Добровольский В.И. Расчёты на прочность, жёсткость и устойчивость элементов конструкций
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gxoltoMrrlsoe.
3. npo8eprrb |{ rtpr Heo6xotrr,rMocrn
o6ecneqfiTt aufloJlHexre
yoroBxt
xecr-
rocTr 6ankr.
48
49
2MA=Pl-ql
0,5l
P zl-Mo+RB
4l=o, RB=o'344P;
,MB=P
5l+qt
4,5l-RA
4l Mo+P
2l=o, n,{
=1906P
nposepka:
t
v
=
-P-ql+l,9o6P
-
P +0,344P
=0
3. Bbr6ripaeM
a6c$rccbr
zr, zr, zr Ha
yeaccxax n MeroAoM
ceqeHni onpeA€nteM
3aKOHLr
r.BMeHeHr.x
onep€qHHx
ct',t t x3ff6a()uxx
MoMeHroB
IlepsHt
yqacrox;
tv=-P
q1
Qt=0,
Qr=-P szt;
0
M,
Plrc,4.4.
Pac'{erHai
cxeMa6anxu,
snropH
nonepo'lHHx
cun
n l$r[6a]ourtx
MOlleFmB
PEIIIEHI.IE
l. B6r,{ep,{nBaeM
nHlrBuryanrHylo
pacrrerHyrc
cxeMy
6ant(l{
(pnc 4 4) B coor-
BeTCrBns
c lrcxorHHMq
aal{HBIMn,
OnP€AenteM[rM[
no
uropax
HoMepa
sapx-
AHTA.
2.
Bbrq ctteM
onopBHe
peal(qllfl
(pl'c.4.4)
no flonyq€HHbfM
3Ha.{eHraM
crpour ttttop$
A,
E M'
(pnc.
4 4) B ntrepa-
rype
crporrenbHoro
npoolrfl! oc6
M, HanpaBttercr
BHl'3
(pnc.4.4).
4. BHqncnreM
,lonycrceM6|e
HopManbaoe
t KacaretsHo€
HanptxeFnt
t"l-
9'
-
!99
- 36s
yn4
hl-
L
=
-0J"'
=
05
-600
-
rso vnu.
2
"n,
n, 2
5. Han6onbrnre
HopManrHHe
Haflptxesrt
Bo3nnxarcr
B.Hat6onee yaaieHHLlx
roqxax onacHoro
ceqeHHt
Ha neBofi
onope,
rr€ M-
*
=
|
-1
'l25Pl
|
.
Ih
yctto'
Br.u
npoqHocrx no
HopMarI6rHM
HanptxeH[tM
lM-.1 l-r.125P4
r r
*"^
-i7=
n
.t"t
HaxoaxM
pacqerHHn
oceBofi
MoMeHT
conpo Bn€H[t
ce'{eH
t
6anxx
l,l25Pl
1,125.4.30.1l0r
rynz1-0,s1
Qr1=
t,12sP, M,t= A,s3tPI;
nptzl= I
Qt=
-1,25P,
M"=-l,lzsPl.
Ma
ZM
ct
=
Pzt +q4 0,521+
M
n
=o,
M
a
=
-Pt,
O,sqzt'1
BHnyrsar xBaaparHat
napa6ona.
Ilpt' zt
=
0
Qlt=
P,
Mr=o:
Q'i
Bropofi
)
{acroKl
Zv
--P-ql+t,906P-Q'r=0,
Qyz
=o,6s6P:
ZM
c,
=
PQ + z1)+
qt(o,st +
z1)
-l,906Ptz+
Mn
=O,
M
,,
=
-1,125
Pl
+
0,656
Pz
t
.
llpt, 22:0 M,7=
-l,l25P;
npt22'21
M'z:0,188Pt.
tY
=
Q,!
+ RR
=0,
Q4=-0,344P;
LM tt
=
-M
t
+o,344Pzt
=
0,
Ilpu
4=
0
Mi=o;nPA?3=21
Mt:0,688P1.
5l
0,688
0,188
Tperrn
rlacmri
50
300.100
=
450
10-6u3
=450
cxl
W
6.2. KBaApar:
'w
6.3.
Kpyr:
,w
6.4.
KonE{o:
3alaaxcr
lnr
onp€aenefi o$u D
=2d;
o=!
