Belka ze skratowaniem 3.pdf

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3U]\NáDG%HOND]HVNUDWRZDQLHP
3ROHFHQLHZ\]QDF]\üUHDNFMHSRGSRURZHGODSRQL * V]HMEHONL]HVNUDWRZDQLHPREFL * RQHM
REFL * HQLHPFL Já\PRVWDá\PQDW * HQLX
q .
q
l
l
l
2 l
l
l
Przyjmujemy oznaczenia podpór: A i B 1DWRPLDVWSRá F]HQLDSU]HJXERZHR]QDF]DP\
cyframi: 1 , 2 , 3 i 4 .
q
A
1
2
3
l
4
l
B
l
2 l
l
l
5R]ZL ]DQLH]DGDQLDUR]SRF]\QDP\RGXZROQLHQLDXNáDGXRGZL ]yZ]DVW SXM FSRGSRU\
UHDNFMDPL*yUQDSRGSRUDR]QDF]RQDOLWHU
A MHVWSRGSRU WHOHVNRSRZ =DWHPZSXQNFLH A
R A SURVWRSDGáDGRNLHUXQNXPR * OLZHJRSU]HVXZXRUD]PRPHQW M A .
'ROQDSRGSRUDR]QDF]RQDOLWHU
G]LDáDUHDNFMDSR]LRPD
B MHVWSRGSRU SU]HJXERZ QLHSU]HVXZQ :SXQNFLH B
Z\VW SXM GZLHQLH]DOH * QHRGVLHELHVNáDGRZHUHDNFMLSLRQRZD
V B i pozioma H B 2EFL * HQLH
q ]DVW SXMHP\GZLHPDZ\SDGNRZ\PL W 1 = W 2 = q  l = 2 ql .
FL JáHRVWDá\PQDW * HQLX
W 1
W 2
R A
M A
A 1
2
3
I
l
y
H B
4
l
B
V B
x
l
l
l
l
l
7U]\UyZQDQLDUyZQRZDJL]DSLVDQHGODFDáHJRXNáDGXQLHZ\VWDUF] GRZ\]QDF]HQLDZDUWRFL
czterech niewiadomych: M A , R A , V B i H B -HG\QLHUHDNFM V B PR*HP\Z\]QDF]\ü]UyZQDQLD
89765485.033.png 89765485.034.png 89765485.035.png 89765485.036.png 89765485.001.png 89765485.002.png 89765485.003.png
U]XWyZVLáQDRSLRQRZGODFDáHJRXNáDGX
0
å i
P
iy
=
: V B í q  l = 0
Þ
V B = 4 ql
1DVWSQHUyZQDQLHUyZQRZDJL]DSLV]HP\GOD
I F]FLXNáDGX
W 2
3 l
l
.
V 2
I
10 l
2 3
H 2
1
sin . =
l
10
.
4
cos . =
3
l
l
10
S 1
B
2 GODF]FL I XNáDGXZ\]QDF]\P\ZDUWRüVLá\
S 1 G]LDáDMFHMZSUFLH B í 4 0RPHQW\RGG]LDá\ZD V 2 i H 2 Z]JOGHPSXQNWX 2 VUyZQH
]HUXJG\*OLQLHG]LDáDQLDW\FKVLáSU]HFKRG]SU]H]SXQNW
2 =DSLVXMFUyZQDQLHPRPHQWyZ
2 GODF]FL I XNáDGXVNRU]\VWDP\]WZLHUG]HQLD9DULJQRQD:W\PFHOX
Z]JOGHPSXQNWX
S 1 MHMVNáDGRZ\PLSLRQRZLSR]LRP
]DVWSXMHP\VLá
W 2
V 2
I
2 3
H 2
S 1 ÂFRV .
l
4
S 1 ÂVLQ .
B
l
l
5yZQDQLHPRPHQWyZZ]JOGHPSXQNWX
2 GODF]FL I XNáDGXPDSRVWDü
å
M
I
i2
=
0 : í S 1 ÂFRV . Â l í W 2 Â l = 0
Þ
S 1 = í
2
10
ql
3
i
.ROHMQHUyZQDQLH]DSLV]HP\GODZ]áDSRGSRURZHJR
B .
