A History of the Theory of Elesticity Volume- II Part -i (1893)

773

description

A History of the Theory of Elesticity Volume- II Part -i (1893)

Transcript of A History of the Theory of Elesticity Volume- II Part -i (1893)

TM

5-3810-294-20

C1

CHANGENo.1

"\

HEADQUARTERS DEPARTMENT OF THE ARMYWASHINGTON, DC, 8 January 1982

/

Organizational Maintenance Manual

CRANE-SHOVEL, TRUCK MOUNTED; 3/4 CUBIC YARD; 20 TON; WITH CLAMSHELL, DRAGLINE, AND BACKHOE

ATTACHMENTS;

G.E.D.

(HARNISCHFEGER CORP MODEL NSN 3810-00-151-4431

M320T2)

ITM 5-3810-294-20, 5 April 1974,is

changed as follows:

Page Page

/v,1

2-72.

following number 2-72 add the following: Air cleaner service 2-84.

AutomotiveWarren,

Command,48090.

ATTN:

DRSTA-MBP,

MI

A

reply will be furnished to you.

v, following number 2-105 add the following: 2-105.1 Adjusting front and rear drum brakes. 2-110. 2-1 10. 2-105.2 Location of chains and chain shafts. .

Page(3)

2-3;

paragraph 2-4e(3). Following subparagraph

add.

CAUTIONWhenreeving a three or more part line, position the cable outside the boom point cable

Page4

1-1.

TM

Paragraph 1-4 740-90- 1".

line 1.

Change

t4

TM

7480-90-1" to

Paragraph

1-5

is

superseded as follows.

guards. This will prevent the cable dragging on the inside rear of the guards.

1-5.

Reporting Errors and Recom-

Page

2-25,

paragraph

2-10'J

-3

we reduce

this last pair of

^=/iWl .............................. (v),S> = 61

are roots of the quadratic //, (/+ e) p, +fe - h = 0. Such is substantially Saint- Yenant' s reduction. It is obvious, however, that this result follows at once when a known problem as to

where^ and ^

2

a

the invariants of a conic

is

applied to the work-function.

remark as to isotropy on p. 272 (t) bearing on the uni-constant controversy:

A

may be reproduced

as

1'isotropie paralt rare.

Non-seulement

les corps grenus ou vitreux, refroidis bois, les fers ^tire's ou forge's, mais de la surface au centre apres leur fusion, peuvent presenter des

0.

I2.

PITCH BRAC.E COTTER/ NUT AND P|N

LINE UP PITCH BKAC HOLE

RgTRACf CABLE

PITCHC? COTTER

JAM NUTADJUSTING NUTPITCH

COTTER P

AND

PIN

ME

3810-294-20 '2-33

Figure 2-88. Rake angle and retract cable adjustment.easiest

point will be at the

boom

foot

drum

stalled,

the dipper trip

pushbutton switch

is

sprocket, since the chain is accessible

and sup-

mounted on a bracket on the front drum clutchleveor. If closing the dipper trip pushbutton will not actuate the dipper trip mechanism, first check the batteries (para 2-53).

ported by the sprocket. To open the chain, chisel off the cotter pin (fig. 2-36) and drive out the chain connecting pin at the point shown. To reinstall

the pin,

wrap the chain around

the two

sprockets as shown- Make sure the chain points in the direction shown in figure 2-37. Then support the chain on one side with a heavy hammer or steel plate while installing the connecting pin

6. Refer to figure 2-40 and replace the dipper trip motor megnetic switch and wire leads.

2-30. Dippera.

and Dipper Teeth Replacement

and a new cotter pin.6. Repair. If a single section of unworn chain should break, refer to figure 2-38 and repair the chain by replacing the broken link.

Dipper Replacement Refer to figure 2-41 and remove or replace the shovel dipper.6.

Dipper Tooth Replacement Drive out the

attaching pins and replace dipper teeth.

2-29. Dipper Trip

Motor Magnetic Switch and

NOTEDipper teeth can be kept sharp in service by regularly reversing them, top for bottom, as they wear. However, when teeth are worn to about one third their original length, they must be replaced.

