Year: 1885

page_text: I, WILLIAM CHARLES CARTER, of 129 Pottinger Terrace, Albert Bridge Road,
Belfast, Ireland, Engineer, do hereby declare the nature of the said invention, to be
as follows:-
My invention has reference to a special arrangement of calculating logarithmic
scales with slides, by the movement and setting of which, the several equations for
any particular strength of rivet joints of steam boilers or other work are indicated
at once, without the labour of resolving these by actual calculation.
That is (amongst others) for finding the value of p, the pitch of rivets in the
ordinary equation-
P
P = pitch of rivets.
n = No of rows of rivets.
a = area of rivet.
=
thickness of plates.
<:
And which instrument I hereinafter term a "Boiler joint calculator" or
"Calculator."
Referring to the accompanying sheet of Drawings, Figure 1 shows a front view
of this "Boiler joint calculator" complete, with its two slides * 1 and * 2 working
in grooves in the upper and lower parts A¹ and A' of the body of the scale and
edge to edge at their centre joint over a centre rib at A in the body part so that
their division lines touch each other, and may be made to coincide or indicate the
incidence or divergence from the coincidence of this. While Figure 2 is a back
view of the lower slide 2 which has division scales on this side also for being
reversed and touching the divisions on the upper slide, to find the strength of the
joint for either the plates or the rivets. And Figure 3 is a transverse section of
the calculator Figure 1..
In addition to solving the simple formula given above, this calculator is so
graduated as to allow (1) for single or double shear rivets, (in any ratio of from
1 to 2 times the shearing area for rivets in single shear; the Board of Trade and
D
071

page_text: Lloyd's allowance being 14 times for double shear) and (2) for any proportionate
value of shearing strength to tensile strength that the Designer may wish, the
Board of Trade ratio for steel rivets in steel plates being for one square inch in
shear of steel in tension as shown by line B (of the lower slide Figure 1 on
the fixed scale below) while that of Lloyds is indicated in like manner by the
line L.
The divisions and lines marked 1 and 2 on the upper fixed line A¹ of the scale
indicate the value of rivets in double shear as compared with rivets in single shear
in any proportion desired and the divisions are proportional to the logarithms of
the numbers.
The divisions and lines marked Nº of Rows on the upper edge of the upper
slide 1 indicate the number of rows of rivets 1 to 5 in the joints and they are
divided proportional to the logarithms of the respective numbers, the position of
the figure 1 on the slide * 1 being opposite to the figure 1 on the slide * 2
(Thickness of plate).
The divisions on the lower edge of the upper slide marked "Size of rivets," are
proportional to the logarithms of the areas of the sections of the rivets.
The divisions and lines marked "Thickness of Plate" on the front upper edge of
the lower slide * 2 indicate the thickness of the plates of the joints from 0 and
inch up to 1 inches, proportional to the logarithms of the numbers indicating
the thicknesses of plate as regards the divisions to the right of the figure 1, those
to the left being proportional to the logarithms of the reciprocals of the numbers
indicating the thicknesses of plate.
."
"
The divisions and lines marked "value of rivet section on the front lower edge
of the lower slide indicate the per centage, (marked 50 to 100%) of value of plate
area in tension, allowed for the rivet area in shear and are divided proportional to
the reciprocals of per centages expressed as fractions thus-the divisions marked,
50% is proportional to the logarithms, of the reciprocal of 10 set off to the left
hand of figure 1.
°
The divisions and lines marked 50 to 100% per centage of joint, on the left of
the lower fixed scale, indicate the per centages of joint for plate or rivet, and are
divided proportional to the reciprocals of per centages expressed as fractions set off
to the left of Figure 1 as above.
1
The divisions on the lower part of *1-size of rivets are-as stated-pro-
portional to the areas of rivets, but the line (imaginary) which would represent
the 1' from which the divisions are stepped off coincides with the 1 of the scale
No of rows
on the upper edge of this slide and represents that diameter of rivet
which would give an area of 1.square inch.
"
°
"
On these scales "size of rivets," "Thickness of plate," "Value of rivet section,"
" age of joint," all the divisions to the left of the I are proportional to the
reciprocals of the respective numbers; those on the right to the logarithms of the
numbers themselves. The scale "Pitch" is set off with divisions proportional to
the logarithms of the numbers themselves but from left to right as is the "No of.
Rows" scale.
י
To prevent confusion, and make these scales more easily understood they are not
subdivided into such small proportional divisions as they would be in reality for
practical use.
In the first instance assume the slides to be closed up the calculator gives the
theoretical pitch which would be correct for equal strength of plate and rivet.
Having found the nearest possible pitch to which the joint will divide out, then
the actual per centages of the pitch adopted are found.
The way to use the Calculator is as follows:-
>
To find the pitch of the rivet holes of a rivet joint in single shear, place the
"No of Rows" on the upper edge of the upper slide 1' to coincide under the
line SS, of the upper index. line A, then bring the "Thickness of Plate" on
the upper edge of the lower slide * 2, under the size of rivet on the lower edge

