Belka ze skratowaniem 2.pdf

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Microsoft Word - Przyk³ad 2.6.doc
3U]\NáDG%HOND]HVNUDWRZDQLHP
3ROHFHQLHZ\]QDF]\üVLá\ZSU WDFKGZXSU]HJXERZ\FKGODSRQL * V]HMEHONLREFL * RQHMVLá
VNXSLRQ
M = Pl
P
2 l
l
l
l
2 l
l
2 l
Przyjmujemy oznaczenia dla podpór: A i B GODSRá F]HSU]HJXERZ\FK 1 , 2 , 3 i 4 , a dla
SRáF]HQLDWHOHVNRSRZHJR
5 .
A
M = Pl
2
3
5
4
B
P
2 l
1
l
l
l
2 l
l
2 l
5R]ZL]DQLH]DGDQLDUR]SRF]\QDP\RGRVZRERG]HQLDXNáDGXRGZL]yZ]DVWSXMFSRGSRU\
A MHVWSRGSRUSU]HJXERZQLHSU]HVXZQ=DWHP
w punkcie A G]LDáDMGZLHQLH]DOH*QHRGVLHELHVNáDGRZHUHDNFMLSLRQRZD V A i pozioma H A .
3UDZDSRGSRUDR]QDF]RQDOLWHU
B MHVWSRGSRUSU]HJXERZSU]HVXZQ:SXQNFLH B
R B NWyUHMOLQLDG]LDáDQLDMHVWSLRQRZDSURVWRSDGáDGRNLHUXQNXPR*OLZHJR
Z\VWSXMHUHDNFMD
przesuwu).
M = Pl
A
2
3
5
4
B
H A
P
y
V A
R B
2 l
1
x
l
l
l
2 l
l
2 l
:SROHFHQLXGR]DGDQLDQLHVZ\PLHQLRQHUHDNFMHSRGSRURZHMHGQDN*HZ\]QDF]HQLHUHDNFML
V A lub R B MHVWNRQLHF]QH=DSLV]HP\UyZQDQLHPRPHQWyZZ]JOGHPSXQNWX A GODFDáHJR
XNáDGX]NWyUHJRZ\]QDF]\P\UHDNFM
A .
2 P
å
M
iA
=
0 : R B Â l í P Â l í M = 0 Þ R B = 3
i
Po wyznaczeniu reakcji R B PR*HP\REOLF]\üZDUWRüVLá\ S 3 G]LDáDMFHMZSUFLH 1 í .
P oraz momentem skupionym M = Pl .
UHDNFMDPL/HZDSRGSRUDR]QDF]RQDOLWHU
R B 0RPHQW\VLá H A i V A Z]JOGHPSXQNWX A VUyZQH
]HUXJG\*OLQLHG]LDáDQLDW\FKVLáSU]HFKRG]SU]H]SXQNW
89765484.048.png 89765484.049.png
I
M = Pl
A
2
3
5
4
B
H A
P
V A
R B
2 l
1
l
l
l
2 l
l
2 l
1 í]DVWSXMHP\VLá S 3 NWyUDG]LDáDZW\PSUFLH:SRáF]HQLXWHOHVNRSRZ\P 5
Z\VWSXMHPRPHQW
M 5 LSR]LRPDVLáD R 5 SURVWRSDGáDGRRNáDGHNWHOHVNRSX5HDNFMD R B -
MDNRZLHONRü]QDQD±R]QDF]RQDMHVWNRORUHPF]DUQ\P
I
3 l
90 o
.
M 5
M = Pl
5
4
B
2 l
13 l
R 5
.
S 3
R B
2 l
2
sin . =
13
1
3
cos . =
l
2 l
l
2 l
13
:FHOXZ\]QDF]HQLDVLá\
S 3 ]DSLV]HP\UyZQDQLHU]XWyZVLáQDRSLRQRZGOD I F]FL
XNáDGX
å
P
I
iy
=
0 : R B í S 3 ÂVLQ . = 0
Þ
S 3 =
13 P
i
3R]RVWDáHGZLHQLHZLDGRPHVLá\G]LDáDMFHZSUWDFK
1 í 2 i 1 í 3 Z\]QDF]\P\]GZXUyZQD
1 .
UyZQRZDJLGODZ]áD
2
3
4
l
cos =
1
S 2
5
S 1
2 l
13 P
5 l
2
S 3 =
sin =
3
5
.
1
6Lá
S 1 PR*HP\Z\]QDF]\ü]UyZQDQLDU]XWyZVLáQDRSR]LRPGODZ]áD 1 .
0
å i
P
1
ix
=
: í S 1 ÂFRV + S 3 ÂFRV . = 0
Þ
S 1 = 5 P
2VWDWQLQLHZLDGRPREOLF]\P\]UyZQDQLDU]XWyZVLáQDRSLRQRZGODZ]áD
1 .
å
P
1
iy
=
0 : S 1 ÂVLQ + S 2 + S 3 ÂVLQ . = 0
Þ
S 2 = í
8 P
i
2
3UW
3
3
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S 1 i S 3 PDMZDUWRFLGRGDWQLHF]\OLLFK]ZURW\V]JRGQH]]DáR*RQ\PLD]DWHPVWR
VLá\UR]FLJDMFH1DWRPLDVWVLáD
S 2 MHVWXMHPQDDZLFMHM]ZURWMHVWSU]HFLZQ\GR
1 í 3 MHVWFLVNDQ\
=HZ]JOGXQDSROHFHQLHZ\]QDF]RQH]RVWDá\MHG\QLHVLá\
]DáR*RQHJR3UW
S 1 , S 2 i S 3 RUD]MDNRZLHONRü
pomocnicza reakcja R B 1LHPR*HP\ ]DWHPEH]GRGDWNRZ\FKREOLF]HZ\NRQDü
VSUDZG]HQLDSRSUDZQRFLUR]ZL]DQLD
3
6Lá\

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