Wire Leadsa.

figure 2-39.

Refer to the dipper trip wiring diagram, When the shovel attachment is in-

2-43

46

SAINT-VENANT.

[56

of course are only true for these excepexpressions (v) tional sections, which can never occur in pure torsion as sections of cases of flexure combined with torsion danger, while in practical or slide they are frequently found to be specially strengthened

The

(e.g.

built-in ends).

[56.]

We will now enumerate the examples(1).

Saint-Venant gives

of the above condition of safety. Consider a rectangular prism (cross-section 26 x 2c) subaxis of a (or side 20). Let the a force to parallel to the jected only built-in terminal of the prism be so fixed that it can be distorted by Then if the length of the prism be a, and 2 slide-moduli, supposing, however, that bJ]T s neglects also the flexural slide-components.

cj

'jj.

.l

flexural

moment

at section x,

*~~_3

we'

M

easily obtain for the stretch s the value /z cos y sin reatment of combined strain.1

Saint-Venant terms this

sollicite

licular to this the

prism

is sollicite

de champ. a plat.

When

the load-piano

in

porpnn-

TM 5-3810-294-20

a!

^;%w'v'v\, ?m&t\.

v^w^T^-

t"^**. LEADS tI

^H

s

J;

^K,^

'.

DISCONNECTLEADS.

STEP 2.STEP 3.

REMOVE CAPSCREWS AND LOCKWASHERS. REMOVE MAGNETIC SWITCH.ME3810-294-20/2-40

Figure 2-40. Dipper

trip

magnetic switch, removal.

2-39

52

SAINT-VENANT.

[6468

[64.]

ire particulars

In the same volume of the same Journal, pp. 2201, of the memoir on the Flexure of Prisms communi-

sated to the SocittJ Philomathique.

In the same volume of this Journal, pp. 396 398, is mother communication of Saint-Venant's to the Sociitd PhiloThis deals with the formulae for the nathique (July 8, 1854).[65.]

lexure of prisms and for their strength, when the cross-section It gives the general equations loes not possess inertial isotropy. a of case the treats md rectangular cross-section: see specially;he

A,o

Legons de Navier, pp. 52 58 and our Arts. 1581*, 14 and 171. final paragraph to the paper points out that the resistance

torsion varies

more nearly inversely than directly as the:

axial

noment[66.]

of inertia

see our Art. 290.

428 31 of the same volume of th$ same Journal communicates to the Socttti Philomathique (July 8 md October 21, 1854) the results obtained from the stretchThese results were afterwards published in condition of strength. see our Arts. 53 et seq. ;he memoir on Torsionpp.Saint- Venant:

On

[67.]

-esults

of the

Volume 23 of the same Journal, pp. 24850. Further memoir on Torsion communicated to the SocUti

Philomathique (April 12 andi

May

12, 1855), notably the case of:

prism on an equal-sided triangular base

see our Arts 40

2.

The same volume of the same Journal, pp. 440 442. [68.] Diverses considerations sur I'&asticiti des corps, sur lex actions vntre leurs moUcules, sur leurs mouvements vibratoires atomiques,par la chaleur. An account of a memoir October 1855, to the Sori&A Philomathiqve contain20, presented on remarks the rari-constant theory of intormolccular ing general The expression for the velocity of sound on p. 441 h action.&t

sur leur dilatation

should bep.

^J

and not A/'this subject

^: sec L'lnstitwt, Vol.

24,

215.

Saint- Venant refers to the labours of:

Newton, Amperepoints out that

and others on

see our Art. 102.

Ho

in order to explain heat by translational vibrations, tho second differential of the function which expresses the law of intermo-

lecular force

must be

positive: see our Arts. 20t Lon fhe Aittzan, Vol \\n pp 269-90, London, 16 >9 Tied Cylmdtfs & ol(l On tilt hham hiiyiue, ^ ^Ib-JO, gives a foimuli foi the propei thickness of east non e^lmdeis and pipes subjected to sti xiu iiising fiom[962]

F

1

)

650

MAHISTKE.

