Ka^egpa texho.noruqeckux mamuh u o6opygobahun

OHHHAfl OE^EPAflbHOrO rOCy^APCTBEHHOrO BW^ETHOrO OBPA3OBATE^bHOrO y^PE^EHHfl BWCmErO OBPA3OBAHHH «HA^HOHAflbHBIH HCCHE^OBATEnbCKHH yHHBEPCHTET «M^H»
B r. CMOHEHCKE
Ka^egpa «TexHoaoruaecKue MamuHM u o6opygoBaHue» HanpaBaeHue nogroToBKu 13.03.02 «^aeKTpo^Hep^eTUKa u aneKTpoTexHHKa»
3A^AHHE
Ha KypcoByro paOoTy cTygeHTa ATaKumueBa ^.A. (rpynna PT-20)
TeMa: PacaeTM Ha npoaHocTL MexaHuaecKux KoHcTpyKgufi Cogep^aHue pacaerao-noacHuTeaLHofi 3anucKu:
1. BBegeHue.
2. 3agaaa N1: nocTpouTL ^^ropM npogoaLHtix cua, Hanpa^eHufi u nepeMe^eHufi nonepeaHtix ceaeHufi 6pyca.
3. 3agaaa N2: nocTpouTL ^^Mpy KacaTeaLHtix Hanpa^eHufi.
4. 3agaaa N3: nocTpouTL ^^ropy nonepeaHtix cua u u3ru6aro^ux MOMeHTOB.
5. 3agaaa N4: nogoOpaTL nonepeaHoe ceaeHue 6aaKu.
6. 3agaaa N5: nog6op guaMeTpa Baaa npu u3ru6e c KpyaeHueM.
7. 3aKaroaeHue.
nepeaeHL rpa^uaecKoro MaTepuaaa:
1. ^^MpM K 3agaae N1
2. ^^MpM K 3agaae N2
3. ^^MpM K 3agaae N3
4. ^^MpM K 3agaae N4
5. ^^MpM K 3agaae N5 ^aTa Btigaau 3agaHua: 8.09.2021
/
PyKOBOflHTeHb -—-
3agaHue npuHaaa K BtinoaHeHuro:
CTygeHT
^aTa 3a^uTM KypcoBofi paOoTM 28.12.2021
- EopucoB A.B. ATaKumueB ^.A.
CMoaeHcK 2021

AHHOTa^H
B KypcoBOH pa6oTe paccMaTpHBaMTcn MexaHH^ecKHe KOHCTpyKgHH, gnn KOTOPMX BMnoaHHMTCH npo^HOcratie paOTeTM npu cnegyro^Hx Bugax ge^opMagHH: pacTH^eHHH (c^aTHH), Kpy^eHHH, H3rH6e, H3ra6e c Kpy^eHHeM.
Pac^eTHO-noHCHHTenLHaH 3anucKa KypcoBOH pa6oTM COCTOHT H3 28 CTpaHHg, 5 npHno^eHHH, BKnM^aM^Hx pucyHKH K 3aga^aM, 7 nHTepaTypHMx HCTO^HHKOB.
Knro^eBLie cnoBa: 6anKa, ^^Mpa, pacra^eHHe, Kpy^eHHe, H3rH6, npo^HOcrt.
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.

£Z ............................................................................KHH9M<0I/'Hdn
ZZ .................................................iadAxedaimf HtMaAeai/'oiiDH MODHU^
\Z ..............................................................................................9HH9h(HI/'5n?£
8T ...............................................................................85N ehei/ee
PI ...............................................................................p°bl eMi/ee
IT ...............................................................................85N ehei/ee
8 ...............................................................................^ehetfee
9 ...............................................................................T5NBhBtfe£
c; ...................................................................................................9HH9b,9ag
:9HHPM