page_text: of the upper slide, then opposite the "value of rivet section' adopted on the lower
edge of the lower slide, will be found the "Distance between rivet holes
lower fixed scale A¹.
"
on the
To find per centage of joint (1) for plate,-Reverse lower slide (the divisions
scales of which are shown in Figure 2) and place the 1 of the line of "pitches" on
the lower edge, over the "Distance between rivet holes," and below the pitch of
said line on the lower line A' will be found "per-centage of joint" (plate). (2) To
find per centage of joint for rivet in single shear, place "No of Rows" under the
line S. S. then bring Thickness of Plate (of the back scale Figure 2) under "Size of
rivets," and under the "Pitch" will be found per centage of joint for rivet.

page_text: Resolving the Problems Connected with the Rivet Joints of
Steam Boilers and other Rivet Work.
I, WILLIAM CHARLES CARTER, of 129 Pottinger Terrace, Albert Bridge Road,
Belfast, Ireland, Engineer, do hereby declare the nature of my invention for
A NEW OR IMPROVED ARRANGEMENT OF CALCULATING 'SLIDES FOR RESOLVING THE
PROBLEMS CONNECTED WITH RIVET JOINTS and in what manner the same is to be
performed, to be particularly described and ascertained in and by the following
statement:
My Invention has reference to a special arrangement of calculating logarithmic
scales, with slides, by the movement and setting of which, the results of the several
equations for any particular proportion of rivet joints of steam boilers or other
work, are indicated at once, without the labour of resolving these by actual
calculation.
That is, firstly, for finding the value of d, the distance between rivet holes, in
the ordinary equation d = 1ª when d distance between rivet holes n = number
па
=
of rows of rivets or number of rivets
t = thickness of plate.
in each pitch, a = area of rivet section
Secondly, for finding the value of P₁, the percentage of strength of plate in the
joint, in the ordinary equation p₁ =
d) where p = pitch of rivets, d = diameter
of rivets.
100 (P
P
-
Thirdly, for finding the value of p, the percentage of strength of rivet in the
joint, in the ordinary equation p₁ = * xa x 100
where n = number of rows of rivets,
pxt
or number of rivets in each pitch, a = area of rivet section, p =
t:
-
thickness of plate.
pitch of rivets,
And this Instrument I hereinafter term 8 "Boiler Joint Calculator," or
"Calculator."
Referring to the accompanying sheet of drawings.
Figure 1 shows a front view of this "Boiler Joint Calculator" complete, with
its two slides B₁ and B₂ working between the upper and lower portions of the
scale A, and A., which are fixed and held together by the brass plates 2, x, those
plates which come to the front of the Calculator being cut away as shown so as to
avoid obscuring the figures marked upon the slides B, and B. These slides, B₁
and B, work together edge to edge at all the joints so that their division lines
touch each other, and may be made to coincide in any position required.
Figure 2 is a back view of the lower slide B, which has division scales on this
side also for being reversed and touching the divisions on the upper slide B₁ and
the lower fixed scale A., to find the strength of the joint for either the plates or
the rivets,