[963

one-half of a cylinder to be heated unequal expansion. Thus he supposes 300 F. higher than the other half. Tredgold's formula and his method are both very questionable. Gray points out a slip in his algebraical work and gives a corrected formula based on the same hypothesis. The whole procedure seems to me so questionable that I place no faith in formula. Winkler has attempted Gray's corrected version of Tredgold's a similar problem, in a manner which I think inadmissible also, but see our Art. 645. The problem is certainly better than Tredgold's: of some importance and ought, I think, to admit of a solution by accurateanalysis.

imprinter

des chemins de fer, sans avoir & craindre la rupture T. XLIV., pp. 610-13. des rails. rendus, Paris, 1857. Comptes This paper after referring to the Portsmouth experiments on the

[963.]

Mahistre

:

Mennoire sur

les

Unities des vitesses qu'on pent

aux trams

flexure of railway rails under a travelling load (see our Art. 1417*), proceeds to develop a formula for the maximum load which can cross with given velocity a doubly built-in rail without destroying its elasticefficiency.

Mahistre treats the railway

rails as built-in at

by a process which does not seem to me free from doubtful hypotheses the following formula for the maximum load which can andfinds

the sleepers,

travel with velocity

V

along the rail

:

p_

21 is the length of the rail, b its vertical diameter, EWK? its flexural rigidity, h the height of the centre of gravity of the travel-

where

the limit to elastic tractive stress, the Q ling load above the rail, stretch-modulus of the. material of the rail, and 47* the part of the weight of the locomotive which rests on the most charged pair ofwheels.If 2h/b be small compared with be, this formula reduces to

T

E

Ef l\ as I think

r

it

would generally

Ewhich I have deduced from This may be compared with a formula for Saint-Venant's result (xiii^) for a doubly supported beam given in our Art. 375. Putting the Q of that article = 2F, I find approximately for

P

P

:

Thus the

difference occurs in the factor 4/3 of tho

term V"/y.

Mahistre neglects the inertia of the rail; he assumes it at each instant under the transit of the load to take the statical form which

would be produced by the force

2P+-

2jr>

y*,

where r

is

the radius of

964]

MALLET

651

curvatuie of the curve described by the centre of gravity of the load, and he further appears to assume that the centies of curvatuie of the path of the load and of the curve of deflection of the rail at the point of contact with the wheel must coincide at each instant I do not think either the first equation of his (1) or his equation They apply rather to one simply (3) holds for a doubly built in lail suppoi ted, and this on the assumption that the cross section has its centroid in the mid point of the vertical axis of symmetry JTurthei I do not follow the argument by which it is shown that the envelope of the successive curves of deflection is a circle , nor if it be a circle do I understand why equation (4) for the deflection and curvature of the strained foim at any instant must hold My surprise is rather that the author comes so close to the right lesult than that he differs from the foimula of Phillips and Saint-Venant

[964] Bobeit Mallet On the increased Deflection of Gwder$ w Bridges exposed to the Transverse Strain of a rapidly passing Load This paper was read at the Institution of Civil Engineers of Ireland and will be found printed in The Ciml Lnginee? and Architect'* Jouiiial, Vol xxiu pp 109-110 London, 1860 Mallet lefers to the labouis of Willis and to the experiments of James and Galton, and then adopts Morm's foimula for the deflection, which is leally due to Cox It supposes the beam see our Arts 1417*-24*, 1433* and 881(6) to take its greatest deflection when the travelling load is at the centre and the deflection then to be that which would be due to a central load equal to the weight of the tiavellmg load, together with a load equal to the instantaneous 'centrifugal force' of the tiavellmg load If the load statically placed at the centre of the beam would produce a bend s there, then I find 011 this theory that the bending ing moment moment D when it is travelling with velocity 7, is

M

M

,

EUK ywheie EUKis

as usual the flexiual iigidity of the

beam

Hence

if

M

(}

be the safe bending moment,

we must have

^f"Butif

w

In thet

weight of the tiavellmg loid and01,

21 the length of the

beam, J/ s = \ul

652

LEMOYNE.