BBegeHue
^aHHaa pacaerao-rpa^uaecKaa, KypcoBaa paSoTa aBaaeTca uroroM
caMOCTOHTeaLHoro u3yaeHua yaeSHwx MaTepuaaoB, noayaeHHwx npu KoHTaKTHofi pa6oTe c npenogaBaTeaeM, u pemeHua 3agaa no gucgunauHe «npuKaagHaa MexaHHKa» Ha TeMy «PacaeT Ha npoaHocTL MexaHuaecKux KoHcTpyKgufi».
^atro BtmoaHeHua paSoTw aBaaeTca ocBoeHue MeTogoB pacaeTa Ha npoaHocTL KOHCTpyKgHH npu pa3HMx cayaaax ge^opMaguu: pacTa^eHHu(c^aTHu), KpyaeHuu, H3rH6e, H3rH6e c KpyaeHueM. B xoge BtmoaHeHua pacaerao-rpa^uaecKofi pa6oTM, 6LMH BtinoaHeHti pacaeTti, gaa nocTpoeHua ^^Mp BHyTpeHHux cuaoBtix ^aKTopoB gaa npuBegeHHMx BMme BugoB ge^opMaguu. A TaK^e cgeaaHti aepTe^u, HeoSxoguMtie gaa pacaeToB, B KOTOPMX npegcraBaeHLi ^^ropM gaa Ka^goro Buga ge^opMaguu. Etiau onpegeaeHti npoaHocratie xapaKTepucTUKu KoHcTpyKgufi, nogoSpaHM onTUMaaLHtie ceaeHua u cgeaaH aHaau3 npoaHocTu KoHcTpyKgufi.
KaroaeBtie caoBa npu BtinoaHeHuu KypcoBofi paSoTti:
EaaKa - 6pyc, Haxoga^ufica nog geficTBueM H3ru6aro^ux ycuaufi, B aacraocra, nonepeaHtix cua, MoMeHToB u pacnpegeaeHHtix Harpy3oK.
^^ropa - ocoStifi Bug rpa^uKa, noKa3tiBaro^HH pacnpegeaeHue BeauauHti Harpy3Ku Ha o6teKT.
PacTa^eHue - Bug npogoaLHofi ge^opMaguu cTep^Ha uau Spyca, Bo3HUKaM^ufi B TOM cayaae, ecau Harpy3Ka K HeMy npuKaagtiBaeTca no ero npogoaLHofi ocu (paBHogeficTByro^aa cua, Bo3geficTByro^ux Ha Hero, HopMaaLHa nonepeaHoMy ceaeHHM cTep^Ha u npoxoguT aepe3 ero geHTp Macc).
KpyaeHue - oguH H3 BugoB ge^opMaguu Teaa. Bo3HHKaeT B TOM cayaae, ecau Harpy3Ka npuKaagtiBaeTca K Teay B Buge napti cua (MoMeHTa) B ero nonepeaHofi naocKocTu. npu ^TOM B nonepeaHwx ceaeHuax Teaa Bo3HHKaeT ToaLKo oguH BHyTpeHHufi cuaoBofi ^aKTop — KpyTa^ufi MoMeHT.
H3ru6 - TaKofi Bug ge^opMaguu, Korga nog geficTBueM BHemHux cua B nonepeaHwx ceaeHuax cTep^Ha(fipyca) Bo3HHKaeT u3ru6aM^ufi MoMeHT.
npoaHocTL - ^TO OTOCOSHOCTL KoHcTpyKguu Bwgep^uBaTL 3agaHHyro Harpy3Ky, He pa3pymaacL.

3aga^a N1 ^aHo:
a _ 0; 6 _ 9; e _ 7
E _ 2405 Mna
[6] = 160 Mna = 1,6 • 108 na
CxeMa 7;
Pi = 17 KH, P2 = 19 KH;
Ai = 2,0 CM2, A2 = 2,9 CM2, A3 = 2,7 CM2; a _ 0,8 M, b _ 0,7 M, c _ 0,6 M.
PemeHHe:
nyHKT 1: nocTpoeHue ^^MpM npogoaLHMx cua Nz.
y^acTOK 1 AB: NAB _ P1 = 17 KH
y^acTOK 2 BC: NBC _ P1 = 17 KH
yqacTOK 3 CD: NCD _ P1 - P2= 17 KH - 19 KH = -2 KH
yqacTOK 4 DE: NDE _ P1 - P2= 17 KH - 19 KH = -2 KH
nyHKT 2: nocTpoeHue ^^ropM HopMaatHMx Hanpn^eHHH 6.
y^acTOK 1 AB: 6AB
y^acTOK 2 BC: 6BC _ y^acTOK 3 CD: 6CD _ y^acTOK 4 DE: 6DE _
nyHKT 3: nOcTpOeHue ^^MpM nepeMe^eHHH nOnepe^HMx ce^eHHH 6pycaA li.
A l
^ li
1 E
A lE = 0
y^acTOK 4 DE: A lD= AlE +
O' DE ^ lD
' DE lDE r, , -7,4 '0,6 _
E
D lC
■= 0 +
2-105
= -2,22^ 10 M
yqacTOK 3 CD: A lC = AlD+ ^CD ±CD = -2,22^0-5 + -6,9 50,35 = -3,4275M0-5 m
E
2^105
18. KP. 13. 03. 02. nM.
-R3-
^MCT
6

y^acroK 2 BC: AlB=AlC+
y^acTOK 1 AB: AlA=AlB+
0"BC lB
'BC 'BC _ T A^r -,n-5 , 58,6 '0,35 _ _ „ _-5
E
-= -3,4275-10J +
= 6,8-10J M
^AB'1^^,, ,n-5 , 85 '0,8 _ „ ,._-5
= 6,8-10 +
2-10
= 40,8-10J M
E 2-103
BMBog: TaK KaK |6max| < [ 6] ^85 < 16°, TO CTep^eHL Btigep^HT npHao^eHHLie Harpy3KH.
18. KP. 13. 03. 02. nM.
-R3-
^MCT
7

