Добровольский В.И. Расчёты на прочность, жёсткость и устойчивость элементов конструкций
Подождите немного. Документ загружается.
a,
Pflc. 10.4. BH)"rpeHHne
cuoBhre
QaKropH
n HanprxeHHoe cocmrHre
onacHo-
ro 3neMeFra kpyrnoi
IrnacTnH6r rrpu
ynpyroM (d)
!{ rlpe]le]lbHoM ruracTtilre-
crcM
(6)
leoopMr.rpoBafi
,rI{
0,0776.44?00.
t,
.
t2.
{l-
03r
|
^^^^^_
_
r
-=:r=0,002e6M>
[w]=0.001
2a=0.002u.
2.t0,.10'.0,04,
BuAHo,
.rro
ycnosne
xecrxocut
He Bf,Ilto'lrureTcr, BbrqncnreM
nolycxaeMLri
pacnpereneHHHl
MoMetIr
[z].
m
ycnoBHr
x€crxocrfi [nacruHEr
lo.ottono,l
Dtu=i
^
|
sl'li
tDl
o
t62
t63
(r0.26)
=
zeroolr .
Oxonqaren6Ho rrpfinrMaeM
MHHHMarbHoe
3HarreHx€
lonycraeMoro
pacnpele-
nefiHoro MoMeEra
[ ]
=
[n]-i.
=
26800 HM / M. I,lcnofiL3yr
{opMynu
(10.22)
n
(10.23),
BHqrcnreM
pa6oq[e
Hanprxcfir{r B oracHof, mqKe
ruacrnHH:
*o.
=
100
Mna;
-"06
=
36,6 Mna;*a,-.
=
122 Mna.
PaccMotp&
pacqer
Ba
npoqfiocTL
Jrotr xe nnacrsHU
no Melotry npeAorF
H6rx
(pa3pyuapsrlrx)
HarpyroK flpx
3roM xecr(ocr! nnzrcrllHH He
HopMr,tpy-
erct, B coomerErsnr c r€oprel
ruracTxrrHofin A.A. IlnHourxta
npk npe-
lenbfioM
Irnac cqec(oM
AeoopMnpolaHnn,
xorAa flnacrfiqect(xe
aeoopMaqxn
pacnpocrpaHr,lrrHcs
Ha Bcro Bhrcory olacHoro
o6a€Ma .['lacrHHH
(puc.
10.40,
nnTeHcHaHocT6
npeAenbr$rx rlarlprxeHnn
paana
cxeMam3xpoBaBBoMy
npe]le-
ny r€ryqecrn oa
=
a,
r-
o,np
:
vMo4D
+m
o;p
-trh
one.M
c€rD
-
og
npl' n3B€crHoM
13
ynpyrom
peureHxi (10.22)
orfiorreHnt
nn!6e/nds.
=
-io6€,D/*o'p
=
-0,366
ti3 nocnealref,
{opMyns
nony_
qaeM
3llaqeHnr npeaerr6HHx HanprxeBni (p
c. 10.40:
*sD=0,8166-
=
359
Mna;
.i,o,t!D
=
-O,299a8
=
-l3l
Mna.
Pac.rer rrracrxH c
)AeroM
MacTrrecxnx
Aeoopxaufifi
noBHrnagT
Aorryc-
KaeMtrc Harp)3rry
B 1,5
pa3a
flo cpaaHeHno c aHanorrqHHM
peyn[Taro
no
Meroay
aorryc&aeMdx
HanprxeHrtr. CneAoBarenbHo,,4ofiycr€eMul
pacnpete-
J'eHHHf, MoMeFr
no Merory npea€nlHlrx Ha.p)3ox
prleH
trl-
=
l,st,,tl.
=
1,5
32000
=
48000 HM /x.
I0.4. PACqETHO.NPOEKTI,IPOBOqHA' PAEOTA
(PACqETbI
HA NPOqHOCTI, H XECTKOCTb
I(PYfNOfi SETOHHOft
NIACTHHbI NPH
OCECTIMMETPIqHOM I43|I'EE,)
3.Artro:
pa3MepH (a
=
2 M;b=0,5a=1Mi h
=
0,160 x) n xarepxan
(6smH:
,
=
0,2 10' Mna;
p
=
0,1?5; o.'
=
3
M[a;
o-
=
3l Mna) Kpyrron rr'IacrrflH c
BHPe3oM B
qeHrpe,
uapH&pno 3aKperuefinoi no Hap)ri(HoMy KoFrypy n Ha-
rpy:r(eHHofi
no Bq,rp€HneMy Korrypy MoMenroM n; KosoorqnetIr HaaexHo-
ctl,/.,
fo
=
2,50:,
aorrycKaeMbrF
nporu6
[-]
=
0,001 2d
=
0,004 M;
pacqerHarr
cxeMa
(pHc.
10.5) r
ypaBHeHrc
cpeAfiHfion noBepxHocrx rnacfliHLr
l"b l*lEh'
t t"=
ofri?=..r.{-rtr,o1iu}
o.oo:. z. ro5
.
t06
.o,o4l
r2.tr- o,irI0,0776.l':
^.,i
I
nlry,\
|
.
,t
l.,ll
'ltr--r-
'
\X
-t')ol
t-Y 2(l t
}l,
I
'Tpe6yercc:
nocrpol{rL 3rtropH rt, n Mo B
rontx
z,3mopy,-{r) B
aontx
na'/D; orrp'-,let''rb
torycl(aeMUtr
MoMero
[rr1l,
yaoBnerBoprrcuti
ycrosrtM
nPoqt{ocTn n xecTKocTH llnacTt'sLr,
BbIBOA
YPABHEHHJT CPEAI-IHHOfi
NOBEPXHOCTh.
