Układ belkowy złożony 3, Budownictwo Studia, Mechanika(1)

[ Pobierz całość w formacie PDF ]
3U]\NáDG8NáDGEHONRZ\]áR
*
RQ\
3ROHFHQLHZ\]QDF]\üUHDNFMHSRGSRURZHRUD]RGG]LDá\ZDQLDZSRá
F]HQLDFKSU]HJXERZ\FK
LZWHOHVNRSLHGODSRQL
*
V]HJRXNáDGXREFL
*
RQHJRREFL
*
HQLHPFL
Já\PRVWDá\PQDW
*
HQLX
q
1
=
q
i
q
2
= 2
q
VLá
VNXSLRQ
P
= 2
ql
oraz momentem skupionym
M
=
ql
2
.
M
=
ql
2
q
2
= 2
q
cos
.
=
5
3
P
= 2
ql
q
1
=
q
4
sin
.
=
5
1
cos
=
= 45
o
.
2
sin
=
1
l
2
l
2
l
l
2
l
2
l
2
Przyjmujemy oznaczenia dla podpór:
A
,
B
,
C
i
D
RUD]GODSRá
F]HSU]HJXERZHJR
1
i
teleskopowego
2
.
q
2
= 2
q
cos
.
=
5
3
P
= 2
ql
M
=
ql
2
q
1
=
q
4
A
sin
.
=
5
1
2
B
C
D
1
cos
=
= 45
o
.
2
sin
=
1
l
2
l
2
l
l
2
l
2
l
2
8ZDOQLDP\XNáDGRGZL]yZ]DVWSXMFSRGSRU\UHDNFMDPL2]QDF]RQDOLWHU
A
podpora jest
A
G]LDáDMQDVWSXMFHUHDNFMHUHDNFMDSLRQRZD
R
A
SURVWRSDGáDGR
NLHUXQNXPR*OLZHJRSU]HVXZXRUD]PRPHQW
WXOHMDZLFZSXQNFLH
M
A
. W miejscu podpory przegubowej
przesuwnej
B
G]LDáDUHDNFMDSLRQRZD
R
B
SURVWRSDGáDGRNLHUXQNXPR*OLZHJRSU]HVXZX
podobnie w punkcie
C
G]LDáDUHDNFMDSLRQRZD
R
C
3UDZDSRGSRUDR]QDF]RQDOLWHU
D
, jest
SRGSRUSU]HJXERZQLHSU]HVXZQ]DWHPZSXQNFLH
D
G]LDáDMGZLHQLH]DOH*QHRGVLHELH
V
D
i pozioma
H
D
2EFL*HQLHFLJáH
q
1
=
q
]DVWSXMHP\
VNáDGRZH UHDNFMLSLRQRZD
W
1
]D
q
2
=2
q
dwiema wypadkowymi
W
2
i
W
3
.
Z\SDGNRZ
W
2
W
3
W
1
M
=
ql
2
P
= 2
ql
M
A
A
1
2
B
C
D
H
D
y
R
A
= 45
o
R
B
R
C
V
D
.
x
l
2
l
2
l
l
2
l
2
l
 :\SDGNRZHREFL*HQLDFLJáHJRZ\QRV]
W
1
=
q
1
Â
l
=
q
Â
l
=
ql
W
2
=
q
2
Â
l
= 2
q
Â
l
= 4
ql
W
3
=
q
2
Â
l
= 2
q
Â
l
= 4
ql
']LHOLP\]áR*RQ\XNáDGEHONRZ\QDEHONLSRMHG\QF]HSRGXNáDG\WZRU]FVFKHPDWSUDF\
UR]SDWU\ZDQHJRXNáDGX:SRáF]HQLXSU]HJXERZ\P
1
G]LDáDMGZLHQLH]DOH*QHVNáDGRZH
V
1
i pozioma
H
1
3RGREQLHZSRáF]HQLXSU]HJXERZ\P
C
Z\VWSXM
GZLHQLH]DOH*QHVNáDGRZHRGG]LDá\ZDQLDSLRQRZD
RGG]LDá\ZDQLDSLRQRZD
V
C
i pozioma
H
C
1DWRPLDVWZSRáF]HQLX
teleskopowym
2
Z\VWSXMHRGG]LDá\ZDQLH
R
2
RNLHUXQNXSURVWRSDGá\PGRRNáDGHNWHOHVNRSX
oraz moment
M
2
.
I
I
M
2
W
3
II
H
1
1
2
R
2
V
1
90
o
H
C
H
D
.
C
D
P
= 2
ql
M
=
ql
2
V
C
V
D
M
A
A
1
W
2
H
1
W
1
IV
R
A
V
1
III
R
2
V
C
90
o
B
C
H
C
2
M
2
R
B
R
C
.
l
2
l
2
l
l
2
l
2
l
-DNRSLHUZV]H]DSLV]HP\UyZQDQLHU]XWyZVLáQDRSR]LRPGOD
III
F]FLXNáDGXZFHOX
H
1
w przegubie
1
.