[965

T uK /h,2 Q

we have

w} himself scitws twenty yeais previously, concluded thit the lesistincc of wooden wxs dm to the shearing xnd not to the bending stiength of tin tine id Thus if S be the ibsolute sheaiing strength of the mateual, M< oughtis

w

to ha\ e instead of

(i)

P = $J>c

(u)

llnhlnnnn (Zeitwhnft de? AichihLtrn u Inynueni Veifim* f d tin ills of J\omc/ieu/t //tpunovn, Hd M Hoft 2 u ^, \\lieie tli< (let

654discussions will be found,

GRASHOF.

[967

a periodical unfortunately inaccessible to formulae (i) or (ii) will be as the that considers ^true according me) He then proposes thread does not or does accurately fit the matrix. 154 of his Leqons, for combined to use a formula given by Navier, in This formula is erroneous, so that no weight can be flexure and shear. In the course of his paper he refers to laid on Rtihlrnann's results. certain experiments on wrought-iron made in 1834, the details of which are published on S. 228 of the Mittheilungen des Gewerbe- Vereins f. d. that the absolute shearing Konigreich Harmover^ 1835, showing strength of wrought-iron is from 68 to 80 per cent, of its absolute tractive a result not very far from the |- obtained by extending the strength, results of uniconstant isotropic elasticity to the phenomena of cohesion:

see our Arts.

879

(d)

and 903.

Such was the state of the problem when Grashof took it up. [967.] considers (ii) to be the correct formula for tightly fitting screws, and that it is impossible to apply (i) to the case of a beam the height of

He

It is whose cross-section is of the same dimensions as its length. necessary, he holds, in the case of a metal screw, which does not fit so closely as a wooden one, to take into account both the flexure and He supposes the pressure P to be distributed shear of the thread. on a cylinder round the spindle of the screw, the radius of which is slightly greater than the mean between the radii of the spindle and I hardly see that he justifies this assumption (S. 290). the thread. He then, after demonstrating at some length the error of Navier's a fact long before known from Saint-Venant's researches formula, proceeds to apply Saint-Yenant's formula for combined flexure and shear He attributes this formula to to the case of the thread of a screw. Poncelet and says he first found a rational treatment of combined flexure and shear in Laissle and Schiibler's work (see our Art. 889)! He then gives a numerical table showing the influence of shear and This table is similar to one which flexure respectively on short beams. had been previously given by Saint- Yenant and which we have already cited in a later form (see our Art, 321 (d)). Grashof concludes from into which, however, he has not introduced the differhis formula, ences between the stretch and slide moduli, and between the absolute tractive and -shearing strengths, that if a screw thread is not to give way by flexure we must have

P'

= 0'rf"

"'//'

for () It is thtie sho^n to be piictically small but tlu toiMonal diifeicnces noted by \\ohlci \\tic also(

)

JIM

674wherestress

WOHLER.

[1000of the wheel, the longitudinal'

A

is

the diameter of the axle and

d

due to

C

being neglected.

For the torsion of the same wheel,

centners produces a Wb'hler says a rim-load of 29 tiussersten Fasern' of 52 centners. Now if S be the shear and not the traction at thefind

Spannungc

der'

outer fibre

I

and

S has

the value 52 centners.

So that there is a radical difference between the two stresses of 252 and 52 centners both of which Wohler speaks of as Faser spanning.

He

proceeds as follows

:

Die Mb'glichkeit des Falles^vorausgesetzt, class die grossten Krafte auf Biegung und auf Verdrehung gleichzeitig wirkten, ist dann nach den vorstehend ermittelten Zahlen die gro'sste aus diesem Zusammenwirken resultirende = V252 2 +52 2 =257 Centner pro D Zoll (S. 644). Faserspannung der AchseI do not understand why the maximum stress at any point should be the square root of the sum of the squares of the maximum traction

and

shear.