page_text: Figure 3 is an end view of the Calculator, Figure 1, In addition to solving the
simple formula giving above, this Calculator is so graduated as to allow. (1) for
single or double shear rivets (in any ratio of from 1 to 2 times the shearing area
for rivets in single shear, the allowance under the Board of Trade, & Lloyd's
Surveys being 14 times for double shear) and (2) for any proportionate value of
shearing strength to tensile strength that the designer may wish the Board of
Trade ratios for steel rivets in steel plates being, for 1 square inch in shear,,,
or 38 of steel in tension, according as the strain allowed upon the plate in tension
is 28, 29, or 30 tons on the square inch respectively, the ordinary allowance of
being shewn by the line B, while that of Lloyd's for steel plates and rivets, of
85 per cent is indicated in like manner by the line Ļ.
5,
The divisions and lines marked 1 and 2 on the upper fixed scale A, indicate the
value of rivets in double shear, as compared with rivets in 'single shear, in any
proportion desired, and the divisions are proportional to the logarithms of the
numbers set off from left to right.
"
The divisions and lines marked N° of Rows, on the upper edge of the upper
slide B, indicate the number of rows of rivets 1 to 5 in the joints, or the number
of rivets to each pitch, and they are divided proportional to the logarithms of the
respective numbers, the position of the figure 1 on the slids B₁ being opposite to
the fig. 1 on the slide B, (Thickness of Plate).
The divisions on the lower edge of the upper slide marked "Size of rivets" are
proportional to the logarithms of the areas of the sections of the rivets, but the
line (imaginary) which would represent the 1 from which the divisions are set off
coincides with the 1 of the scale "No of Rows" on the upper edge of this slide and
represents that diameter of rivet which would give an area of 1 square inch.
The divisions and lines marked." Thickness of Plate" on the front upper edge of
the lower slide B, indicate the thickness of the plates of the joints from inch up
to 1 inches, the divisions being proportional to the logarithms of the numbers
indicating the thicknesses of plate as regards the divisions to the right of the fig. 1,
those to the left being proportional to the logarithms of the reciprocals of the
numbers indicating the thicknesses of plate, assuming the divisions to be set off
from the fig. 1 in each case, those of a greater value to the right and those of a less
value to the left.
.
The divisions and lines marked "value of rivet section" on the front lower edge
of the lower slide B, indicate the percentage (marked 50 to 100°) of value of
plate area in tension, allowed for the rivet area in shear, and are divided pro-
portional to the logarithms of the reciprocals of the percentages divided by 10
thus the distance between the division marked 50%, and that marked 100% is
proportional to the logarithm of the reciprocal of 5 set off to the left hand of the
fig. 1 or 100.
°
The divisions and lines marked 50 to 100 % "per centage of joint," on the left
of the lower fixed scale, indicate the percentages of joint for plate or rivet, and are
divided proportional to the reciprocals of percentages divided by 10 set off to the
left of fig. 1 as above.
31
On these scales "Size of rivets" "Thickness of plates "Value of rivet section
"Percentage of joint," all the divisions to the left of the 1 are proportional to the
logarithms of the reciprocals of the respective numbers; those on the right to the
logarithms of the numbers themselves.
The scale "Pitch" is set off with divisions proportional to the logarithms of the
numbers themselves, but from right to left as is the N° of rows scale.
To prevent confusion, and make these scales more easily understood, they are
not subdivided into such small divisions as they would be in reality for practical
use.
In the first instance assume the slides to be placed with the faces as shown in
Fig. 1. The Calculator, by moving the slides so as to bring the lines indicating
the scantlings of the joint into coincidence, gives the theoretical pitch which would
be correct for equal strength of plate and rivet. Having found the nearest possible

page_text: pitch to which the joint will divide out, then the actual percentages of the pitch
adopted are found.
The way to use the Calculator is as follows-
To find the pitch of the rivets in a joint with the rivets in single shear, place
the division line indicating "No of Rows" in the upper edge of the upper slide B₁
to coincide with the line S. S. on the upper fixed scale A, Then bring the division
line indicating the "Thickness of Plate" on the upper edge of the lower slide B,
under the division line indicating. the "Size of rivet" on the lower edge of the
upper slide B₁-then, opposite to the line indicating "Value of rivet section "
adopted, on the lower edge of the lower slide, B,, will be found the "Distance
between rivet holes" on the lower fixed scale A, By adding the diameter of the
rivet the Pitch is found.
To find the percentage of joint (1) for plate-
Reverse the lower slide (the divisions then uppermost are shewn in Fig. 2.) and
place the 1 of the line of "Pitches" on the lower edge over the " Distance between
rivet holes" and below the line indicating the Pitch, will be found on the lower
fixed scale A, the " Percentage of Joint" for plate. (2) To find percentage of joint
for rivets in single shear. place the division line indicating No of Rows "under the
line S. S. then bring the line indicating "Thickness of Plate" (of the back scale
Fig. 2) under the line indicating "size of rivets" on the lower edge of the upper
slide, and below the line indicating the Pitch will be found on the lower fixed
scale A, the "Percentage of Joint" for rivets.
Having now particularly described and ascertained the nature of my said
Invention, and in what manner the same is to be performed, I declare that what
I claim is
t
(1.) The application of sliding logarithmic scales with special divisions as herein-
before described, to the solution of the equation d = a.
na
=
100 (P-
(2.) The application of sliding logarithmic scales with special divisions as
herein before described, to the solution of the equation p₁
d)
(3). The application of sliding logarithmic scales with special divisions as herein-
before described, to the solution of the equation p. nx ax 100
Dated this Twentythird day of July 1886.
=
Pxt