Anooep€HuxanL8oe
ypaaHeHse
cpe4rHHor
noBepxHocrH Kpy Iof, turacr!-
Hll npn ocecnMMerpnqHoM l'3rn6e xMeer BHI
daw
2d1w t d'w I dw
o0l
d,^
';77-7
d,'
-
,'
d,
=
D
'
rle
9(/)
-
raxoH tl3veHeHrr
pacnpetreneHHot
HarplB(ni D
=
Eh, l2(l
-
t"l
-
urjrrrurpnqeckar xecfiocrL cc'{cfiur ruacrnHu:
E,
F
-
Morynh
yrrpymcrn.
rog$<plurerr nyaccoHa, O6nlee
peueHrc
rroro ueolHoporHoro
)?aBneHrt
npeAnaraercr B BrI€
rr{r)=
q
+
crln'
+ car'? + CnrzlnLr
+wr(r)
,
r,[e Cl, Cr, Ca, C.
-
nocrotHlr!|e fiHrerpxpoaaHrl', olpeIenteMLl€
r{3 rPaHIrq-
Hbrx
yctoBnfi
anr
xoHKperHot
3a,qaqn.
qacrHoe
p€ueHxe
vt(.) MoxHo npe,q-
."+l+{d..[l,rr4]"1"
c
yqeroM
3Toro
ypaBHeHrr
cpe4r ol noDepxHocrti norryareHH lr
npsBeaeHEl
B
l
re6Hnxax tr clpaBoqHrKax
rrr
Hafi6on€€ xapaKrepHsrx c.,ryqaet 3a&pellne-
Hwt H HarplDrcHff
(pyrnHx
|rllacTnH.
noxaxeM MeroAlKy KolrkperH3aqnx
)?aBre
fi, cpeauHHo[
noBepxHocin
nnacrrHs. Ilocxon6(y noneFeqHar Harp)3ra
(g(r)
=
0,
p
=
0, P
=
0) 8a
ro,a-
crnny He
Aef,crByer,
ro
qacrHo€
p€ureHre vr(r)
=
0.
npeacraBnteM
)?aDHeHre
cp€anHHofi
floBepxHocru
B o6qeM Brue
4r)=
ct
+Czlw +C{2 +C{zliv
'
n,u
onpelener&r
qerBrpex
nocrorufiLrx
HHr€rpnpoBaHtt Ct, Cr, Cr, Ca 3ann-
c6l0aeM
qerHp€
rpasnqHbrx
ycroBnr:
l. nqn r=a
w=0
(onopa);
2. nplr r=d
M.=0
(uapHrpfi(r€
3arpeuekhe)i 3.
np', Fb M,=n
(ycroBre
Harp,t€Hnt);
4.
npr
r=6
O,=0
(nonepeqHar
HarpylKa Ha BFyrpesHeM
xoHrype orc)"rcrByer).
._dwc,^
Hd(o.rsM npo}r3BolHHe: w'
=
+
-
3
+2Ctr
+Car\zlw
+l)i
t4=-\*rr,*"
n(ztnr+:);
T=7,=
d3w C, 2C^
C
JaremM
9Toro
noryraeM
pacnp€AencHqrc non€pctlfiyto cuty
- -(
at.
td'zw
I dn\
4Dc'
u-=-it-
+---=-i=--
-
\dt'
r&'
r'dr)
Ilcnonb3yr
4f6EnqHoe
ycnoane
4, nxeeM
q
=
-4DC1lr
-0
tt c4
=0.
HaxoA
n r|3rr6aloqxf,
oMelrr
B oxp)DxHoM
ceqeHxx
".
=
-J
4+, Ya\--rf-
(t,r')6,
-4r
-sp,1
\d,'
tdt)
L
.-
I
C
)AeroM
r?aHr.tHHx
ycnoBrtr
2 n I flon)ryaer
*",
='
",
=
-4-+c,
*z(r*v16,]=0.
*",
=
t u,
=
-{-trl.c,.z(r*u)c,]='
Peuat coBM€crrD
nocJreartrt6
ypaBEel{tt,
Haxorllll
flocrlotlluHe
B
cooreercrsru
c rpa nqHNM
yctostcM I npH r
=
c ltM€€M
^
^o2t'|
I
tno
t
l
orxyra
nocm'Bna' .'
-
6r:FFr
I
_1,
-t(i[)l
C
J
{eroM
Hafr,[eHB[|x 3HaqeHxf,
nocmi
HHx Cr,
C1, C] C.
nonyqaeM
xoHxpe-
TnxxpoBanHo€
)?asflcdte
cp€anlrfiotr
floBepxxocrt
nlacTllELl
,,
.o2br
tr"(./,)
('
-"/,')l
",r,,
=
GL_'F Ll;
-
_F;ilj.
qTo
coBnaAaeT
c
Bhlpai(ell'|eM,
npeacTaBne]rflslM
B
yoloBl{g
3aaaqlt.
PEIIIEHI,IE
l. HaxolnM
pacnpeteneHHLln r3rx6aloufii
MoMem
M' B oxPyxfiblx
ceqefiux
'npr,r
BLtnonHeHu
PnP fie flpoBo4rrcr.
r64
165
..
-(
a'-
u
a')
a"
^oztz
I
t
'
I
',
=
-\E'
*'
*
1,
i
=
V
_;,pLr
-nF'
G,,Fl'
r\ du)
^o'b'
f u u I
;7=G';TLo;F.[+F]'
<ro27)
d2w
^o't'
I I
t
I
-
=
ri'-----ir-l
-
t-------i_i
+
----i--i
| ;
dt'
\x-b'pL
(l-Ff' (l+IF
l
cneAosaren.Ho ,..rh6aroulrf, Moue..r
",=
-
ur-oLl|
-
rl.
nptl r
-
0.5a oxoHqaren68o no,DAaer
M,
=
0,3331-
-
t
l.
(10.28)
2, Onp€lenren
pacnpcaetcfinutr
t|3no&oqrtr
*o""rr, t
"
paaxulbHrrx
..