The maximum

stretch s

is,

I think, given by

a

~V $2+ *utraction,

/?*

l^2

'

and therefore thedirection of the'

maximum',

which

is

not of course in the

fibre

by

or, for

uniconstant isotropy,

S as compared with T enables us practically to neglect its effect on the maximum stress. Wohler remarks that the maximum stress of 257 centners in these cast-steel axles of 3J" diameter would have produced set in iron axles, the elastic limit of which he takes at 180 centners per Q". The above results were for four-wheeled wagons. For six-wheeled wagons he found that these stresses were increased in the ratio of 6:5; while for covered four-wheeled as compared with open fourwheeled wagons they were increased as 10 9. For the 5" diameter axle the maximum traction was 156 centners and the maximum shear 35 centners, so that the result appears rather close to the elastic limit of iron as stated by Wohler above. Further, with these axles the maximum stress seems to have been often repeated. Wohler reduces these stresses to percentages of the total load of wagonIn Wohler' s results the smallness of: .

and cargo

(S. 646).

10011002][1001

WOHLER

675

not,

The number of repetitions of the maximum stress does ] Wohler considers, exceed one per German mile 1 and he reckons the life of an axle at 200,000 miles Hence he reduces his pioblem to the following one To how great recurring positive and negative,

times without

an axle of given dimensions be subjected 200,000 its breaking ? He describes (S 647-8) the method by which he proposes to answer experimentally this problem Thus we see the ongin of his later experiments on repeated loading Two points are to be noticed in the problem as Wohler statesstresses canit

First,

he supposes that

therefore unrecordedrapidity with

by

his apparatus)

destruction of the axle

maximum (and do not conhibute to the Secondly, he takes no account of theall

loads less than the

which the loads are repeated Would 200,000 loadings and reloadmgs of an axle in a day represent the same wear as 200,000 like maximum loadings occurring while the axlemiles, thatis,

? spread out over its whole life load repeated many times a minute may lead I believe not to a vibratory accumulation of stress, this accumulation is im-

was running 200,000

A

possible if the

same load recuis only at long intervals For both these reasons Wohler's latter experiments do not seem to me so useful as they might otherwise have been

The memoir concludes withthe experiments (S 647-52)

tables of the numerical details of

Vetsuche zui Enmttelung der anf die Eiseneinwwkenden Krafte und dei Widei standsbahnwagen-Achsen dei Eibkains Wagen-Achsen fahigkeit Z&itschnft fw Bauwesen, The first portion of this Berlin, 1860 Jahrgang x, S 583-616 memoir (S 58S-6) is entitled Vei suche zui Ei mittelwig dei auf die Wagen-Achsen einww'LendenKiafte, and it details expenments made with a slightly modified foim of the appaiatus refened to

[1002]

Wohler

in

998-1000, necessitated by its application to the of Only passenger tiams moviug at a greater speed carriages flexure experiments were made as it \\as considered that the firstset of

our Arts

expenments had demonstrated tint the

torsional btiess

was

In the case of the ixles of passenger carnages the maximum stress a 4 5" non a\le was found to be 173 centners pci a", and it was reckoned that the mean stress ^ isof small account

m

from

tSO

to

110 centners1

\bont fne Fiv hsh miles

43- 2

676

WOHLER.

[10031004vollkommen ausreichend

Ein Durclimesser der Achse von 4'5 Zoll in der Nabe darf daherbei

WagenThe

der Art, wie der benutzte, fur(S. 586).

erachtet

warden

details of the

experiments on the axles of passenger

Further experiments, confircarriages are given on S. 603-4. matory of the previous ones, on the 3f" steel and 5" iron axles of goods wagons are given on S. 601-2.

