Pacnetbi ha npohhoctt mexahhneckhx kohcrpy^hh cogep^ahhe

OH^HA^ OE^EPA^bHOrO rOCY^APCTBEHHOrO BM^ETHOrO OBPA3OBATE^BHOrO YHPE^EHHfl BBICmErO OBPA3OBAHHH «HA^HOHA.HbHBIH HCC^E^OBATE^bCKHH YHHBEPCHTET «M^H»
B r. CMO^EHCKE
HanpaBaeHne nogroTOBKH 13.03.02 «^.aeKTpo^Hep^eTHKa H ^.aeKTpoTexHHKa»
3A^AHHE
Ha KypcoBym pa6oTy CTygeHTa ATaKHmueBa. ^.A. (rpynna PT-20)
TeMa: PacneTbi Ha npoHHOCTt MexaHHnecKHx KOHcrpy^HH Cogep^aHHe pacHeTHo-noacHHTeabHoH 3anHCKH:
1. BBegeHHe.
2. 3agana N°1: nocTpoHTb ^^mpbI npogoabHbix cna, Hanpa^eHHH H nepeMemyHHH nonepenHMx ceneHHH 6pyca.
3. 3agana N°2: nocTpoHTb ^^mpy KacaTeabHbix Hanpa^eHHH.
4. 3agana N°3: nocTpoHTb ^^mpy nonepenHbix CHH H H3ru6a.mm.Hx MOMeHTOB.
5. 3agana N°4: nogo6paTb nonepenHoe ceneHHe 6anKH.
6. 3agana N°5: nog6op gnaMeTpa Bana npH H3rn6e c KpyneHHeM.
7. 3aKamneHHe.
nepeneHb rpa^nnecKoro MaTepnana:
1. 3nmpbi K 3agane N°1
2. 3nmpbi K 3agane N°2
3. 3nmpbi K 3agane N°3
4. 3nmpbi K 3agane N°4
5. 3nmpbi K 3agane N°5 ^ara Bbigann 3agaHHa: 8.09.2021
Ka^egpa «TexHoaorHHecKHe MamHHbi H o6opygoBaHHe»
PyKOBO,n,HTeab - —
3agaHHe npHHaaa K BbmoaHeHHm:
CTygeHT
^ara 3amHTbi KypcoBon pa6oTbi 28.12.2021
EopncoB A.B.
ATaKHmneB ^.A.
CMoaeHCK 2021

AHHOTaUHH
B KypcoBOH pa6oTe paccMarpnBaroTca MexaHnnecKne KOHCTpy^nn, gna KOTopbix BbmonHamTca npoHHOCTHtie pacneTbi npn cnegymrnux Bngax ge$opMa^HH: pacTa^eHHH (c^arnn), KpyneHHH, rornde, rornde c KpyneHneM.
PacHeTHO-noacHHTenbHaa 3anncKa KypcoBOH padoTbi COCTOHT H3 28 crpaHH^ 5 npnno^eHHH, BKamnammux pncyHKH K 3aganaM, 7 nnTeparypHbix HCTOHHHKOB.
KnmneBbie cnoBa: danKa, ^^ropa, pacra^eHne, KpyneHne, rornd, npouHOCTb.
Annotation
The coursework discusses mechanical structures for which toughness calculations are performed assuming that the following types of deformation occur: tension (compression), torsion, bending, bending and torsion.
The explanatory note on the calculations of this coursework comprises 28 pages, 5 applications, which include drawings for the tasks, and 7 literary sources.
Keywords: beam, diagram, tension, torsion, bending, strength.

Cogep^aHHe:
BBegeHHe................................................................................................... 5
3agana N°1............................................................................... 6
3agana N°2............................................................................... 8
3agana N°3............................................................................... 11
3agana N°4............................................................................... 14
3agana N°5............................................................................... 18
3aKawneHHe.............................................................................................. 21
CnncoK Hcnoab3yeMOH aHTeparypti................................................. 22
npHHO^eHHa............................................................................ 23
18. KP. 13. 03. 02. nM. n3
Pacve Tbi Ha npo HHOcTb MexaHUHecKux KOHCTpy^MM