3agaaa N2
K CTaaLHOMy Baay npuao^eHM Tpu u3BecTHMx MOMeHTa: Ti, T2, T3. Mogyat cgBura G = 0,8 • 105 Mna
TpeOveTca:
1) CgeaaTL qepTe^ Baaa no 3agaHHMM pa3MepaM B MacmTaOe;
2) CocTaBHTL gaa Ka^goro yaacTKa Baaa B ceaeHuu aHaauTuaecKue Btipa^eHua H3MeHeHHH KpyTHigux MOMeHTOB T, KacaTeatHtix Hanpn^eHHH T u yraoB 3aKpy^HBaHHH 9;
3) nocTpoHTL ^^MpM npogoatHtix ycuauH T, KacaTeatHtix Hanpa^eHufi T u yraoB 3aKpy^HBaHHH 9;
4) CgeaaTL BLiBog o npoaHocra cTep^HH npu [T]=50 Mna
HcxogHLie gaHHMe
CxeMa no pucyHKy: 7 PemeHue:
1) CocTaBHM gaa Ka^goro yaacTKa Baaa aHaauraaecKue BLipa^eHua u3MeHeHua KpyTH^ux MoMeHToB T u nocTpouM ^^Mpy KpyTHigux MoMeHToB.
Mz =T3 =0,29 KH-M;
Z AB
M =T3-T2 =0,29-0,17 = 0, 12 KH-M;
BC
Mz =T3-T2 = 0,12 KH-M;
"CD
M =T3-T2 + T. = 0,29-0, 17+0,19= 0,31 KH-M .
ZDE 3 2 1
2) CocTaBUM gaa Ka^goro yaacTKa Baaa aHaauTuaecKue BLipa^eHua u3MeHeHUH KacaTeaLHMx Hanpa^eHUH T u nocTpouM ^^Mpy KacaTeaLHLix Hanpa^eHUH.
M
T
i W
Pi
1
T-
rge i - KacaTeaLHoe Hanpa^eHue Ha yaacTKe 1;
Mz H .
zi - KpyTH^uH MoMeHT Ha yaacTKe 1;
Wp .
pi - MoMeHT conpoTuBaeHua ceaeHua yaacTKa 1, KoTopoe onpegeaaeTca
BMpa^eHueM:
nd.3
WPi==0-2 d-
-rge
d
guaMeTp ce
IOHHH y
aacTKa 1
M3M.
aMCT
N° goKyM.
nognMC
flaT
18. KP. 13. 03. 02. nM.
-R3-
aMCT
8

AB
—Zab = 0’29'10 3 =0,0537-109 na = 53,7 Mm;
WPAB 0,2 • (3-10-2)
BC
—— = 0-12'10 =0,0048-109 na=4,8 Mna;
-2 3
WPBC 0,2-( 5-10-2)
M
CD
0 1 2 103
— = - = 0,0028-109 na = 2,8 Mna;
WPCD 0,2-(6-10-2)
TDE
_^de = 0,31-10 = 0,0072-109 na = 7,2 Mna.
-2 3
WPDE 0,2-( 6-10-2)
3) CocTaBHM gaH Ka^goro yaacTKa Baaa aHaauTuaecKue Btipa^eHua yraoB 3aKpy^HBaHHH ^ u nocTpouM ^^ropy yraoB 3aKpyauBaHHH. yroa 3aKpy^HBaHHH onpegeaaeTCH no ^opMyae:
M •/.
z. i
0 = 1 ,
GV
rge li - gauHa yaacTKa i, M;
G - MogyaL cgBura, Mna;
Jpi - MoMeHT HHepguu yaacTKa i, KoTopaH onpegeaaeTCH no ^opMyae:
Jp = 0,1 d,,
0E 0 (T.K. ^TOT Kpafi 3aKpenaeH);
Mz •l
0 D 0 E + 0 ED = 0 + '
zEDlED = 0,31-10360,18 _n n/1 ,„-3
ED 0,8-10116 0,1- 6-10-2)
= 0,54-10 3 pad;
M^=0,54-10-3+0,12:10! 60,42.
GJ
D T E 'r ED - GJ
0C = 0D+ 0DC=0,54-10 J +
= 1,0310-3 pad;
0B=0C+0CB=1 > 03-10"3+^ZCB >CB =1,03-10-3+0 ’12'10 60,5
PDC
0,810u 6 0,1-(6-10-2)4
GJ
PCB
0,8-10“ 6 0,1-( 5-10-2 )4
=2,2310-3 pad;
0A=0B+0BA=2,23-10"3+7rrL-— =2,23-10-3+0’29'10 60,7
GJ,
BA 0,8-10“ 6 0,1-3-10"2)4
=33,53 10-3 pad;
4) H3 ^^ropM KacaTeaLHoro Hanpa^eHHH MaKCHMaaLHoe Hanpa^eHue paBHo:
T max = TAB = 53 - 7 Mn°;
npoBepuM npo^HocTL crep^HH npu gonycKaeMoM HanpaweHHu ITl_50 Mna
18. KP. 13. 03. 02. nM.
m
a^cT
9