-(
ta* a2*\
ta*
^"'o'
I
l I
I
M
e
=
-
\;
T
*
Yei
)t
; e
=
V
-;,pLtr -g -
[
*Fl'
d'w .ottt I u u I
u-=t--l_:---i-+- li
'
d,'
\r'-b'lPL
(l-ul' (l+F,rl
(10.29)
nb' lo' I
Ma=_r_11_+tl.
-
la'-b'l\" )
np{b
=
0,5d oxoxqsrenlHo
norD rrcn M€=-{)J33"{++ll.
(10.30)
\r)
B 3roM npr epe noncpeqHar cllla
g,
=
0.
npx
aFIcrBtn
Ha ntamflry
4(t),
p
xnH
P
3Ha{eHne
g.
*
0. OaHaxo olpcAetcHxe
O
xox||o onycrrfl[,
nocxo,Ibxy
Bn$tgxe
e.
Ha npoqHocrL nracrtHu o6HqHo
ge3$!.r|{tcrLttoc.
3,
3a.aariHoe
ypaBHcBnc
cpcltlxHoft nos€pxEocu
nr&Tr,firH fipn b
=
0,54
l|
]r
=
0, |
75
npl,|Boanrcr x El,r.e/
;'t= lo.rol'r
-o.u/,
-4'il!4
''
L
a
\
x))D
(r0.31)
no
oopMynaM
(10.28), (10.29)
u
(10.31)
Haxo4{x Ben
qffiu
M^
Me n
{r)
!n,
prla
3Haqorrln z Pe3ynbmr
Blrqxcn€Hrl cro,r'tx B rafnrtry
I0.5 I,r
crpolrM 3nFpu
(prc.
10.5) M. M6
r,(r)- nonox'nE LHH€ sfiaqe||xt tmop
noxa3aHH Ha
pacrrHyE[
cnorx
Macr rN x Hao6opor.
0
0,259
t,667
0,926
0,667
0,387
0,178
0
w\r
)
-o'fD
Pxc, 10.5.
SrDopH
pacnpeleneHfi[rx
Ir3 6aloqtrx
MoMeBms
B
oxpyxHoM
M'
rr DitluanbBoM
M. CeqeHntx,
3mopa
nPorl'6oB
x'(/) xot6qe6ofi
lrnacrnnu
Ta6r.
10.5.
0.5a
0.625a
0.750a
0.8754
1.00
0,520
0-259
0. t02
0
1.667
-l
187
4.926 -.0.769
4,661
u'lr\/kd/D\
-{.38?
4.271 -{.178
-{,0872
0
166
t61
4. Aaanst ?firop
M, i Me no(a3uBaer,
{ro onacHLIMH
6y,q}'r HaI|6oJI€e
y!a_
,€HHHe
01 Cp€ll{Hxof,
ntocxocTr aepxHne
toqk{ anF?eHHero
toFTyPa
rula-
crnHH.
B
oKpecruocrx
onacHol
roqxt B[uorxM
tleMcl{mpHHfi
o66eM
(pl{c.
10.6). 3Kcrp€xat6l$Ie
EarptxeHxt
s onacxux
rotrxru
paaHU
-^
_6Mool
__6
t,667m
-lon
..".-1,
---]r--
I
=",,
02=ui
6M--
6n
^-",=-F=-v=o'.
5, npoBepteM
BHnonHeHrc
ycnoBlrl xecrlosru
nnacrl,|llH
. I
o.:rr,ll-o;r9[,'lg'.$;p]l=
*^*=f
D l=-- Eh'
_
0.1?s.2900:2:
!2.(r--0.r75?
)_
0.000617 M
<
[.]-o.oor.zo_o.oo+u.
o-2.lor
'
I0"
.0.160'
Bnaro,
.rro
ycnoBxe xecrxocrr
4llt
6emnHofi
rulacrfinhl
BunoJrHterct
Oxotl_
qarerbHo
nDufiNMa€M
3naqeHne trolrycxaeMono
MoM€Hra
[n]
=
[tn].
=
29fi)
HM/M.
6sroH
rBmeTt
xpynxnx
Marepuano
,
n@mMy
pactlsr
nnacrHHsl
c
yq€_
ToM
nnacr|{.l€cKflx aeoopMaqfin
He tunojlHtcrcr'
(r0.32)
Pxc.
I 0.6. K aHanBy
lranptxaflfloro cocrotHxt
a oKpecrHosd{
onacHotr
roqt(r
njlacT{HH
H3 aflanna
BIrrBo,
rrro
MarcpxaJr
ntaqfltflu
Pa6oraqr
a
ycnoafitx
llJlocKom
HanptxeHHono
cocrotHlrt.
B
coorBercrrnl|
c ncmfi
(O.
Mopa)
T€opficfi
npoqEocrn
ycjloBlle
lpoqtro_
CTI{ UM€CT
BNA
*o-'
=6'
-*or
<bl,
(10.33)
rAe I
=
o',
/ o-
=
3,00
/
3l
=
0,0968
-
ro3ooliqnefll
HepaBHonpo'rHocrn
6e-
mfia
Irp}I
pacrrxeH
n s cxaflrx;
[o],
=
o.o/10
=
3,00
/2,50
=
1,20 Mna
-
rorrycKa.xoe
anptxeHne
Ha
pacrtx€l
tc. C
y,{€loM
sToro
no,r)^€eM
*.*.
=
!!3
-o.o*{
-F)=
#
=td,
(10.34)
AoflycxaeMlrfi
pacnpelene$H$tr
MoMeFr
IB
ycnoBHt
npoqfiocrx
(10.34)
pa8eH
l^l
=l"ln'
lrc,e
-r,z0
106.0,|60'!110,6=2e0oHx/M.
(10.35)
l6E
1I. PACqETbI
HA
NPOqHOCTb
I{ XECTKOCTb
nPtMOvrOJIbHl,lx
IUIACTI{H
nPu
H3II{6E
3reMeHr6r
koticrpyxurtr
B BHAe nptMoyronbHbtx
lulacrllH
u{poxo
rcnonl-
rylorl:,
B
crporr€nscrBe {Il,lxrbl,
naHenfi rnaHnfi
fi coopyxeHtrk).
