STK
469
STR
« a 1 other as 3, 2, 1 ; hence, the relative strength of beams,^cording to the system of Mariotte, is two-thirds of Galileo ’s ;irt i ’ acc P r ding to the supposition of the axis fracture being,l. le middle of the beam, the relative strength is'only one-of Galileo ’s, or half of Mariotte’s.ij worthy of notice, that, although the relative strengthV f r ^ different on the three suppositions, yet in each it isbit' * e breadth, duplicate ratio of the depth, and reciprocalai) !° of the length. This relation is the most important;1, ; exactly true, would answer every purpose : for, byS j 0 ln o the weight that a piece of timber of any given dimen-gj v s will carry, that which a piece of timber of any otherh„ ® 11 dimensions would bear, might be ascertained, withoutany attention to the absolute strength.
Is r i Ver y commodious formula may be had froi' g°hows :—
^Ppose a piece of timber, a foot in length and an inch0 (| ‘ re > Would carry w pounds ; let l be the length of anyin , r Piece of timber in feet, b the breadth, and d the depth'•tubes j and let W be the weight in pounds that these
, b d 2 w
,s >ons will carry ; then W = — j —,
'toy 1 X li b d 2
• 1
fe lap ' S> t ' le strength
iom this analogy,
for,
by this ana-b cP w
.. w : w ; therefore, w_ ^
.,__of any piece of timber is equal to the
1( ,j lv ® strength of a piece of timber a foot in length and an^dh S( l Uai ' e > multiplied into the breadth and square of thedivided by the length.
to **mpU. —Suppose a piece of timber a foot in length and
Pi.
> a el
e 1 square, would carry 500 pounds, how much will ae e ight feet in length and five inches square carry ?e w = 500, 5 = 5, and d = 5 ; therefore,
5 x 5 s X 5008
= 7812.5.
hei n ' Pieces of timber of the same length, the relative strength,4 V(,( as the breadth and square of the depth, differs but inhut J s mall degree from that which actual experiment gives;S fi(1 pi'der to show how far the practical carpenter mayJet s a 1,1 the rule just found from the theory, we have twoj ^ x P ei 'iments, made on oak timber, one by the cele-'v drench engineer Belidor , on a small scale, the other' ’ be Buffon, much more extensi
The pieces tried by
h'^lt'c^ 6 buffon, muc h more extensive, with which the>|j,j uu »d by rule may be compared.
Were sound, evenly-grained oak, and tolerably well. > and the relative strength resulting from the variousV\ 0n a tried, are exhibited in the following Table;’ u must be observed, the lengths are in the second
>ti c - • i
■ \ s j c °lumn, under L, on the left, and the other dimen-l he columns under the initials b and d. The weight|%i 0 1 *0 break the beams is given in lbk in the fifth
’ ^‘Ift ** - - * p 1 - 1 *- - - - i— - - - 3 J
"lean
■Three pieces of each dimensions were tried, andSe taken. The experiments were of two kinds ;\(j_ "dtk the ends loose, the other with the ends firmlyla t]
Jf 0i j e following table—
if 0 . , an d 2 show the strength to be as the breadth.
\ j ar *d 3, as the square of the depth.
. ^o, 4 an< f 4, nearly as the reciprocal of the length.
"’t&t'B „ atl( l 5, nearly as the breadth multiplied into thej < of the depth.
.. an d 5, nearly as the breadth multiplied into the((Ha , depth, divided by the length.
lower numbers, 7 and 8, show the increase of
V
s ^ derived from fastenin
tto.
the two ends. By com-
H, , ” f with No. 7, and No. 4 with No. 8, the strength
*• 6 D
of the loose bar to that of the fixed one, appears to be in theratio of 2 to 3 ; but the theory shows it to be in the ratioof 1 to 2, that is, as 2 to 4 ; though a difference in the man-ner of fixing may produce this deviation.
Table I.
N.
L.
B.
D.
lb.
Medium.
401
\
i
18
i
i
415
406
405
810
2
18
2
i
795
805
812
1570
3
18
1
2
1580
1580
©
1590
O
—
185
4
36
1
1
195
187
w
180
1550
5
36
2
2
1620
1585
1585
1665
6
86
If
2*
1675
1660
1640
«
600
7
18
1
1
600
608 i
624
-6
X
V
<G
285
a.
8
36
1
1
280
283 1
c
1
285
The following Table is an abstract of experiments onbeams of four inches, by Buffon. The first column containsthe length of the bar in the clear, between the props. Thesecond, the weight of the bar, the next day after it was felled,in pounds. The third column exhibits the number of poundsnecessary for breaking it in the time shown by the fifthcolumn. Column the fourth shows the inches bent in theact of breaking; and the fifth, the time required to breakeach beam. Two bars of each length were tried, and eachof the first three pairs were cuts of the same tree.
Table II .—Experiments on Beams Four Inches Square.