CnegoBaTenLHO, ycnoBue npo^HOcra He BLinonHaeTcn (cTep^eHL paOoTaeT B ycnoBHH neperpy3KH).
IT max [ T1
n=—-—
■ 100 % =|50 53 ’7| =7,4%
50
18. KP. 13. 03. 02. nM.
-R3-
^MCT
10

3aga^a N3
nocTpoeHue ^^Mp BHyTpeHHux ycuaufi B cTara^ecKu onpegeauMwx 6aaKax.
Tpe6veTca:
HanucaT
Ka^goro y^acTKa B o6^eM Buge;
2) nocTpouTL ^^MpM nonepe^Hofi cuaw Qy u u3ru6aro^ero MOMeHTa Mx;
1) HanucaTL Bwpa^eHun nonepe^Hofi cuaw Qy u roruSaro^ero MOMeHTa M gan
CxeMa no pucyHKy: 7 PemeHue:
1) OnpegeauM peaKguu onop. ^an onpegeaeHun peaKgufi cocTaBaneM ypaBHeHun cyMMw MoMeHToB Bcex cua oraocuTeatHo To^eK A u B.
c+d
£ Mi = 0:P a + RBi(b + c) + m-q-( c+d)
b+
i = 1
RB =-
P a-m+q-(c+d)•(b + c+ d ) b+c
\
2
= 0;
2 7 +10
-10-1,0-19 + 7-( 2,7 + 1,0 )•( 2,9 + - )
2,9+ 2,7
P-( a+b +c)+m+q-( c+d)
= 16,79 KH;
RA =
A b+c
c+d 2
d
10-( 1,0+2,9+2,7 ) + 19 + 7-(2,7 + 1,0 )•
2,7 +1,0 2
1,0
/
= 19,11 KH .
2,9+2,7
3HaK naroc y peaKgufi RA u RB noKa3MBaeT, ^TO HanpaBaeHue peaKgufi 6wao BwSpaHo BepHo.
npoBepKa no ycaoBuro paBHoBecun:
n
£ Fiy=0: - P+RA+RB - q-( c+d )=0;
i =1
-10+19,11 + 16,79-7-2,7 + 1,0)=0 .
>
0=0.
2) OnpegeauM nonepe^Htie cuaw Qy u nocTpouM ^^Mpy nonepe^Htix cua. nepBmfi ygacTQK:
18. KP. 13. 03. 02. nM.
ne
^MCT
11

0
BTopoH ygacTQK:
0
TpeTuH ygacTQK:
0 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.
^eTBepTfcrn ygacTQK:
0
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) Onpege^HM H3ru6aM^ue MOMeHTM Mx u nocTpouM ^^Mpy H3ru6aM^ux
MOMeHTOB. nepBHH ygacTPK:
0
npu z 1=0: Mx 1=0 KH-M;
npu z1= 1,0: Mx 1= -10-1,0 = -10 KH-M;
BTopofi ygacTPK:
0
npu z2= b=2,9 M : Mx2=-P-(a+z2)+RA-z2=-10-( 1,0+2,9) +19,11-2,9= 616,42 KH-M;
TpeT
HH ygacTPK:
0
z
zn
npu z3= d = 1,0 M : Mx3 = m-q-z3- — = 19-7-1,0-- =15,5 KH-M;
10
2
^eTBepTHH ygacTPK:
0
z 4 +d
2
2
2
(z 4+ d)
npu z4 = c = 2,7 M : Mx4=m + RB-z4-q-- =19 + 16,79-2,7¬
7 (2,7+1,0)2 ,6 42 ,,
-7- =16,42 KH-M;
2
18. KP. 13. 03. 02. nM.
ne
^MCT
12

^^ropa 6ygeT HB^HTLCH napaSoaoS BLinyKnocrtM BBepx c MaKCHMyMOM B TO^Ke, rge Qy4 0 . HafigeM ^Ty Tomy:
Q R . . d . i 0 RB-q d 16,79-71,0 „ 398
Qy4 = -Rb+ q-\d+z4) = 0^z4=-=---= 1,398 M;
q7
z_1 398
nogcTaBHM 4_ ’ B aHaaHTH^ecKoe ypaBHeHue gan H3rH6aro^ero MOMeHTa Ha
qeTBepTOM y^acTKe:
Mx max_m + Rb 1 ,398_q.l1 ■ 398+ dI =19 +16,79.1,398_74 ’398 +1,01 _
2
=22,34 KH.M .
18. KP. 13. 03. 02. nM.
-R3-
^MCT
13

