N AK

229

N AK

raf ter x „ ,

^hethe • < oes not rest exactly upon its middle, the fulcrum,aruj r ^ sustains one-half the weight of the rafter at x,placed at 161 ° n t ' le wa " ! tben also the half of the burden is

“It

A, t 0 ^ 18 obv >ous, from this calculation, that the joinings aboutthe p a a, f- tbe m lddle of the framing, press most of all. Sincer;ift er; . r n ' cu ' ar weight of these is about nine of the longerto eaeli f Ut tbe others, less by a ninth part of the wood)raft er f °* w *uob there will be added, half the weight of thehre a k 01 '? l lTlneS3 deducted, lest by its own weight it shouldlying’ u and Moreover one-half of the weight of the joint cby conn?°” I*®* 11 ? about four of the rafters. And so,ter sin? u' n ° tbe whole, the strength requisite, lest a raf-the wein-t £' ve way, will equal more than thirteen timesS *t of the rafters, and be about fourteen times9 2 7lQi

3^ + 4 394549_ _ . 503313_ _ 167771

cop, 1360668 “ 1360668 - 453556

“ No*^ 011 * n Wu 'ght of each rafter.

0, igest ° U ) t can now remain that the rafters, even theS ' lst ain’a < ?' n n ' a< ^ e of such firmness as shall enable them tofourth? ^ e 'ght that may be placed upon them individually

the

a ” v “ u *' 'Aiuj mv/ j/mwu uyv»» tiiotu uiui» tviuaiij'

t *°Ulited the weight of the whole; neither can it be

C! *“ possibl at ra ^ ter ' n o °1 tb's description is the safest that*° can,-; ^j' Je a PPl' et l t0 P UI 'P oses where great weights are

tin Mother f

°lhcr f 0| . m j. 1 ™ of this construction. Figure 6 exhibits

■ l . 6 endg 011 ?’ differing from the preceding in this, that where^'Oed by -°‘ tWo of the rafters lie upon a third, they arellotc bed a 'T° distinct dovetails ; into these a third rafter is*t. . j, e n d all are so placed as to be supported by those

<v ° othov. C , e to die middle part of each rafter are fastened“ ers > but tn „--

p. ~‘°t but to opposite parts.

exhibits the lateral face; thei ° n ’i° u s from Figure 6.

“ t! eri pd') and similar amonbe . ut here, as ‘

upper face is suffi-All these rafters are of anthemselves.

"injure 0 e> . as ‘ n the preceding construction, the work may’ be... . tess extpnrle/i nr.A _

ee 9u U exten ded, and the condition of the timberb "*8bt n a ..y determined both as to the aid it gives and the

- Tn . • - -

th

>8 «

O

th e b * can T' For, as in the protracted area, the num-tli c ° n stru f ams j s augmented, so is also the weight. Buttl, 6 b eatp s > ° I* attended with a disadvantage from bothill? bur dcn lying upon one, which having to endure

’•"'o

b tb at

to

done • ” r ““-““>“'6 C “ UU1C

p r lnc *ividual part of the beam, it is more stre-v,j e d: that is, it lias to sustain the entire weight

ends n -* -- — ...

of °® e entire beam ; for, in this construction, equal' 10 be la ' b > which in the preceding was not borne, isat one and the same point ; on thisb 6g > b y bei*,, w °°d at that mortise is. very much weak-Whi c }, ® cut away to enable it to support the twose e ^ reat their tenons in one place. This in some8t ty e d tow ar j bo be compensated by the resting timbers beingit J av t s °PPosite parts, which in the n receding eon-

opposite parts, which in the preceding con-I,’ 8 Hot J Awards the same parts ; although, in this alsoCb^ 8 * test- rnuc ' 1 consequence, especially if the ends of t ebu! tl p § on the others, are not extended toward theai- 1 b is ^Pt pretty close to the outer part of the framing,i, tect. aSll y done by the judicious management of the& Ut *b‘ .

kl P'an *? '“convenience forms no substantial objection to

to , ... 8,t ' c e tb- - - -

Vlf\

%

hi

f *. * «ui C a it —ouMotaiiiiai uujcouun iu

^ tb° 8ll Pport he ra fter8 are sufficiently strong and wellla \ s " b ioin a ?y P ro P or tionate weight, as will be obviousc eg ^ -'kioy mvestigation of their strengt

gth.

e former of these--vtung ttt what is before ns. re & disposed

.At n, eins the stronger, because the ' , e „ e ^ while wt

^ ktte r V ^^ liman 8 bip is more obvious ^ intervals areVoi,, B 't 18 scarcely distinguishable,

3 s

so varied as to give the work a distorted appearance : yet inboth they are squares ; and in the latter the spaces beyondthe half-rafter from the wall-beams are also resolved into thesame figure.

“The calculation in this construction, will result fromthe same principles as in the preceding ; but here it willbe much more expeditious, because, as all the timbers areof the same length, and they support the weight of the cor-responding timbers about the centre, they are almost allpressed by an equality of weight about the same part: allwhich conduce to render the results more readily to beobtained.

“ Calculation adapted to this construction.

“ With respect to the facility of this calculation, it may beobserved, that the points (whether five or four) which aresimilarly posited in respect of the scheme, and on thataccount support an equality of weight, are designated by thesame symbol that was adopted in the preceding problem.But, here, on account of the individual pieces of wood sup-porting the same weight, and that too about the same part,the two ends of each rafter have to support the same weight ;these ends we shall therefore express by the same symbols,the equal weight being denoted by a similar sign. Othermethods of proof might be mentioned, but the foregoingwill be sufficient for our purpose.

“ SYNOPSIS OP THIS CALCULATION.

1. A = a= |T + B.

2. B = P = iT + lK + }r

3. C = 1 T + A.

4. D = S =£t + L.

5. E= £ =iT + l/3-flK.

6 . r=|T+ic + |G.

7. G=y=^T + E.

8. h = 1t + |« + |d.

9. I = . = |T + h + lN,

10. k = * = Jt+1h +*I.

11. L = X = ^T-|- £ K .

12. M = p = i T 4- £ P.

13. N = v — It + i\ + ^M.

14. P = Jr = iT +

15. Q = At. +

16. E=p = ^T + ^7r-f^Q.

17. c = t 4- b, by 3, 1.

18. d = t -(- i k, by 4,11.

19. f = i t 4- \ b 4 - X e, by 6, 7,17.

20. h = A t 4- 4 b 4- } k, by 8, 1, 18.

21. M = | t 4- by 12, 14.

22. n= T 4- + 4 P, by 13.11, 12.

23. N = | t 4- J k 4- l i, by 22, 14.

24. Q = | t 4 - £ e, by 15, 7.

25. k = | t 4- | e 4- i«, by 16, 14,24.

26. b ~ |t 4 - £ b 4 - £ e 4 - £k, by 2, 19.

27. B = 9 ; + 2 6 B + 4 3, by 26.

28. e = t + e + J i -{- } k, by 5, 25,27.

29. e = 8 7 t + 6 i +J 6 k 28 _

34

30. H r= 2 T 4- £ e 4- A x, by 20, 27.

31. i = «t 4- f£ 4- tb i + by 9,23.

32. x = 17* + 8 £ + 2_*

15

K = ftT + *E 4--248 t + 42 eK ~ 77

, by 31.

k, by 10, 30, 32.by 33.