90 o
l
1
sin =
S 2
5
S 1
2 l
5 l
2
cos =
.
5
H B
V B
2
=UyZQDQLDPRPHQWyZZ]JOGHPSXQNWX
89765485.004.png 89765485.005.png 89765485.006.png 89765485.007.png 89765485.008.png 89765485.009.png 89765485.010.png 89765485.011.png 89765485.012.png 89765485.013.png 89765485.014.png 89765485.015.png 89765485.016.png 89765485.017.png 89765485.018.png 89765485.019.png
3U]\MPXMHP\RSURVWRSDGáGROLQLLG]LDáDQLDVLá\
S 2 Z\VWSXMFHMZSUFLH B í:
B MHG\QQLHZLDGRPEG]LHVNáDGRZD
pozioma H B :FHOXXSURV]F]HQLDREOLF]HQLDU]XWXVLá\ S 1 QDR]DVWSXMHP\VLá S 1 jej
VNáDGRZ\PLSLRQRZLSR]LRP
UyZQDQLXU]XWyZVLáQDWRGODZ]áDSRGSRURZHJR
90 o
l
sin
=
1
S 2
5
2 l
S 1 ÂVLQ .
5 l
cos =
2
.
5
H B
S 1 ÂFRV .
V B
=DSLVXMHP\UyZQDQLHU]XWyZVLáQDRGODZ]áDSRGSRURZHJR
B .
å i
P
B
i
=
0
: V B ÂVLQ
í H B ÂFRV
í S 1 ÂFRV . ÂFRV
+ S 1 ÂVLQ . ÂVLQ
= 0
Þ
H B =
11 ql
3R]RVWDáHUHDNFMHZ\]QDF]\P\]UyZQDUyZQRZDJL]DSLVDQ\FKGODFDáHJRXNáDGX5HDNFM
SR]LRP
R A REOLF]\P\NRU]\VWDMF]UyZQDQLDU]XWyZVLáQDRSR]LRP
11 ql
å i
P
ix
=
0
: R A + H B = 0
Þ
R A = í
3
Moment podporowy M A ZPLHMVFXSRGSRU\WHOHVNRSRZHMPR*HP\Z\]QDF]\ü]UyZQDQLD
PRPHQWyZGODFDáHJRXNáDGXZ]JOGHPSXQNWX
B .
W = W 1 + W 2 = 4 ql
M A
R A = í
11 ql
A 1
2
3
C
3
l
11 ql
4
l
H B =
3
B
V B = 4 ql
l
l
l
l
l
5yZQDQLHWRPDSRVWDü
å
M
iB
=
0 : í R A Â l í M A í W Â l = 0
Þ
M A = í
14 ql 2
3
i
6SUDZG]HQLHSRSUDZQRFLSU]HSURZDG]RQ\FKREOLF]HZ\NRQDP\]DSLVXMF UyZQDQLH
UyZQRZDJL]NWyUHJRZF]HQLHMQLHNRU]\VWDOLP\0R*HWRE\üQDSU]\NáDGUyZQDQLH
PRPHQWyZGODFDáHJRXNáDGXZ]JOGHPSXQNWX
C .
å i
M
iC
=
0
: H B Â l í V B Â l í M A + W Â l =
11 ql  l í ql  l í ( í
3
14 ql 2 ) + 4 ql  l =
=
22 ql 2 í ql 2 +
14 ql 2 + 8 ql 2 = 0
3
5yZQDQLHVSHáQLRQHMHVWWR*VDPRFLRZR
3
3
3
3
89765485.020.png 89765485.021.png 89765485.022.png 89765485.023.png 89765485.024.png 89765485.025.png 89765485.026.png 89765485.027.png 89765485.028.png 89765485.029.png 89765485.030.png 89765485.031.png 89765485.032.png

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