3aga^a N4
^nn 3agaHHofi 6anKu H3 3aga^H N 3 Tpe6yeTcn:
1. BtmepTHTL B MacmTa6e 3agaHHoe ce^eHue 6anKH c yKa3aHueM qucneHHtix 3Ha^eHHH pa3MepoB. Onpegenurt nono^eHue geHTpa TH^ecru ce^eHun u BtiqucnuTt
MOMeHT HHep^H Ce^eHHH OTHOCHTentHO HeHTpantHOH ocu.
2. nocTpouTL ^^MpM HopMantHtix Hanpn^eHHH, pacnpegeneHHtix no BticoTe
ce^eHHH gnn ce^eHun c MaKcuMantHMM H3ru6aM^uM MOMeHTOM Mx, B3HTMM H3 3aga^u N 3.
3. Hcnont3yn ^^MpM H3ru6aro^ux MOMeHTOB Mx, nocrpoeHHtix B 3aga^e N 3, onpegenuTt H3 pac^eTa Ha npo^HocTt HOMep npo^unn gByTaBpoBofi (npu 3Ha^HTentHOH Hegorpy3Ke npuHHTt gnn 6anKH ce^eHue B Buge mBennepa) npoKaTHofi 6anKH. MaTepuan 6anKu - cTant CT.3, [a] = 160 Mna.
4. npu TOM ^e 3Ha^eHuu gonycKaeMoro Hanpa^eHun onpegenuTt nO ycnoBuro npo^Hocru pa3Mepm nonepe^Horo ce^eHun B $opMe:
a) Kpyra guaMeTpa d;
d
6) Kontga c OTHomeHueM guaMeTpoB
c o = -J= 0,6
h
k = b = 1’9
B) np^MoyrontHuKa c OTHomeHueM CTOPOH b
5. CocraBurt Ta6nugy OTHomeHufi nno^agefi yKa3aHHtix ce^eHufi K nno^agu gByTaBpoBoro npo^unn.
HoMep ce^eHun: 7
1) OnpegenuM geHTp TH^ecra OTHocuTentHO HefiTpantHofi ocu Ox:
n
X Ai-yc. n
y(
i = 1
A
■,A = X A,,
i=1
zde A, -nno^adb i- mozo ceueHun, MM ; yc - paccmoRHue om ocu Ox do i-mozo yeumpa mnwecmu, MM .
yc=■
A1 y c 1 + A2 ^ yC2 + A 3 ^ y C 3
A1 + A 2 + A3
zde A1 = B-4C=22-4-26=2288 MM2;
A2=3B2C = 3-22-2-26=3168 MM2;
= n (1,5 B )2 3,14- 1,5-22 )2 855 2
A 3 = = =855 MM
3 4 4
18. KP. 13. 03. 02. nM.
ne
^MCT
14

B =22
2 =
3 B
yc = EC, = = =11 MM;
Jc i 1 2 2
yc = EC2 = ^ + B= 2 + 22 = 55 MM;
3-22
2
yc = EC3 = 3B=3-22 = 66 MM;
A i'yc i + A26 yC2- A 3 6 y C3 2288-11 + 3168-55-855-66
yc=- = =31,1 MM;
Jc A1 + A2-A3 2288+3168-855
2) OnpegeauM MOMeHT HHepgHH ceaeHHa OTHOCHTeatHO OCH Ox:
2 2 2 Jx = Jx + A1 6 a1 + Jx + A2 6 a2 + Jx + A3 6 a3 ’
^^e a 1=CC1=yc-yc =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;
3 3 C^
b16 h1 4 CB3 4-26-223 4 4
Jx = — 1 = - = - - =92283 MM4 = 9,23 CM4,.
x1 12
3
''2 6 h2
12
12
, b26h 2C-3B)3 2-26-(3-22)3 124r816 4 58 4
J = = = =1245816 MM =124,58 CM ;
x2 12 12 12
, nd4 n-(1,5B)4 3, 14-1,5-22)4 r8184 4 5 82 4
J,, = = = =58184 MM = 5,82 CM ;
x3 64
64
64
2 2 2 J xC= J xC + A1 6 a1 + JxC + A2 6 a 2 J xC - A3 6 a3 =
=9,23+22,88-2,012+124,58 + 31,68-2,392-5,82-8,55-3,492=297,25 CM4;
3) HopMaatHtie Hanpa^eHHa npu H3rH6e no BMCOTe ceaeHHa pacnpegeaeHM no aHHeHHOMy 3aKOHy u B aroSofi Tome ceaeHHa onpegeaaroTca no ^opMyae:
„ Mz max
ai=—, ■■ y,’
xC
ede Mz-u3eu6aK>w,uu MOMeHm e ceueHuu,KH-M;
J4
XC - MOMeHm unepOuu cemenub OMWcume OCU,CM ;
\S \S \S •
y-paccmORHue Om HeumpaAbHOu OCU OO paccMampueaeMOu mOUKu I,MM.
CTPOHM ^^ropy HopMaatHtix Hanpa^eHHH gaa onacHoro ceaeHHa: yD = CD = 56,9 MM;
yE=CE = 31,1 MM;
M
'D= J,
_ z max 22,34-103 6 0,0569 427 6 Mn
oD= -yD = -8 = 427,6 Mna;
297,25 10-8
xC
M
x3
_ ' z max 22,34-1060,0311 „„„ ^ J/rrT
oy= -yE = - =233,7 Mna.
E J.
xC
297,25 10
18. KP. 13. 03. 02. nM.
n3
aMCT
15
1
2
3