MauHHo'
crpoeHIrn
(3neMeHrhr
rexEojlornqec((x
nprcnoco6neHti),
aBnaqfil{r
cylo-
crpoeHHH
(o6lxlBXI{
DIaH€pa
CaMOner4
xopnyca
KoPa6nt, 3neMeflrH
F,e3ep-
ByapoB)
n
apyrB
o6nacrtx rexHlrxx-
I I.I.
OCHOBHbIE
IIOJIOXEHH'
PACqETOB
HA IPOI{HOCTb
H x(E.
CTKOCTb
NP'MOY|OJIbHbIX
IUIACTI,IH
TIPh I,I3|HEE
Pacqerbl
Ha npoqHocrE
rI xec ocr$
mHXI{x ruacTHH
ocHoaaHH
Ha cte-
.6'lourlm AoryueHl{tx.
,{p6at
rptMa{, HopManEBa,
x cpe4tHHoii
ruocl(osrt
Ao
aeoopMaut,
ocmerct
nocre
Ae{Dopvaus{
nptMof,'
HopManbHo{
I( cpe-
aHHHoii
noBepxHocT[.
HanptxeHttMn,
ae[cfB]ToI{HMI'l
nepnes4[xynrpHo
It
cpeariHsofi
noBepxHocT&,
MoxHo flpere6peqE
B nonepe,tH6rx
ce'Iefi tx
nnacrrHh' .I0z,
/Oz
(ptc
ll.l)
Bo3Htir€Ior
pac_
npeAeneHHhre
no
lrlrHe
n3rt6aroqli€
M,, M, n xpyrtu
e M"
=
-M!'
MOMeI{'
T6r,
pacnp€aenekHHe
nonepeqHble cruIH
o,, 0)"
xomP$e B3atMocBtBarH
c
cooTBeTcnyroqr
Il HopMiurlHHMn
o,, o,
It KacaTeIbxLIMn
BanprxeHnrMu
cJIeA/IOUIIM O6pa3oM
+0.5,
r4,5rt
M,=
J6,zd,.
M,=
la!2d,.
Mry-
!1,,2d,.
-0.5/'
-0,5/'
0t,
+05i
{t,l
^
I
l, *. {lll)
U'-
Jr'az'
vt=
t"
-0.5,
{,t,
Hanprx€Hrt
B nponBonbHoM croe
IUIacr{H6t c
oPAnHaron
z
paBHbl
t2M.z
t2M
yz
l2M,'z
o,=,r I
",=-T-
1.,,-
/'F
\"2,
Han6on[lllne
Hanprxefitt
Bo3HnKaIor B
Hari6onee
ylrn€HHoM
cnoe
npu zo*
=
0,5h
6M,
6M,
6M,,
"*
-;i,
"*-
=
I
,
'*-
=
-;t
6tw
^
daw aa-
dx.y)
-- --+
z
----'+ ------
=
-
t
d d-oy- oy
u
npeanoxeHHoro Coor
)I(epMeH n Xo3eooM JIarpaHx€M. 3aec6
4(.x;r)
- Aet-
crByroqa,
Ha ruacrnty
pacnpeaet€HHai
HarpFI€; D
=
Eh"/ l2(1
-
$'\
- \u-
nrH,qprlrec(a, x€crxocG
ceqetfr, rutacrlHN. ToqHHe
p€ueHHt
]?aaHefltu
(11,4)
norryqeHr'r
ant
npocreiuux cn).IaeB
3axpennefl t $ {arp}rrcHqt
nnl'
cT|H.
Arr
rpyMx
cn)"raeE
nonyqarcr np{6nroKeHfiue
p€ueHHt
auooepeHuH-
an6Horo
ypaBueH&r (
I | ,4),
flcflonL3yt
aBofiHLIe
fink o! HapHue
rpl{roHoMer"
pnlrecxne
prlbr,
Baprra4{oHHhre,
qficreHH6le
n
lpyme
Meroas.
tF--
+,"
(r
|.4)
Pnc. I L l. B|{},rp€HHne
clrj|o8He
oa'(topH
tr HaIDtxeHHoe cocrotHne
3neMeH_
m npcMoyronLHofi
nnacT[Hbl
Ecnti
]?asHeBne
cpeauHHofi
noBepxfiocT,
nna€rnHH ]t(I
-)/)
ruBesrHo,
ro
BnyrpeHRre
csnoBr,re
OaKropH
B
c€qeHn
x.toz,
yoz ruEcrr'rHbt
(ptc. l1.l)
onpeaerrrcrcr
no
oopuyraM:
ri3rn6arculi€
MoMel{rbt
noA
aencrB||eM
BHeurfieil sarpy3xn
rl,lacrnna
nporl6aerct,
a cpeltHHas
nnocxocrb
npeBpaqaerct
B cpeaFfiryo
noBepxHocr!
OyHru}ilo
ryorn6o8
w(r:yr
rnr
cpel]rHHo, noBepxHocrr
nonyqa]or
B
p$ynbmr€
peueHrt
trxoo€'
peHrrnajlhHoro ypaBHeHnt
8ru6a
nptMoyronrHofi
rlnacrunLl
(11.3)
".
=
4#.,#),
"
"
='4#.r#),
kpynrqre MoMenrbl
u,,
=
Ur=-'O1t-V)ffi:
(1r.5)
(l
l .6)
i\r L
Yfl--
,/(w
170
t7l
^
Ja'*,
u'").o
-_Jl:,
j!.
1.1r,.ry
nonepeqHUc
cH.n6l
r.--1*t,
a!dr)-
):v,-
"\axs
ayax').",
Il3
Dnc.