The second part of the paper is entitled Versuche [1003.] zur Ermittelung der WiderstandsfdhigJc&it der Wagen- Achsen (S 586-600 with tables of results S. 605-16).:

first series of experiments on repeated and we loading, postpone their consideration for the present, in order to deal with his complete researches in the decade 1860-70. The present experiments are on repeated flexure and the stress

These are Wohler's

positive value through zero to negative value, and then back to zero again, once in about every four seconds (S. 586). Other matters in the memoir, not exactly bearing on repeated loading, are the erroneous treatment of the stretch-squeeze ratio on S. 592 where ititsits

changed from zero to

maximum

maximum

assumed that the volume of a bar under flexure does not change, the deduction of the form of the strained cross-section, and a not very lucid discussion of the relation of set to clasticis

strain.

Wohler holds thatstress,

elastic

strain

is

always in linear

proportion to

and

is

in

itself

quite independent, of the

amount

of set (S. 600).

GROUP D.Memoirs relating more especiallyto

Bridge

F. W. Schwedler: TJwne toi iqm det> pi ui [1009 ] on solutions conceinant I'eqiuhbie des voilte^ T x\xv, pp 404-502, pp 5 31-540, and pp 577-587 7 end u^

Pans, 1852 This is a very valuable criticism of the vanous theones of the u ch piopoumlul up to lcS52, and is ot pecuhai inteiest db noting T^rJ the CXtdlt to whlfh thp^< thrmipv lu1

1

682

MINOR MEMOIRS ON BRIDGE STRUCTURE.

[10201022

De

Olercq, Winkler, Arts. 1017, (see our

nor Wohler take into account in their analysis 1026 and 1028). In all cases the theoretical

stresses in the bracing bars are calculated

and tabulated. The of strength due to multipleincrease the show great experiments Lobse the riveting together of the bracing bars. bracing and to for him numerous to his enough does not consider experiments numerical the details but and propound any general formula, the general results are perhaps more likely to be of practical service than the lengthy analytical investigations to which wehave previously referred. Resume des G-. Wolters:

resultats obtenus dans les epreuves [10201. Annales des travaux publics de Belgique, de quelques pouts en fer. Tome xv., pp. 145-75. Bruxelles, 1856-7. This is translated into German under the title Bericht uber die Ergelnisse der Belastungsproben in the Zeitschrift des b'sterreichischen Ingenieureiniger eiserner Brucken S. 185-195. Wien, 1858. It gives details ofVereins,

of the deflection of various railway bridges experimental determinations The girders of the bridges were chiefly of cast-iron with in Flanders. The results do not there was one of plate-iron. openings in the web ; seem to have any permanent theoretical importance.

Jahrgang

x.,

In the same volume of the Annales is an article by Houbotte [1021.1 entitled Experiences sur la resistance des longerons en tole (pp. 403-26). It is translated into German in the same volume of the Zdtschrift, S.:

195-201. The girders were of plate-iron, and the object of the experiments described was to test the best relative dimensions for the flanges and web in the case of girders of JL section. The span of the model l'5m. to 3m. and their heights varied from -2 to girders was from 49 m. The load upon them was gradually increased up to rupture weeks the duration during a period amounting in some cases to several;

of load, the elastic and set deflections one set of experiments on a girder in

were all noted There is also which the web was replaced by

bracing.

Houbotte concludes from this experiment that the bracing is than the plate-web. The rupture occurred in the plate Houbotte endeavours to construct a girders by buckling of the web. formula which will give the proper strength for the web of such a moreefficient

girder, but neither the range of experiments his formula seems very satisfactory.

nor his method of obtaining

Abe

numberthe

of articles

lattice girders, the latter in the

by J. Lunger ou wooden and iron form of arches with braced ribs, etc;, willdes

found

in

Zeitschrift

Merreichinchcn

/tnjatlctir- IVm'y/*,

Jahrgang

113, 135, 152. Wien, 1858-9. Juhr^uig M., S. (>9, These give a Inigtiiy theory of the 127, 153, 186, 206. Wien, 1859. braced arch. Further projects for braced arches will be found in Jahrgang xn., S. 29, 91, 125 and 193. In several of those projects,x., S.