BBegeHue
^aHHaa pacaerao-rpa^uaecKaa, KypcoBaa pa6oTa aBaaeTca uToroM caMocToaTeabHoro u3yaeHua yae6Hbix MaTepuaaoB, noayaeHHbix npu KoHTaKTHoa pa6oTe c npenogaBaTeaeM, u pemeHua 3agaa no gu^unauHe «npuKaagHaa MexaHHKa» Ha TeMy «PacaeT Ha npoaHocTb MexaHuaecKux KOHCTpy^HH».
^abro BbmoaHeHua pa6oTbi aBaaeTca ocBoeHue MeTogoB pacaeTa Ha npoaHocTb KOHCTpy^HH npu pa3Hbix cayaaax ge$opMa^HH: pacTa^eHHu(c^aTHu), KpyaeHuu, u3ru6e, u3ru6e c KpyaeHueM. B xoge BbmoaHeHua pacaeTHo-rpa^uaecKoa pa6oTbi, 6biau BbmoaHeHbi pacaeTbi, gaa nocrpoeHua ^^rop BHyrpeHHux cuaoBbix ^aKTopoB gaa npuBegeHHbix Bbime BugoB ge$opMa^HH. A TaK^e cgeaaHbi aepTe^u, Heo6xoguMbie gaa pacaeTOB, B KoTopbix npegcTaBaeHbi ^^ropbI gaa Ka^goro Buga ge^opMaguu. Ebiau onpegeaeHbi npoaHocTHbie xapaKTepucTUKu KoHcTpy^ua, nogo6paHbi onTHMaabHbie ceaeHua u cgeaaH aHaau3 npoaHocru KoHcTpy^ua.
KawaeBbie caoBa npn BbmoaHeHuu KypcoBoa pa6oTbi:
EaaKa - 6pyc, raxogamuaca nog geacTBueM roruSarorngx ycuaua, B aacTHocTu, nonepeaHbix cua, MoMeHToB u pacnpegeaeHHbix Harpy3oK.
3nwpa - oco6bin Bug rpa^uKa, noKa3biBaromuH pacnpegeaeHue BeauauHbi Harpy3Ku Ha o6beKT.
PacTa^eHue - Bug npogoabHoa ge$opMa^HH cTep^Ha uau 6pyca, Bo3HHKarom,uH B TOM cayaae, ecau Harpy3Ka K HeMy npuKaagbiBaeTca no ero npogoabHoa ocu (paBHogencTBywmaa cua, Bo3gencTBywmux Ha Hero, HopMaabHa nonepeaHoMy ceaeHuw crep^Ha u npoxoguT aepe3 ero ^mp Macc).
KpyaeHue - oguH u3 BugoB ge^opMaguu Teaa. Bo3HHKaeT B TOM cayaae, ecau Harpy3Ka npuKaagbiBaeTca K Teay B Buge napbi cua (MoMeHTa) B ero nonepeaHoa naocKocTu. npu ^TOM B nonepeaHbix ceaeHuax Teaa Bo3HHKaeT ToabKo oguH BHyTpeHHHH cuaoBoa ^aKTop — KpyramuH MoMeHT.
H3ru6 - TaKoa Bug ge$opMa^HH, Korga nog geacTBueM BHemHux cua B nonepeaHbix ceaeHuax cTep^Ha(6pyca) Bo3HHKaeT roruSaromua MoMeHT.
npoaHocTb - ^TO cnocoSHocTb KoHcTpy^uu Bbigep^HBaTb 3agaHHyw Harpy3Ky, He pa3pymaacb.

3agana N°1 ^aHo:
a = 0; 6 = 9; B = 7
E = 2105 Mna
[G] = 160 Mna = 1,6 ■ 108 na
CxeMa 7;
Pi = 17 KH, PI = 19 KH;
Ai = 2,0 CM1, A2 = 2,9 CM1, A3 = 2,7 CM1; a = 0,8 M, b = 0,7 M, c = 0,6 M.
PemeHHe:
nyHKT 1: nocTpoeHHe ^^ropbI npogontHtix CHH NZ.
YnacTOK 1 AB: NAB = P1 = 17 KH
YnacTOK 2 BC: NBC = P1 = 17 KH
YnacTOK 3 CD: NCD = P1 - PI= 17 KH - 19 KH = -2 KH
YnacTOK 4 DE: NDE = P1 - PI= 17 KH - 19 KH = -2 KH
nyHKT 2: nocTpoeHHe ^^wpM HopMantHbix Hanpa^eHHH 6.
NAB _ 17103 _ 0 _ 1A7
YnacTOK 1 AB: GAB = — =
AAB 2,0H0-‘
= 8,5-10 na = 85 Mna
YnacTOK 2 BC: GBC = -— =
_NBC _ 17103 _ 1A7
ABC 2,9-10”
= 5,8640 na = 58,6 Mna
YnacTOK 3 CD: GCD = — = = -6,9-106 na = -6,9 Mna
ACD 2,9-10-4
3
YnacTOK 4 DE: GDE = — = = -7,4406 na = -7,4 Mna
DE ADE 2,7^10-4
nyHKT 3: nocTpoeHHe ^^ropbI nepeMern,eHHH nonepenHbix ceneHHH 6pyca Al,.
°rli
U £
ME = 0 ;
YnacTOK 4 DE: UlD = AM ^4^ = 0 + -74-06 = -2,2240-5 M
lE+ E
2H0
5
YnacTOK 3 CD: AlC = AlD + = -2,2240-5 + -6,9 ^ = -3,427540-5 m
C D T7 ’ 0.1A5 *
E
2^10
18. KP. 13. 03. 02. nM. n3
Guam
6

YnacTOK 2 BC: MB = MC+ = -3,4275-10'5 + 58,6 '0f5 = 6,840'5 m
B C E 2405
YnacTOK 1 AB: bdA = MB+ = 6,840'5 + 85:0,8 = 40,8-10'5 m
A B E 2-105
Bbreog: TaK KaK |6max | < [5] ^85 < 160, to crep^eHt Btigep^HT npnno^eHHbie Harpy3KH.