=s.5,
17,
=146
-o.1=
oro
"",.
D
"
:t2 '
llu/
D
=
rl;-+
=
t?.0 cri d= 8.5 cM: f.
=
t 70 cMr.
tqr-u
,
6.5.
tllDeruep: B6r6npaeM, HarprMep, npoornl
Ns
40;
no m6n. n.4
,nr
u8er-
neDa JS 40 HaxornM
W,
=
13,4 cn3-
F.
=
61,5 cM':.
v
6. Onp€lenreM
pa3MepH
Han6onee
pacnpocrpaHeHHhrx
ce'{ertlrn
6arox.
6, |, nprMoyronrH{(: 3a.qaeMcr
luu
oflpetrerefiEocrv h
=
2b:
,
=
2 8,80 cM; Fr
=
155 cMr.
A]-
4
=7=lso
cu':
b=rli4
={e.an =n,s.M-
Fz= 193 ev-'z
w-
=:::-=450
cNt :
"32
?.
O{ennEaex xalepraro€xrocrE 6arox c no&6panHhrMx
ceqeHmMu,
npn-
nxMax nnoqirAr rraf,x€srur€ro
(aayraopo8oro)
ccqetjnA n lO0
o/ol
(q
I
F),{F,
/
F"r,(F,t F"\:(F4
I
F6lt(f.,
/
FJ{f.6
/
F)
=
=333,4lS
It65 |366:'t
:100
(./o\.
Aan[Helm€
Fcqcr6|
Bunonfifiorcr
rrr
6anxn
lEjrra8posoro
(Han6oree
3lro-
rroMr{qHom) ce,{e
|!. Bugt|c,ne rtaxc'{ arbHoc
pa6oqee
Hanpr)f,eHne
*6*
'/*
-1125
4 30 1 10'=286.10'na
286Mnq
lY^
472.104
xoropo€ r.eHbure
AonycxneMoro
Hanprrrcdlrr
t|a
A
-
*"fi
'
bl
l00%
=2Y,1oo
1sv"
'
a.67
',5.
161
300
8. Harr6onbllre l(acar€rErcrc mrprx€Hrr Bo3fifixtrror
B ro.rxa( HehpanhHoii
txHrn ofttcrpfl) ceqesx, 6anKr na
neDofi onop€,
rAe
18 n-l=
l25P
=1,25.4q1.
npeaDaptnetHro m
ra6r. n-5
.Enr aByraspa
]{e 30
Haxo4rv: J,
=
7080 €r.';
Sg
=
26t
c|r!
;
d
=
0,65 cM. npoBeplex npo,r-
{ocrr 6atm
AB)aaDposoro
ceqeHxr no xacmenlH6rM sanprxe
r{rM
=
87,4 105na
=
=8?'4
Mna
<
[t]
=
I 50 Mna'
9- Alral''3l'!yt 3';lo!p'J
Qt
x M! HaxoAlor
npelnonaraeMo€ onacHoc c€qeHne
no ?m{aiuclttr$ Hanprxefifirr, :narctrqrr Kax
oT HopMut6riHx, Tar & xa-
c{r€n[HUx
r€rtptr(edrl.
Ktx rpaBxno, onacnoc ceqeHse ro, rAe Bo3HnKa€T
Ha$6on6unf, |t3r$6atouxn xoxcllr MlE n sHaqFrer6xar
(rc
o6'3a1erl$o
xrxcmranLHar)
mneF,rHar
crina
9F-
B
pacclar!*.acMoM
npnnepe onacHoe
(no
fxarsai€Illtfix HarprxcHl|'x) c€.reHse
pacnonoxe|o
fia ncBofi onope
6€nrn, rlc /l/-
=
-1,
| 25 Pl tr
8F
=
-l25P.
10.
Apy.aapoBoc
cc,rc{nc .l& 30
JrcnoBfio
npeAcmBnreM
(puc.
4.5) B Erne
rpex
nplxoymftsxxioa:
JEyx
noror
parxepax{
,
x
t r cIeHru
pa3Meprxs (,
-
2a)
x
d. C
yqdor
aa6nh|sr n.5
,o|'
a8yr'arpr
lft 30 saxoauM:
,
=
13,5 cM; r
=
I,02 cx; ,
=
l0 cr.; d
=
0,65 cx.
