :
Failure of plate.
Failure by rivets tearing out.
x = s/d.h (c/f)
Use x for lap joints only.
Use 2 x in place of x for butt joints with single or double cover-plates.
SingleShearing x = s/0,7857. d2. (g/f)
Use a:for lap joints only.
Use 2 x in place of x for butt joints with single cover-plate.
x = s/1,5714. d2.(g/f)
Use 2 x or butt joints with double cover-plates.
x = s.h/0,1964.d3 (k/f)
Use x tor lap joints only.
Use 2 x for butt joints with single cover-plates.
x=s.h/0,7857. d3.(k/f )
' The fourth decimal given in formulas is not quite right, but is made to correspond with fractions used in Table I.
Use 2 x for butt joints with double cover-plates.
Tension on Plate h = s/b.(t/f)
Use ( c/f) instead of ( t/f) if plate is in compression.
Shearing end of plate.
f = s/2.h.(g/f)
(If more than one rivet use s/x instead of s for distance of each rivet from end as shown in Figure 171.)
Where s = the whole load or strain, in pounds, to be transferred from one side of the joint to the other.
Where d= the diameter of rivet-hole, in inches. Where h= the thickness of plate, in inches. Where more than one plate is used, take for h the least aggregate sum of thicknesses of all plates acting in one direction. (The sum of cover-plates should at least equal this aggresrate in thickness and should be larger, where the net b of cover-plates is smaller than the net b of connected plates.)
Where b = the net breadth of plate, in inches, that is the breadth, less rivet-holes, at the weakest section ; where more than one plate is used they should all of course be of same breadth. The net b of cover-plates will frequently be much less than that of original plates, as they lose the greatest number of rivet-holes at their centre, where they are carrying the full strain.
Where x = the total number of rivets required at the joint for lap joints, and the number required each side of joint for butt joints with single or double cover-plates; that is in the latter two eases 2x will be the total number of rivets required.
Where y=in inches, is the length A B or C D (Figure 171) from any rivet to free edge of plate; where more than one rivet is used, insert s/x in formula, in place of s. It will only be necessary, of coarse, to calculate y for the line of rivets nearest free edge.
Where ( c/f )= safe compression stress, per square inch,
Where ( t/f. ) = safe tension stress, per square inch,
Where ( g/f)= safe shearing stress, per square inch,
Safe Stresses on Rivets and Pins.
The writer uses the following values, as a rule for rivets and pins.