3agana N°2
K CTantHOMy Baay npnno^eHbi Tpn H3BecTHbix MOMeHTa: Ti, T2, T3. Mogyab cgBHra G = 0,8 • 105 Mna
Tpe6yeTca:
1) CgeaaTb nepTe^; Baaa no 3agaHHbiM pa3MepaM B MacmTa6e;
2) CocTaBHTt gaa Ka^goro ynacTKa Baaa B ceneHHH aHanHTHnecKHe Bbipa«:eHHa H3MeHeHHa KpyTarn,Hx MOMeHTOB T, KacaTenbHbix Hanpa^eHHH T H yraoB 3aKpyHHBaHHa 9;
3) nocTpoHTb ^^wpM npogonbHbix ycnnHH T, KacaTenbHbix Hanpa^eHHH T H yraoB 3aKpyHHBaHHa 9;
4) CgeaaTb BbiBog o nponHocra cTep^Ha npn [T]=50 Mna
HcxogHbie gaHHbie:
CxeMa no pncyHKy: 7 PemeHHe:
1) CocTaBHM gaa Ka^goro ynacraa Baaa aHanHTHHecKHe Bbipa^mna H3MeHeHHa KpyTam.Hx MoMeHToB T H nocTpoHM ^^ropy Kpyramux MoMeHToB.
Mz = T3 = 0,29 KH • M;
zAB 3
M^ = T3 - T2 = 0,29 - 0,17 = 0,12 KH • M;
Mz = T3 - T2 = 0,12 KH • M;
zCD 3 2
M^ = T3 - T2 + T1 = 0,29 - 0,17 + 0,19 = 0,31 KH • M.
2) CocTaBHM gaa Ka^goro ynacraa Baaa aHanHTHHecKHe Bbipa^mna H3MeHeHHa KacaTenbHbix Hanpa^eHHH T H nocTpoHM ^^ropy KacaTenbHbix Hanpa^eHHH.
M„
1 W
WPi
rge xi - KacaTeabHoe Hanpa^eHHe Ha ynacrae i;
M - KpyTamHH MoMeHT Ha ynacrae i;
Wp - MoMeHT conpoTHBneHHa ceneHHa ynacTKa i, KoTopoe onpegeaaeTca BMpa^eHHeM:
W
^di r\ 1 3
p. = —— = 0,2di .
pi 16 ^
rge di - gnaMeTp ceneHHa ynacraa i;

M,
1AB -
W
0 29 10^
0,29 •10 - 0,0537 ,io9 na - 53,7 Mna;
PAB
M,
xBC
xCD
LDE
0,2 -(3 • 10 ■2 j3 0,12 -103
W
PB
M,
W
PC
M,
0,2 -(5 -10 _2 j3 0,12 • 103 0,2 -(6 • 10 _2 j3
0,31 -103
WPDE 0,2 -(6 -10 _2 j3
0,0048 -109 na - 4,8 Mna;
0,0028 -109 na - 2,8 Mna;
0,0072 -109 na - 7,2 Mna.
3) CocTaBHM gaa Ka^goro ynacraa Baaa aHaaHTHnecKHe BbipmeHHa yraoB 3aKpyHHBaHHa 9 H nocrpoHM ^^ropy yraoB 3aKpyHHBaHHa.
Yroa 3aKpyHHBaHHa onpegeaaeTca no ^opMyae:
Mzi - li 9 --i-,
^ G - JPi
rge li - gaHHa ynacraa i, M;
G - Mogyat cgBHra, Mna;
JPi - MOMeHT HHep^HH yaacraa i, KoTopaa onpegeaaeTca no ^opMyae: Jpi- 0,1d,4;
9E - 0 (T.K. ^TOT Kpan 3aKpenaeH);
9D - 9E + 9ED - 0 +
MZED - lED
0,31 -103 - 0,18 1A_3
0,54 -10 3 pag;
G - JPED 0,8 -1011 - 0,1 -(6 -10 _2 j4
Mz -1
9C - 9d + 9dc - 0,54 -10_3 + zDC DC - 0,54 -10_3 4
_3 , M^ -IDC Ac„ 1A_3 0,12-103 - 0,42
G - J
PD
0,8 -1011 - 0,1-(6 -10 _2 j4
-1,03 -10 3 pag;
, Mz - l™ . 012-103 ^ 0 5
9b - 9C +9cb -1,03 -10_3 + zcB CB - 1,03 -10_3 + , ,
G - J
PC
0,8 -1011 - 0,1 -(5 -10 _2 )
- 2,23 -10 3 pag;
, Mz - lRA . 0 29 -103 ^ 0 7
9a - 9b +9ba - 2,23 -10_3 + zBA BA - 2,23-10_3 + , ,
G - J
PB
0,8 -1011 - 0,1 -(3 -10 _2 )
- 33,53 -10 3 pag;
4) M3 ^^ropbI KacaTeatHoro Hanpa^eHHa MaKCHMaatHoe Hanpa^eHHe paBHo:
xmax - xAB - 53,7 MMB;
npoBepHM npoHHocTt CTep^Ha npn gonycKaeMoM Hanpa^eHHH [x]- 50 Mna xmax - 53,7 Mna > [x] - 50 Mna;
18. KP. 13. 03. 02. nM. n3
flucm
9
AB
BC
CD
DE

CnegoBaTentHO, ycnoBHe npoHHoern He BbrnonHaeTca (cTep^eHt pa6oTaeT B ycnoBHH neperpy3KH).
%
“max
[xl |50 - 53,7 100% = ' 1
max
50
= 7,4%
18. KP. 13. 03. 02. nM. n3
Rucm
10

