STR
472
STR
Table IX.
1st.
2nd.
3rd.
4th.
Table X.
7
11570
11570
0
8
9968
9838
130
L.
4 In. sq.
5 In- sq.
6 In. sq.
7 In.sq.
9
8722
8365
357
7
5312—
10375+
17928+
28469+
10
7725
7189
536
8
4568—
8925+
151K —
24481 +
12
6230
6152
78
9
3989—
7791 +
13464—
21380+
14
5162
5389
227
10
3526+
6887 +
11901—
18899-1-
16
4361
4452
91
12
2832 +
5531 +
9558—
15177 +
18
3738
3815
77
14
4462+
7884—
12519+
20
3240
3353
113
16
3835+
6628—
10525+
22
2832
3116
284
18
3270+
5652—
8975 +
24
2492
2316
176
20
2818+
4870+
7734+
28
1958
1954
4
22
2448+
.
24
2140+
From the above rule, which is only applicable to the five-
28
1656+
inch bars, another mort
general one
has been derived ; which
IS. S :
651 bd*
’’ l
10 b d\
This formula is founded on the following observations : aconstant number may be added to each column, which willincrease the numbers therein contained in .the reciprocal ratioof their lengths : the constant additive number of one columnis to that of another as the cube of the side of the beams ofthe former to the cube of the side of the beams of the latter :therefore, 5 3 : l 3 :: 1245 : 9.96, or 10 nearly, for the additivenumber to a bar of an inch square. Again, 5 3 : 4 3 :: 1245: 6.37, or 6.40 nearly, for the additive number to a beam offour inches square; consequently, the relative strength of apiece of a foot in length, and an inch square, taking 5312 for
... , . 5312 + 640 X 7 ...
a radical number, is-—-10 r= 641.
o4
The relative strength of a piece in general will, therefore,
10 d\
, 651 bd* ,, . 651 d 3
be-;-10 b d, or, in square beams,
l
l
Example .—What weight will be required to break an oakbeam twenty feet long and eight inches square ?
651 x 8 3 . ,
That the reader may judge properly of the application ofthis rule, the following Tables have been calculated. Thefirst contains the numbers according to calculation ; thesecond, the differences between the first Table and the Tableof experiments ; where it may be observed, that six, seven,and eight-inch beams differ less and less from the experiment,as the beams are longer : the greatest difference is in theseven-inch beam of seven feet long, which is somethinggreater than one-ninth, and less than experiment.
This rule is sufficiently exact for practical purposes, as inmost cases it gives a solution within the fifteenth part ofwhat would result from experiment: though the principleupon which it is founded cannot be admitted to be just, for
when the length is 65.1 the quantity —-- :and, consequently, the strength would be nothing.
10 b d *
Table XI.
L.
7
89
10
12
14
16
18
20
22
24
28
4 In. sq.
5 In. sq.
6 In. sq.
7 In.sq.
0
+ 1150
+ 1022
+3731
+ 18
+ 866
+ 108
+1569
+ 36
+ 517
— 314
+ 970
+ 86
+ 238
— 651
+ 576
+ 155
+ 544
— 458
+ 998
+ 738
— 409
+
--3
O
03
+ 515
— 266
+ 475
+ 430
_ 90
+ 270
+ 407
+ 80
+ 641
. + 527
_
+ 22
_ .
+.119
rinc'P
lies.
other P rl f tl' e
The succeeding Table is calculated u P on , s qu» re 0viz. that the strength is as the breadth a fifth P 0 fdepth, and reciprocally as the fourth root o ,j, 0 f a be
of its length ; and that the mean relative s i °. g found . 0 {oak, one foot in length, and an inch s<l ua ,,/ive str eI1 » g s*1,000 lb. nearly; therefore, let s be the re '. , thena piece of timber, b the breadth, and d the a jith'
This formula is exceedingly eas 7 ’ 0 fl°fP}”
metical operation will be much simplified ^7 . j on ® (fidrithms. The radical number, 1000, is 01 foot 1°
experiments, and is reduced to a piece
of one