I l.l
BHAIro,
{m Marepsan
rlnacrnHLl
pa6oraer B
ycnoafitx flnocKo_
ro HanDixeEHofo
cocmiHnt.
Ecn[ IUlacrnHa
lt3tomanefia
[l3
lrtacrHrlRoro
Marepxana,
To
B
coorBercrtnH
c
'{crDeprof,
(3rieprer
qecKotr)
r€op,ei
ycto_
sre
[poqHocT,
B onacHofi
Toqxe
fiMeeT Bg]l
*
o,-
=Jol*ol
",o,*:.1,
s[o]
(l
|.8)
sfl
c
yqeroM
Oopiry,
(l1.3)
no,ry'raeM
h'--;----
-,,o,
,
=\Juj""*
u'zN- M,-M,
"+1M;,""
<16l.
(|r.e)
h"
rae M,-,
Mr.,,
M,!."
-
rtm6alourxe
u xp)'rturfi
MoMesrH
a oflacHoM
ceq€-
.qlr
rllacruH
tB
xPynKoro
Marepsana
ncnorb3yerct
mrai
(O.
Mopa)
reo_
*6-5
=or
-xo3
s[o].
(l1.lo)
6M
npl^ a>
b Mr""
>
M^
n o,on=#=or,
or=o,
","=YP-=o
o.""n
*",,",
=uyri"
=l,L
(t
l.l l)
3Aecr
lol
=
o, /t.,
[o]D
=
a,D /
Yo
-,qonycraeMue
lrarpt*eHl{t l.rll
ruracrrtiHoro
n xpynxoro
MarePnarloB;
,r,
1o
-
Ko3Qouqterru
3anaca npo'rHocrH
H Halex-
IIOCTH.
OnacHyo
roqKy onp€lejltlor
B
Pe3yrsmr€
aHarrca
smop M',
4'
M,!
Ecrn
orHo3Haqfioe
onpeAeneHue
oflacHo[
To'{xl'l 3arPyrHeHo'
ro npellBaptr_
Ten6Ho
HaMe'{a}or
Heckothr(o
fipeanonaraeMHx
onacHf,lx
ro'rex. 3areM
sbt'{l{c-
rilor
&!r
ulo( 3(BHsaneHTHUe
HanptxeHb
H
AeJlaror
oKonvarcnhnut
su6op
B
prle
crryqaeB
ffacruHa
tronxHa
6urL
He ron6xo
npoqHof.
Ho x
rocm-
To'rHo xecrxofi.
ycnoB
e xecfiocrg
n
l:lcrHH_ Mesr
alltr
rl*
=
-
<
l"i,
(rl.l2)
u€
-^*
=l*-*lq.^
lD.
"^1*.",1e"'lD.
**
=l^**.plP"2lD, .*
=l*..^l.a'lD ko3qqru$eHrH'
orp€-
rerrreMHe
n1 rruopH
npoflt6oB
w
npl nctcrBt'tx
Ea(Pyjxu
q
lww'1l
wt
p
(fVM),
P
(H),
,,
(HM/M);
a
-
ra6apsrl$Itr
pa3Mep
ruacfl{HH;
[n]
- lonycxae-
Mbln
nporr6. 3aBlrctuHg
or
HetHaqeHlr,
runcrl,|HH
.[l4t
mfiKl,( ruacrxH
B
pire
crry{aeB .4onycra€Mtfi
rporH6
[]tl=(0,00
I . . 0,002)d.
npri oqeHxe
pa6orocnoco6fiocrn rt,acrHH
xaPaKrepsr,I
rpli tapnaHra
llep-
BNft:
n3
ycnoBfifi
npoqriocrx
x xecrxocrx
al|qxcrltror aolrycxae*6le
HarPylxn
fi oKoErarenlHo
B6r6npabr
MeHluee
3Ha'reHle.
BToPofi:
1r3
ycroBnfi
opoqHo-
crx
n xecrrocrn
olrpe]lerrK]r
ro:IllllrHy
ruacrrutrl
[r].,
[r]"
x oroxqarenhBo
npxHrMalgr
6onr'ure€
3Ha.reflx€.
Tperrn:
eofi rcaecrHH
pa3
epH nt{rcflHEl,
,ledcrByrorrne
Harp,3K{
tr MarepRaJI,
m BtIIoJIHtrolct
npoDepoqnHe
PacqerH
Ha rporrHocn
xecrxocrL,
a 3ar€M
lBetclr
rarunoqeHrc
o
pa6mocnoco6Hocrn
Pacqcr
nprMoyronbHtx
lrracrtH
lto
[Peaet6HLIM
cocrotHnfi{
c
)4eroM
ffacrxqecxm( teoopMaqHfi
coBepu€Hlro
aHanorn'reH
PaHce
peccMo'IPeHHoMy
M€Tory
lJn
(pyrn6|x
nnacrnH. B coorBgrcrstu
c rEoprcf,
uacrtlrHocrs
A_A'
Urr}or|rl,tHa
fipn
npercJl[8oM
lrnacr,FtecxoM aeooPM[poBaHxs'
xoraa
lrnacflt-
,r€cKHe
.qeoopMaunt|
pacnpocrpafiMrcr Ea
Bcto
BHcory olacHoro
oobeMa
ruracuru
(pac.