3agaaa N°3
nocTpoeHHe ^^rop BHyTpeHHHx ycnaHH B cTarnaecKH onpegeaHMbix 6aaKax. Tpe6yeTca:
1) HanncaTb Bbipa«:eHHa nonepeaHoft cnabi Qy H H3rH6arom,ero MOMeHTa Mx gaa Ka^goro yaacTKa B o6^eM BHge;
2) IIocTpoHTb ^^wpM nonepenHOH cnabi Qy H H3rH6arorn,ero MOMeHTa Mx; HcxogHbie gaHHbie:
CxeMa no pncyHKy: 7 PemeHHe:
1) OnpegeaHM pea^HH onop. ^aa onpegeaeHHa pea^HH cocTaBaaeM ypaBHeHHa cyMMM MoMeHToB Bcex cna oraocHTeabHo ToaeK A H B.
^ c +
XMiA = 0: P • a + RB • (b + c) + m - q • (c + d) ■
i=1
b +
v 2 J
= 0;
RB =
- P • a - m + q •(c + d)• (b + c + d)
b + c
-10 -1,0 -19 + 7 -(2,7 +1,0)- (2,9 + 2,7 +1,0)
2,9 + 2,7
2-= 16,79 KH;
P •(a + b + c)+m + q •(c + d )•
f
R
c + d
d
A
b + c
10 • (1,0 + 2,9 + 2,7)+19 + 7 • (2,7 +1,0)
2,7 +1,0 2
A
1,0
J _
= 19,11 KH.
2,9 + 2,7
3HaK naroc y pea^HH RA H RB noKa3biBaeT, HTO HanpaBaeHHe pea^HH 6biao Bbi6paHo bepHo.
npoBepKa no ycaoBHW paBHoBecna:
XFiy = 0: -P + RA + RB - q •(c + d) = 0;
i=1
-10 +19,11 +16,79 - 7 ‘(2,7 +1,0)= 0;
0 = 0.
2) OnpegeaHM nonepeaHbie cnabi Qy H nocTpoHM ^^ropy nonepeaHbix cna. nepBHH yqacTQK:
0 < z1 < a = 1,0 M Qy1 =-P = -10 KH;
18. KP. 13. 03. 02. nM. n3
aucm
11

BTOPOH ygacTQK:
0 < z2 < b = 2,9 M QY2 =-P + RA =-10 +19,11 = 9,11 KH;
TpeTHH ygacTQK:
0 < z3 < d = 1,0 M QY3 = q• z3;
npu z3 = 0: Qy3 = 0 KH;
npu z3 = d = 1,0 M : QY3 = q • z3 = 7 • 1,0 = 7 KH.
ReTBepTHH ygacTQK:
0 < z4 < c = 2,7 M QY4 = -RB + q •(d + z4 );
npu z4 = 0: Qy4 = -RB + q • d = -16,79 + 7 • 1,0 = -9,79 KH;
npu z4 = c = 2,7 M : QY4 = -RB + q •(d + z4) = -16,79 + 7 • (1,0 + 2,7) = 9,11 KH.
3) OnpegenHM roruGammue MOMeHTti Mx u nocTpouM ^^mpy H3rH6a.mm.Hx
MOMeHTOB. nepBHH ygacTQK:
0 < z1 < a = 1,0 M MX1 =-P• z:;
npn z1 = 0: Mx1 = 0 KH • M;
npn z1 = 1,0: Mx1 = -10-1,0 = -10KH• M;
BTOPOH ygacTQK:
0
npu z2 = b = 2,9M: MX2 =-P•(a + z2)+RA • z2 =-10•(1,0 + 2,9)+19,11 • 2,9 = = 16,42 KH • M;
TpeTHH ygacTQK:
z
0 < z3 < d = 1,0 M MX3 = m - q • z3 •-^ npn z3 = 0: Mx3 = 19 KH • M;
7 1 0
npn z3 = d = 1,0 M : MX3 = m - q • z3 • — = 19 - 7 • 1,0 • — = 15,5 KH • M; 2
2
2
J3 = d = A,0 M : Mx3
MeTBepTtiH ygacTQK:
z + d
0 < z4 < c = 2,7 M MX4 = m + RB • z4 - q(z4 + d)• 4
2
npu z4 = 0: Mx4 = m - q • d •d = 15,5 KH • M;
2
npH z4 = c = 2,7 M : MX4 = m + RB • z4 - q •
(z4 + d )2
2
19 +16,79 • 2,7
■7 •
(2,7 +1,0) 2
16,42 KH • M;
3nmpa 6ygeT aBnaTtca napaGonofi BrnnyKnocTtm BBepx c MaKcuMyMOM B TogKe, rge Qy4 = 0. HaHgeM ^Ty TogKy:
U fA \ n RB - q • d 16,79 - 7 4,0
Qy4 =-RB + q •(d + z4 )= 0 ^ z4 ^-B-=-= 1,398 M;
y q 7
18. KP. 3 03. 02. nM. n3
^ucm
12

nogcraBHM z4 = 1,398 M B aHanHTHnecKoe ypaBHeHHe gna H3rH6arorn,ero MOMeHTa Ha neTBepTOM ynacTKe:
Mxmax = m + RB ■1,398 - 9
(1,398 + d )2
2
19 +16,79 ■ 1,398 - 7 ■
(1,398 +1,0) 2
= 22,34 KH ■ M.
18. KP. 13. 03. 02. nM. n3
Rucm
13
2