REOLF]HQLDRGG]LDá\ZDQLDSR]LRPHJR
1
å
P
III
ix
=
0
:
2
ql
Â
í
H
1
= 0
Þ
H
1
=
ql
2
i
H
1
]DSLV]HP\UyZQDQLHU]XWyZVLáQDRSR]LRPGOD
(
I
F]FLXNáDGX]NWyUHJRREOLF]\P\ZDUWRüRGG]LDá\ZDQLD
R
2
w teleskopie
2
.
3RZ\]QDF]HQLXZDUWRFLRGG]LDá\ZDQLD
I
I
M
2
H
1
=
ql
1
2
V
1
90
o
R
2
.
2 l
2
I
å
i
P
I
ix
=
0
:
H
1
í
R
2
ÂFRV
o
í
.
) = 0
Þ
R
2
=
4
5
ql
=UyZQDQLDU]XWyZVLáQDRSLRQRZGOD
I
F]FLXNáDGXPR*HP\MX*Z\]QDF]\ü
V
1
w przegubie
1
.
RGG]LDá\ZDQLHSLRQRZH
3
ql
å
i
P
I
iy
=
0
:
V
1
+
R
2
ÂFRV
.
= 0
Þ
V
1
=
í
4
Ostatnim równaniem zapisanym dla (
I
F]FLXNáDGXEG]LHUyZQDQLHPRPHQWyZZ]JOGHP
punktu
2
]NWyUHJRREOLF]\P\ZDUWRüRGG]LDá\ZDQLD
M
2
w teleskopie
2
. W równaniu tym
QLHZ\VWSLRGG]LDá\ZDQLD
H
1
i
R
2
SRQLHZD*OLQLHG]LDáDQLDW\FKVLáSU]HFKRG]SU]H]SXQNW
2
.
3
ql
2
å
M
I
i2
=
0 :
M
2
í
V
1
Â
l
= 0
Þ
M
2
=
í
2
i
R
A
na podporze
A
PR*HP\Z\]QDF]\ü]UyZQDQLDU]XWyZVLáQDRSLRQRZ
dla (
III
F]FLXNáDGX
P
= 2
ql
M
=
ql
2
III
M
A
A
1
H
1
=
ql
R
A
V
1
=
í
3
ql
l
2 l
å
P
III
iy
=
0
:
R
A
í
2
ql
Â
1
í
V
1
= 0
Þ
R
A
=
4
1
ql
2
i
W celu wyznaczenia momentu podporowego
M
A
w tulei
A
zapiszemy równanie momentów
Z]JOGHPSXQNWX
A
dla (
III
F]FLXNáDGX
å
M
III
iA
=
0
:
í
M
A
í
2
ql
Â
1
Â
l
í
M
í
V
1
Â
l
= 0
2
Þ
M
A
=
4
1
ql
2
i
5HDNFMSR]LRPQDSRGSRU]H
D
REOLF]\P\]UyZQDQLDU]XWyZVLáQDRSR]LRPGODFDáHJR
XNáDGX
å
i
P
=
0
: 2
ql
Â
1
+
H
D
= 0
Þ
H
D
=
í
ql
ix
2
C
dla (
II
F]FLXNáDGXZ\]QDF]\P\UHDNFM
=UyZQDQLDPRPHQWyZZ]JOGHPSXQNWX
V
D
na podporze
D
:UyZQDQLXW\PQLHZ\VWSLRGG]LDá\ZDQLD
V
C
i
H
C
oraz
reakcja
H
D
JG\*OLQLHG]LDáDQLDW\FKVLáSU]HFKRG]SU]H]SXQNW
C
.
SLRQRZ
W
3
= 4
ql
II
H
C
C
D
H
D
=
í
ql
V
C
V
D
2 l
3
5HDNFMSLRQRZ
4
 å
i
M
II
iC
=
0
:
V
D
Â
l
í
W
3
Â
l
= 0
Þ
V
D
= 2
ql
.RU]\VWDMF]UyZQDQLDU]XWyZVLáQDRSLRQRZGOD
II
F]FLXNáDGXZ\]QDF]\P\
V
C
w przegubie
C
QDWRPLDVW]UyZQDQLDU]XWyZVLáQDRSR]LRPGOD
(
II
F]FLXNáDGXZ\]QDF]\P\RGG]LDá\ZDQLHSR]LRPH
H
C
.
å
RGG]LDá\ZDQLHSLRQRZH
P
II
iy
=
0
:
V
C
+
V
D
í
W
3
= 0 Þ
V
C
= 2
ql
i
å
i
P
II
ix
=
0
:
H
C
+
H
D
= 0 Þ
H
C
=
ql
$E\Z\]QDF]\üUHDNFM
R
B
]DSLV]HP\UyZQDQLHPRPHQWyZZ]JOGHPSXQNWX
C
dla (
IV
)
F]FLXNáDGX
W
1
=
ql
W
2
= 4
ql
IV
R
2
=
4
5
ql
3
ql
2
V
C
= 2
ql
M
2
=
í
2
B
C
90
o
H
C
=
ql
2
R
B
R
C
.
l
2 l
å
M
IV
iC
=
0 :
R
2
ÂFRV
.