11,36),
urfreHcmHocra
[p€aenbHNx
lranplxeHnfi
on'p
paBHa
cxeMarKrpoBaHHoMy
Irpeaerry
rexyqecrn
ort
=
6r
l,'-
o,,"
=
J
*
ofo
+*
oj- -*
",''
*
","
*:*.L
=
"*
np{
x3BecrHux
,$
ynpyroro
peMHIrt
(10.3)
orlrouerutx
"r*/o*
=
*oro/*c-c
tr
1{,w
/o'fu
=
@Ir'D/I*one
t3
nocnenHen
OopMynH
MoxHo
Ilo.,IJAmh
3flaqeHHt
np€A€nLHHx
Haflptx€sfl*
AfianorfiqHo
xpyrnHM
pacqer
llplMoyrojlsllnx
fltzlctltH
c
)AeroM
Macr[qe_
cl(I|x
AeoopMalrd
noBhllraer rorryc&aeMylo
Harpluxy
t l'5
Pa3a
no
cpaarc-
Hrrc
c
P$ynEBroM,
I|oD
refiHstM
IIo Memry
Aonycxaer'l'Ix
Ha[Ipf'*eHl,n'
I I .2. BAPI-IAHTbI
PACTIETHO-NPOE(TI-IPOBOT{HLIX
PAEOT
(PACqETbt
HA
nPOqHOCTb
ri
XECTKOCTb
nPtMOvrOJIbHbx
flIACTNH
NPH
fi3F'IEE'
3rArHo:
pa3MepH t MexaHnqccxre
xapaKr€pncrlKu
xarepsana
npfio_
yronhHofi rlnacrtHH:
xorooxuye|rr
3anaca
npoqHocrr
,' tl't't
Ko3oouul|eFr
Harexsocrk
Yo
(m6r.
I LI,
I L2):
pacqe.ruat cxcMa
r
)TasHcH
e cpelHHHol
noBeDxnocrt
IrtacrliHH
(ft6n
11.3);
aorycKaer'{Dln
nporrl6
['l<0'001 '
0.002)a.
Tp€6yerct:
nocrpoxrh
B xapaKrepHLlx
ceqe8ntx
ln|opht
pacnPelcneHHLlx
'r3rx6a|oulrc(
M. Mr H
kp)'rtuero
M! MoMeHroB
a
aon
x
qd
ntB
pa'
m'
r'
,rnopH
npofl.t6os
',(r;
l,)
s
aottx
qa"tD tttiM
pd/D,
'd/D'
Pd/Di
ofipe!en,,|16
6M
.^"
o-.
=
ri=o:,
t72
173
lorryckaeMyo
HarpFKy
I
ql (WM'z) t
rA
lPl Ot'\r), Lt ]
(HM/M),
[P]
(H), yaoBne-
rBoprroqyro
ycnoBfitM
nPoqHocrn I{ r(ecT(ocrt
nnerrH6r-
0'
Ta6n. I . I . l,lcxoru6|e
.4aHnHe anr
PnP
E=2
Un0pa
J{e
l-r
uropa
]G
Eapra 2-, Irltopa Ns Bap-T-.
l-r
urO.
J{-o BaD.
4-r
qxQ.
I! BaD.
b, CTanr
Mna
I t. t0 0.550
0,020 l8rn 0.340
235 2.40 t0
2 l-20 0,600 0,022
20 0.330 270
2.50 9
3 1.30 0.650
0.024 BCr3 0.J20
275 2.60 8
4 I.40 0.7000.026
09f2c 0,310 370
2-to 7
5
l-50 0.750 0.028 30
0.300 380 2.80
6
6 1.60 0.800 0.030
l512 0.290
440 2.90 5
7 1.70 0.8500.032
40 0.280 500
3.00 4
8
r.80 0,m0 0.034 45 0.270
l. t0 3
9 1.90 0,950
0.036 t2t2c 0260 590
3-20 2
0 2.00 1.00 0.038 50
0,250 650 3.30
I
a6n, I l 3, PacqcrHLre cxeM$ n
Ne
YpaBHenm
cpe,nnHHofi
noBepxHocrn
2
J
e'r=)ff(n
2
"k;v)=
n*'(t."".?sl'-"*?)
o^(r_r:1,.4)o
|
," b'.)
3
r:'v
'oTCgnSt /
x
------>",/*
/ ,2\
64q"1
'!':-8F+
|
I D-t
urlxivl=_=+<
'
'
""V'
-$v'
lD
r[,'"orE *
a'*r{l
\
c
D)
%
m,-|-lm, ,
m1-Umt
,
s,tr:vl=--r+r-
-+
Y-.
zl
-r"
D
zl-t"
lo'
mt=m, mz
=2m
5
"\":
v)=
q",'a'Ir
*,?.sl,i"
q
\
a)
-l$;;*..b^T
Ta6nI1.2I,lcxo,qHhte
.qaHHHe !,!r
PnP
Il}l0pa
]{
l-'
q'Opa
Nr BaD-m
2-r
qnopa
)$ Batrra
3-r
uxQ.
4-,
uuo.
Xe BaD-Ta
b,
Mna Mn!
Mfla
4.002.U) ).1600.t50 10'
0.1501.00I 1.0 1,00
l0
2 4.202.to).1700.t60 t0'
0,t55l-t0 15.0 2.90
9
3
4.402.201.1800.170 10'0.160
1.50r9.0 2.80 8
4 4,602.30,.19c0.180.r0'
0.1652.0023,0
2.to 1
5 4.802.40c.20c0.190.t0'
0-1702.5027
-0
2,60
6
6 5.00
2.500-2lc 0.200 10' 0.1753,00I
r.0 2.50 5
1 5.202.600,22(0.210.t0'
0.1803.5016.0
2.40 4
8 5,40
2.700.21c0.220.10'0.t85
4.0040.0 2.30 3
9 5.602.80t.24(0,230.t0'
0.1904.50
44.0 2,20 2
0
5.802,90
j,25t
0.240.10'0.195
5.0048.0 2.10
I
l'14
t15
Ta6n.