3agaaa N4
^aa 3agaHH0H GaaKu u3 3agaau N 3 TpeGyeTca:
1. BbinepTHTb B MacmTa6e 3agaHHoe ceaeHue GaaKu c yKa3aHueM aucaeHHbix 3HaneHHH pa3MepoB. OnpegeauTb noao^eHue ^HTpa Ta^ecTu ceaeHua u BbiaucauTb MOMeHT HHep^HH ceaeHua OTHOCHTenbHO HeHTpanbHOH ocu.
2. nocTpoHTb ^^ropbI HopMaabHbix Hanpa^eHun, pacnpegeaeHHbix no BbicoTe ceaeHua gaa ceaeHua c MaKcuMaabHbiM roruGarornuM MOMeHTOM Mx, B3aTbiM H3 3agaau N 3.
3. Hcnoab3ya ^^ropbI roruGarornux MOMeHTOB Mx, nocTpoeHHbix B 3agaae N 3, onpegeauTb u3 pacaeTa Ha npoHHOCTb HOMep npo^uaa gByraBpoBon (npu 3HanHTeabHOH Hegorpy3Ke npuHaTb gaa GaaKu ceaeHue B Buge mBeaaepa) npoKaraoH GaaKu. Marepuaa GaaKu - cTaab CT.3, [a] = 160 Mna.
4. npu TOM ®:e 3HaneHHH gonycKaeMoro Hanpa^mua onpegeauTb no ycaoBuro npoHHocTH pa3Mepb nonepeaHoro ceaeHua B $opMe:
a) Kpyra guaMeTpa d;
do
G) Koab^ c oTHomeHHeM guaMeTpoB c0 = —
od
B) npaMoyroabHHKa c oTHomeHHeM cTopoH k
= 0,6
h
b
= 1,9
5. CocTaBHTb TaGaH^y oraomeHun naom,agen yKa3aHHbix ceaeHun K naorn,agu gByraBpoBoro npo^uaa.
HcxojHbie gaHHbe:
HoMep ceaeHua: 7
1) OnpegeauM ^HTp Ta^ecra oTHocuTeabHo HeHTpaabHon ocu Ox:
2 Ai • yCi n
yc = —,A = i Ai,
A i=i
rge Ai - naorn,agb i - Toro ceaeHHa, MM 2;
yc - paccToaHHeoT OCH Ox go i - Toro ^rnpa Ta^ecra, MM.
A1 • yC1 + A2 • yC2 + A3 • yC3
yC =
A1+A2+A3
rge A1 = B• 4C = 22 • 4• 26 = 2288 MM2;
A2 = 3B • 2C = 3 • 22 • 2 • 26 = 3168 MM 2;
A^
*(1,5B)2 3,14 • (1,5 • 22)2 2
_ -= 855 MM
4
4
B 22
yc = EC = - = —= 11
JC1 1 2 2
MM;
n

f 22 = 55 MM;
yc
_ 3B _ 3• 22 y p — EC 9 — h B —
JC2 2 2 2
y^ — EC3 — 3B — 3 • 22 — 66 MM ;
Ai • yc + a2 • yc - a3 • yc 2288-11+3168 • 55 - 855 • 66
A1 + A2 - A3
2288 + 3168 - 855
31,1MM;
2) OnpegenHM MOMeHT HHep^HH ceneHHa OTHOCHTeatHo OCH Ox: 2 0 0
Jxc — JxCl + A1 • a1 + JxC2 + A2 • a2 + JxC3 + A3 • a3 ,
rge a1 — CC1 — yc - yCj — 31,1 -11 — 20,1 MM; a2 — CC2 — yc - yc — 55 - 31,1 — 23,9 MM; a3 — CC3 — yc - yc — 66 - 31,1 — 34,9 MM;
, b1 • h3 4C • B3 4 • 26 • 223 m,0, 4 n ,, 4
K — ——1 —-—-— 92283 MM — 9,23 CM ;
12
12
12
b2 • h2 2C • (3B)3 2 • 26 • (3 • 22)3
12
12
12
1245816 MM4 —124,58 CM4;
— ^ — *• (1>5B)4 — 3>14•(U•22)4 — 58184 MM4 — 5,82CM4;
x3 " A ' ‘ ‘ ’ ’
64
64
64
xC
2 2
Jx + A1 • a1 + Jx + A3 • a3 — Jx
xC1 1 1 xC2 2 2 xC3
2
3 • a3
A~i • a
— 9,23 + 22,88 • 2,012 +124,58 + 31,68 • 2,392 - 5,82 - 8,55 • 3,492 — 297,25 CM4;
3) HopManbHbie Hanpa^eHHa npn H3rn6e no BbicoTe ceneHHa pacnpegeaeHbi no HHHeHHOMy 3aKoHy H B HM6OH Towe ceneHHa onpegeaaroTca no ^opMyae:
M,
a
Lzmax
J
• y^
xC
rge Mz - H3FH6arom,HH MOMCHT B ceneHHH, KH • M;
T 4
J - MOMeHT HHep^HH CeHCHHfl OTHOCHTeabHO HeHTpaabHOH OCH, CM ;
yi - paccToaHHe OT HeftTpaabHoft OCH go paccMaTpHB aeMOH TOHKH i, MM. CTPOHM ^^ropy HopMaabHbix Hanpa^eHHH gga onacHoro ceneHHa: yD — CD — 56,9 MM ; yE — CE — 31,1 MM ;
_ Mzmax 22,34 403 • 0,0569
aD —--yD —-^— — 427,6 Mna;
J>
M,
297,25 40
A3
-8
_ Lzmax 22,34 403 • 0,0311
aE —--yE —-^— — 233,7Mna.
J.
297,25 40
-8
4) OnpegeaHM MoMeHT conpoTHBaeHHa ceneHHa Wx 6aaKH:
M„
a
lzmax
max
<
W„
[4
18. KP. 13. 03. 02. nM. n3
flucm
15
J
x
2
C
C