10231024]giaphical methods might

DAVIES

DECOMBLE

683

now be usefully employed The designs* would form very good exercises in the calculation of stresses foi advanced engineering students even at the present day

[1023 ] Thomas Davies Wrought and Cast Iron Seams The Civil Engineer and Architect's Journal, Yol xx pp 20-23, and pp 41-44 This paper was read at a meeting of the Architectuial London, 1857 Institute in Edinburgh, February, 1856 It commences with some account of the want of confidence felt in,

only experiment a "plate beam" (one of section?) Davies proposes to supply this want of information with regard to the strength and elastic pioperties of wrought-iron beams, in order that they may be more generally understood and adopted The experiments given in the first part of the paper may have technical, but they hardly have theoretical or physical value , the load was applied over as much as of the length of the beam, and was brought into play by putting on the top flange non railway bars The author agrees "zequiring two men at each end to lift them" with Tate that the upper and lower flanges of a wrought iron beam should have practically equal areas (p 23) The second portion of the papei cuticises the lesults of Hodgkinson's experiments on the beam of greatest strength see our Aits 244*, 875 and 1016 The wnter contends that the ratio of the sectional aiea of the flanges ought to be as 3 5 or 3 to 1 and not 6 to 1 as suggested by

cast-iron beams, and of the superiority of malleable lion beams owing to their lightness and sensible Fairbaira having yielding befoie rupture one on given in his work on cast- and wi ought iron

X

enteis into no theoietical im estigation of the stiength does he adduce any expenmental e\idence beyond He considers Hodgkinson's results enoneous because Hodgkmson's the lattei left out of account the diffeience the thicknesses of the webs of his individual beams when deducing conclusions fiorn his It seems to me that Hodgkmson was light and quite expenments

Hodgkmson

He

of such beams,

1101

m

justified in doing this, as the web added little to the flexinal stiength of the beam Thus the ratio of the areas of the flanges ought to be

ncaily that of the compie&sive to the tensile strength of cast-lion, according to Hodgkm&on about 6 1

i

e

[1024

]

Decomble

Sur

les

dioites enjont?

Annales desponts

meilleiw es formes d, donnei aui pouhes et chaubseei, 2 Semestie, pp 257-319

Pans, 1857Tinsis

icbistuice,tlu

a long memoir mvestig iting a theoiy ol the solid of when the tensile and compiessive stiengths of theclifFeient,

gieatest material

ue supposedstretchedtlio

ind

and the solid squeezed 'hbus'

is

designed so tint the luptmes ofit

occm

the

sime lo\d

Apait

of tl tsticit\ issuinption invohcd in ipplymg the theoiy seveial points to the phenouuni of luptuie, the diseussion seems be reiched of value by i theoiy of tins veiy doubtful, ind ill tint

horn

m

em

684

MINOR MEMOIRS ON BRIDGE STRUCTURE.

[10251027

kind has been better given by Saint- Venant in his Legons de Navier, and our Arts. 176, 177, (6). There are, however, a pp. 102, 142-56, number of experiments on the rupture of cast-iron beamso

interesting various shapes and cross-sections, which may possibly have practical The editors of the Annales remark in a note appended to value still.:

the memoir

soit en opposition, sur Quoique la partie theorique du me'rnoire precedent les principes g&i&alement adinis, la commission des plusieurs points, avec Annales a cru devoir le publier tel qu'il a dte prdscnte par 1'auteur, 2i raison des details int&essants qu'il renferme sur les poutres on fonte et sur le moulage

de la fonte en general

(p. 319).

British Association.

Report of Twenty-Seventh (Dublin)

Meeting, 1857. The titles of two articles in this Report maybe noticed: C. Vignoles: On the Adaption of Suspension Bridges to sustain the passage of Railway

P. W. Barlow: On the Mechanical fiffect of Trains, pp. 154-158. combining Girders and Suspension Chains, and a comparison of the weight of Metal in Ordinary and Suspension Girders, to produce equal deflections with a given load, pp. 238-48, Both these papers discuss the adaption or modification of suspension bridges when built for the transit of railway trains. They turn principally on stiffening the platform till it becomes a girder, or on special arrangements of the suspending bars. The bridges at Niagara and elsewhere built as girder suspension-bridges,

had gone far to destroy the old misti'iist in suspension-bridges for railway traffic ; and the authors of the above papers endeavour to show that equal strength may be obtained with far less material from a suspension-girder than from a pure girder bridge.[1026.] poutres en

Clercq Note sur les phenomenes d, la flexion des Annales des travaux publics de JJelyiqiw, T. xv., pp. 198-214. Bruxelles, 1856-7. This is another of those memoirs which deal with the lattice-girders, which were rapidly taking the place of the older clouble-T girders with a:

G. A.

De

treillis.

solid web.