I I .3
(oKoHqsHre). PacqerHde cxeMLI
I{
ypaBHeHtt cpe4tHHot
2
3
",a(r-""'?e{r-*.fJ
"'\";t\=
l.--a'*a{
-.^)^
I
I /)......._
+JoJ
ll,,
I
o'b'
)
F-'I
--
7
4)=#(,5-'*.,*)'
q,
=
co'la
8
"t
,rl=lo,o",.o,*ls(f
-
')],
,9..T['-*.#)
ffi,"=.'"92
-'7Vr?-r??-?-2-?"-=
pv
*{,;/)
=lo,orre
* o.oor
r{;-
r)],
'9.'"?['-"r;)
ffil
l0
f / A\]
",(';
r)
=
lo.ooerl
+ o.ooezl
t
-
:.1.1
'
obt nx
w
I I.3. PACqETHO.IIPOEKTI,IPOBOqHA'
PAEOTA
(PACqETbI
HA DPOIIHOCTb
I.l XECTKOCTb CTAIbHOff
nPtMovrOJIbHOR
mACThHbl nPH
rcrItBE)
3raiBo:
pa3Mephr (d=
1 M;6
=
0,5
M;,
=
0,04 M) n Marcpnar
(cran6
l8f2:
,
=
2
l0' Mna;
F
=
0,30; o,
=
440 Mna) nptMoyrotsHotr
llnacrnHbl, lllapHtP
Ho saKpenneHHoli
no xoBrypy s Harp''xeHHofi
paclpeAeneHHofi
no
cnHycoF
. tt
trv
mM
Harpy3fton
q\t
:
y
)
-
qstn
-
stn
-;
,
kot9QH
qxelfr
pnaca
npoq
Hocrlr ,rr
-
3,0;
aorrycKaeMHft
npofl6
[v]
=
0,002,
=
0,002 M;
pac,icrHat
cxeMa
(pnc.
11.2)
lr
)?aaHeH
e cpeAnHHo*
noB€pxHocrll
aao
bn fi' nv
nr(x;
/,=
---
r
----------
srn-sur--.
nalat +bzf
a
b
Tpe6yercr: s xapaKrePltr'Ix
ceqeH rx r0z,r9z
(pl'c.
I1.2) nocrpol{rL
lrtro_
pN paclpeaereH
Erx LBm6doruD(
M', ,t4 fi Kp,'rtuero
M,/ xoMeHToB E
aontx
ql,
enop$
nporr{6oB }r,(.r;
y)
t
wntx
qa'/D;
or!,erctl{r6
aorycKaeM}ro
Ha-
rppKy
[st
(HAr'), yAoBnerBopircus o
ycrloBxtM
npoqHocrlr
t x€crKocrx
IUTACTT'HLI.
BLrBoil vpABHEHItt cpE,ul'lHHofi
noBEPxHocrH'
Anr
orp€aeneHrr
ypaBHeHx,
cp€anHHoi
noB€pxHocrg
x,(r,
/)
xc'onl3yeM
!n(!4€pc
uianLHoe
ypaBH.nne
B
qacrHllx
npolBBoaltxx
(l
L4)
O'w
^
3'n
a'w
q\x: y)
&.
-
&r ay, ay4
D
rA.
D
=
Eh3/12(l
-
pt)
- uUrxxapavecrar
xectr(ocl[ ceqeHrt
lDlacrriHsr.
PeureHx€
)?asxcfirr
(1t.4)
ant
paccxarpuBa€Moro nprMepa
npetrox€Ho
opaHrry3ckrM
'4eH!tM
Arpr Has6€
(1785
-
1836
rr.) B BuAe
.
1U lry
v(r
j
y.,
=
,osrn
-
srn:
'
(l
l.l3)
rae )ro
-
npor6
B
qemp€
MacrnHH.
an"
no
,t oy
a"ab
a'w
:rn nr rv
-
. I tollcTaBntt
'b4
a b
C
).{groM
(l
l.l3)
nor}"{aeM:
atw
tn
nx nY
-=w.
-Sln-Sln-i_;
ax'd'
-
a'b'
a b
flo.rryqeHHEre
3HaqeHnt
qacTr6lx
npor{3BoaHErx
fi
q(r,
/)
B
(l
I.4), nocne npeo6pa3oDaHrt'
Hzlxoal{
'nprl
BNIIonHeHtx
PnP Ee npoBoArrcr,
'117
t76
cd4b' ./-....\.
eo!]-
sinEsin?.
(n.ul
-"
no
(oz
*a,lz o
"
n,\at
+b'1l'D
qro
coBnatraer
c aHajloruqHLrM
Bh|pa)I(eHteM
npfiaeAeHHElM
B
yCJIOBtrn
3aAaqfl
Pe reHfie
A.
Hasle
(ll.l4)
sBnterct
3reMeHmpE
M florloMy'
qm qerHHe
rracrHHe
ltporriBoaHNe
or
r,(r;
/)
cosnaaslor
c mqHocrhlo
'qo
nocrotHHux
uro*llrenifi
c
taronov
rcMesexnx
fiarpFxt
9(r;
y).
PEIIIEHI,IE
l. Onperente
pacnpeF eHHLle
{3rt6aroqne
MoMe{rt't
M', MvB
'e'r'Hfi'
rx
z,)Oz
(prc. t 1.2)
,
=-Jt+-,+),
".--l+--+l
-le,
'
6yz
)
'
\ay'
d''
)
Anr
3roro
c
yqero
ypalheHlrt
(l
l.l3) B6lqlrcnteM
aropHe
npou3DoaHHe
44
=
-\
*",^r-,,7,
fr
=
$^,-i,^i
cneroBal€nLHo,
pacnpeaerelrrble
rl3rlr6aroun€
MoMerfr}I
paBHr'I
t.
="o..fl*4lsinrrsin?
I
"\a'
t')
a
b
"
="'-"[+-l]inlr,ing.
"\a'
t')
a
b
np'r,
=
o,5a
ri
F
=
0,3 t{3
noc,IeaHrd
BLlpaxeHnn
nonyqaeM
. rr
,ry
.,
1.0t?4aa2sin9sing.