I
I.
OrycAp.ffey
Hopr.arlHn€
Hrnprxcdnr B )(.ptu(repHHx roq[ax onacHoro
ceq€Hxr
(prc.
4.5), rcnonByr
oop.yny
l,n*|
a'
=
---;-
y"
h=216cu'.
CneAoBar€rhHo,
Heo6xofl.tMoe
'txcno
MennepoB ff 40 nu
-
450/73,4^6,
F5=661,5=369cM'.
6,6,
AByraBp:
no ra6r. n,5 naxo,otM HaH6oree noaxo,[,urri
@y"aBp
.l.|! 30,
xMercUlxn cnelyroule neoMcTpnqec(ne xapar1€pncrn*n
Wn
=
472 cM'; F6
=
46,5 cM' .
52
53
,d
281
Mn4 a1
=
-f
4,7 MTt4
04
=
13'
c,ot D
-
D ar
=
8? M[a, ar
=
87 Mfla,
.to
=451cnor
E-,or
=
14,7 Mn4
sr
=
-281
Mn4
qo:
-t3.;cno,
F-
For=
0,{X
Mn4 ar
=
267 MIIa,
ao
=-{,665d;
cror
C Co,=0,or=
286 Mna,
uo
=
_0.
Crpor{M
amrc{MMerpnqHHe
srmpH
rnasHL,x
HanprxeHnfi
or,
or
(pr.rc.
4.5).
14.
Hcnor!3yr
rlaoo-aHanHT}'qecrsfi
Memr
O. Mopa,
orpeaenreM
BenlrqrH6r
r Hanpasu€HK
rraBHLrx
sanprxeHl|i
I,|r
xapa$epHLrx
roq€r
q
D l,
6 c no-
MourEto xlryra
HanI'{xeHnf, (o6parHar
3aaaqa),
(ax
noKa3aHo
Ha
puc.
4.6.
Mna
ot,ol,
Mna
65
14,7
0,04
Pkc. 4.5, 3mopu FopMarbHhrx, KacareJrb{brx r{ rnaBHr,rx fiallprxeHafi ! o[ac-
HOM
CeqeHnX
layiaBpoBon
6arKfi
rAe
y,
--
opAHnaTa
paccMaTpfiBaeMHx
mqex ceqeHHr.
F[a
uoaB A
-
I tr G
-
G
),i
=
+
I 5 cx,
croeB
8
-
r,
C
-
C u E
-
E,
F
-
F
y,
-
+0,5(,
-
2t
=
*l
3,98 cM. C
yqemM
3roro norrlqaeM: o/
=
286 MIla;
o,
=
oc
=
267 Mlla, aa=0;6t= 6t=
267 Mna: ac
=
186 Mna. no norl^reHflhrM lHaqeHmM
crpo,M srrropy sop-
Mar[Hux Eal|p')reHttfi
(p
c.4.5).
12. HcnonL3yx
oopMyny
A.ll.
X]?aBcxom
r'
-------:---
,
JtDi
onperejlreM xacaletsHHe xanprxcHui B
yxasaHHErx
Burle roqftax.
IIp{ 3ToM
Qr""
-
-l,25P;
J,
=
7080 cM'. IlpeaBapmenDHo HaxoAxM crarrqecxxe MoxeH-
rEr
orceqeHHErx
nnournae*:
anr
mqex
/
r
c s:'
=
0;
rnr
loqek
4
c, E H F
sI"
=
r.r.0,5(r-r)= 13,5.1,02 0,5(30
*
l,o2)
=
199 cMr;
4n'
rorrKH D lR
Ta6n. n.5
.!ri
aB'.r.spa
N! 30 nor)AaeM S$,
=
268 cMr.
C
y.rerox
rroro
au-
qHctieM:
r,i
-0;tr=tr=
3,1 Mna;k=rr=-{5 Mna; rD=-87 Mna.
CTposM 3fllopy racarenLHHx HanprxeHs,
(prc.
4.5),
13, Onperenr€x aerx.i{Hu Ir HanpaBreHrr maBr6tx Eanprxefid no
QopMy-
o,
l
,'22
,
re2.to
=
--
o,
B
psynbrare
BHqrcneHrfi nonlAaeM
ur:
cnor ,,1
-
.{ or
=
286 Mna, 03
=
0,
qo
=
0: clto B
-
B at
-
267 Mn4 03
=
-{,M
Mna,
qo
=
0,665';
cror
C
-
C o'
=
65
0,04
14,7
267
281
8'l
ao@
n.a. 03
JI.A.