Mzmx 22,34 -103 3
W =—r-i—= — -— = 139,6 CM3
Bbi6epeM coraacHo rOCT 8239-89 gByTaBp N18: Wx = 143 CM 3,A = 23,4 CM 2.
[a] 160 -106
M coraacHo rOC
Hanpa^eHHe B ^TOM cnynae 6ygeT paBHo:
Mzmax 22,34'1^ m9rT mum
a =-=-— = 0,15622 -10 na = 156,22 Mna.
Wv
143-10
-6
Hegorpy3 B ^TOM cnynae 6ygeT paBeH:
M-^ -100% = 160 -156,22 -100% = 2,4% < 20%
[a] 160
ran
Hanp^eHHe b ^TOM cnynae 6ygeT paBHo: a = Mzmax = 22,34 -10 = 0,14697 -109 na = 146,97 Mna.
3 2
ECHH npHHOTb 6amy B $opMe mBennepa N20: Wx = 152 CM ,A = 23,4CM .
W
x
152 -10
-6
Hegorpy3 B ^TOM cnynae 6ygeT paBeH:
[a] a -100% = 160 ^146,97 -100% = 8,1% < 20% ^ y mBe^^ep Hegorpy30o^bme,
[a]
160
neM y gByraBpa, ^o^TOMy 6epeM gByTaBp N18. 5) OnpegenHM nonepenHoe ceneHHe 6anKH B $opMe Kpyra:
W =
n- d3
~12
^ d > 3
32 - M
zmax
= 3
n-[a] V
32 - 22,34 -10
3
3,14 -160 -10
= 112,5 MM;
= 99,35 CM2;
_n-d2 _ 3,14-11,252
AKP = 4 = 4
OnpegenHM nonepenHoe ceneHHe 6anKH B $opMe Konb^:
-4'
WY
= ^_d_|1_Co],rgeC0 = ^ = 0,6 H ^-c4j=^1 -0,64j=
0,87, T.e.
n-d3 -0,87 _ ,
W =-— ^ d > 3
32
32-M
zmax
=3
n - [a] - 0,87 y
32 22,34 10
3
3,14 -160-106-0,87
2 0,87 0,87 - 3,14 -11,782 2
—— = —-----= 94,77 CM2 ;
44
= 117,8 MM;
A.
n
- d2 - (1 - c02 ) _ n - d2 -
4
nog6epeM ceneHHe B $opMe npaMoyronbHHKa (h = 1,9-b):
b-h2 _b-(1,9-b)2
W
0,6 - b3 ^ b = 3
6 6
h = 1,9-b = 1,9-61,5 = 116,8 MM;
Anp = b-h = 6,15-11,68 = 71,83 CM2
M
zmax
[a]- 0,6 \
22,34-10
3
160 -106 -0,6
61,5 MM;
CocTaBHM cpaBHHTenbHyw Ta6nn^ ceneHHH:
18. KP. 13. 03. 02. nM. n3
Rucm
16

3agana N5
CTanbHOH Ban BpamaeTcn c nOcTOnHHOH nacTOTOH n u nepegaeT MO^HOCTB N. Tpe6yeTca:
1) OnpegenuTb Harpy3Ku, geftcTByromue Ha Ban;
2) nocTpoHTt ^^wpM KpyTnm.Hx MOMeHTOB, ^^ropbI u3ru6arom,ux MOMeHTOB B gByx nnocKocTnx (BepTUKanbHOH u rOpu3OHTanbHOH);
3) nogo6paTb guaMeTp Bana, ncnonb3yw TpeTbw Teopnro nponHocTH, ecnu H3BecTHO gonycKaeMoe Hanpn^eHue [a] = 170 Mna
HcxonHbie gaHHbie:
CxeMa no pucyHKy: N7 PemeHHe:
1) OnpegenuM BenunuHy Kpyrnm,ero MOMeHTa: rr_A/r _N _nn
T MKp ; Q ;
Q 30
T =
30 • N 30-17-10
3
= 271H • M = 0,271 KH • M;
nn 3,14 • 600
OnpegenuM BenunuHbi OKpy^Hbix u paguanbHbix can Ha 3y6naTbix Konecax:
T 2T
0,5D D
2T 2•271
Ft = — =-= 6775 H = 6,775 KH;
11 D1 0,08
2T 2•271
Ft = — =-= 2464 H = 2,464 KH;
2 D2 0,22
Fr = Ft • tga = Ft • 0,364, rge a = 20°
Fr = Fti • 0,364 = 6,775 • 0,364 = 2,466 KH; Frz = Ftz • 0,364 = 2,464 • 0,364 = 0,897 KH;
2) nOcTpOHM ^^ropbI u3ru6a.roinux MOMeHTOB B nnOcKOcTnx xOz u yOz. ^nn ^TO^o HafigeM OnOpHbie pea^uu: a) PaccMOTpuM BepTUKanbHyro nnOcKOcTb:
n
Fr + Ft = 0; r2 t1 ’
I Fyk = 0; - R
k=1 n
Ay RBy
I = 0; - F^ • 3a + F^ • a - RBy • (3a + b) = 0;
k=1
r2
t1
By
18. KP. 13. 03. 02. nM. n3
flucm
18