4) OnpegeauM MOMeHT conporaBaeHua ceaeHua W x 6aaKu:
M
a max= -zmL <[ a ] ,
max
W
x
W -z max 22,34-103 139 6 3
Wx=, 1 = —-6— = 139,6 CM
x [ a] 160106
Bbi6epeM coraacHo rOCT 8239-89 gByTaBp ^18 Hanpa^eHue B ^TOM cayaae 6ygeT paBHo:
a=—USSL.=22I34v10 =0,15622.109 na = 156,22 MUa. Wx 143-10-6
Hegorpy3 b ^TOM cayaae 6ygeT paBeH:
^ 100 % =160 —156,22 . 100 % = 2,4% <20 %
[a] 160
ECHH nPUH^Tb 6aaKy B $opMe mBeaaepa N°20: Hanpa^eHue B ^TOM cayaae 6ygeT paBHo:
a=—™=22,34'10 =0,14697-109 na=146,97 Mna.
: W= 143 CM3, A = 23,4 CM2.
W= 152 CM3,A=23,4 CM2.
W,
152 10
-6
Hegorpy3 B ^TOM cayaae 6ygeT paBeH:
[a] a -100% = ——146,97 .1qq% = 8,1%<20%^ y meejnep nedocpy3 dojbwe, [a] 160
m y gByTaBpa, ^o^TOMy 6epeM gByTaBp N°18.
5) OnpegeauM nonepeaHoe ceaeHue 6aaKu B $opMe Kpyra:
J32—
ae
3
Wx=—^ d >
x 32
z max
n
•[ a ]
3 32-22,34-10 _ _
_ 1----=112,5 MM;
3,14-160-106
Akp== 3 ’ ^ ^=99,35 cm2;
OnpegeauM nonepeaHoe ceaeHue 6aaKH B $opMe Koabga:
W,
_nd 3-(1—c Q)
d
32
, ede c0 = ~d~=0,6 u (1— cQ) = ( 1—0,64)=0,87 , m. e.
W = nd-0,87 ^ d> 332'-zmax
x=32 ^ “
_ 332-22,34-10
n-[ a-0,87 |3,14-160-106-0,87
_K'd -(1 — Co2)_ n-d 2-0,87 _ 0,87-3,14-11,782 _
= 117,8 MM;
KOJI 4 4 4
nogSepeM ceaeHue B $opMe npaMoyroabHUKa (h = 1,9/b):
94,77 CM ;
18. KP. 13. 03. 02. nM.
-R3-
aMCT
16

Wx= „
x 6
bh2_ b-( 1,9 b|
=0,6-b3 ^ b=3 = 322,34-10- =
3
6
h= 1,9-b = 1,9-61,5 = 116,8 MM; Anp=b h=6,15 11,68=71,83 CM:
\a ]-0,6 160-106-0,6
=61,5 MM;
CocTaBHM cpaBHHT&nbHyro Ta6.^H^y cegeHHH:
18. KP. 13. 03. 02. nM.
ne
^MCT
17

3agaaa N5
CTaatHofi Baa Bpa^aeTca c nocToaHHofi aacTOTofi n u nepegaeT MO^HOCTL N. TpeSyeTca:
1) OnpegeauTL Harpy3KH, geficTByro^ue Ha Baa;
2) nocTpOHTL ^^MpM KpyTR^HX MOMeHTOB, ^^MpM H3rH6aM^HX MOMeHTOB B gByx naocKocrax (BepTuKaatHofi u roprooHTaatHofi);
3) nogoSpaTL guaMeTp Baaa, ucnoaL3yro TpeTLro Teopuro npoaHocTu, ecau u3BecTHO gonycKaeMoe Hanpa^eHue [a] = 170 Mna
HcxogHLie gaHHLie
CxeMa no pucyHKy: N7 PemeHue:
1) OnpegeauM BeauauHy KpyTa^ero MoMeHTa:
N nn
T = M =— ;a =—;
Kp a 30
30-N 3017103
T=30-N=3°-17-^=271 H-M=0, 271 KH-M; nn 3,14-600
OnpegeauM BeauauHM oKpy^HMx u paguaatHtix cua Ha 3y6aaTtix Koaecax:
F = _T_=2T.
t = 0,5 D = D ’
2 T 2-271
Ft = = =6775 H=6,775 KH ;
f1 D1 0,08
2 T 2-271
Ft = = =2464 H=2,464 KH;
12 D2 0,22
Fr =F-tga=F-0,364, ede a=20°
F =Ft i0,364=6,775-0,364=2,466 KH;
r 1 11
Fr =Ft i0,364=2,464-0,364= 0,897 KH;
r 2 12
2) nocrpouM ^^ropM u3ru6aro^ux MoMeHToB B naocKocTax xOz u yOz. ^aa ^TO^o HaHgeM onopHtie peaKguu: a) PaccMoTpuM BepTuKaaLHyro naocKocTL:
n
Z Fy. =0 ; - RAy - RBy - Fr 2 + Ft, = 0;
k =1
18. KP. 13. 03. 02. nM.
ne
aMCT
18