O
Ol
286
oo@
T
n.A.
ol
d\
o
x
0or
Pnc.4.6.
Kpym
O. Mop.
Anr
sneMeHroB
C,
Dn
f
flocrpoeHne
xpyros
O. Mopa
norcHxM
ta nprMepe
ro,rl(I{
C
(pxc.
a.6):
BH6l,|paeM
xoopAxHarHue
ocs o
-
lj B MircurTa&
mKrarhrBae
HanorxeHm
oc, rc r
0.
-rc;
coerhHreM
nojlfreHHue
ro,{K,
nprMon l,r ortxc8Bae;
oqyx-
I
n.A.
ol
aoo
Q
+n"l
54
55
r u,
rr; coearHreM
nony{€HHHe
Toqrfi dprMoi
n onficbrBaeM
orp}rkHocrL.
(rrpc1xr,
orc€fteMs€
oxpyxHoclHo
Ha
ocn o, npeAcraBrlrror
co6of, s Mac_
urra6c
rnasHEre
HanprxeHy,,
or
=
28 | Mna
n or
=
-
| 4,7
Mna. 3ar€M
FaxornM
'rcp(lnbHhre
npoerqnr
ro'rex c
(oopftHamMn
(oc;
rc) }l
(0,
,tc)
Ha
oxpyx-
'rocrr;
qepd
rovrx
c kooplHHaraMH (or;
0) r
(ac;
-rc)
npoBoarM
nriHxH
!ei-
cralu (n,a)
[naEH6,rx
HanprxeHlfi
ol I 03, xorop6re
onpeaenfloT
ncxoMLtf,
y,on
oo
=
lld,
nocne
rrom noxa3HBaeM
raflprxeHHoe
cocrorHr{e
6:UI|fi,3a-
aaHHo€
Ha
DraBHHx nJiouaakax
Fanprx€H[rMn
sr n or
(prc,
4,6, BH],rp€HHxr
i(y6r&).
BuHo,
qro
xpyr
sanprxefist
coBepurerHo
aHanorrqeH
rqyry
{rep-
usr O. MoDa-
15. Arann
snlop o x
1
(puc,
4.5)
noM3hrBaer,
,{To
Han6onsr
ne 3xBxBan€m-
HLre
HanprxeHqr
Bo3H&rabr
B cjrotx
c
_c
n
E E.3anucNBaeM ycnosn€
npo{Hoc
6anKn no
3xBr[ajeHrHuM
HanprxerrHrM,
trcoors3y,
Tperbro
r€o_
xe, so
npornBorronoxso
HanpaBreHHyD.
A6cuHccu
yqacrxoE
6an|(l, xtM€llr_
torct
B np€A€nax:
0
S
zr
S
I; l3
zr'3l;31
S
4<
5/. HanpaBreHr.n
BHeuHxx
sarpFotq
coorBe.rcrsyroulHe
norox&TenbHbrM
3lra(aM cnameMhrx
vDaaHeHrfi
r
4.I0, (4.
|
|r. nora3aHH Ha p{c.
4.2. C yqerov
,roro ynru"p.-in".
ypu"-
HeHUr (4.10)
{
(4.1l)
r(oHreerr.BrpyeM
cn€nyrorruM
o6pa3oM
^
^
P(,, o)'
q("
-
ol R,1.
.
tll
oh
-
tf
2tEJ,
31.A,,t 2tA"
3tLJ,
,,.
,
M.t!:)!I
P9
:f!)
\ta,
2'.EJ,
|tl
^
p(,
oI
qG_o\f
R.l,-rl
qt,_rf
)',=''a.va']=--_.-:--*lL-
3lEl
4lEJ,
tt
3tU, 4lEJr
t,,
+MoQ4r)'_*4ty
2tEt,
3tEJ.,,,,
17,
Ha onopax nporu6u
parHhr
Hymo,
CreAoBar€rbno,
rpaHrqHHe
ycnoBnt
Meftra
4l.zt=l
y=0i2.zx=51
J4
=
0.IlorcraBnrr
rpaH{qfibre
yc-
noBnx B
X)aBHeHNr
nporr6oB
lrr
fiepBoro I{
Tl,erbero
)AacTr(oB
r coBMecrHo
peura,
l,|\.
nony'{aeM HaqarbH6re
napaMeTpH:
Oo=
|
l,l2spF,f,J,;
y{=-l,948PP
/EJ,.