- Fr ■ 3a + Ft ■ a - 0 897.3.019 + 6 775 • 019
R^ =—b-L = 0,897 3 0,19 + 6,775 0,19 = 1 kH.
By 3a + b 3 ■ 0,19 + 0,17
RAy = -RBy - Frz + Fti = -1,049 - 0,897 + 6,775 = 4,829 KH; npoBepKa:
n
I M = 0;F ■ b - F. ■ (2a + b) + RAy ■ (3a + b) = 0;
k=1 B 2 1
0,897 ■ 0,17 - 6,775 ■ (2 ■ 0,19 + 0,17) + 4,829 ■ (3 ■ 0,19 + 0,17) = 0;
- 0,001 * 0;
6) PaccMOTpHM ropu3oHTaabHyro naocKocTb:
n
I Fxv = 0;RAX + RBX -F -Ft9 =0;
k=1 n
I MyA = 0; Fr ■ a + F^ ■ 3a - RBX ■ (3a + b) = 0;
k=1
t2
RBx =
Fr ■ a + Ft2 ■ 3a _ 2,466 ■ 0,19 + 2,464 ■ 3 ■ 0,19
= 2,53 KH;
3a + b 3 ■ 0,19 + 0,17
RAx = -RBx + Fr + Ft2 = -2,53 + 2,466 + 2,464 = 2,4 KH; npoBepKa:
n
I MyR = 0; - Fr, ■ (2a + b) - Ft2 ■ b + RAx ■ (3a + b) = 0;
k=1 1 2
- 2,466 ■ (2 ■ 0,19 + 0,17) - 2,464 ■ 0,17 + 2,4 ■ (3 ■ 0,19 + 0,17) = 0;
0,001 * 0;
nocTpoHM ^^ropy H3ru6arom,Hx MOMeHTOB B BepTHKaabHoft naocKOCTu:
I ygacTOK:
0 < ZX < a = 190MM;
MxAC =-RAy ■ Z1. npH Z3 = 0 ^ MxAC = 0;
npH Z3 = 190 MM ^ M^ = -4,829 ■ 0,19 = -0,917 KH ■ M;
II ygacTQK:
0 < Z3 < b = 170 MM;
xDB By 3’
npn Z3 = 0 ^ MXDB = 0;
npn Z3 = 170 MM ^ M^ = -1,049 ■ 0,17 = -0,178 KH ■ M;
nocTpoHM ^^ropy H3ru6arom,Hx MoMeHToB B roproomaabHoft naocKocTu:
1 ygacTPK:
0 < Z3 < a = 190 MM ;
MyAC = RAx ■ Z1.
18. KP. 13. 03. 02. nM. n3
flucm
19

npn z3 = 0 ^ = 0;
npH z3 = 190 MM ^ M^ = 2,4 • 0,19 = 0,456 KH • M;
II ygacTQK:
0 < z3 < b = 170 MM;
MyDB = RBx • z3;
npH z3 = 0 ^ MyDB = 0;
npH z3 = 170 MM ^ M^ = 2,53 • 0,17 = 0,43 KH • M;
3) OnpegenHM gnaMeTp Bana ncxoga H3 ycnoBHa o6ecneneHHa npoHHocTH no
TpeTteH Teopnn:
no TpeTten Teopnn npoHHocTH:
M,KB = JMX + My + 0,75T2;
M
3KB,
M
3KB
B
= J M2A + M2A + 0,75T2 =yl (-0,917)2 + 0,4562 + 0,75 • 0,2712 = 1,051 KH •
= JM2B + MjB + 0,75T2 =yj(-0,178)2 + 0,432 + 0,75 • 0,2712 = 0,521 KH •
M;
M;
M3KB A ^ M3KB B ;
CnegoBaTentHo, pacneT Heo6xogHMo Becra B ceneHHH A. 3KBHBanemHoe Hanpa^eHHe npn H3rn6e onpegenaeTca Btipa^eHHeM:
M,
a
3KB
3KB A
W"
, rge Wx = 0,1d ;
d > 3
M
3KB
A = 3
0,1[a] V
1,051 • 10
3
0,1 • 170 -10
6
0,03954 M = 39,54 MM;
OKpynraeM go GnHHafiraero 6ontmero cTaHgapTHoro 3HaneHHH gnaMeTpa Bana: d = 40 MM.
18. KP. 13. 03. 02. nM. n3
Rucm
20

