ME C

157

ME C

CoW- ’ ^ ' s plain that nothing is concerned here but theau(j ;! 0n °1' the wires; for the beam is sawn through at A,Inst ^ arts are perfectly moveable round b and c.keep t * 1 ' s process, apply the piece A h below A, and

on a "here by straining the same wire, bhc, over it: layan<J ei SEt, which must press down the ends of b a and c a,inst ar , aUS ,? tbe pi ece aH to strain the wire bhc. In theb c jn 0 ^ rac ture of the same wire, its resistances, h b and^eak^ a, l* e equal to Ay and A g, and the weight h H, whichlast] em ’ must ' 3e e( l u al to A a.

8atn e employ all the three pieces, f b, ah, g c, with theth at t ^ Ire attached as before. There can be no doubt buta A ® height which breaks all the four wires must be =or twice a a.

8atn e offl reader eannot but see that the wires perform the verythe Cf w 'tli the fibres of an entire beam, l m, held fast inJ n uoles, D b c, and e, of some upright posts.ba rs Q j. ® ex periments for verifying this, by breaking slenderirig t | le llne deal, we get complete demonstration, by measur-ed d CUrvatures produced in the parts of the beam thussioipl T n> and com pariug them with the curvature of a beamCllr *ous ,ai ^ 011 tbe P r0 P s B an< l c i an< l there are manyW e ln *erences to be made from these observations,that I) , rtl . a y ul'serve, by the way, that we learn from this case,into the nS &re t0 CSLTT 7 twice the load when notched'vh; c h - e ^fters, that they carry when mortised into them,the bind - 1 . mos t usual manner of framing them. So would»e 8s 0 p ' n S joists of floors ; but this would double the thick-ly le _ flooring. But this method should be followed inPtflarg e ca8e > suc l 1 as bres-summers, lintels over severalthe s ;Jj e c * These should never be cut off and mortised intot^hich otf ever y upright ; numberless cases will occur"VV e ° w the importance of the maxim.

C or e*" 6 reinar ^> that the proportion of the spaces b c andtlm i, c an d L b, has a verv sensible effect on the strengthta th< b6!

earn b c :

has a very sensible effect on the strength. , but we have not yet satisfied our minds as

' v ith \\^ lona ^ e °f this effect. It is undoubtedly connectedii'aotiu.g 6 8 ® r 1 P er 'tine form of the curve, of the beam beforedie S p r ^ d his should be attended to in the construction ofa tftiddl “ S .°* carr iages. These are frequently supported atj* c 8rtai n ^ 0Int ( an d it is an excellent practice), and there isb ody 0 p P ro P°rtion which will give the easiest motion to theta at ( ] e . le , carr 'age. We also think that it is connected withf X P ei 'itn ' atlon from the best theory observable in Buffon’s0t Ce of (i* tS 0,1 v arious lengths of the same scantling. The^ l °Pon; 6 bear us diminished much more than in the inverse°f their lengths.

Pieces'^ Seen <dlat depends entirely on the position ofat tb e d’ res P ec f °f their points of ultimate support, andi. , rec , t ‘ on of the external force which produces the° f of„) Whet her . -

-*■ of ' ' “' :u »er any particular piece is in a state of extensionffromv 0t . n P r ession. The knowledge of this circumstance mayS/„ 1: f'fluence us in the choice of the construction. In“ e ato g a3( r a w e may substitute slender iron rods for massive, ^t’7 1,en the piece is to act the part of a tie. But we“ctg a ot JOvert this disposition ; for when a piece of timberV trut > ar) d is in a state of compression, it is next to' ‘''oiinii ‘ at ft is not equally compressible in its opposite sidesP^Ssino. (• tvhole length of the piece, and that the com-® rce on the abutting joint is not acting in the most111 eithJ^I'Her all over the joint. A very trifling inequality

Ot tllOOn ~t- '

a P r ess n p ( ese circumstances (especially in the first) will

Thisg concave

C0,tl ei-e

'>tt' t ' 0 * ; he^' e Jteam more on one side than on the other.

(Amt 8 j ( j Vltlout the beam’s bending, and becomingg 0 j‘Pen S) t | ® ^n which it is most compressed. When thisto r . ra ®e is in danger of being crushed, and soonUln - It is therefore indispensably necessary to2 s,

make use of beams in all cases where struts are required ofconsiderable length, rather than of metal rods of slenderdimensions, unless in situations where we can effectually pre-vent their bending, as in trussing a girder internally, wherea cast-iron strut may be firmly cased in it, so as not to bendin the smallest degree. In cases where the pressures areenormous, as in the very oblique struts of a centre, or archframe, we must be particularly cautious to do nothing whichcan facilitate the compression of either side. No mortisesshould be cut near to one side; no lateral pressures, even theslightest, should be allowed to touch it. We have seen apillar of fir, 12 inches long and 1 in section, when loadedwith three tons, snap in an instant when pressed on one sideby 16 pounds, while another bore 4^ tons without hurt,because it was enclosed (loosely) in a stout pipe of iron.

In such cases of enormous compression, it is of greatimportance that the compressing force bear equally on thewhole abutting surface. The German carpenters are accus-tomed to put a plate of lead over the joint. This prevents,in some measure, the penetration of the end fibres. M. Per-ronet, the celebrated French architect, formed his abutmentsinto arches of circles, the centre of which was the remote endof the strut. By this contrivance the unavoidable change ofform of the triangle made no partial bearing upon either angleof the abutment. This always has a tendency to splinter offthe heel of the beam where it presses strongest. It is a veryjudicious practice.

When circumstances allow it, we should rather employ tiesthan struts, for securing a beam against lateral strains. Whenan upright pillar, such as a flag-staff, a mast, or the uprightsof a very tall scaffolding, are to be shored up, the depen-dence is more certain on those braces that are stretched bythe strain than on those which are compressed. The scaf-folding of the iron bridge near Sunderland had some ties veryjudiciously disposed, and others with less judgment.

Figuie 25.—1. When a beam, a b, is firmly fixed at theend, a, and a straining force acts perpendicularly to its lengthat any point, B, the strain occasioned at any section, C,between b and A, is proportional to c B, and may therefore berepresented by the product w X C b ; that is, by the productof the number of tons, pounds, &c. which measure the strain-ing force, and the number of feet, inches, &c. contained inc b. As the loads on a beam are easily conceived, we shallsubstitute this for any other straining force.

2. If the strain or load be uniformly distributed along anypart of the beam lying beyond C (that is, farther from a), thestrain at c is the same as if the load were all collected at themiddle point of that part ; for that point is the centre ofgravity of the load.

Figure 26.—3. The strain on any section, d, of a beam a b,

AD x D B

resting freely on two props, a and b,is»X - — -•

4. The strain on the middle point, by a force applied there,is one-fourth of the strain which the same force would pro-duce, if applied to one end of a beam of the same length,having the other end fixed.

5. The strain of any section, c, of a beam resting on twoprops, A and b, occasioned by a force applied perpendicularlyto another point, d, is proportional to the rectangle of the

ac X db mi

exterior segments, or is equal to in X • -there-fore the strain at c, occasioned by the pressure on d, is thesame with the strain at d, occasioned by the same pressureon c.

6. The strain on any section, d, occasioned by a load uni-

v