XMx = 0; -Fr 6 3a+Ft 6a-RBy6(3a+b)=0;
k = 1
RB =-
By
F - 3 a+Ft 6 a
_-0,897-3-0,19+ 6,775-0,19 _
3 a + b
+
r2 L1
3-0,19 + 0,17
= 1,049 KH;
RAy=-RBy-Fr + Ft1 =-1,049-0,897 + 6,775 =4,829 KH;
npoBepKa:
n
X Mx =0; Fr 6b-Ft 6(2a+b) + RAy6(3a + b)=0;
k = 1
0,897-0,17-6,775-(2-0,19+0,17)+4,829( 3-0,19+0,17 )=0; -0,001« 0;
6) PaccMOTpuM ropH30HTa^LHyro nnocKOCTb:
n
X Fx,=0 ;RAX+RBX- Fr, - F, =0;
k =1 n
XMy =0; Fr 6 a+Ft 63a-RBx6(3a+b)=0;
k= 1 A 1 2
F - a+Ft 6 3 a
RB =
Bx
r 1 ~ _ f2
_ 2,466-0,19+2,464-3-0,19 _
3 a + b 3-0,19+0,17
R=-RBX + Fr_ + Fu =-2,53+2,466+2,464=2,4 KH;
2,53 KH;
' 1 2
npoBepKa:
n
X My = 0; -F 6(2a + b)-F,;6b+R.x6(3a + b)=0;
k=1 B 1 2
-2,466 •( 2-0,19+0,17 )-2,464-0,17+2,4-( 3-0,19+0,17 )=0;
0,001^0 ;
nocrpoHM ^^Mpy H3ra6aM^Hx MOMeHTOB B BepTHKa^bHofi nnocKQCTH: I ygacTQK:
0 < z1
Mx.C = -RAy 6 z 1 >
'AC
npu z 1=0 * Mx =0;
v AC
AC
z =190 MM * M =-4,829-0,19=-0,917 KH-M;
npu 1 x.
II ygacTQK:
0
M =- RBy 6 z
By 3’
npu
npu
z3= 0 * Mx =0;
DB
z3= 170 MM * Mx =-1,049-0,17=-0, 178 KH-M;
18. KP. 13. 03. 02. nM.
ne
BMCT
19
1
2
DB

nocrpoHM ^^ropy H3rH6aro^Hx MOMeHTOB B roprooHTanLHoH nnocKocTH:
I ygacTOK:
0
MyAC= RAx LZ1 ;
z = 0 ^ M = 0; npu 1 ^ AC
z. = 190 MM ^ M =2,4-0,19=0,456 KH-M;
npu 1 ^ AC
II ygacTOK:
0
MyDB = RB*L z 3 :
^ z3= 0 ^ M = 0;
npu 3 yDB
z3= 170 MM ^ M =2,53-0,17= 0,43 KH-M;
npu
DB
3) OnpegenHM gHaMeTp Bana HCxogH H3 ycnoBHH oOecneHeHHH npo^Hocra no
TpeTLefi TeopHH:
no TpeTLefi TeopHH npo^Hocm:
M =+ M2+ M2+0,75 T2:
3K8 x y
MKD = JM2* + M2 + 0,75 T2 =V(-0,917 )2+0,4562+0,75-0,2712 = 1,051 KH-M;
3K8A A A
M^a =JM2X + M2V + 0,75 T2 = V(-0,178 )2+0,432+0,75-0,2712 =0,521 KH-M;
3KeB B B
M _ > M
A
' 3K6B 9
CnegoBaTenLHo, pacneT HeoOxogHMo BecTH B ceneHHH A. ^KBHBaneHTHoe Hanpn^eHHe npu H3ru6e onpegenneTCH BMpa^eHueM:
M
1 KB
, zde Wx =0,1 d3;
o =
3Ke W
7 3 M3K8. 3 1 051-103
d> A =3 _ =0,03954 M = 39,54 MM;
0,1 [o ] 0,1-170-10_
OKpyrnneM go Onu^anmero Oontmero CTaHgapTHoro 3HaneHHH guaMeTpa Bana: d=40 MM .
18. KP. 13. 03. 02. nM.
ne
^MCT
20