3aKaroaeHHe
B xoge BbmoaHeHHa KypcoBOH pa6oTbi noayaeHM caegyrornue pe3yabTaTbi:
B 3agaae 1 paccHHTaHa npoHHocTb 3aKpenaeHHoro cTep^Ha, Haxogarn,eroca nog geHCTBHeM cna. npoBepHB npoHHocTb cTep^Ha npn gonycKaeMOM Hanpa^eHHH, cgeaaH BMBog HTO, ycaoBHe npoHHocTH BbmoaHaeTca.
B 3agaae 2 paccHHTaHa npoHHocTb 3aKpenaeHHoro cTaabHoro Baaa, Haxoga^eroca nog gencTBHeM Kpyra^nx MOMeHTOB. npn npoBegeHHH npoBepKH Ha npoHHocTb CTep^Ha npn gonycKaeMOM Hanpa^eHHH cgeaaH BMBog HTO, Baa He Bbigep^HT Harpy3KH.
B 3agaae 3 nocTpoeHM ^^ropbI nonepeHHbix cna H H3rH6arorn,Hx MoMeHToB H onpegeaeHo onacHoe ceaeHHe.
B 3agaae 4 gaa 3agaHHon 6aaKH 3agaan 3 onpegeaeHM npn gonycKaeMoM Hanpa^eHHH no ycaoBHW npoHHocTH pa3MepM nonepeHHoro ceaeHHa B $opMe gByraBpa H mBeaaepa. H cgeaaHa cpaBHHTeabHaa Ta6an^ oraomeHHH naom,agen pa3aHHHbix ceaeHHH, gaa onpegeaeHHa caMoro BbirogHoro npo^naa ceaeHHa, KaKoBMM oKa3aaca mBeaaep.
B 3agaae 5, ncnoab3ya aeTBepTyw Teopnro npoHHocTH (Teopnro HanSoabmnx KacaTeabHMx Hanpa^eHHH), MM paccHHTaan gnaMeTp Baaa no H3BecTHoMy gonycKaeMoMy Hanpa^eHHW [6] = 160 Mna, KOTOPMH 6bia oKpyraeH go San^anmero 6oabmero 3HaaeHHa H3 cTaHgapTHoro paga rOCTa.
27.12.2021
(gaTa) (nognucb)

CnncoK Hcnont3yeMOH aHTepaTypbi
1. HocnaeBHH r.E. npHKaagHaa MexaHHKa: ^aa CTygeHTOB By30B.
[3aeKTpoHHbift pecypc] : / r.E. HocnaeBHH, n.A. .He6egeB, B.C. OrpeaaeB. -3aeKTpoH. gaH. - M. : MamHHocTpoeHHe, 2012. - 576 c. - Pe^HM gocTyna: http://e.lanboook.com/books/element.php?p11 id=5794
2. CTenHH n.A. ConpoTHBaeHHe MaTepnaaoB [3aeKTpoHHbift pecypc] : yne6HHK. - 3aeKTpoH. gaH. - Cn6. : .barn, 2 14. - 340 c. - Pe^HM gocTyna: http://e.lanboook.com/books/element.php?p11 id=3179
3. KapHMoB H. ConpoTHBaeHHe MaTepnaaoB. 3aeKTpoHHbift yae6HbiH Kypc gaa cTygeHTOB OHHOH H 3aoHHob $opM o6yneHHa [3aeKTpoHHbift pecypc]. Pe^HM gocTyna: http://www.soprotmat.ru
4. EeaaeB H.M. C6opHHK 3agaa no conpoTHBaeHHro MaTepnaaoB [3aeKTpoHHMH pecypc] : yae6Hoe noco6ne / H.M. EeaaeB, .b.K. napmuH, E.E. MeabHHKoB [H gp.]. - 3aeKTpoH. gaH. - Cn6. : .barn, 2011. - 431 c. -Pe^HM gocTyna: http://e.lanboook.com/books/element.php?p11 id=2022
5. Mnpoaro6oB H.H. ConpoTHBaeHHe MaTepnaaoB. noco6ne no pemeHHW 3agan [3aeKTpoHHbin pecypc] : yae6Ho-MeTogHHecKoe noco6ne / H.H. Mnpoaro6oB, 0.3. AaMoMegoB, H.A. Kyp^HH [H gp.]. - 3aeKTpoH. gaH. -Cn6. : .baHb, 2014. - 512 c. - Pe^HM gocTyna: http://e.lanboook.com/books/element.php?p11 id=39150
6. ^yKoB B.r. MexaHHKa. ConpoTHBaeHHe MaTepnaaoB [3aeKTpoHHbin pecypc] : yae6Hoe noco6ne. - 3aeKTpoH. gaH. - Cn6. : .baHb, 2012. - 415 c. Pe^HM gocTyna: http://e.lanboook.com/books/element.php?p11 id=3721
7. KapHMoB H. npHKaagHaa MexaHHKa. 3aeKTpoHHbin Kypc gaa cTygeHTOB OHHOH H 3aonHofi ^opM o6yneHHa ^aeKTpoHHbin pecypc]. Pe^HM gocTyna: http: //www. prikladmeh.ru

A, =2,0 CM'
-19 KH
b=Q7n
0, N:,KH, (l(N:}=2.
o, a, Mfia, /i(oj=\
o. AUIO~5MR (Ai}=i-
npHno^eHHe 1
^epTe^; K 3agane N°1
R-
P>-n
18. KP. 13. 03. 02. nM. n3
Rucm

npnno^eHHe 2
^epTe^; K 3agane N2

npnno^eHHe 3
^epTe^; K 3agane N3
18. KP. 13. 03. 02. nM. n3
^ucm

npnno^eHHe 4
^epTe^; K 3agane N°4
18. KP. 13. 03. 02. nM. n3
^ucm
27