STR
475
STR
‘ Example 2. — Required, the weight that would break thetiii 6 ^ eam > when supported at each end, rejecting the defi.ee-n < which is very inconsiderable.
% Formula 2,
8 fad 8 x 13,000 x .732 x 366 _ noo1u
' r - 30 - y 8
^ 1 Example 3. —Required the weight that would break the, e beam, fixed at each end.
’■Rejecting the deflection, we have, by Formula 3,
^ 12 fad 12 X 13,000 x .732 x 366
l ~ 30 - 1492 lb>
k Note .—We have assumed 13,000 for the force of direct„ ea ion ; this, however, rather exceeds the greatest strength(( which varies from 10,000 to about 13,0001b.
Un ,Example 4. — Assuming the direct cohesion at 13,000,4^ the specific gravity of fir at 720; how long must a beampi l hat is two inches deep and one inch broad, which, when^ with one end in a wall, will just break with itsl Weight?
■Let x be the required length of the beam in inches ; its
Coh,
* ei ght
will be
tttd
«tie
2 a; X 7201728
90 x
5 x
ounces, orp^ = — pounds
this weight will have the same effect as if it acted all at
Point on the centre of the beam, or at the distance \ t>Renee, by substituting for w, in Formula 1,
192
5 a?
96 =
X 2
2 X 13000
96
X .732 x .366
X 13000V 1337285
X *.732 X
or,
5 a? z=
.366 = 133728 ; whenceinches, or 47 feet.
'IJ
,/nthis case, the angle of deflection is not introduced.
«a Se 'hen the deflection is considered, as it should be in this’ "'o find it to be, from the data of Example I., and the
° r ®tn for the deflection, as 30 s : 5 : : \ x 3 : ;
25 a; 2 \
(1800)/ !
5 , 2 X 13000 X. 732 X. 366
10 h becomes --
6ftce the cosine
Vt;
= V(!
and the above
96
Pr.
W(i _
a cubic equation, whence the value of x may be
. •i ined -
® an l fS ) after many experiments made, at various' °n the real and comparative strength of oak, fir, and- as deduced the following inferences : the worst, orloot l St> P' ec e of dry heart of oak, one inch square and oneV> ' )ore 6601b., though it was much bent, and 21b.
. °ke it. The strongest piece he tried, of the sameV e ^ l0t1s > broke with 9741b. The worst piece of deal^ols ’ but br °ke with little more. A bar of the
\l? st kind of cast-iron, of an inch square and a foot long,'"T| 6a k with 21901b.
Wo jj ' e following are some of the experiments he mentions ;
“ .g ai 'ks On the Power of Machines.)
^il j*P e riment 1.—T wo bars of cast-ir
feet long, were placed upon a horizontal bar, so as1(1 a cap at the top, from which was suspendedthese bars made each an angle of 45° with the
25 x 3 ^(1800// 5
which
\ h:
-iron, one inch square
base-plate, and of course formed an angle of 90° at the top ;from this cap was suspended a weight of 7 tons, which wasleft for sixteen hours, when the bars were a little bent, butvery little.
“ Experiment 2. —Two bars of the same length and thick- !ness, were placed, in a similar manner, making an angle jof 22^° with the base-plate ; these bore 4 tons upon the !scale; a little more weight broke one of them, which was iobserved to be a little crooked when first put up. In this icase the pressures would be as the sines of the angles ofelevation, viz., as 3826 to 7071, and as 3826 : 7071 : : 4tons : 7.6 tons; that is, if the second bars broke with 4 tons,the first ought to have taken 7.6 tons to break them ;and it is likely that such would, if tried, have beenthe case.
“Experiment 3.—Another bar was placed horizontallyupon two supporters, exactly three feet distant, which bore6cwt. 3 qrs. or 6751b. but broke when a little morewas added. i
“ Experiment 4. —The same experiment repeated with the ;same result. j
“ Experiment 5.—The bearings were 2 feet 6 inches apart, Jthe bar broke with 9 cwt. ,
“ Three more experiments were tried at three feet, the javerage result was 6 cwt. 2 qrs. and 6£ lb. I
“ Mr. Banks made some experiments on the strength of :cast-iron, at Messrs. Aydon and Elwell’s foundery, Wake- '
field. The iron came from their furnace at Shelf, near jBradford, and was cast from the air-furnace ; the bars, one Iinch square, and the props exactly three feet distant ; one {yard in length weighed exactly 9 lb. or one about half an jounce less, the other a very little more ; they all bent an inch
before they broke.
. lb.
1. The first bar broke with . 963
2. The second bar with . 958
3. The third bar with. 994 j
4. A bar made from the cupola . 864 j
5. A bar equally thick in the middle, but the ends
formed into a parabolic form, weighing 6 lb. 3 oz. 874
“ The same gentleman, after many other experiments,concludes from the whole, that cast-iron is from 3^ to 4^times stronger than oak of the same dimensions, and from5 to 6£ times stronger than deal.
“We shall only observe here, (says the writer of theStrength of Materials , in Rees’s Cyclopcedia,) tha»Mr. Banks ’s pieces of oak exceed very considerably thespecimens we had an opportunity of trying, while his fir fallssomething short of ours.”
The following Tables of Experiments on the strength otvarious materials under different circumstances will befound useful. They are extracted principally from Tredgold,to whose works, and those of Barlow, we would refer forfurther information :
Cohesion of a Square Inch, pulled asunder in a directionperpendicular to the Length of the Fibres.