Â
l
í
M
2
í
R
B
Â
l
+
W
1
Â
5
l
+
W
2
Â
l
= 0
Þ
R
B
=
41
ql
i
-DNRRVWDWQLQLHZLDGRPZ\]QDF]DP\UHDNFM
R
C
]UyZQDQLDU]XWyZVLáQDRSLRQRZ
zapisanego dla (
IV
F]FLXNáDGX
å
P
IV
iy
=
0
:
R
C
+
R
B
í
R
2
ÂFRV
.
í
W
1
í
W
2
= 0 Þ
R
C
=
21
ql
i
IV
)
F]FLXNáDGX=DSLV]HP\WRUyZQDQLHZFHOXVSUDZG]HQLDSRSUDZQRFLZ\NRQDQ\FK
REOLF]H
å
P
IV
ix
=
0
:
R
2
ÂFRV
o
í
.
)
í
H
C
=
4
5
ql
Â
4
í
ql
=
ql
í
ql
= 0
i
5yZQDQLHVSHáQLRQHMHVWWR*VDPRFLRZR
W
1
=
ql
W
= 4
ql
+ 4
ql
= 8
ql
P
= 2
ql
M
=
ql
2
1
ql
2
M
A
=
4
A
1
2
B
C
D
H
D
=
í
ql
R
A
=
4
1
ql
= 45
o
.
R
B
=
41
ql
R
C
=
21
ql
V
D
= 2
ql
8
8
l
2
l
2
l
l
2
l
2
l
4
2
8
8
:UR]ZL]DQLX]DGDQLDQLHZ\NRU]\VWDOLP\UyZQDQLDU]XWyZVLáQDRSR]LRPGOD
5
'ODVSUDZG]HQLDZ\QLNyZVNRU]\VWDP\UyZQLH*]UyZQDQLD]DSLVDQHJRGODFDáHJRXNáDGXQD
SU]\NáDG]UyZQDQLDPRPHQWyZZ]JOGHPSXQNWX
D
:UyZQDQLXW\PPR*HP\]DVWSLü
W
2
i
W
3
Z\SDGNRZ
W
EGFLFKVXPNWyUHMOLQLD
Z\SDGNRZHREFL*HQLDFLJáHJR
C
.
G]LDáDQLDSU]HFKRG]LSU]H]SXQNW
å
M
iD
=
0
:
í
M
A
í
R
A
Â
l
+ 2
ql
Â
1
Â
l
í
ql
2
+
W
1
Â
2
9
l
+
W
Â
l
í
R
B
Â
l
í
R
C
Â
l
=
L
=
í
1
ql
2
í
1
ql
Â
l
+ 9
ql
2
í
ql
2
+
ql
Â
9
l
+
8
ql
Â
l
í
41
ql
Â
l
í
21
ql
Â
l
=
=
ql
2
(
í
1
í
5
+ 9
í
9
+ 16
í
41
í
2
21
)
= 0
3RZ\*V]HUyZQDQLHWH*VSHáQLRQHMHVWWR*VDPRFLRZR
=HZ]JOGXQDZ\VWSRZDQLHSRGSRU\SU]HJXERZHM
C
ZPLHMVFXSRáF]HQLDSU]HJXERZHJR
II
) i (
IV
PR*HP\UyZQLH*SU]\MüLQQ\VFKHPDWSUDF\XNáDGX
F]FL
I
I
M
2
H
1
1
2
V
1
90
o
R
2
.
W
2
W
1
IV
R
2
90
o
B
C
H
C
*
2
M
2
R
B
V
C
*
.
W
3
II
M
=
ql
2
P
= 2
ql
M
A
A
1
V
C
*
H
C
*
H
D
H
1
C
D
R
A
V
1
III
R
C
V
D
l
2
l
2
l
l
2
l
2
l
1
i teleskopie
2
QLH]DOH*RG
Z\ERUXSU]\MWHJRGRREOLF]HVFKHPDWXSUDF\XNáDGXEHONRZHJR MHGQHJR]GZX
V
C
*
:SLHUZV]\PVFKHPDFLHSU]\MW\PGRUR]ZL]DQLD]DGDQLDVWRRGG]LDá\ZDQLD
Z\VWSXMFHSRSUDZHMVWURQLHSRGSRU\
C
EGUy*QH
V
C
C
:SRZ\*V]\PVFKHPDFLHRGG]LDá\ZDQLDWH
C
. Gdyby podpora
C
E\áDSRGSRUSU]HJXERZ
QLHSU]HVXZQWRPRJá\E\WH*Uy*QLüVLRGG]LDá\ZDQLDSR]LRPHZSXQNFLH
Z\VWSXMSROHZHMVWURQLHSRGSRU\
C
.
5
2
4
4
2
8
8
4
2
2
4
:DUWRüUHDNFMLSRGSRURZ\FKRUD]RGG]LDá\ZDZSU]HJXELH
SUH]HQWRZDQ\FK1DWRPLDVWZDUWRFLRGG]LDá\ZDSLRQRZ\FKZSU]HJXELH
  [ Pobierz całość w formacie PDF ]

  • zanotowane.pl
  • doc.pisz.pl
  • pdf.pisz.pl
  • emaginacja.xlx.pl

    •