(
.15)
M,
=
0.00891qa'sin
-sm
t:
My=t
b
2,
HnxoArM
pacnpeAeneHHfie
xplniqne
MoMeHTH
M,,
=
M)'
6
'eqe{sax
xoz'
u,,
=
l,Oosslea1ns9rrrsff
(lLr6)
3. KoHrpern3xpyeM
)?aBHeHne
cpearnHofi noBepxHocrn
(I
L14) npH,=0,5a
4
v)=
qo'(o,so\
r' ny
",Qz*1n,5,1t1
p'
.- t
*.{'; y)
=
o.oooq t tgLsin
IIsin I
(r
l.l7)
4. no
oopMyraM
(l
l.15) ...
(lLl7)
HaxoarM Bejln{a'd.bt M' M,, M,, tt\x:
y)
Ara
t
=
0:
0,25a; O,5a;
0,7 sai a i
t
=
0; 0,25bi 0,56; 0,?5r; 6. 3ar€M
pe3yn6m-
rf,r
pacqeroa
cBoAr.rM B ra6rrrv I1.4 n crponM smopH
(pxc.
I1.2).
fur
yAo6-
crBa Bo6paxesnr nonoxI{rcnbHLr€
3HaqeHrr
3rtrop Mb My M,, oKa3aHr' Hz
cxarHx croD( rnacrnHH
s
Hao6opoT.
5, Ararr.r3 3rrop mr'l6a|onll.sx M,, M! ra Kpyr'Iulero Mry MoMeHmB noxa3r,rBaer,
qm
oflacHofi roqXa B
ueHrpe
rlnacrus;I, rle M-"
=
O,OO&glqt, MN
=
o,Oll4ql, Ms"
=
0.
BbuenlrM 3neMeHmpxErn o6!eM
liddl B or(pecrHocrll onacHof, To'rxr
(p
c, I l3), npercmMreM fiopManbHbre
Ir xacar€nbHhre HanprxeHHr B
onacHotr
roqK€ n racr[H6r
AM 6M-,- 6M,.--
*o,
=:_+!'l
*6"
=--r=
i
tp
=
-----jl::
=
0.
h' h' h'
Bnado,
'rro
Marepna, ruacrsHH
pa6oracr
s
ycroBux
rrrockoro HaflprxeHHo-
B comssrcrBlrlr c
.rerB€pmfi
(3Heprernqecxofi)
rmpHeft
ycno-
BUe
rlpoqfiocTn Moxfio [peAcTaagTL
ol
+
a2,
-
a,o,
+ztj, <laj wu
6 F1----
^".*
-
;:,1u'z*"
t u')."
-
M,""M
r"
iM:* <tal.
rae
Ial
=
a" /n,
=
44OB
=
147 MIIa
- lorycmeMoe
HanprxeHhe. C
)qeroM
x16seruq M,on
Mr
t M,,nn 3aqncuEaeM
ycroare
[poqHocrH
0.0905o42 , ,
ms
o
,s!
=
-:--
.-
<
lo I.
CreroBaren6Ho,
aorrycxaeMar
pacnpeaeneHHai
Harpy3,(a Ha lrnacrHrly
paBHa
6Y=
l"h'
=
-'ot'ot
oyt
-r.uo
,oo4.
"-
0,0905a' 0,0905 l'
)Oz
nnacruHH
(Prc l1.2)
=-r,=-4-r\#
C \qeroM
ypaBHeHxt (I
I 13)
Haxorr
Bropyro
npomBoaHro
A.w ft'w" M
try
--
-cos-cos:
dtdY
ab
a
b
np{ 6
=
O,sa
n
u
=
0,3,
c
yqercM
(
I 1.14)
H nocneaHKx
ahlPaxeHni
notrirraeM
.
",
q,'(o.sll
"o.9"o"y
_n
"o\o'
"1o,so\'f
ooo.so
M
,,
=
-
D\t
-0,3)
178
t79
Ta6n.
I 1.4.
I
M,
;F
n7
v=o
0
0
0 -0.00568
0
o,25
0
0 -{.00402
0
0,50
0
0
0
0
0.75
0
0
0.00402
0
0
0
0.0056E
0
y=025b
0
0
0
{.00402
0
0,25
0,00445
0,00870 -o.00284
0,000206
0,50
0.00630
0.0123
0
0,000291
o.7s
0,00445
0.00870
0,00284
0.000206
I
0
0
0.00402
0
y=
0,50b
0
0
0
0
0
0,25
0,00630
0.0123
0
0.000291
0,50
0.00891
0.0 t74
0
0.00M1I
0.75
0-00630
0.0123
0
0.000291
0
0
0
0
y-0,15b
0
0
0
0,00402
0
o25
0.00445
0-00870
0.00284
0.000206
0,50
0.00630
0.0123
0
0.000291
0.75
0,00445
0.00870
-{.00284
0,000205
I
0
0 -4.00402
0
0
0
0
0.00568
0
0.25
0
0
0.00402
0
0,50
0
0
0
0
o-75
0
0 -4,00402
0
I
0
0 -{,00568
0
0,0174
0,0123
0,00891
0,00630
-
0,00568
-
0,00402
0,00402
0,00568
0,000291 0,000411
Psc.
I
1.2.
3mopH
pacnpeaereHHHx
Brfi6arourx Mr, Mrv kpyrxulero M,,
MoMesroB, 3firopH nporn6oB w(r;
.),)
rprMoyronLHot nnac-rtrHEl
M*
qa2'
M.,
;7
-0
M,y
^^z
0
M,
6.
IlposeptcM
shr[onHe
re
ycjloDut *ecrxocrn
ojlacrnrir,|
nPn
F
=
0'3
*.*
=o,oo*t'$
=
o'ooon"d*&
=
_
z.oo.ro1
r',tz(t -g.l!
)
=
0,er
r.l0-3
M,
2.to'
lo'.0,04'
qro
MefiDrIc
aolrycKae
oro
nporr6a
[Yl
=
2 10_r
M
EcJu{
xefl(ocrb
llnacrn-
HH
H€ o6€cncqeH4
To
aorrycraeMyo
HarpFry
[4]"
BLIq{crIlIor
It3
yc'IoBllt
qao
lD
180
l8l