3aKnro^eHue
B xoge BMinonHeHuH KypcoBofi paSoTMi nony^eHMi cnegyro^ue pe3ynLTaTMi:
B 3aga^e 1 pacOTuraHa npo^HocTt 3aKpenneHHoro cTep^HH, HaxogH^erocH nog geficTBueM cun. npoBepuB npo^HocTt cTep^HH npu gonycKaeMOM HanpH^eHuu, cgenaH BMiBog ^TO, ycnoBue npo^Hocra BtmonHHeTcH.
B 3aga^e 2 pacOTuraHa npo^HocTt 3aKpenneHHoro cTantHoro Bana, HaxogH^erocH nog geficTBueM KpyTH^ux MOMeHTOB. npu npoBegeHuu npoBepKH Ha npo^HocTt cTep^HH npu gonycKaeMoM Hanpn^eHuu cgenaH BMBog ^TO, Ban He BMigep^uT Harpy3KH.
B 3aga^e 3 nocTpoeHM ^^ropM nonepe^HMix cun u roruSaro^ux MoMeHToB u onpegeneHo onacHoe ce^eHue.
B 3aga^e 4 gnH 3agaHHofi 6anKu 3aga^u 3 onpegeneHM npu gonycKaeMoM HanpH^eHuu no ycnoBuro npo^Hocra pa3MepM nonepe^Horo ce^eHuH B $opMe gByTaBpa u mBennepa. H cgenaHa cpaBHurentHaH TaSnuga oraomeHufi nno^agefi pa3nu^HMx ce^eHufi, gnH onpegeneHuH caMoro BMrogHoro npo^unH ce^eHuH, KaKoBMM oKa3ancH mBennep.
B 3aga^e 5, ucnont3yH ^eTBepTyro Teopuro npo^Hocra (Teopuro HauSontmux KacaTenLHMx HanpH^eHufi), MM pacc^uTanu guaMeTp Bana no u3BecraoMy gonycKaeMoMy HanpH^eHuro [6] = 160 Mna, KoTopMfi Skin oKpyrneH go Snumfimero Sontmero 3Ha^eHuH u3 cTaHgapTHoro pHga rOCTa.
27.12.2021
(gaTa) (nognucb)

CnucoK ucnon^yeMofi nuTepaTypti
1. HocuneBH^ r.E. npuKnagHan MexaHHKa: ^nn cTygeHToB By30B. PneKTpoHHtrn pecypc] : / r.E. HocuneBuq, n.A. .HeOegeB, B.C. CTpenneB. - ^neKTpoH. gaH. - M. : MamuHocTpoeHue, 2012. - 576 c. - Pe^HM gocTyna: http://e .lanboook . com/books/element.php?p11 id=5794
2. CTenuH n.A. ConpoTHBneHue MaTepuanoB ^neKTpoHHMH pecypc] : y^eOHHK. - ^neKTpoH. gaH. - Cn6. : .HaHt, 2 14. - 340 c. - Pe^HM gocTyna: http://e .lanboook.com/books/element.php?p11 id=3179
3. KapuMOB H. ConpoTHBneHue MaTepuanoB. ^neKTpoHHLIH y^eOHMH Kypc gnn cTygeHTOB O^HOH H 3ao^Hofi $opM oOy^eHHH ^neKTpoHHtrn pecypc]. Pe^HM gocTyna: http://www.soprotmat.ru
4. EenneB H.M. COopHHK 3aga^ no conpoTHBneHuro MaTepuanoB ^neKTpoHHMH pecypc] : y^eOHoe nocoOue / H.M. EenneB, .H.K. napmuH, E.E. MenLHHKoB [u gp.]. - ^neKTpoH. gaH. - Cn6. : .HaHt, 2011. - 431 c. -Pe^HM gocTyna: http://e.lanboook.com/books/element.php?p11 id=2022
5. MuponroOoB H.H. ConpoTHBneHue MaTepuanoB. nocoOue no pemeHHM 3aga^ PneKTpoHHtm pecypc] : y^eOHo-MeTogu^ecKoe nocoOue / H.H. MuponroOoB, 0.3. AnMoMegoB, H.A. KypuguH [u gp.]. - ^neKTpoH. gaH. -CnO. : ^aHL, 2014. - 512 c. - Pe^HM gocTyna: http://e.lanboook.com/books/element.php?p11 id=39150
6. ^yKoB B.r. MexaHHKa. ConpoTHBneHue MaTepuanoB ^neKTpoHHtrn pecypc] : y^eOHoe nocoOue. - ^neKTpoH. gaH. - CnO. : .HaHt, 2012. - 415 c. Pe^HM gocTyna: http://e.lanboook.com/books/element.php?p11 id=3721
7. KapuMoB H. npuKnagHan MexaHHKa. ^neKTpoHHMH Kypc gnn cTygeHToB O^HOH H 3ao^Hofi ^opM oOy^eHHH ^neKTpoHHtrn pecypc]. Pe^HM gocTyna: http://www.prikladmeh.ru
8.

ripnnO>KeHHH
18. KP. 13. 03. 02. nM.

npHno^eHHe 2
^epTe^ K 3aga^e N2

npHno^eHHe 3
^epTe^ K 3aga^e N3