18. Pa36rBar
6anry Ha 10.{acT€i
n
lAr,rruBar
3haqeHur Oo lryo,
no KoHry€rri-
3xp@aHHErM
ypaEHefirutM
BHtrncnreM
yrr6r
noBopoTa
r nporr6H
6anrl{,
pe_
3ynrrars BDl'rrcnesxt cEor{M
E ra6nrrry
4.3.
Ta6nfiqa
v
261'1 +a(-6s)'z
=
2e6 Mna
<
Iol
=
300 Mna.
Ta(xl, o6pa3oM,
n!'oqHocrh
6anxn no HopMarrhruMj
(acarenbHLrM
t,| 3|(BnBa-
reHTIrhrM
HanprxeHrtM
o6ecneqeHa.
16. npoBonxM pacqer
!!).raBpoBon 6arKx Ha
x(eoxocrr.,lln,
onD€Aene8n,
yrnoB
noBopora
fi nporr6o8
ncnonL3yeM yHnBepcarLHEre
ypaBHeHH,
(4.10)
n
(4.11).
B coorBercrBr.rH
co
coopMynHpoBaHtrHxr
BHrle
rpe6oEaHxiMn
co-
cEBJrieM pacqerHyro
cxeMy 6anxr
lnr
oflp€aereRri
fl€peMeurerrn] (pr,c.4,7),
Pxc. 4.7.
Pac{erHar
cx€Ma
r cocraBneHrro
yHnBepc€nrFlrx
ypaBH€H{n
yrnoB
noBopora
ceqesfifi I|
npor[6oE 6ar(N
flps
3roM
Ba,raro l(oopAnHar pacnonaraBM
B rgatrHeM
neBoM
ce{esrl{
6arxn, a
pacnpeA€r€HFyrc
Harpy3Ky
4
npoAnreM
Ao
t(oBro
6an(H u
lo6aBnrex Takyto
OxoHqarerurc npercraBnrei,
6anKy
(ptrc.4.8)
s crpor rruopH
0,
M", O, n
)!
c
]/.|erol{
pacqer@
'r
ArooepeflumrEHhrx
3aBllc$Mocrer
Mex/y
qr,
Qy
M",
O, n
/,.
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npaanna xoHrponpnrop,
npoE€pr€M
npas}r,hHocrh npo-
BCIEHHEIX
DIICqETOB.
n€peMeqe-
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2l 2.st
3.5/ 4t 4,51
n
? ?
"1
?
f
x
i
?
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6L
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56
51
0,2t3
0,0535
Ptc. 4.8, Pacqerrai
cxeMa
6anxn, 3moplr non€peqHux
cfin, Brn6arollnx Mo-
MemoB,
yrnoB
noBopora l,l nporu6oB
19, AHanrclpyr
3flropy rDorr.{6o8,
HaxoayM
onacHoe no xecrxocrfi
ceqefixe
(B
paccMarprBaeMoM
npxMepe
kpafiHee neloe
c€{eHhe), npoBepreM Bunon-
HeHxe
ycroBxr
xecTxocrn
6aJrr(x
=0,00803
M
<
t]=
0,01 M.
BraHo,
qro
ycnosfie
xecrkocrl
6arrKx ENnoJtllrercr.
B nporuBHoM
cnygae u3
ycnosnr
xecrftocT[
BHqrcJrreM pacq€rHHt
MoMe&T l,|Hepqsn
4
x
no m6n,
fL5
okoH'rarenlHo
sH6rpaeM
HoMep
asymBpa.
5. PACqETbI
HA nPOqHOCTb
BPyCt
EB nPIt BHEUOHTPEHHOM
PACT.SXEHT,II'
(CXATfi
U)
Mfiorue
3neMesru
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pa6orarcr B
ycrloBtltx
coBMecrt{o.o
lefi-
cTBnr
npocrhrx snaoB
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(pacrtxeHfit
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