The writer of the memoir supposes the bracing bars rigidly attached to the booms, and deduces by what does not scum to me \ cry conclusive reasoning, that a bracing bar after flexure will take tin? foim of a spiral of Archimedes (p. 201). C. Wiukler (sec our Ait, lO^S) had, I think, read De Clercq before writing the second part of his paper;he extends, however, the latter's results. The piesrnl paper is clearly written as compared with Winkler's, but it deals with a simpler case. At the same time to consider the special conclusions deduced by hoth these writers from their somewhat doubtful hypotheses would carry us beyond our limits.0. Knoll: Theorie der Gitlerbalketi. [1027.] Zeitung, Jahrgang xvi., S. 13-5. Stuttgart, 185D. This is

Zw

/i'/V';/Wm-

an analytical

10281030]booms

WINKLER

STONEY

685

calculation of the sti esses in the bracing of lattice gliders with straightparallel

Wmkler TJmrw der eisemen Gitterti ager Forst&rs [1028] Allgememe Bauzeitung Wien, 1859 Jahigang xxiv S 191-222 This memoir on lattice-girdeis is divided into two parts The first deals with the stiesses in the booms and bracing bars when the biacing bars are not nveted to each other In this case we have only to con,

sidei the flexure of the

booms, for the bracing bars aie, if buckling be Wmkler proceeds excluded, in pure tensile 01 compressive stress analytically to the discussion of the stresses, and points out an erroi of Scheffler's (see our Art 651) The treatment appears sound, and theresults,

may

although havmg only special technical interest and application, be of service (S 191-9) In the second part of the memoir the biacing bars are supposed riveted or pinned where they cioss each othei, and the result is thatstill

now subjected to flexure The calculations, heie of course necessarily analytical, become more complex, and I confine myself to referring to Winkler's analysis which I have not verified (S 199-206) far his fundamental hypotheses similar to those of De Clercqthese bars are

How(see

our Art 1026), approach the truth, especially foi the second case on S 199-200, I have no means of judging, they seem to me The memoii concludes with the somewhat bold, not to say dubious application of the lesults obtained to a numbei of numerical cases of The exact treatment of these lattice- gliders, lattice giideis (pp 206-22) in which the frames have a gieat numbei of supei numeral y bais, would be an extremely difficult analytical problemstated

the Calculation

Stoney On the Application of some new Formulae to of Strains in biaced Gwdeis Proceedings of the Royal This paper \\as Irish Academy, Vol vn pp 165-172 Dublin, 1862 road in 1859 Pp 165-9 deal by the simplest statical methods with the stiesses in the diagonal bracing of a Warren girdei when some 01 all of the nodes There is nothing that calls foi special at the upper boom aie loaded[1029],

B B

comment

Pp 1G9-72processes

tie it of Lattice

Gilder and use only ordinal}

static il

discussion, howevei, seems to me obscuie, especially It is in cises impossible to find the exact th( final paiagiaph stitsscs in 1 \ttice gliders without appeal to the theoiy of elistieity, and

The

mmy

this point docs not

seem

to

have been iccognised by Stoney

[1030]

Another papei byentitled

B B

Stoney may be just refeued to

IKK,

it

is

On

the Relative Deflection oj Lattice

and Plate,

(linln** ind is published in the Tiauwction* of flu Royal Academy Yol Ihe pinti wxs \\iv pp ISO-OS of Dublin, Ih71 I, Science to contim nothing of sufficient It does not ic id JniK J3, INGJ

Put,

\nnal